middle atmosphere

Middle Atmosphere

1989

Edited by R. Alan Plumb Robert A. Vincent

Springer Basel AG

Reprint from Pure and Applied Geophysics (PAGEOPH), Volume 130 (1989), No. 2/3

Editors' addresses:

R. Alan Plumb Center for Meteorology and Physical Oceanography Massachusetts Institute ofTechnology Cambridge, MA02139 USA

RobertA. Vincent Department of Physics University of Adelaide Adelaide, SA 5001, Australia

Library of Congress Cataloging in Publication Data

Middle atmosphere I edited by R. Alan Plumb, RobertA. Vincent p. cm. »Reprint from Pure and applied geophysics (PAGEOPH), volume 130

(1989), no. 2/3« --T. p. verso. Includes bibliographies.

1. Middle atmosphere. 1. Plurnb, R. Alan, 1948 -. H. Vincent, R. (Robert), 1942-QC881.2.M53M528 1989 551.5--dc19 89-81

CIP-Titelaufnahme der Deutschen Bibliothek

Middle atmosphere / ed. by R. Alan Plurnb; Robert A. Vincent. - Reprint. -Basel; Boston; Berlin : Birkhäuser, 1989

Aus: Pure and applied geophysics ; Vol. 130

NE: Plurnb, R. Alan [Hrsg.]

This work is subject to copyright. All rights are reserved, wh ether the whole or part of the material is concemed, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use a fee is payable to »VerwertungsgesellschaftWort«, Munich.

©1989 Springer Basel AG Originally published by Birkhäuser Verlag Basel in 1989. ISBN 978-3-7643-2290-8 ISBN 978-3-0348-5825-0 (eBook) DOI 10.1007/978-3-0348-5825-0

Contents

149 Introduction, R. A. Plumb and R. A. Vincent

151 Earlier days of gravity waves revisited, C. O. Hines

171 A note on some early radiosonde temperature observations in the Antarctic lower stratosphere, H. R. Phillpot

181 The impact of base-level analyses on stratospheric circulation statistics for the Southern Hemisphere, D. J. Karoly

195 Comparison of data and derived quantities for the middle atmosphere of the Southern Hemisphere, W. L. Grase and A. O'Neill

213 Some comparisons between the middle atmosphere dynamics of the Southern and Northern Hemispheres, D. G. Andrews

233 On the seasonal cycle of stratospheric planetary waves, R. A. Plumb

243 Body force circulations in a compressible atmosphere: Key concepts, T. J. Dunkerton

263 Satellite data analysis of ozone differences in the Northern and Southern Hemispheres, M. A. Geiler, M. F. Wu and E. Nash

277 Further evidence of normal mode Rossby waves, T. Hirooka and 1. Hirota

291 Monthly mean winds in the mesosphere at 44S and 78S, G. J. Fraser

303 Radar observations of prevailing winds and waves in the Southern Hemisphere mesosphere and lower thermosphere, A. Phi/Ups and R. A. Vincent

319 Comparison of geostrophic and nonlinear balanced winds from UMS data and implications for derived dynamical quantities, T. Mi/es and W. L. Grose

343 A review of gravity wave saturation processes, effects, and variability in the middle atmosphere, D. C. FrUts

373 Theory of internal gravity wave saturation, T. J. Dunkerton

399 A theory of enhaneed saturation of the gravity wave speetrum due to inereases in atmospherie stability, T. E. VanZandt and D. C. Fritts

421 The effeet of horizontal resolution on gravity waves simulated by the GFDL "SKYHI" general eireulation model, Y. Hayashi, D. G. Golder, J. D. Mahlman and S. Miyahara

445 Laboratory observations of gravity wave eritieal-Iayer flows, D. P. Delisi and T. J. Dunkerton

463 Wind fluetuations near a eold vortex-tropopause funnel system observed by the MV radar, S. Fukao, M. D. Yamanaka, H. Matsumoto, T. Sato, T. Tsuda and S. Kato

481 Internal gravity wave seleetion in the upper troposphere and lower stratosphere observed by the MV radar: Pre\iminary results, M. D. Yamanaka, S. Fukao, H. Matsumoto, T. Sato, T. Tsuda and S. Kato

497 High time resolution monitoring of tropospherie temperature with a radio aeoustie sounding system (RASS), T. Tsuda, Y. Masuda, H. Inuki, K.

Takahashi, T. Takami, T. Sato, S. Fukao and S. Kato

509 Falling sphere observations of anisotropie gravity wave motions in the upper stratosphere over Australia, S. D. Eckermann and R. A. Vincent

533 Constraints on gravity wave indueed diffusion in the middle atmosphere, D. F. Strobel

547 Temperature and heat flux speetra in the turbulent buoyaney subrange, C. Sidi and F. Dalaudier

571 Interpretation, reliability and aeeuraeies of parameters dedueed by the spaeed anten na method in middle atmosphere applieations, W. K. Hocking, P. May and J. Röttger

605 Full-eorrelation analysis of turbulent seattering layers in the mesosphere observed by the MV radar, M. Yamamoto, T. Sato, T. Tsuda, S. Fukao and S. Kato

PAGEOPH, Vol. 130, Nos. 2/3 (1989)

Introduction

0033-4553/89/030149-D2$1.50 + 0.20/0 © 1989 Birkhäuser Verlag, Basel

Our knowledge of the stratosphere and mesosphere has progressed dramatically in the past fifteen years. The intense effort aimed at understanding the structure, dynamics and chemistry of the region has been motivated primarily by the need to understand the complex interplay of processes which control the distribution of atmospheric ozone and to provide assessments of the impact on ozone of stratospheric pollutants. On the organizational level the Middle Atmosphere Program (MAP) has encouraged a more coherent effort, particularly for the observational component. The MAP subprograms GRATMAP (Gravity Waves and Turbulencej MAP) and MASH (Middle Atmosphere of the Southern Hemisphere) were the subjects ofworkshops held consecutively at the University of Adelaide in May 1987; most of the papers in this special issue of PAGEOPH were presented at those meetings. This issue thus presents an up-to-date summary of current research in these two important aspects of the dynamics of the stratosphere and mesosphere.

This issue begins with two historical perspectives from pioneers of the study of atmospheric gravity waves and of the circulation of the southern stratosphere. Aside from their intrinsic interest, these papers remind us of the difficulties faced by early workers, when observations were spar se and infrequent and the very existence of gravity waves in the atmosphere was not widely acknowledged.

The large-scale circulation of the northern stratosphere is now reasonably weIl documented. The Southern Hemisphere, however, has received much less attention, partly because of the poorer observational base and partly because interest in this region has been intrinsically weaker (though the Antarctic ozone depletion has recently changed all that). On large scales the ground-based observational network in northern mid-Iatitudes is sufficiently den se that satellite radiances can be used to build up geopotential analyses (from which winds may be estimated via geostrophic or other assumptions) with a fair degree of confidence. This is not the situation in the Southern Hemisphere and so an important part of the research effort there must be aimed at understanding the possibilities and limitations inherent in the available data. This is all the more important if one is to try to use the data to derive quantities such as potential vorticities or wave fluxes which may be very sensitive to data quality. The extent to which such calculations are reliable for the southern stratosphere is discussed in three papers here. Despite such issues, we are now beginning to understand better the southern stratosphere and to recognise that there are substantial differences between the two hemispheres. Differences in the structure of the two hemispheres, in planetary wave activity and ozone are addressed. Quite apart from the intrinsic importance of increasing our knowledge of this half of the

150 Introduction PAGEOPH,

stratosphere, these differences provide us with new evidence, interpretation of which can materially help to advance our understanding of stratospheric dynamics in general.

It is now weil established that smaller-scale motions-in particular gravity waves and turbulence-are of fundamental importance in the general circulation of the mesosphere; they seem to be similarly, if less spectacularly, significant in the troposphere, and probably also in the stratosphere. Our understanding of these motions, their effects on the mean circulation and their mutual interactions is progressing rapidly, as is weil illustrated by the papers in this issue; there are reports of observational studies, especially with new instruments such as the Japanese MV radar, reviews of the state of theory, a laboratory study and an analysis of gravity waves and their effects in the high resolution "SKYHI" general circulation model. There are good reasons to suspect that gravity waves may be of crucial significance in making the stratospheric circulation the way it is (modeling experience being one suggestive piece of evidence for this). Direct observational proof has thus far been prevented by the difficulty of making observations of such scales of motion in this region; in one study reported here, falling sphere observations are used to obtain information on the structure and intensity of waves in the upper stratosphere.

Finally, we note that publication of this issue is the end product of efforts by a large numberof colleagues. We particularly wish to acknowledge the efforts of David Fritts and Alan O'Neill, the convenors respectively of the GRATMAP and MASH workshops; we also thank all the contributors and reviewers for helping to bring the issue together.

R. Alan Plumb M.I.T. Cambridge, MA 02139 V.S.A. June 1988

RobertA. Vincent Vniversity of Adelaide Adelaide, Australia

PAGEOPH, Vol. 130, Nos. 2/3 (1989) 0033--4553/89/030151-20$1.50 + 0.20/0 © 1989 Birkhäuser Verlag, Basel

Earlier Days of Gravity Waves Revisited

COLIN O. HINES

Abstract-The means whereby the author came to be involved in the study of atmospheric gravity waves, and then came to involve others in that study, are outlined. In particular, events leading up to, during and following the International Symposium on Fluid Mechanics in the Ionosphere, of July 1959, are described.

Key words: Atmospheric dynamies, atmospheric waves, gravity waves, upper atmosphere, history of atmospheric science.

I greatly appreciate the opportunity accorded me to recall in public "the early days of atmospheric gravity waves". However, as I responded at time I received the invitation, I can give only my own recollections of what was a very personal involvement, for I have never researched the full history. And I can do even that only for the earlier days of gravity waves, since I was not involved in the earliest days nor do I believe that the early days are yet past. Those caveats now in place, I give warning to expect that this indulgence in nostalgia will contain an introductory or warming-up phase, a major climax that can be dated as midmorning on Monday, July 13, 1959, and aftermaths ofimmediate and longer term. Let me begin at what was, for me, the beginning.

I first became aware of atmospheric gravity waves through a paper by DAVID MARTYN (1950) that I read in the spring of 1952 in Cambridge, England, some six or eight months after arriving there to pursue doctoral research.

That was the Cambridge of Hermann Bondi, Tom Gold and Fred Hoyle, with their exhilarating and widely promulgated cosmological theory of continuous creation; the Cambridge of the graduate students Francis Crick and James Watson, as yet unknown to the world at large or even to much of the university community, with their nascent unraveling of the double helix; the Cambridge, in radio studies, of Martin Ryle (with Tony Hewish, then also a graduate student) and his interferometric response to the massive Jodrell Bank radio telescope, and of Jack Ratcliffe (known to all as JAR) and his ionospheric group-one of the

I Arecibo Observatory, Arecibo, PR 00613-0995, U.S.A.

152 c. O. Hines PAGEOPH,

most productive ever assembled-which included Basil Briggs, Ken Budden, Phil Clemmow and Kenneth Weekes on staff, Sid Bowhill, Owen Storey, David Whitehead and many more as students, and visitors such as Jules Fejer, then from South Africa, passing through.

I was loosely associated with this last group throughout my two doctoral years, having made my arrangements for supervision in Cambridge by way of Ratcliffe at the instigation and as a requirement of my prospective financial sponsor, the Defence Research Board (DRB) of Canada. (Prior to its proposal of sponsorship, I had been accepted for research in fundamental physcis with R.E. Peierls, in Birmingham.) These initial arrangements with Ratcliffe had been superseded by others, however, the financial sponsorship having foundered on terms I found unacceptable and I having discovered that Ratcliffe expected his graduate students to be in their places "by nine in the morning". With the concurrence of my new financial sponsor-my tolerant and hard-working wife, Bernice-I turned to certain studies in fundamental electromagnetics I wished to pursue. This was done under the newly arranged, formal supervision of Bondi, whose department, Mathematics, had no office space for staff or students and so had no place in particular for me to be at nine in the morning (or at any other time, for that matter).

My first avenue of study, pursued with Bondi's indulgence and despite his skepticism, involved Ritz's ballistic theory of electromagnetism and relativity. It proved to be a dead end. Next on my agenda had been the proper derivation of Maxwell's (macroscopic) equations from Lorentz's (microscopic) equations of electromagnetism-a topic on which I turned out to be scooped by a year when I eventually completed it, alm ost twenty years later. (This derivation is now employed, for example, in the text by JACKSON (1975).) Also bypassed at this time and consigned ultimately to limbo-for quite different reasons-was my proper explanation for the absence of the Lorentz polarization term from magneto-ionic theory.

Unnerved and demoralized by the outcome of my Ritzian work, and beginning to feel the temporal pinch imposed by the financial pinch, I turned to the generalization of Alfven's recently introduced theory of hydromagnetic waves-a generalization (to ionized gases from collision-dominated conducting fluids) that I had begun before reaching Cambridge, and one whose value as thesis material was certain, even if somewhat debased from fundamental electromagnetism.

Because of its origins in magneto-ionic theory and its possible application to ionospheric processes, the hydromagnetic work brought me into closer contact with Ratcliffe's group once again. Much of the effort of that group was directed toward the observation and interpretation of moving irregularities in the ionosphere, the cause of the irregularities being unknown and the movement itself being termed a "drift" in order to avoid prejudgment of its actual nature as a wind, a wave, or whatever. The observations were all made with radio waves reflected by the ionosphere, and so pertained to its underside. Similar observations, attributed to

Vol. 130, 1989 Earlier Days of Gravity Waves Revisited 153

moving irregularities in the high ionosphere or in interstellar space, were being made by Ryle and his group at the same time through the reception of radiation from radio stars. All such observations provided active discussion in the tea room of the Cavendish.

Turbulence was already a burgeoning area of fluid dynamics, and one of its foremost investigators was George Batchelor, yet another of the Cambridge luminaries of the day. Batchelor was not, so far as I know, directly involved with the ionospheric data, but his nearby presence no doubt enhanced the awareness of turbulence in Ratcliffe's group, as it did in me. In any event, wind-borne turbulence was recognized as one of the mechanisms potentially relevant to the observations. A second mechanism invoked electrostatically induced motions of ionization in a possibly windless atmosphere, while it left the source of the irregularities themselves unspecified. Waves of some sort constituted a third contender, but they too were of an unspecified nature. And the observations were so diverse that more than one interpretation might weIl be needed in the end, each applicable to its own body of data.

A wave interpretation was in fact suggested by oscillatory variations in some of the observations, notably those of the traveling ionospheric disturbances (TIDs) described in so me detail by GEORGE MUNRO (1950) from Australia. (The earliest published data clearly suggestive of waves appear to be those of PIERCE and MIMNO (1940), who in fact proposed an atmospheric "pressure wave" associated with the sun's terminator as the underlying mechanism.)

The TID observations included the now-famous characteristic of an apparent descent of the disturbances through the ionospheric F layer as if from above. Their source might then reasonably be postulated to be some form of hydromagnetic interaction with interplanetary ionization that we would now identify as the solar wind. Ratcliffe, knowing of my earlier and renewed hydromagnetic studies, suggested that I look at Munro's paper and attempt an interpretation based on hydromagnetic waves. I soon found that such an interpretation, though attractive at first encounter, lost its allure when the relevant numbers were inserted: amongst other things, hydromagnetic waves would be too fast to match the observations.

Munro's paper led me to Martyn's, however. Martyn, invoking a smattering of meteorological papers that had previously dealt with atmospheric waves in the presence of gravity, derived a dispersion relation for such waves and showed its compatibility with the horizontal speed of propagation of Munro's TIDs. He also postulated some mechanism of reflection at a height above the F peak to produce a horizontal ducting of wave energy within the F region in what he termed a cellular wave, and he sketched a means whereby the apparent descent of the disturbance might be produced in such a wave by the geomagnetic field acting on the ambient ionization in its enforced motion.

Martyn's theory of cellularity was in places ad hoc at best, it failed to account for the apparent descent of disturbances not traveling equatorward, and it was


neither pursued nor pressed but instead soon abandoned by MARTYN (1955) hirnself. It did, however, lead me to add gravity and pressure gradients of the neutral gas to my hydromagnetic formulation, which until then had incorporated only electrodynamic forces and collisional interactions between the various ionospheric species. This combined melange would have been too complex for me to treat analytically except for its one redeeming feature: with numbers appropriate to the observations, the combined acoustic-gravity-hydromagnetic system could be approximated by a loosely coupled pair of systems, the one acoustic-gravity (as with Martyn before me, he having ignored the hydromagnetic interaction) and the other hydromagnetic. Seeing nothing better to do, I sought a resonance between the two and obtained results that were, if not convincing, at least publishable (HINES, 1955) and, for thesis purposes, defendable. I did pursue this line of enquiry one more stage (HINES, 1956), by introducing pressure gradients into the ionized species (emphasizing, incorrectly, electron pressure rather than ion pressure ); but, like Martyn before me, I did not press the theory on others, for it was too weakly based.

Following my thesis defence and a year of post-doctoral shenanigans in London (financially sponsored, at last, by DRB), I returned to Canada and to the Radio Physics Laboratory (RPL) of DRB in the summer of 1954. There, though I was allowed to finish my TID papers for publication, I found my colleagues quite uninterested in this li ne of study. The most attractive alternative-one that was urged on me and that I accepted in due course-was an involvement with Peter Forsyth (my immediate supervisor) and his group, who were studying radio signals scattered by the ionization of meteor trails. This project had a strong bias toward basic research, whose theoretical aspects I was supposed to untangle and exploit, but it also had important practical applications. It was, in fact, the basis on which Canada was developing a new system of beyond-the-horizon radio communications, code-named JANET.

Those were the days, one must recall, at the peak of the Cold War between East and West; the days when Canada was allowing the USA to build a Distant Early Warning (DEW) line across its northern mainland (without simultaneously allowing the USSR to build one across its southern mainland-a move that I have always thought might have reduced some of the political paranoia already so evident); the days before communications satellites had been designed, much less launched; and hence the days when any secure and reliable means of communication southward from the DEW li ne to some more civilized portion of the country would be considered a major contribution to the nation's defence-a prime plum to be picked by DRB in its quest and in its duty to justify its existence to the government. (Normal short-wave signals were neither secure nor, because of auroral and other disturbances of Canada's ionosphere, reliable. Transmissions of very low frequency, though reliable, permitted only low rates of information transfer.)

JANET functioned in a bi-directional mode (whence its name, transmuted from Janus). The intended recipient transmitted a continuous VHF radio signal, one that


would normally penetrate the ionosphere and travel off into space. But, when a suitably oriented meteor trail of sufficient magnitude was formed, near the 100 km level, the signal scattered by it would be received at the intended transmitting station, weil beyond the horizon. (One thousand kilometers was a typical path length.) That station, triggered to the knowledge that a communication path was now available, at least for the moment, would automatically transmit its stored information in a broad-band bürst that the intended recipient could in turn receive. The bursts of signallasted typically only a tenth of a second and occurred typically only a few times aminute, but they were thought to be re1atively sec ure (in that a spy station was unlike1y to have a suitably oriented meteor trail, of sufficient magnitude, available to it during the short burst) and relatively reliable (in that, at the frequencies employed, ionospheric disturbances were thought to be of little consequence). The JANET system (FORSYTH et al., 1957) ultimate1y lost favor in Canada when, in the week of its first operational trials, it was hit by the strongest of all solar proton events recorded up to that time-one that sparked a small explosion scientific research, incidentally-and JANET was blacked out just as thoroughly as were all other HF and VHF communications over northern Canada. Financial constraints within DRB then took their toll. Meteor-burst systems neverthe1ess continue under development (elsewhere) to this day.

JANET itself plays no part in the gravity-wave story, but it did bring the RPL group into elose association with others in the field of meteor studies, most particularly (for present purposes) with a group at Stanford University (VILLARD et al., 1953) that was working toward a communication system similar to JANET (VINCENT et al., 1957). Of that group, the members most relevant here are Von Eshleman and Larry Manning. But I must digress for a moment before explaining their role.

A second form of radio communication then being developed, in part for application to the DEW line, was that provided by forward scatter from naturally occurring small-scale irregularities of refractivity in the atmosphere and ionosphere. This avenue had been opened by studies, in 1945, of the propagation of radio waves of a few centimeters wavelength over the ocean east of Antigua, at the eastern end of the Caribbean Sea. A ducting of the waves was found, limited to heights of ten or twenty meters, the ducting being associated with water evaporated from the ocean's surface. On propagation paths exceeding 120 km or so, however, the characteristics of the received signal alte red (KATZIN et al., 1949) in a manner that could be accounted for by scattering from turbulence (PEKERlS, 1947). The theory of radio scattering by turbulence in the troposphere was then developed by BOOKER and GORDON (1950). The thought that similar scattering from the ionosphere might be used for long-distance communications had been expressed long before by ECKERSLEY (1932), and it was now pursued with some urgency in the USA (BAILEY et al., 1952, 1955; the final page of the latter gives a revealing insight into the "security" status of this and other, unpublished work of the time).


Perhaps through his participation in this work, Henry Booker undertook a more thorough study of the possible implications of turbulence at ionospheric heights and developed an almost all-encompassing picture of its dominance in irregularities at those heights (BOOKER, 1956). In doing so, he employed as the large-scale end of his turbulence spectrum the irregular wind patterns (with scale size of one kilometer and more) derived by LILLER and WHIPPLE (1954) from photographs of long-enduring (several seconds) meteor trails. This step led hirn to infer persistence time scales of the order one minute and a turbulence dissipation rate of about 25 W /kg. He then went on, in collaboration with Bob Cohen, to develop a more detailed theory of turbulence effects in long-enduring meteor trails and to support that theory with certain radio observations (BOOKER and COHEN, 1956).

The inferred dissipation rate, as it happens, transcribes into a heating rate of about 2000 K/day-an intolerable value, one that would have eliminated this turbulence interpretation of meteor-trail deformations immediately, had it been calculated at the time; but it was not. The first signs of trouble came from quite a different quarter. In retrospect, they might have been anticipated, for Booker and Cohen had taken exception to a well-constructed interpretation of meteor-trail echoes that happened to be in conflict with their own-one previously expressed and supported observationally by Eshleman and Manning, to whom we now return.

These two had presented evidence (ESHLEMAN and MANNING, 1954) that the characteristics of long-enduring radio echoes from meteor trails could be explained on the basis of fairly large-scale deformations of the type revealed by Liller and Whippie, whereas Booker and Cohen were calling upon smaller-scale eddies of comparable strength to render the trails rough for their purposes. Manning and Eshleman soon published a rebuttal (MANNING and ESHLEMAN, 1957) whose abstract reads, in full: "The experimental evidence offered in support of Booker and Cohen's theory is examined point-by-point. It is concluded that the theory does not accurately represent the properties of meteoric echoes. "

The paper went on to include one of the most devastating diagrams ever published, one that might by itself have put an end to the Booker-Cohen theory and one that simultaneously established a place of prominence for quite a different model, already developed and subsequently published by MANNING (1959), in support of the original Eshleman-Manning contentions. It also contained several other pithy statements about the points at issue, and concluded: "However, the theoretical method in Booker and Cohen's paper appears sound. If small-scale turbulence did exist, their conclusions would doubtless be valid. Thus, it appears that they have proved that small-scale trubulence of significant velocity does not exist in the ionosphere at meteoric heights."

In response, BOOKER (1958) reaffirmed his earlier position, countered the arguments that had been made against it, and went on to say, inter alia, "The assumptions of Manning satisfy the equation of continuity of fluid mechanics, but in all probability they satisfy no other principle of fluid mechanics."


One need not be adept at reading between lines to deduce that the debate was, at times, heated to say the least-not only in print but even more in open scientific sessions. Lest there be room for doubt, one final quotation (BOOKER, 1958) should serve: "The fact that the application of principles of fluid mechanics to meteoric phenomena (i.e., by Booker and Cohen) led to results in discord with current thought in the field (i.e., that of Eshleman and Manning) naturally led to heated discussion. The only such discussion to appear in print so far is that of Manning and Eshleman". Needless to say, Manning and Eshleman's was no longer the only such discussion to appear in print, now that Booker's was available.

I followed this debate (insofar as it was conducted in print) from the outside only until, in the course of 1958, I was asked by Millett Morgan to prepare a review artic1e on "Motions in the lonosphere" for a special issue of the Proceedings of the Institute of Radio Engineers that was to commemorate the International Geophysical Year, then nearing its end. (As a footnote: Morgan had first invited Martyn, who had at first accepted but then, at a la te date, withdrawn. Had he not withdrawn, I very likely would have had no further contact with gravity waves.)

I had previously had the vague thought that, though the winds of Liller and Whippie certainly looked irregular enough, still they could be Fourier decomposed into a superposition of sinusoids and so might simply represent a noisy system of waves. The acoustic-gravity waves of my earlier work were the obvious contenders, and I was intending to mention them in my review in the context of TIDs in any event. I therefore performed a back-of-the-enve1ope calculation to confirm that the perturbations winds of these waves might well be predominantly horizontal, as meteor-height winds were known to be (and as they should be, I found, if the wave periods were sufficiently long), and that the vertical scale sizes, which were believed to be considerably shorter than the horizontal scale sizes, were compatible with the theory. This done, I inc1uded in my review (HINES, 1959a) the suggestion that the deformations required by Manning and Eshleman could indeed be waves, and that the waves would have the appropriate properties. I went on to say: "But the amplitudes involved (which would be the "winds" observed) are appreciable fractions of the phase speed deduced, so the oscillation would at best be nonlinear. Some form of turbulence might be expected as a result, but probably not of an isotropic nature. It is certainly not c1ear that the usual criteria for turbulence would apply." This was, in part, an attempt to allow the two sides to find common links, if not common ground.

I might well have abandoned the subject at that point-for I had by then taken on responsibilities as Superintendent of RPL that ate into my research time-were it not for the happenstance of a visit by Clemmow, who had been one of my thesis examiners and badminton-playing buddies in Cambridge. He was on his way (with his family) for an extended stay with Kip Siegel's group at the University of Michigan in Ann Arbor, but he made a stop in Ottawa en route. At the end of an afternoon's tour around RPL and talk of this and that, and with fifteen minutes left


to kill while waiting for the buses to leave, I sketched to hirn the basis of the wave interpretation of meteor-height irregular winds. To my horror, my attempt to rederive the earlier back-of-the-envelope calculation produced only an inverted result: the predominantly horizontal winds were to be associated with horizontal scales that were smaller, rather than larger, than the vertical scales. In front of this witness, I had shown that my just-published speculation was based on nonsense!

Needless to say (in retrospect), once Clemmow and I parted that evening I was able to discover my current error and regain my former conclusion. This had a most peculiar psychological effect on me: it led to the conviction that I must be on the right track. This conviction in turn led me to pursue that track more diligently, now in the early spring of 1959.

Again I must digress. Booker had spent an extended time (perhaps a sabbatical leave) in Cambridge at some point during the preceding few years, I believe in some form of association with Batchelor and with the purpose of increasing his understanding of turbulence. Moreover, the ever-growing supply of unresolved data relating to motions at ionospheric heights had prompted a move by the International Scientific Radio Union (URSI) for a joint study of the field by ionospherists and fluid mechanists. This move, however it began, resulted in the International Council of Scientific Unions requesting Booker to organize an appropiate meeting, to be sponsored by URSI in collaboration with the International Union of Theoretical and Applied Mechanics (IUT AM) and the International Union of Geodesy and Geophysics (IUGG). Booker was soon joined by Batchelor (as IUTAM representative), and together with an organizing committee they made preparations for the International Symposium on Fluid Mechanics in the lonosphere, to be held Thursday-Wednesday, July 9-15, 1959, at Cornell University, Booker's horne base at the time; Ralph Bolgiano, Jr., was organizing secretary. Roughly speaking, the ionospherists (which term included those studying meteors) were to set out the nature of their medium and the observations requiring explanation, while the fluid mechanists (which term included at least one admitted and prominent meteorologist) were to educate the ionospherists on the likely bases of explanation and to provide such explanations as might come to mind (BOLGIANO, 1959). The meeting was intended to be the major focus ofinternational attention in this field for some years to come-the springboard to further advanceand it was to be attended by invitation only.

I had received a second-hand invitation to attend, if I wished, as a representative of DRB. At the time of this invitation, I had little of my own to say on the subject, little commitment to the subject, and no desire to participate as a representative of DRB, which had absolutely nothing to say on the subject and no commitment to it. I had therefore declined, and DRB was to go unrepresented. But now, in the early months of 1959, my interest had suddenly blazed afresh; I might weH have something to say of significance to the symposium, even if it must be presented by proxy.


At some point in the course of these developments, I had come to recognize both the fact and the observational significance of that property of gravity waves whereby vertical phase and energy propagation proceed in opposite directions. Many TIOs had revealed not just one but a regular succession of ripples descending through the F layer (e.g., MUNRO, 1958). These, it seemed, must be phase progressions, so the energy, if carried by gravity waves, must be propagating upward. This was an attractive conclusion, for energy sources above should have produced only the unacceptable hydromagnetic waves whereas those below should include meteorological processes, wh ich would always be present and therefore always able to launch the required waves. They would, moreover, surely launch waves into various azimuths, as had by now become required by TIO observations. (The large-scale TIOs that pro pagate equatorward from auroral latitudes were not yet emphasized as they are now, probably because of different observational biases as between the ionosonde detection of the time and the more prominent incoherentscatter detection of today.)

With meteorological sources now in my mind, the importance of the inherent exponential growth of wave amplitude with height at last struck horne: the ionospheric regions would be like a light-weight tail wagged by a very massive dog, and they must respond to almost any disturbance created below. This growth was al ready known and accepted for tidal oscillations, which I had studied in the works of WEEKES and WILKES (1947) and WILKES (1949), and those oscillations became, through growth to nonlinear amplitude, a further possible source of their cousins, the shorter-period gravity waves now of concern.

But, if the waves were growing with height, how did the noisy spectrum of meteor altitudes give way to the relatively quiescent wave field of the F region? The only reflecting barrier I knew was that of the mesosphere, as in the theory of the semidiurnal tide, and nonlinear breakdown seemed likely to be as much a source of new waves as it would be a sink for old. I needed dissipation, but at the time knew nothing of kinematic viscosity or its growth with height. Indeed, I knew very Iittle of fluid dynamics-which I had never before studied-and I had forgotten most of the thermodyamics I had once been taught. It was clear that I needed education in these matters, but time was pressing if I was to make any contribution to the international symposium without risk of humiliation through ignorance of some fundamental edict of nature. I needed time to work, time away from my desk at RPL.

Good fortune was with me. Siegel had previously arranged matters with ORB so that I would visit his group for a month during Clemmow's stay. Offically, I had been called upon as a consultant on heavy-ion effects in the propagation of whistlers-a subject on which I had recently published and one that Siegel had a research contract to pursue (for the purpose of transpolar detection of nuclear explosions or other major disturbances affecting the ionosphere). But the time required of me for this purpose was minimal-others were doing the real work-


and I was left free to develop the gravity-wave thesis on my own. (Various clues have led me to believe that the V.S. Oepartment of Oefense was weIl aware of gravity waves already, vis-a-vis atomie-bomb testing (see Note 8.1 of HINES, 1974), and that V. H. Weston, who was working for Siegel at the time, was studying them for sueh purposes, probablyon another eontraet of Siegel's (see WESTON, 1961). None of this was ever diseussed with me, however, despite my mandate from The Queen in Right of Canada to reeeive information classified up to---but not beyond -"seeret".)

By the end of my stay in Ann Arbor, I had viseous dissipation weIl under eontrol and thermal eonduetion in hand by extension. The Lagrangian time averages of energy density and dissipation rate given in my 1960 paper (HINES, 1960), for example, were worked through in the eourse of that month. They revealed that moleeular dissipation, at any rate, eould not invalidate my thesis for meteor-height winds but would serve nieely to narrow the observable speetrum at F-region heights to seales eharaeteristie of F-region TIOs. The story was essentially eomplete and, to my mind, almost irrefutable by virtue of its many eontaets with observation. Its one missing link was the range of wave periods to be assoeiated with the irregular winds of Liller and Whippie: I needed thirty minutes or more, in order to make these winds quasi-horizontal, whereas the only time seale then in vogue was the one-minute seale inferred by Booker. Could anyone be persuaded that the appropriate times were as long as thirty minutes?

But still to be faeed was the problem of no invitation. Rather absurdly, perhaps-but what else eould I do?-I wrote to Booker with a summary of my conclusions and with a preprint of a short paper (HINES, 1959b) in whieh Irestated the wave interpretation of meteor-trail d~formations and extended it, through nonlinearities, to suggest an isotropie/anisotropie duality in the nature of turbulenee analogous to that of the aeoustie and gravity ranges of aeoustie-gravity waves. On the merits of these submissions, I asked that he or some nominee present my views at the symposium. He, greatly to his eredit, responded that it was obvious I should attend if I eould, and he issued me an invitation. (This he immediately extended to Fejer on learning that Fejer had reeently joined me at RPL and would like to partieipate, so ORB ended up with two representatives.) The way was now open.

It has been said that diseovery is seeing what everyone else has seen and thinking what no one else has thought. To that, I would have to add: and publishing first.

I feit I had already sueeeeded in diseovery, aeeording to the first definition, but I was in danger of losing out to the addendum. The observations, whieh had so neatly fallen into plaee for me, were about to be set before leading meteorologists and fluid dynamieists, any one of whom (in my imagination) might eome to be in a position to think what only I, until then, had thought.

In order to stake at least some claim to priority, I prepared a one-page summary of my work, and, arriving the day be fore the symposium opened, I managed to have


a copy inserted into the envelope of material each participant would receive upon registering. I also requested time on the program-twenty minutes or more-but was dissuaded with the ass uran ce that there would be plenty of time for discussion and that no formal listing for me need be made.

Things did not work quite that way. For the first three days-Thursday through Saturday-the mornings were programmed to carry two major tutorials by ionospherists and the afternoons were devoted to two corresponding tutorials by fluid dynamicists. Moreover, the fluid-dynamic side of the discussion-and much of the ionospheric side, when an interpretation was presupposed-was oriented, as might have been expected, toward turbulence. To quote Batchelor, on introducing the first afternoon session: " ... at this stage we are not absolutely clear which parts of fluid mechanics are going to be relevant. We will start, however, with the preconceived notion that turbulence is bound to be the most imponant single topic, so that the objective of the six fluid mechanics speakers is to give a short course on turbulence-turbulence, of course, in a broad sense, allowing for the effects of the earth's magnetic field, the density gradient, and several other factors as weil." (TRANSACTIONS, 1959, p. 2044.)

This predisposition toward turbulence was not all bad from my point of view, of course, for it would misdirect attention until, perhaps, I had had my say. But when to have it? There was discussion time, to be sure, but given over primarily to elucidation of the tutorial material as each side tried to understand the other's perceptions and preconceptions. There certainly was no point in the discussion at which I feit I might rise and in effect declare that the tutorial just given, while no doubt of value, was missing the key ingredients that I would now introduce for the instruction of all. Instead, like the young ci vii servant I then was, I steadfastly held my peace and my place. The Transactions record only one furtive claim-staking entry by me during those opening days, and that on the opening day itself (p. 2047): "The distortions of meteor trails that have been observed can be explained fairly weil by wave motions. This will be discussed in more detail later. However, to answer Dr. Martyn [who had enquired about the density variations that might accompany turbulence and had been told they would be negligible], these wave motions are accompanied by strong density variations and could be the source of the observed density changes. This leads to the question of whether random waves with strong coupling (as these have) are the same as turbulence. By your earlier comment, Professor Batchelor, did you mean the coupling of waves does not lead to transfer of energy from large-scale to small-scale motions?" (To which Batchelor is recorded as replying: "My comment referred to uncoupled waves. When the waves are coupled there would be generation of small-scale motion, a condition elose to turbulence.")

The inner elation with which I had arrived at the symposium reached new heights when, during the second tutorial of the Friday morning, J. S. Greenhow introduced 100 minutes as the decorrelation time for the winds at meteor heights:


the long time scale I had expected to introduce only as a postulate had been dropped in my lap! Moreover, Greenhow went on to give the horizontal scale size as a factor of twenty or more greater than the vertical scale size, just as it should then be (GREENHOW and NEUFELD, 1959). But, if my elation grew, so too did my anxiety. For anyone in the audience familiar with the characteristics of gravity waves would now be in a position to combine an atmospheric buoyancy period of 5 minutes with a decorrelation time of 100 minutes (= a quarter to a half wave period), to emerge with that factor of "twenty or more" and with winds that would be quasi-horizontal, as Greenhow was now describing them! Should I speak out immediately, having already tipped my hand on the preceding afternoon? Would it be fair to Robert Long, who was to give, that very afternoon, a tutorial on fluid flow over obstades, and who might weil have prepared his talk with the intent of explaining the Greenhow and Neufeld data as being a consequence of mountain waves? Again I held my peace: if Long had not thus prepared, it would have been foolish of me to give hirn a furt her nudge and a lunch-time of opportunity in wh ich to do so.

Long's tutorial (LoNG, 1959), when it came, was aimed more at laboratory tank studies of an incompressible fluid than at the equivalent atmospheric processes, and it treated the gravity waves more as a formal solution to a boundary-value problem than as a dass of waves in their own right, free to pro pagate as they might. He said nothing of their growth with height in the atmosphere, nothing of their vertical phase and energy opposition, nothing of their tilts in relation to their periods. The dosest he came to breaking through occurred in the discussion afterward, when, in response to prodding by Ratdiffe, he is recorded (TRANSACTIONS, 1959, p. 2055) as saying, " ... the experiments and theory indicate that disturbances of stratified fluids lead, typically, to jet-like motions. Such motions are indeed observed in the troposphere, and there is every reason to believe they occur in the ionosphere. In fact, they would explain many of the observations presented this morning." But this line was not pursued by anyone.

Following the Saturday sessions, safely past, I spent the Sunday filled with apprehension, now for fear that my single sheet of summary, inserted in the delegates' envelopes, would come to be examined on that day of free time and would, for some one or more of the delegates, combine with the observations to trigger their own thought patterns into a new outpouring before I could have my say.

On Monday morning, I asked again to be scheduled but was told now there was no significant time available; there were working groups to report, and so forth. I should speak to some session chairmen, if I insisted, and see if any of them would slot me in.

The chairman of that morning's session was to be Ratdiffe. He allowed me five or ten minutes. I said I needed twenty at least: there were many features of the theory and many facts of the observations to be correlated. He told me no one


could give me twenty minutes at this stage, but he would allow me the full ten. In his favor, I should add that, the last time he had seen me lecturing on these waves (as a post-doc, from London, revisiting Cambridge for the purpose), I had transcribed 1t radians as 90 degrees: he had little cause for confidence in me.

In desperation to make the impact my analysis deserved but time constraints would now preclude, I opened my remarks with: "I have been given ten minutes in which to explain to you half of the observations that have been described here. The work is outlined on a sheet you will have received in your envelopes at registration time."

A flurry of motion, of search, gave me heart that I had gained the audience's attention. I proceeded to outline the nature of the waves I was treating; their exponential growth with height and the magnitude of its implications if meteorological sources were at work-a factor of 103 for meteor heights; the vertical phasejenergy opposition and its implications for TIOs; the verticaljhorizontal structure and wind ratios implied by Greenhow's introduction of a 100 minute decorrelation time; the likely relevance to noctilucent cloud patterns and to drifts in E-region studies; and the role and implications of dissipative processes in narrowing the spectrum seen at meteor heights to that revealed by TIOs a hundred kilometers above (RINES, 1959c).

All of this took more than ten minutes. Ratcliffe, presumably recognizing the import of what I was saying, left me to continue to my own ending some twenty minutes or so after my opening. And then the questions began.

Many, if not most, were sharply put: Wh at would be the sources of these presumed waves? On what grounds could I contemplate retaining a3 a valid solution a wave that grew exponentially as it propagated away from its source? And more, more than are recorded in the Transactions. Though I thought I had already covered the points raised, I repeated and expanded in my answers. Rad I known that meteorologists, though aware of gravity waves beforehand, had already consigned them to a minor role-specifically, to such boundary-value problems as flow over mountains and ducting below an inversion layer-and that they had already revised their operational equations to preclude the generation of these unwanted waves in their large-scale numerical modeling, then I might have been better prepared for the surprise that met my claims of ubiquity. Rad I known that the exponential growth with height would discommode some, as it did, primarily because they commonly used the Boussinesq approximation (of which I had no knowledge at the time), whose solutions yielded no such growth, then I might have converted their skepticism more readily than I did. But, as things were, the somewhat heated debate continued in open session for some time and then again in the corridors afterward. But the critical tones gradually abated, and some favorable upwelling could be perceived.

(Compared with my feelings about it when at its focus, this debate as recorded in the Transactions reads as if edited and expurgated in the fashion of the


Watergate Tapes. Certainly the Transactions lost some of the flavor of all the discussions, as was inevitable of course. One example in particular I would eite quite altruistically, simple for the record. A tutorial 1ecture was given by Gold on hydromagnetics in the ionosphere. In a summarizing statement on the final day, Jim Dungey is reported in the Transactions (p. 2087) as having said, on closing. "In my opinion, the future of hydromagnetics in the ionosphere is excellent." In fact he said, with a self-depricating smile that requested the indulgence of his audience, "In my opinion the future of hydromagnetics in the ionosphere is Golden.")

By the end of the symposium, gravity waves had been accorded a fairly respectable, but only provisional, acceptance as the most appropriate channel of study for the observations I had addressed, while turbulence had retreated to a much more limited role, as in the rapid expansion (rather than distortion) of meteor trails. Booker (TRANSACTIONS, 1959, p. 2089) was able to emphasize this latter role, when he came to summarize events, while Manning (ibid.), following hirn, was able to say: "I have been pleased with the picture of motions in the atmosphere that has been formed at this conference. If we interpret the predominant motions as gravity waves, and assurne that turbulence with velocities no more than 5 or 10 per cent of the wave velocity is driven by the shears, a satisfactory agreement is obtained with the meteor data as I know them."

In a summarizing review of the symposium (BOLGIANO, 1959, p. 2040), the following conclusion was reached: "Although significant progress was made during the symposium, it is possible, in retrospect, to recognize some aspects of it that may justifiably be criticized. Perhaps the most serious criticism that might be made is that the overall problem of fluid mechanics in the ionosphere was approached from a position somewhat too firmly entrenched in preconceived notions. As a result a disproportionate amount of attention may have been directed toward turbulence, as the mechanism, and toward meteor data, as the source of information. It is possible that even greater progress would have resulted had more emphasis been placed on the study of organized motions (waves), and had other radio so unding techniques, such as direct backscatter experiments, been relied on more heavily for the factual data. On the other hand, some of the prineipal conclusions reached in the meeting might never have materialized under those eircumstances."

The immediate aftermath of the symposium falls into three classes in my mind, distinguished by (l) fluid dynamieists and those studying meteors, (2) meteorologists, and (3) ionospherists. The fluid dynamicists, so far as I know, accepted that the ionospherists' problems they had been convened to disentangle were now fairly weIl in hand, with large-scale waves and small-scale turbulence available for their respective roles, though further development of both topics was obviously still needed. Those studying meteors appeared to agree (TRANSACTIONS, 1959, pp. 2084-2091) .

Meteorologists, few of whom were present, exhibited a wide spectrum of responses and do so even to this day. Prototypical of the best was Jule Charney.


Though not a participant in the symposium, he soon had word of what I had argued, soon had me invited to lecture on it in the forthcoming meeting of the American Meteorological Society, and soon had me visit the Massachusetts Institute of Technology to discuss the picture in detail with hirn and his colleagues. I believe he was aleader among those who had written gravity waves out of the equations for large-scale circulation, but I also believe he was a leader in giving me and my thesis credibility in the meteorological community. He told me, in later years, that his own paper with Philip Drazin on planetary waves (CHARNEY and DRAZIN, 1961) was prompted in part by my story; that, though he had wondered before what happened to the energy of planetary waves at high altitudes-energy that would have created a terrestrial corona at low ionospheric heights, were it to get there-he had not seriously pursued the matter until my tale of other waves ascending to the ionosphere had reached hirn. And he spoke words encouraging me to keep apart from the meteorological community, or at least from its prejudices, in that my special contribution to the field-or much of my charm, as he called it, in his own charming way-derived from my quite different point of view.

(The meteorological hierarchy of the day had in fact already induced me to keep somewhat apart, for it had excluded aeronomy from the International Association of Meteorology and Atmospheric Physics (IAMAP) during the restructuring of the IUGG in the early 1950s, on the grounds that the upper atmospheric levels neither were nor could be of consequence to meteorology. As a result, I as an aeronomer have often found myself with the previously orphaned aeronomers who had, for stability, then joined the geomagnetists in what became the International Association of Geomagnetism and Aeronomy. I continue to find myself somewhat apart, not just for this reason but for others as weIl; for example, because I refuse to employ the ambiguous and therefore unscientific adjective and adverb "westerly" and its cousins. Dictionaries define "westerly" as both "to the west" and "from the west"-in that order, in my Webster's. What translators into other languages do with the word, I have no idea. The excuse that the word has historic meaning in application to winds, even if acceptable to the scientific community at large, does not carry over to directions of wave propagation and suchlike. If there be any doubt, I would revert to an earlier paragraph and ask: would meteorologists have expected Canada to seek a northerly flow of information from the DEW line? In my opinion, aeronomers should show pride in their science and hold firm to unambiguous terms such as "westward", and meteorologists would do weIl to join them. All that having been said, I should doubtless add that so me of my best friends have been meteorologists.)

At the other end of the spectrum of meteorologists was one senior individualone who had participated in the symposium, I might add-who went out of his way to attend a talk I gave at the 1960 URSI meeting in London. This talk had been specially invited, presumably to broadcast to the ionospheric community the nature and importance of gravity waves. At the end of my talk, the gentleman in question


rose and announced that gravity waves might, of course, be genera ted from time to time by things like airflow over the Gibraltar peninsula; but, as far as widespread generation by meteorological processes was concerned, we might better forget them. In essence, he was saying they did not occur in his atmosphere. My response-inwardly or aloud, I forget which-was: "And yet they do occur." (Bob Roper, on hearing this anecdote, immediately and correctly identified the meteorologist in question, who apparently had dismissed gravity waves in almost the same terms when serving subsequently as an assessor of his-Roper's-Ph.D. thesis.)

The ionospherists, for their part, were left with a confusion of mixed messages. The impact of the wave thesis at the symposium had been clear enough to those present, and yet sufficient reservation had been expressed publicly by some individuals (and not withdrawn publicly by those same individuals) that there was room for doubters to doubt. This situation was not eased by the incident at the URSI meeting, where other ionospherists were witness to the reactionary view. (Nor had it been helped in 1960 by the American Geophysical Union's spring meeting, an annual meeting where many new theses leap into life. There, my paper opened a session being held in a hotel basement still being converted by carpenters into the complex of auditoriums that had been promised, and my microphone was still being connected as I delivered my talk by a technician who could not get the thing right. I have been informed that I was inaudible beyond the second row.)

Among the points of the gravity-wave thesis most difficult to seIl to ionospherists, or at least, to some ionospherists, was the downward phase progression as a manifestation of upward energy flow. This puzzled me, because the magneto-ionic theory of radio propagation was weIl known to ionospherists and incorporated much the same behavior (with respect to the component of whistler propagation across the magnetic field, for example). But, in the end, I feit obliged to put their opposition to rest by means of a movie film (made in collaboration with and principally by Dave Fultz of the University of Chicago and shown first at an international symposium in St. Gallen, I believe, in 1967). This film exhibited a laboratory tank simulation in which water having height-varying salinity modeled the atmosphere's height-varying density. A rocking paddle at the top of the tank acted as the source of waves and so produced a downward energy flow. It was seen to be producing ripples of phase that progressed downward-in complete accord with normal experience but in complete contradiction of my accompanying patter on gravity waves! Or so it seemed, until a burnt-out match appeared on the screen, collected smoke from thin air, burst spontaneously into flame, and then was struck back into its pristine, virginal state. This entropy experiment was then repeated, but with time now progressing and the phase ripples ascending toward their source, as advertised. And, lest my credibility were in doubt regarding the (alleged) source, a third sequence showed the system initially at rest, the source being turned on, and the region disturbed by the waves gradually descending through the tank as phase ripples rose within that region, being borne out of nothing at its bottom, to meet the


source in perfect synchronism. But the battle had already been won with the first match: I have never, since then, heard this aspect of gravity-wave theory cited as an objection in application to TIDs, or in any other application, for that matter.

Though hydromagnetic waves, in place of graviy waves, were proffered in explanation of TIDs on one later occasion, they were readily dealt with and, I believe, eliminated from further contention. There seems now to be no remaining hesitancy in the acceptance of TIDs as a manifestation of gravity waves, sometimes meteorologically and sometimes aurorally generated. Probably the only serious remaining question about the application of the theory to ionospheric measurements concerns the E-region (and lower) scattering and drift measurements. Even that question lost much of its polemic with the c1ear identification of superimposed waves in the total-reflection E-region results of PFISTER (1971). It continues today only where it should, at the lower levels (typically studied by partial-reflection systems) where turbulence is known to exist and to provide wind-borne irregularities of refractivity, which may or may not be those producing the radio returns and may or may not be revealing their motions directly.

The development of gravity-wave studies spread only slowly in the first years after the Ithaca symposium, for which land some of my former students and post-doctoral fellows can be grateful: the way was left free for us to skim much of the cream. One theoretical step previously made by SAWYER (1959), drawing attention to the upward launching of substantial momentum by mountain waves, seems to have made but little impact on meteorological studies of the day, though it gradually gained force through the sixties and seventies and has blossomed anew in the past decade in application to the middle atmosphere. Earl Gossard, who had spent some years studying gravity waves associated with tropospheric inversion layers, reanalyzed apart of his data and validated the troposphere as a likely source of emissions upward to the ionosphere (GOSSARD, 1962), but again there was no great spin-off of new studies. Clear-air turbulence (CA T) was a topic of great and growing interest in the early 1960s, and it quickly became fashionable to attribute the generation of such turbulence to gravity waves. Bumpiness (as distinct from jiggling) in aircraft flights was often identified as a direct manifestation of these waves, a sort of pseudo-turbulence produced by a broad spectrum of waves in superposition as at meteor heights. These processes came under study by radar, but their complexity defied detailed interpretation save in rare occurrences, and most of those occurrences were (probably) examples of in situ generation of the long-established, evanescent gravity waves in a shearing flow, Kelvin-Helmholtz waves.

As the ubiquitous nature of gravity waves became more accepted in the meteorological community, even to the point that I thought it was beyond attack (in the mid sixties), a new challenge came from a surprising direction: that of the diurnal tide, whose full nature was just then being elucidated by Susumu KA TO (l966a,b) and Dick LINDZEN (1966, 1967). In particular, Lindzen showed that the 1,1 and 1,3 and 1,5 modes of that tide, when superimposed with the amplitudes and


phases his calculations determined, yielded a wind profile at meteor heights remarkably similar to that of one "irregular" wind pattern obtained by Liller and Whipple-the very one, in fact, that Booker had employed to provide the largescale end of his turbulence spectrum and that I had used as being illustrative of gravity waves. Perhaps gravity waves weren't needed after all?

Lindzen presented this result and this suggestion at (amongst other pi aces) an international symposium in Vienna, if I recall the locale correctly. Though the gravity-wave thesis stood on far firmer ground than just the wind profiles of Liller and Whipple-how could a decorrelation time of 100 minutes be produced by a diurnal oscillation, for example?-nevertheless Lindzen's presentation on this occasion was impressive and likely to snare the unwary. I happened to be in the audience, and I happened to have at the tips of my neurons an immediate response, based on my own prior involvement with the diurnal tide (HINES, 1966; reprinted with the relevant calculations in Hines, 1974, Paper 21 and its Postscript). After congratulating Lindzen on the main body of his work, I proceeded to state the fundamental failing of its application to the data of Liller and Whippie: the 1,3 and 1,5 modes would have been effectively dissipated by viscosity-molecular, never mind turbulent-at heights below those at which Lindzen now wanted them. They simply could not produce the wind structure he attributed to them.

This refutation seems to have fallen on many very dear ears. At least one prominent meteorologist present repeated Lindzen's suggestion to me a year or two later, now in the form, "People are saying that perhaps gravity waves aren't needed-that tides can do it all." His questioning tone indicated that he himself was one of those people. Again I outlined the reasons why tides could not do it all, and indeed could not do even the one little bit that had been explicitly claimed. But by then I was losing interest in the campaign. Time would tell; there was really no need for me to, yet again.

I have been amused, after departing the field a few years later and then returning to it in the mid eighties, to disco ver that discussion of the Liller and Whippie da ta had been brought fuH circle by a newly published paper. In it, the author stated that I had been led to my wave interpretation of those data by the sinuous nature of the wind profiles whereas, in fact, they were really rather irregular and might better be interpreted as turbulence!

I have been amused, too, by other recent evidence of recalcitrance in the meteorological community, this dating back again to the late sixties and early seventies. I had then, in work presented orally more than once and subsequently published (HINES, 1972) and republished (HINES, 1974, Paper 30), pointed out the remarkable rate of gravity-wave momentum deposition at the meso pause implied by very strong wave-induced temperature ftuctuations revealed by THEON et al. (1969). This rate, if accepted at even a tenth its value by the modelers of the day, would have thrown into imbalance their models of mesospheric circulation. But neither it nor any downgraded fraction of it was aHowed into those models. Only later, when the rates of radiative relaxation assumed in the models had to be altered by a


large factor for some reason, were gravity waves invoked as a means to restore the

balance--anew, as if from oblivion, or "in from the cold" in a more popular turn

of phrase. And it was the work of Theon and colleagues (in an earlier presentation

(THEON et al., 1967) that lacked the temporal resolution I had been able to employ

to advantage) that was recalled, in due course, to provide observational estimates of

the available momentum ftux for modeling purposes (LINDZEN, 1981). When I asked yet another prominent member of the meteorological community why my

earlier estimates had not been accepted as suggestive, at the very least, I was told,

"The temperature ftuctuations were too large; they were not believed."

There is little one can do, but be amused. I like to believe that Charney would

have been amused, too. All the same, I am delighted that gravity waves have now

found full respectability and that I am able to participate, in these less contentious

times, in their study once again.

REFERENCES

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BAILEY, D. K., BATEMAN, R., and KIRBY, R. C. (1955), Radio transmission at vh/by scattering and other processes in the lower ionosphere, Proc. Inst. Radio Eng. 43, 1181-1231.

BOLGIANO, R., Jr. (1959), A review 0/ the International Symposium on Fluid Mechanics in the Ionosphere, J. Geophys. Res. 64, 2037-2041.

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BOOKER, H. G., and COHEN R. E. (1956), A theory o/Iong-duration meteor echoes based on atmospheric turbulence with experimental confirmation, J. Geophys. Res. 61, 707-733.

BOOKER, H. G., and GORDON, W.E. (1950), A theory 0/ radio scattering in the troposphere, Proc. lost. Radio Eng. 38, 401-412.

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ECKERSLEY, T. L. (1932), Studies in radio transmission, J. lost. E1ectr. Eng. 71, 405-454. ESHLEMAN, V. R., and MANNING, L. A. (1954), Radio communciation by scattering /rom meteoric

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generated in the troposphere, J. Geophys, Res. 67, 745-757. GREENHOW, J. S. and NEUFELD, E. L. (1959), Measurements 0/ turbulence in the 80 to 100 km region

/rom the radio echo observations 0/ meteors, J. Geophys. Res. 64, 2129 2133. HINES, C. O. (1955), Hydromagnetic resonance in ionospheric waves, J. Atmos. Terr. Phys. 7, 14-30. HINES, C. O. (1956), Electron resonance in ionospheric waves, J. Atmos. Terr. Phys. 9, 56-70. HINES, C. O. (1959a), Motions in the ionosphere, Proc. lnst. Radio Eng. 47, 176-186. HINES, C. O. (1959b), Turbulence at meteor heights, J. Geophys. Res. 64, 939-940. HINES, C. O. (1959c), An interpretation 0/ certain ionospheric motions in terms 0/ atmospheric waves, J.

Geophys. Res. 64, 2210-2211. HINES, C. O. (1960),Internal atmospheric gravity waves at ionospheric heights, Can. J. Phys. 38, 1441-1481. HIN ES, C. O. (1966), The diurnal tide in the upper atmosphere, J. Geophys. Res. 71, 1453-1459.


HINES, C. O. (1972), Momentum deposition by atmospheric waves, and its effects on thermospheric circulation, Space Res. 12, 1157-1161.

HINES, C. 0., The Upper Atmosphere in Motion (American Geophysica1 Union, Washington, 1974). JACKSON, J. D., Classical Electrodynamics (Wi1ey, New York, 1975). KATO, S. (1966a), Diurnal atmospheric oscillation. I. Eigenvalues and Hough functions, J. Geophys. Res.

71, 3201-3209. KATO, S. (I 966b), Diurnal atmospheric oscillation. 2. Thermal excitation in the upper atmosphere, J.

Geophys. Res. 71, 3211-3214. KATZIN, M., BAUCHMAN, R. W., and BINNIAN, W. (1949), 3 and 9 centimeter propagation in low ocean

ducts, Proc. Inst. Radio Eng. 35, 891-905. LILLER, W., and WHIPPLE, F. L. (1954), High-altitude winds by meteor-train photography, In Rocket

Exploration of the Upper Atmosphere (Spec. Supp., J. Atmos. Terr. Phys. 1) pp. 112-118. LINDZEN, R. S. (1966), On the theory of the diurnal tide, Mon. Weather Rev. 94, 295-301. LINDZEN, R. S. (1967), Thermally driven diurnal tide in the atmosphere, Quart. J. Roy. Meteorol. Soc.

93, 18-42. LINDZEN, R. S. (1981), Turbulence and stress owing to gravity wave and tidal breakdown, J. Geophys. Res.

86, 9707-9714. LONG, R. R. (1959), The motion ofjiuids with density stratification, J. Geophys. Res. 64,2151-2163. MANNING, L. A., (1959), Air motions and the fading, diversity and aspect sensitivity of meteoric echoes,

J. Geophys. Res. 64, 1415-1425. MANNING, L. A., and ESHLEMAN, V. R. (1957), Discussion of the Booker and Cohen paper. "A theory

of long-duration meteor echoes based on atmospheric turbulence with experimental confirmation", J. Geophys. Res. 62, 367-371.

MARTYN, D. F. (1950), Cellular atmospheric waves in the ionosphere and troposphere, Proc. Roy. Soc. London, Sero A 201, 216-233.

MARTYN, D. F., Interpretation of observed F2 'winds' as ionization drifts associated with magnetic variations, In The Physics of the Ionosphere (Physica1 Society, London, 1955) pp. 161-165.

MUNRO, G. H. (1950), Travelling disturbances in the ionosphere, Proc. Roy. Soc. London, Ser. A 202, 208-223.

MUNRO, G. H. (1958), Travelling ionospheric disturbances in the F region, Aust. J. Phys. 1l,91-112. PEKERIS, C. L. (1947), Wave theoretical interpretation of propagation of 10 centimeter and 3 centimeter

waves in low-Ievel ocean ducts, Proc. Inst. Radio Eng. 35, 453-462. PFISTER, W. (1971), The wave-Iike nature of inhomogeneities in the E-region, J. Atmos. Terr. Phys. 33,

999-1025. PIERCE, J. A., and MIMNO, H. R. (1940), The reception of radio echoes from distant ionospheric

irregularities, Phys. Rev. 57, 95-105. SAWYER, J. S. (1959), The introduction ofthe effects oftopography into methods ofnumericalforecasting,

Quart. J. Roy. Met. Soc. 85,231-243. THEON, J. S., NORDBERG, W. M., KATCHEN, L. 8., and HORVATH, J. J. (1967), Some observations on

the thermal behavior of the mesosphere, J. Atmosph. Sci. 24, 428-438. THEON, J. S., NORD BERG, W., and SMITH, W. S., Aeronomy Report No. 32 (Aeronomy Laboratory, Univ.

of Illinois, Urbana, 1969). TRANSACTIONS (1959), Transactions of the International Symposium on Fluid Mechanics in the Ionos

phere, J. Geophys. Res. 64, 2042-2091. VILLARD, O. G., Jr., PETERSON, A. M., MANNING, L. A., and ESHLEMAN, V. R. (1953), Extended-range

radio transmission by oblique rejiection from meteoric ionization, J. Geophys. Res. 58, 83-93. VINCENT, W. R., WOLFRAM, R. T., SIFFORD, 8. M., JAYE, W. E., and PETERSON, A. M. (1957), A

meteor-burst system for extended range VHF communications, Proc. Inst. Radio Eng. 45, 1693-1700. WEEKES, K., and WILKES, M. V. (1947), Atmospheric oscillations and the resonance theory, Proc. Roy.

Soc. London, Ser. A 192, 80--99. WESTON, V. H. (1961), The pressure pulse produced by a large explosion in the atmosphere, Can. J. Phys.

39, 993-1009. WILKES, M. V., Oscillations of the Earth's Atmosphere (Cambridge Univ. Press, Cambridge, 1949).

(Received November 6, 1987, accepted November 16, 1987)

PAGEOPH, Vol. 130, Nos. 2/3 (1989) 0033-4553/89/030171-10$1.50 + 0.20/0 © 1989 Birkhäuser Verlag, Basel

A Note on Some Early Radiosonde Temperature Observations In the Antarctic Lower Stratosphere

H. R. PHILLPOT'

Abstract-The behaviour of the Southern Hemisphere stratosphere has attracted considerable interest, and been compared with the Northern Hemisphere, since the International Geophysical Year (1957-58) when the sudden ("explosive" or "accelerated") springtime warming phenomenon in the Antarctic was first observed. Over the years studies of upper air temperature and wind observations have been made, principally through the spring months when the polar vortex breakdown occurs, utilising both ground-based (rawinsonde, rocket) and more recently, satellite-derived data. Although the radiosonde-derived temperature data are li mi ted both by the number of reporting stations, and the practical difficulty of securing observations much above the 100 hPa level, useful records exist from 1956 or 1957. These have shown that in the 1959 southern spring, the lower stratosphere was relatively colder, and the warming rate through the season was essentially more regular, with little evidence of the marked but short-lived temperature fluctuations usually found. Similar, but not quite such wide-spread conditions occurred aga in in the 1961 spring. In another study, 30 hPa temperature fields over the Antarctic continent, wh ich could be drawn for the 1967 spring, showed the complexity of the polar vortex breakdown. These features are recalled because extension of the 100 hPa springtime temperature series for the Australian Antarctic station at Casey (66.rS, 1l0SE) shows that in 1985 and part of 1986, the temperature behaviour there was similar to, but not quite so extreme as that which occurred at Mirny (66SS, 93.0C E) in 1959.

Key words: Antarctic lower stratosphere, polar vortex, springtime warming behaviour, radiosonde temperature observations.

Introduction

In the early 1960's, considerable interest was shown in the behaviour of the Antarctic stratosphere following the first observations of the springtime warming during the International Geophysical Year (1957-58). WEXLER (1959) noted that the stratospheric annual temperature cycle is characterised in the (southern) spring months by a relatively short time period when the temperature rise is very strongly marked. At Amundsen-Scott (the South Pole station) for example, the temperature minimum at the 50 hPa level in 1957 was reached in mid-August and increased through October by nearly 50De, and although at other stratospheric pressure levels

I Department of Meteorology, University of Melbourne, Melbourne Australia.

172 H. R. Phillpot PAGEOPH,

the temperature behaviour was a !ittle different, it pointed strongly to a significant contribution to heating by dynamic processes resulting in subsidence and adiabatic heating.

As part of the pro gram of the International Year of the Quiet Sun (IQSY) of 1964--65, the International Antarctic Analysis Centre, then operating in Melbourne, Australia, was asked to provide warnings of expected stratospheric warming events through the spring periods of those years, and a pre!iminary study of available radiosonde observations up to the end of 1963, was made by the author (PHILLPOT, 1964).

These observations were mainly at the 100 hPa level because flights to heights much above this were not regularly made due, at least in part, to the failure of the balloon fabrics under the very low temperatures ( ~ - 80°C) encountered at lower stratospheric levels in the late winter period.

The work was continued (PHILLPOT, 1967a,b), and furt her extended (1969) when, through the 1967 spring, a daily 30 hPa contour chart sequence could be maintained, and 30 hPa isotherm charts were drawn over the continent through October when the major warming occurred at this level.

Several features of the southern polar vortex and its springtime behaviour were identified. These included: the vortex is cold but the temperature and circulation centres are not usually coincident; stratospheric warming varies from year to year both in time of onset and intensity; warming is evident first at levels above 100 hPa (20 hPa or perhaps higher), and in lower latitudes (around 500 S), and is propagated downwards and polewards with time; early seasonal warming appears to result from displacement of the vortex with warm air invading the continent over East Antarctica, principally from the Australian sector, but possibly also from the Indian Ocean sector (i.e., 0-900 E); available contourjisotherm or streamlinejisotherm charts at the 100 and 50 hPa levels show that the cold air is most frequently displaced towards, or persists in the South American quadrant, extending perhaps to about 40o E; the warming at the highest latitudes (> 800 S) is generally regular making it relatively easy to identify the major warming event, but at stations on the continental coast at about latitude 65°S, identification is made much more difficult by shortlived (almost reversible) warming and cooling cycles superimposed on a gradual warming trend; circulation changes, like the temperature variations, are clearer at levels above 100 hPa, and at 30 hPa in 1967 the vortex became elongated and double centred late in the winter or in early spring, its rate of filling was greatest through the first three weeks of October, the centres showed considerable mobi!ity, in association with this mobility, a travelling two-wave system moved progressively and with remarkable regularity in the westerly stream, the waves being in phase with the short period, almost reversible temperature changes at stations on the sub-Antarctic islands and the continental coast (cold troughs, warm ridges).

It was established that this travelling two-wave system at 30 hPa was by no means uncommon in seasons other than spring, but showed considerable year to year variation. It also appeared plausible to explain a ca se of mid-winter warming,

Vol. 130, 1989 Temperature Observations in the Antarctic Lower Stratosphere 173

thought to have occurred near Campbell Island (53°S, l69°E) in July 1962, as being associated with the passage of a migratory ridge.

In addition to all these features, two particular points emerged which appear worth recalling in the light of the satellite da ta now available. They refer to the complex nature of the vortex breakdown shown at the 30 hPa level in October 1967, and the apparently very low 100 hPa temperatures which characterised the 1959 and (to a rather lesser degree) the 1961 spring periods.

The 30 hPa Temperature Behaviour in Oetober 1967

The change of 30 hPa temperature with time through the 1967 spring was examined (PHILLPOT, 1969) at seven selected Antarctic continental stations each with a reasonably complete flight sequence. The seven stations were Mirny, Vostok, McMurdo, Byrd, Amundsen-Scott, Halley Bay and Molodezhnaya (station

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locations are shown in Fig.I), and it was considered that the peak of the final temperature surge over the continent occurred on about 13 October at Mirny, on 19 October at McMurdo and Amundsen-Scott; and, with slightly lower confidence, on 13 October at Vostok, 17 October at Byrd, 22 October at Halley Bay and 31 October at Molodezhnaya.

At Mirny a more detailed examination of 30 hPa geopotential height, wind speed and direction, and vertical wind shear data between 50 and 20 hPa, or 18.3 and 22.3 km, the highest levels for wh ich winds were consistently reported, also led to the conclusion that whilst no marked shift in wind direction occurred until

Figure 2 Isotherm CC) charts for the 30 hPa surface over the Antarctic continent for specified days in October 1967. Estimated or interpolated temperatures are shown in brackets. The direction of the wind shear is shown by an arrow and the magnitude (expressed in m/s/km) at the end of the arrow. Estimated shears

are shown by a broken arrow (for direction) with magnitude in brackets (from PHILLPOT, 1969).


around 17 November, the fluctuation of wind shear direction following the passage of the ridge on 13 October, and the appearance of northerly to easterly shears indicated the reversal of the normal wintertime thermal gradient. Despite observational limitations over the continent, and their complete absence over the sea therefore, reasonable confidence was feit that 13 October marked the end of the winter thermal regime at this level in the Mirny area,

A set of 30 hPa isotherm charts was drawn for October, and Fig. 2 (from PHILLPOT, 1969) shows twelve selected days. The position of the polar vortex is shown by an L (for each centre separately where the vortex was double centred), and the positions of the two ridges which dominated the circulation through the period are indicated by an encircled A and B. The sequence illustrates that the first warm pool was observed on 6 October, near longitude 130-1400 E in association with a ridge (A), whilst on 12 October a second warm centre, also associated with a ridge (B) in about longitude 70oE, moved across East Antarctica then West Antarctica in the next nine days, but that the cold, mostly double-centred vortex persisted, with one centre evident on the coast near the Greenwich meridian, even on 31 October. This shows both the slow, complex nature of the vortex breakdown, and the persistence of a cold pool in the Weddell Sea-Sanae sector, the position and thermal intensity of which could not be precisely identified.

100 hPa Temperature Behaviour

A detailed examination of the 100 hPa temperature behaviour at Antarctic radiosonde stations was made first for the spring period (I September to mid-December) in each year, and Fig. 3 (from PHILLPOT, 1964) shows this for three selected stations, Amundsen-Scott, Wilkes and Macquarie Island for 1957-62 (inclusive).*

As additional data became available, the record was extended by recognising either Mirny or Wilkes as representative of this sector of the Antarctic continental coast and extending the sequence back to 1956 when Mirny was first opened. The two spring periods of 1966 and 1967 were added later (1969), and Fig. 4 is from the 1969 review.

After the marked stratospheric temperature rise observed in the IGY years (particularly 1957), it was surprising to find that through the 1959 spring no sharp increase in the 100 hPa warming rate occurred at any Antarctic continental observing station. For convenience a smoothed curve, called the "1959 warming

* Note: the practice was adopted of using asolid li ne to join temperature values where the time interval was one day or less, and a broken line where the time interval between successive observations exceeded one but not two days. Where the time interval exceeded two days a complete break in the record was shown.

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Temperature ("C) variation at the 100 hPa level between I September and 15 December in each year 1956--1967 (inclusive), at Mirny (66.5"S, 93.00 E) or Wilkes (66.3°S, I lOSE) (from PHILLPüT, 1969).

The 10-year average is for the period 1956--1965.

rate" was drawn für each station with a sm aB degree of additional smoothing used to give consistency between near-by stations particularly those in about the same latitude. With the ten years of record available in 1967 a lO-year mean (1956-65) cou1d be introduced. For Macquarie Island a 10-year mean (1953-62) was available in 1964.

Figure 4 shows very c1early how far below the 1956-65 average was the 1959 warming rate, and the polar vortex in 1959 must therefore have been much colder than usual, at least through this period. 1961 was also a year when the 1959 warming rate appeared to apply quite weB (Figure 3), but examination of aB the station da ta showed that this was not so general as in 1959.

A further extension of Figure 4 has now been made using readily available

100 hPa observations for Wilkes or Casey up to 1986 (Fig. 5). This shows that not only is there considerable variation in the year to year temperature behaviour, but also in some years (e.g., 1975, 1985 and 1986) the seasonal warming behaviour is similar to that in 1959 for part of the time, although it is not so extreme, if the season is viewed overall.


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In summary therefore, if it is recognised that the 1959 warming behaviour illustrated here for Wilkes and Mirny (Figures 3, 4) was widely observed over the Antarctic in that year; the weIl-below ten-year mean 100 hPa temperatures at Macquarie Island in 1959 (Figure 3c); the much sm aller departures from the smoothed 1959 trend shown by the daily temperatures at Wilkes (and Mirny) through the 1959 season than in 1985; then it appears likely that the lower stratosphere over the Antarctic through the 1959 spring may weIl have been even colder than in the 1985 spring.

This conclusion is based on the extension of the Wilkes/Casey record, and it would be very instructive to extend this study to aIl other Antarctic observing stations. Aseries of charts was prepared in 1964 showing streamline/isotherm fields for the 100 hPa level over Antarctica, for selected days in October and November in each year 1959 to 1963, and these should be extended to 1986 to see whether any significant changes can be detected. In the earlier studies it was found for example, that in 1959 the vortex was centred nearer to the geographie Pole than in other years, there was no marked shift of cold air into the South American sector, and the warming in latitude 50-600 S appeared to be more symmetrical around the hemisphere.

In more recent years of course sateIlite data could also be used, as was done in a study directed mainly to stratospheric contour and derived windfield behaviour over high southern latitudes through the 1983 spring (PHILLPOT, 1984). This included some consideration of thermal fields, particularly those associated with an intense stratospheric high located south of New Zealand on 13 October 1983, but did not address the 100 hPa temperature behaviour over the Antarctic continent.

Acknowledgements

I am indebted to Professor W. F. Budd and Dr. lan Simmonds of this University, and an anonymous reviewer for constructive comments and suggestions. The Australian Bureau of Meteorology kindly provided the additional Wilkes or Casey 100 hPa temperature data to 1986.

REFERENCES

PHILLPOT, H. R. (1964), The springtime accelerated warming phenomenon in the Antarctic stratosphere, International Antarctic Analysis Centre, Tech. Rep. No. 3, Commonwealth Bureau of Meteorology, Melbourne.

PHILLPOT, H. R. (1967a), Some further observations on Antarctic stratospheric warming, Polar Meteorology, W. M. O. Tech. Note 87, 379-406.

PHILLPOT, H. R. (1967b), An examination of polar stratospheric warming using temperatures determined from TlROS VII radiation measurements, International Antarctic Meteorological Research Centre, Tech. Rep. No. 8, Commonwealth Bureau of Meteorology, Melbourne.


PHILLPOT, H. R. (1969), Antaretie stratospherie warming reviewed in the light 0/1967 observations, Quart. J. R. Met. Soc. 95, 329-348.

PHILLPOT, H. R. (1984), Satellite-derived radianee data over high southern latitudes, Met. Dept. Pub. No. 26, University of Me1bourne.

WEXLER, H. (1959), Seasonal and other temperature ehanges in the Antaretie atmosphere, Quart. J. R. Met. Soc. 85, 196-208.

(Received August 17, 1987, revised February 29, 1988, accepted March 3, 1988)


The Impact of Base-Level Analyses on Stratospheric Circulation Statistics for the Southern Hemisphere

DAVID J. KAROLy 1

Abstract-The impact of different base-level analyses on derived stratospheric circulation statistics for the Southern Hemisphere has been assessed. Three different sets of daily operational analyses of geopotential height at 100 hPa for September, 1981 have been used as the base-level analyses, combined with a single set of daily thickness analyses for the stratosphere. The circulation statistics considered inc1ude mean fields, transient eddy statistics, Eliassen-Palm f1ux diagnostics and vorticity fields.

In general, the different base-level analyses do not change the qualitative description of the circulation statistics but they lead to marked quantitative differences, particularly at high latitudes. The statistics which are most sensitive to the different base-level analyses are those which emphasise the shortest space scales through multiple differentiation of the height field and the shortest time scales, such as daily Eliassen-Palm f1ux diagrams or the daily vorticity fields.

Key words: Southern Hemisphere stratosphere, sensitivity of stratospheric circulation.

1. Introduction

Over the past two decades, satellites have provided a vast improvement in data available for the Southern Hemisphere (SH) stratosphere in terms of both the spatial and the temporal coverage. This has permitted a number of observational studies of circulation statistics for the mean flow and transient eddies in the Southern Hemisphere stratosphere; for example HARTMANN (1976), HARTMANN et al. (1984), MECHOSO et al. (1985), RANDEL (1987a) and SHIOTANI and HIROTA ( 1985).

These studies have gene rally derived circulation statistics from geopotential height analyses for the stratosphere. The height analyses have been built up using base-level height analyses for some level in the lower stratosphere, obtained from operational tropospheric analysis systems, and inter-level thickness analyses obtained from satellite radiance data. SALBY ( 1981) has considered the optimal way to choose the base-level for building up the stratospheric height analyses but there appears to have been little study of the impact of the base-level height analyses on

I Department of Mathematics. Monash University, Clayton, Victoria. 3168, Australia.

182 D. J. Karo1y PAGEOPH,

derived stratospheric circulation statistics. In particular, in the Southern Hemisphere, where the differences between operational analyses for the upper troposphere are larger than in the Northern Hemisphere, the impact of different base-level analyses is likely to be larger.

In this study, three sets of daily base-level height analyses for the SH have been used with a single set of satellite-derived thickness analyses for the SH stratosphere to assess the impact of the different base-level analyses on the derived circulation statistics. To save space, the results for a single month only, September 1981, are presented but they are representative of the other months in 1981 in terms of the impact of the base-level analyses. This month was chosen as it had relatively large wave activity. This year, 1981, was chosen as it was prior to a number of improvements in operational tropospheric analysis systems for the SH and long enough after the Global Weather Experiment in 1979 that there were few drifting buoys operational in the SH. Thus, the differences between the base-level analyses for 1981 are likely to be as large or larger than for any year in this decade.

The three sources of the base-level height analyses were the operational SH analyses from the National Meteorological Center, U.S.A. (referred to as the NMC analyses), the European Centre for Medium Range Weather Forecasts (referred to as the ECMWF analyses) and the Australian Bureau of Meteorology (referred to as the AUS analyses). Stratospheric thickness analyses for the SH from the British Meteorological Office (BMO) have been used to build-up height analyses for the stratosphere from the different base-level analyses.

In the next section, a more detailed description of the da ta and computational methods used for the circulation statistics is given. Following this, the circulation statistics obtained using the different base-level analyses are compared, first for the time-mean fields and standing eddy statistics, then for the time-mean transient eddy statistics and Eliassen-Palm (EP) flux, and finally for the daily EP flux and vorticity fields.

It will be shown that the general qualitative description of the circulation statistics is independent of the base-level analyses but that there are marked quantitative differences, particularly at high latitudes. The statistics which are most sensitive to the different base-level analyses are those which emphasise the shortest space scales through multiple differentiation of the height field and the shortest time scales, such as the daily EP flux diagrams and the daily vorticity fields.

2. Data and Analysis

The base-level analyses used in this study were daily 1200 GMT height analyses for September, 1981 from NMC, ECMWF and Australia at 100 hPa. These analyses were used on 5 x 5 degree latitude-longitude grid from lOoS to the South Pole. The stratospheric data were obtained originally from the BMO daily 1200

Vol. 130, 1989 Base-Level Analyses for the Southern Hemisphere Stratosphere 183

GMT height analyses on the same horizontal grid for the SH on seven levels in the stratosphere (100, 50, 20, 10, 5, 2, 1 hPa). These analyses were built-up from the NMC 100 hPa height analyses at the BMO using inter-level thickness fields derived from SSU radiance data. By subtracting the base-level analyses, the 6 inter-level BMO thickness analyses were recovered and used to build-up three sets of stratospheric height analyses from the different base-level analyses.

To derive the circulation statistics, exact1y the same procedure was used for each set of analyses. Geostrophic zonal (u) and meridional (v) wind components were computed from the height (z) analyses using second-order centred differences. It is likely that this geostrophic wind will have larger differences from the real wind than the balance wind computed from the height field (RANDEL, 1987b) but these differences are not important for this comparison of the impact of the different base-level analyses. Temperature (T) was computed hydrostatically from the height analyses using second-order centred differences. To compute the temperature at 100 hPa, height analyses at 200 hPa from NMC, ECMWF and Australia were used. This use of centred differences led to a reduced domain available for the comparison; 6 levels in the stratosphere (100, 50, 20, 10, 5 and 2 hPa) and 15 latitudes from 15°S to 85°S. If further differentiation was required for computing the circulation statistics, such as for the vorticity or the EP flux divergence, second-order one-sided differences were used at the edges so that the domain was not reduced further.

The circulation statistics computed included (i) monthly mean fields, x where x is one of the variables, z, u, v, T and the overbar

indicates the monthly mean; (ii) standing eddy statistics: the root-mean-square zonal variations of height,

[2"*2]1 /2, and the standing eddy heat, [v*T*], and momentum, [v*ü*], ftuxes, where [x] is the zonal mean and x* = x - [x] is the departure from the zonal mean;

(iii) transient eddy statistics: the root-mean-square daily variations ofheight, (Z ' 2) 1/2,

and the transient eddy heat, v'T', and momentum, V'U ' , fluxes, where x' = x - x is the daily departure from the monthly mean;

(iv) EP ftux diagrams (EDMON et al., 1980) showing with arrows the vertical and horizontal components of the EP flux and with contours the eddy-induced torque on the zonal mean ftow. The EP ftux vectors, F, and the torque on the mean f10w DF, are defined as in MECHOSO et al. (1985), using standard notation,

F = (Fv' FJ = p,.a cos <p( - [v*u*],J[v*8*]/[8zD, and

o[u] Tl + ![v] * + ff = DF = v, F/(psa cos <p).

(v) relative vorticity field,

,= ov _ ou. ox oy

184 D. J. Karoly PAGEOPH,

3. Results

(i) Monthly Mean Fields

The monthly mean height field at 100 hPa from the NMC analyses in Fig. shows typical features of the mean SH lower stratosphere, with strong meridional gradient but small zonal variations. The differences of the mean height field from the two other sets of analyses are of order 100 m, with the largest differences at high latitudes. There appear to be some common differences, with the NMC analyses higher than both the ECMWF and AUS analyses over Antarctica, south of Australia and over the south-east Pacific.

(a) i. NMC

Figure I (a) Monthly mean height (2, in m) at 100 hPa for the NMC analyses and the differences from the other

analyses; (b) NMC-ECMWF and (c) NMC-AUS. Negative contours are dashed.


(a) [ul, Me

2

5

Ö

~ 10 .... er ::J 20 Ul Ul

'" er "'-

SO

100 30 60

I ATITUDE [QEG SI

(b) MC-EeMWF

1 o

o

1 30

1 11 I I 11 I I 11 I 1118 111.0 11 I I 11 I I 11 I I 11 II 1-6,4

11. I ~1~;~: \,~ 11 I I 11 I I

60

LRT !lUDE [QEG 5 I

Figure 2

(c) Me-AUS

30

11 11111111 1111 1 111 1111 11 1111881

o ~ 1111"'''' 1 11111111 2 11111111

1""1111 11111111 11111111

60

8'831111

III~tlll1 ~1";';1111 Ir~iY,,1 11111111

LRT !lUDE [QEG 5 I

Zonal mean monthly mean zonal wind ([ü] in ms - I) for the NMC base-level analyses and the differences from the other base-level analyses; (b) NMC-ECMWF and (c) NMC-AUS.

Since the height fields at higher levels are built up from these base-level analyses at 100 hPa using the same thickness fields, the height differences at higher levels are the same as those in the base-level analyses, i.e., the height differences are barotropic (the same at all levels). Also, since the wind has been calculated geostrophically from the height gradients, the differences in the height fields lead to differences in the geostrophic winds which are also barotropic. This can be seen in Fig. 2, which shows the zonal-mean monthly me an zonal wind. The differences of the mean wind are of order 5 ms - I at high latitudes, with the NMC zonal winds weaker than those from the ECMWF or AUS analyses. The temperature field is independent of the base-level analyses at all levels above 100 hPa because it is obtained from the thickness field.

(ii) Standing Eddy Statistics

The standing eddy statistics given in Fig. 3 show that this month had large amplitude standing eddies with root-mean-square zonal variations of height of order 100 m at 100 hPa, growing to more than 500 m at 2 hPa. The differences of the eddy statistics from the different base-level analyses are not the same at all levels because the eddy statistics are quadratic quantities. The NMC base-level analyses give larger standing eddy amplitudes at middle latitudes, of order 10 m, and sm aller amplitudes at high latitudes, of order 20 m, but these differences are relatively small in the middle and upper stratosphere. The poleward standing eddy heat flux obtained using the NMC base-level analyses is larger in middle latitudes than for either of the other analyses, but it is weaker than that from the AUS base-level analyses at very high latitudes.


(a) [l " 2)~. MC NMC-ECMWF NMC-AUS

5

Ci "- 10 :: ~ 20 V> V>

ii! "-

SO

100

(b) [i "t "). NM NMC-ECMWF • MC-AUS

111111 11 1 111111 I I I c>

111111 :" ,~ 5 I \ \ \ \ I 1'/" I

\ \ III ~ '0 ' , I tf I I I I' 10 ' I , I ~ 10 I \I I-i 1 I ,

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~ 20 I I I / I I

V> I \ '/ 1 1 ii! I~ 1 I "- \ ·0." I I

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f\ I 1

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(c) [,. "u"J. NM NMC-ECM"'F NMC-AUS

2

5

Ci "- 10 ~

~ 20 V> ... g:

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100 30 60 30 60 30 60

lAT ITU[)( IDEG SI LRTITUlJE IDEG 51 lRTIlUOE IOEG SI

Figure 3 Zonal mean standing eddy statistics: (a) Root-mean-square zonal variations of height ([i*2) 1/2 in m), (b) heat flux ([v*t*) in °C ms - I) and (c) momentum flux ([v*u*) in m2 s - 2) . The left panel is for the monthly mean NMC base-level analyses and the centre and right panels are the dilferences of the

statistics, NMC-ECMWF and NMC-AUS, respectively.

The differences of the standing eddy momentum fluxes for the different baselevel analyses are relatively larger than for the heat fluxes. This is due to the differences in both zonal and meridional wind arising from the different base-level heights, whereas the temperatures are the same. The momentum flux from the NMC base-level analyses has a complex structure at upper levels, with both poleward and equatorward fluxes in meridional bands of about 20 degree width.

Vol. 130, 1989 Base~Level Analyses for the Southern Hemisphere Stratosphere 187

This indicates that there are regions of strong momentum flux convergence and divergence. However, RANDEL (1987b) has shown that the momentum flux is dependent on the method used to compute the wind from the height field and these regions of flux divergence may be spurious. The largest differences of the momenturn flux occur at high latitudes where, from the AUS analyses, there is stronger poleward momentum flux and no region of equatorward momentum flux at 60oS, as in the NMC and ECMWF analyses.

(iii) Transient Eddy Statistics

A simple measure of the amplitude of the daily transient eddies from the base-level analyses is the root-mean-square daily variations of height at 100 hPa, shown in Fig. 4. This indicates that the standard deviation of the daily height at

(c) NMC·AUS

Figure 4 As in Figure 1 but for the root-mean-square daily variations of height at 100 hPa ((Z'2) 1/2 in m).

100 hPa has a maximum of between about 150 m and 250 m at about 55°S. In the NMC analyses, there is a second maximum over Antarctica, so that the amplitude is twice as large in the NMC analyses over Antarctica than in the other two analyses. There do not appear to be other major systematic differences in the transient eddy amplitudes, although there is some indication of weaker amplitudes

(a) [(/2)1), N:'IC :-1MC·ECMWF :-<MC-AUS

5

Ö a.. :5 10 ... S 20 Vl Vl ... '" CL

50

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(b) [i7f'J, NMC m.1C·E 1WF N:'1C·AUS

2 1111 I I ' \

\ 111' 1 1 ' / /

\ /111 / 1 ' I /

5 I 1111 I I I 1 I I 'I ~ 1 "

I I I \ Ö

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(c) p;7), NMC MC-E MWF NMC-A S

2 I I \ 11111/ 1 '111, I I I I .1111111 ,~II ,I I I 1111111' '1" 1

5 \ \ \1111111 'r1~11:,/ I -h ö "- \ \11111,1 0/"1/ I

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10 " 1\1\"~'Jiit',; I

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50 1 \ - I I

/ -~ I ,I,' /

100 30 60 30 60 30 60

lATITUDE IOfG SI lRTITUDE IDEG 51 lATlTUOE IDEG SI

Figure 5 Zonal mean transient eddy statistics: (a) root-mean-square daily variations of height ([(Z ' 2) ' /2J in m). (b) heat flux ([uT'J in °C ms - ') and (c) momentum flux ([u'u ' in m2 s - 2). The left panel is the monthly mean for the NMC base-level analyses and the centre and right panels are the differences of the statistics,

NMC-ECMWF and NMC-AUS, respectively.

in the NMC analyses over the south Indian Ocean and larger amplitudes over the south Pacific.

The differences of the transient eddy statistics vary with height as shown in Fig. 5. The transient eddy amplitudes are typically about 50% larger than the standing eddy amplitudes (compare Fig. 5( a) with Fig. 3( a». As found from Figure 4, the largest differences of the transient eddy amplitudes occur at very high latitudes, with larger amplitudes from the NMC analyses. The transient eddy heat flux is about half the standing eddy heat flux (compare Fig. 5(b) with Fig. 3(b», with small differences except at high latitudes, where there is a stronger poleward flux from the NMC analyses. The transient eddy momentum flux has a simpler structure and much stronger poleward transport than for the standing eddy momentum flux (compare Fig. 5( c) with Fig. 3( c». Again, the momentum flux differences are much larger than the heat flux differences and they increase with height. The largest differences are at high latitudes, with stronger poleward flux from the NMC analyses.

(iv) Mean Eliassen-Palm (EP) Flux

The effect of the eddies on the me an flow can be represented using EP flux diagrams, which show the EP flux and the eddy-induced torque on the mean flow due to the EP flux divergence. The monthly mean EP flux diagrams for all eddies are shown in Fig. 6 for the three different sets of base-level analyses. There is good general agreement between these three EP flux diagrams. On close inspection, however, there are some marked differences. There is EP flux convergence and a poleward EP flux component from the AUS analyses in the lower stratosphere at

(a) M (b) ECMWF (c) AU

2r-~cl~I~~~~~" ,-~~~~~~~~ r--~~~~~~ ..

5

~ 10

~ 20 <Il UJ

'" a..

so

I I 1 I

60 2 . 0E+'~

LAll TUOE 10EG 51

60 2. OE<')

LAT ITUIJE WEG 5)

Figure 6

60 2. OE<"')

LATITUOE IOEG SI

Monthly mean Eliassen-Palm flux (kgs ~. 2) shown with arrows and contours of the eddy-induced torque on the zonal mean flow (ms- 1 day - 1) from (a) the NMC base-level analyses (b) the ECMWF base-level analyses and (c) the AUS base-level analyses. The scale for the EP flux is shown on the bottom right of

each panel.

190 D. 1. Karoly PAGEOPH,

high latitudes but ftux divergence and equatorward ftux from the other analyses. EIsewhere there are differences of up to 50% in the magnitude of the EP ftux divergence.

(v) Daily Wind Variations and EP Flux Diagrams

A sequence of zonal mean wind fields and EP ftux diagrams from the NMC base-level analyses at two-day intervals from 13 to 17 September is shown in Fig. 7. There was a pronouced acceleration of the zonal mean jet over the first two-day interval and a deceleration of similar magnitude over the second two-day interval. There is a good agreement between the sense of these zonal wind changes and the eddy-induced torque on the me an ftow shown in the EP ftux diagrams. There is EP divergence and an implied acceleration of more than 15 ms - I day - I on 13 September, changing to EP ftux convergence and an implied deceleration of 30 ms - I day - I on 17 September. The EP ftux diagrams for the same days from the ECMWF and AUS base-level analyses are shown in Fig. 8. There is overall agreement in the sense of the major changes over the five days but the differences

(al (,,1. MC, 13 Sept. 15 Sept. 17 Sept.

2

5

Ö ~ 10

~ 20 :::: er "-

SO

100

(1)) EP Hux. 1C

2

5

Q ö ~ 10

~ 20 . -~ '"

~ :::: :l:

50 .. \

100

Figure 7 (a) Daily 1200 GMT zonal mean zonal wind ([u] in ms -I) and (b) Eliassen-Palm flux and eddy-induced torque on the zonal wind from the NMC base-level analyses. The three panels from left to right are for

the dates 13, 15 and 17 September, respectively.


(a) ECMWF, 13 pt.

2 I \ I \ I \

5 ... :/3-1-? ö I , 0

~ 10 Q" l:~-.... er => 20 '" '" .... ce; "-

SO fl- ---

~'O 100

(b) A S

2

5

Ö "- 10 :5 w er :;;;> 20 '" '" UJ er "-

SO

100

15 S pt.

LRT ITUDE

Figure 8

17 ept.

60 5.0E+0

LRT I TUOE IOEG SI

EP flux diagrams as in Figure 7 (b) but from (a) the ECMWF base-level analyses and (b) the AUS base-level analyses.

between these daily EP ftux diagrams are much larger than for the mean EP ftux diagrams in Figure 6. The EP ftux in the lower stratosphere shows marked differences between the different base-level analyses. The eddy-induced torque on the mean ftow has similar overall patterns but its magnitude varies by more than 50% between the different analyses.

(vi) Daily Vorticity Field

All the circulation statistics which have been presented so far have involved some degree of averaging, such as time-averaging for the monthly mean fields , zonal-averaging for the EP ftux diagrams or both. This averaging is likely to reduce the impact of the different base-level analyses. Differentiation tends to accentuate the differences. A particularly severe test of the different base-level analyses is a comparison of the daily relative vorticity field at 100 hPa, which involves the second

192 D. J . Karoly PAGEOPH,

Figure 9 Relative vorticity (( in 10 - 5 S - 1) at 100 hPa at 1200 GMT on 17 September from (a) the NMC analyses, (b) the ECMWF analyses and (c) the AUS analyses. The zero contour is not shown and negative

contours are dashed, with contour interval of 2 x 10 - 5 S - 1.

derivative of the height field and no averaging. The relative vorticity at 100 hPa on 17 September, 1981 from the three different analyses is shown in Fig. 9. There are so me features in common, such as the three major troughs (negative 0 at about 600S at 100E, 1200E and 600Wand the ridges at 300S at OOE and 150°E. EIsewhere, there are many small-scale features in each analysis which are not found in the other two. These small-scale features and the associated wind variations are typical of all the daily base-level analyses. Since these features are apparent at the base-level but not consistent between the different base-level analyses, they lead to similar small-scale differences at all levels. It is possible that so me smoothing of the height fields used for the base-level analyses may remove some of these small-scale features and lead to better agreement.


4. Conclusions

Stratospheric circulation statistics for September, 1981 have been computed from height analyses for the SR obtained from three different sets of daily 100 hPa base-level analyses from NMC, ECMWF and Australia and a single set of daily thickness analyses for the stratosphere from the BMO. In general, there is good qualitative agreement between most of the statistics from the different base-level analyses. The agreement is better if the statistics involve averaging, such as time-averaging or zonal-averaging. The differences are larger for statistics involving no averaging, such as daily fields, or for statistics involving multiple horizontal derivatives, such as the EP flux divergence or the relative vorticity, as this accentuates small-scale features. The quantitative differences for the daily EP flux diagrams and the daily relative vorticity using different base-level analyses are large and place doubt on the reliability of these statistics.

The largest differences for all the statistics occur at high latitudes, over the Southern Ocean and Antarctica, where the differences between the base-level analyses are largest. Routine operational analyses of the SR troposphere and lower stratosphere are least reliable in these regions because of the sparse observational data and the steep topography at the Antarctic coast. There has been improvement in the operational analysis systems for the SR at all three analysis centres since 1981 and it is likely that the differences between the current operational analyses at 100 hPa from NMC, ECMWF and Australia are sm aller than in 1981. Rowever, it is like1y that significant differences still exist and they will be most apparent in the same circulation statistics as described above.

Comparison of the relative vorticity fields has indicated that there are smallscale features in the 100 hPa height analyses which are not common between the different analyses. The effect of these small-scale differences could be reduced by smoothing the base-level analyses prior to their use for building-up the stratospheric height fie1ds. Rowever, there are large-scale systematic differences between the base-level analyses, as shown by the differences of the mean height in Figure I, which lead to significant differences of the circulation statistics and which would not be removed by smoothing the base-level analyses.

This study has shown that circulation statistics for the SR stratosphere are dependent on the base-level analyses, to a varying degree. Statistics involving time-averaging and zonal-averaging are more reliable but derived quantities for individual days obtained from any particular base-level analysis should be treated with appropriate caution.

Acknowledgements

A preliminary version of this paper was presented at the MASR workshop in Williamsburg, Virginia in April, 1986. I would 1ike to thank Bill Grose, Alan


O'Neill and Alan Plumb for encouragement and helpful discussions during the course of this study, Moya Tyndall for assistance with some of the programming and Alison Leicester for typing the manuscript. The BMO thickness data and NMC analyses were provided by Alan O'Neill via the CSIRO Division of Atmospheric Research and the Australian analyses were provided by the Australian Bu.reau of Meteorology. Part of this study was supported by a grant from the CSIRO/Monash University Collaborative Research Fund.

REFERENCES

EDMON, H. J., B. J. HOSKINS, and M. E. McINTYRE (1980), Eliassen-Palm cross-sections /or the troposphere, J. Atmos. Sei. 37, 2600-2616.

HARTMANN, D. L. (1976), The structure 0/ the stratosphere in the Southern Hemisphere during late winter 1973 as observed by satellite, J. Atmos. Sei. 33, 1141-1154.

HARTMANN, D. L., C.R. MECHOSO, and K. YAMAZAKI (1984), Observations 0/ wave-mean f10w interaction in the Southern Hemisphere, J. Atmos. Sei. 41, 351-362.

MECHOSO, C. R., D. L. HARTMANN, and J. D. FARRARA (1985), Climatology and interannualvariability 0/ wave, mean f10w interaction in the Southern Hemisphere, J. Atmos. Sei. 42, 2189-2206.

RANDEL, W. J. (l987a), A study 0/ planetary waves in the southern winter troposphere and stratosphere. Part I: Wave structure and propagation, J. Atmos. Sei. 44, 917-935.

RANDEL, W. J. (1987b), The evaluation 0/ winds /rom geopotential height data in the stratosphere, J. Atmos. Sei. 44, 3097-3120.

SALBY, M. L. (1981), Optimal determination 0/ geopotential base height /or stratospheric temperature sounders, Pure Appl. Geophys. 119, 711-725.

SHIOTANI, M. and I. HIROTA (1985), Planetary wave-mean f10w interaction in the stratosphere: A comparison between the Northern and Southern Hemisphere, Quart. J. Roy. Met. Soc. 111, 309-334.

(Reeeived September 28, 1987, revisedjaccepted Mareh 16, 1988)

PAGEOPH, Vol. 130, Nos. 2/3 (1989) 0033-4553/89/030195-18$1.50 + 0.20/0 © 1989 BirkhäuserVerlag, Basel

Comparison of Data and Derived Quantities for the Middle Atmosphere of the Southern Hemisphere

W. L. GROSEI and A. O'NEILL2

Abstract-Before data from satellites can be used with confidence in dynamical studies of the middle atmosphere an assessment of their reliability is necessary. To this end, independently analysed data from different instruments may be compared. In this paper, this is done for the Southern Hemisphere as a prelude to the dynamical studies of the middle atmosphere being fostered by the MASH project of the Middle Atmosphere Program. Data from two infrared radiometers are used: a limb scanner (LIMS) and a nadir sounder (SSU). While there is usually qualitative agreement between basic fields (temperatures, winds), substantial quantitative differences are found, with more pronounced differences in fields of Eliassen-Palm flux divergence and Ertel's potential vorticity.

The fidelity of the base-level analysis to which satellite data are tied is important for calculating quantities of relevance to dynamical theory. In the Southern Hemisphere, conventional data are sparse and, through the analysis procedure, this introduces errors into derived fields for the middle atmosphere. The impact of using base-level analyses from different sources is assessed. Large discrepancies are found in fields computed by differentiation.

Several techniques are suggested whereby the reliability of fields derived from satellite data may be gauged.

Key words: MASH project, inter-comparison of satellite data.

1. Introduction

For over 15 years, near global measurements of temperature and constituents obtained from satellites have provided information on the thermal structure and distribution of trace species in the middle atmosphere. From these data, it has been possible to infer quantities useful in studies of dynamical and transport processes in the middle atmosphere (e.g., winds, potential vorticity, fluxes of trace chemicals). Data are available for different time periods from several instruments, each with differing spatial coverage and resolution. Before such data can be used with confidence in dynamical studies, an assessement of their reliability is necessary, an indication of which can be obtained from a comparison of data from different

I NASA Langley Research Center, Hampton, VA, U.S.A. 2 Meteorological Office, Bracknell, Berkshire, U.K.

196 W. L. Grose and A. O'Neill PAGEOPH,

sources, e.g., different radiometers on board sateJlites in independent orbit. As part of the MAP PMP-1 projece, a number of such exercises have been completed for the Northern Hemisphere (RODGERS, 1984; GROSE and RODGERS, 1986). For example, a comparison was made of basic temperature data and derived quantities from the foJlowing instruments: the Limb Infrared Monitor of the Stratosphere (UMS); the Stratospheric and Mesospheric Sounder (SAMS); and the Stratospheric Sounding Unit (SSU).

These studies concentrated on the Northern Hemisphere for two reasons. First, the availability of conventional (rocketsonde, radiosonde and baJloon) data for comparison with the sateJlite data was much greater than for the Southern Hemisphere, where conventional data are sparse. Secondly, winter in the Northern Hemisphere is more dynamicaJly active, with striking phenomena such as major mid-winter warmings, and hence has attracted more interest. It is now being increasingly realised, however, that the middle atmosphere of the Southern Hemisphere, despite the absence of major mid-winter warmings, is far from quiescent. Very intense, dynamicaJly induced warmings occur in late winter; the intense polar night vortex may be the seat of instabilities which may affect the circulation on a large scale; and traveJling waves can, on occasions, be clearly seen in the more zonaJly symmetric circulation of the Southern Hemisphere.

The marked differences in the circulation of the two hemispheres afford atmospheric scientists the opportunity to study wh at are, in some respects, two different atmospheres. The elucidation of dynamical mechanisms and transport processes is bound to be furthered by comparison.

Under the auspices of Midd1e Atmosphere Pro gram, the MASH project (Midd1e Atmosphere of the Southern Hemisphere) was initiated to act as a focus for a concerted study of the dynamics and transport in the middle atmosphere of the Southern Hemisphere. An integral part of this project is a comparison of data from different sources, along the lines of that done for the Northern Hemisphere. To this end, an international workshop--involving scientists from Austra1ia, Federal Republic of Germany, Japan, U.K. and U.s.A.-was held in Williamsburg, Virginia in April 1986. In addition to the comparison of satellite data, an important aim of this workshop was to assess the impact of using upper troposheric analyses from various sources as base levels. (A base level analysis of geopotential height, typicaJly at 100 mb4 , is used with the hydrostatic approximation to construct analyses at higher levels.) This is a particularly important exercise for the Southern Hemisphere because of the paucity of conventional measurements in the troposphere.

A comprehensive report on the Proceedings of this workshop is in preparation (O'NEILL and GROSE). It is beyond the scope of the present paper to address aJl of

3 Middle Atmosphere Program Pre-MAP Project 1. 4 The pressure unit is taken as the mh. The equivalent S.1. unit is the hPa.

Vol. 130, 1989 Comparison of Data for the Southern Hemisphere 197

the issues considered and conclusions reached by the many scientists who participated in the workshop, Instead, we have selected a few illustrative examples for this summary to serve as aprelude to investigations that will be fostered by the MASH project. We shall restrict attention here to da ta from two instruments with different viewing geometries: a limb scanner (UMS) and a nadir sounder (SSU).

In Section 2, we briefly describe the data sources. In Section 3, we present some examples of the comparisons of data and derived quantities which typify those made in the workshop. Differences between the various base-level analyses, and the resulting impact on derived quantities, are discussed in Section 4. Finally, we list our conclusions in Section 5 and give recommendations which may be helpful in future studies of dynamics and transport in the middle atmosphere of the Southern Hemisphere.

2. Description of Data Sources

In this section, we give brief descriptions of the UMS and SSU instruments used in this study, and of the methods by which gridded fields were constructed. We list the base-level analyses used, and note the time periods for which the comparisons were made.

2.1 Satellite Data and Method of Analysis

UMS is a limb-scanning, infrared radiometer (GILLE and RUSSELL, 1984). Radiation emitted by the 15 micron bands of carbon dioxide is measured in two spectral channeIs. Temperature is then inferred from the radiances using an iterative retrieval scheme (GORDLEY and RUSSELL, 1981). Synoptic temperature fields at 12 GMT are produced using a KaIman filter technique (HAGGARD et al., 1986). The spatial resolution of gridded fields derived from the instrument is about 3~5 km in the vertical, 4° in latitude, and wavenumber 6 in the zonal direction. Useful data cover the period 25 October 1978 to 28 May 1979, with a latitude range 84°N to 64°S, and an altitude range 15 to 70 km. Fields of geopotential height are constructed from temperature fields using a geopotential-height analysis to 50 mb provided by the U.S. National Meteorological Centre (NMC).

SSU is a nadir-viewing, pressure-modulated, infrared radiometer which scans both sides of the sub-orbital track (PICK and BROWNSCOMBE, 1981). The SSU instrument is part of the TIROS Operational Vertical Sounder (TOVS) system. For the period of the UMSjSSU comparison (May 1979 in this paper), radiances are available only from two out of three channeIs of an SSU-those peaking at 15 and 5 mb. For the period used to assess the impact of different base levels, information from a channe'l peaking at 1.5 mb is also available, together with radiances from another two radiometers: a microwave sounding unit (MSU) and a


high resolution infrared sounder (HIRS-2), most of whose channels peak in the lower stratosphere.

Independent retrievals of the data are carried out by the U.K. Meteorological Office (UKMO) and by NMC. Only the former are used in the present study; at the Williamsburg workshop both data sets were used for comparison with each other and with data from other satellites.

In the UKMO analysis, radiances are inverted by statistical regression (using a reference climatology) to give daily fields of thickness at 12 GMT. For the period of the LIMSjSSU comparison, the regression coefficients do not vary with latitude or season, though they do thereafter. Geopotential heights are obtained by adding the thicknesses to a base-level analysis of geopotential height at 100 mb, obtained (for LIMSjSSU comparison) from NMC. Temperatures are computed by differentiating these heights in the vertical. The spatial resolution of the gridded fields is about 12 km in the vertical, and wavenumber 12 in the meridional (pole-to-pole) and zonal directions. Useful data cover the period from October 1978 to the present, with a latitudinal range from 87°N to 87°S and an altitude range from about 15 to 50 km. Further details of the data analysis and a discussion of the errors involved are given by CLOUGH et al. (1985).

2.2 Base Levels

To assess the impact of using different base levels on derived quantities in the stratosphere, analyses of geopotential height at 100 mb were obtained from archived products at three meteorological centres: UKMO, NMC and the European Centre for Medium Range Weather Forecasts (ECMWF). It is beyond our scope to describe the procedures adopted in producing these analyses (and we are in no position to judge their relative merits). Details can be obtained from the centres concerned.

2.3 Time Periods for Comparison of Data

A constraint dictating the time periods for the comparison of the basic satellite data was the short record (7 months) of LIMS data that is available. At the Williamsburg workshop, comparisons were made for the months of January and May 1979. May is the more dynamically active month, so we expect a higher signal-to-noise ratio then. We shall restrict attention here to the results for a few days in May; they were chosen to be representative of the month.

To examine the effect of the different base-level analyses on derived quantities, UKMO analyses of thickness for September 1985, also a dynamically active month, were added to the base levels from the three sources. Again, results shown (for two days) are representative of the month.

3. Results

3.1 Zonal-mean Temperatures

Latitude-height sections of zonal-mean temperature, derived from SSU and UMS measurements, are shown on 19 May 1979 in Figure 1. (Being based on thicknesses, SSU temperatures are layer means.) Although the fields are in broad agreement, there are significant differences, particularly in the upper stratosphere where SSU temperatures are about 10-15 K colder than those from UMS, and

(a) LlMS

:0-E E

::s ~ E 10 :J

<n Cl 30 <n

-w Q)

I 0:

~~--~------~~------~--~--~~100

(b) SSU

E ::s E

40

~ 30 I

20 -60

40°

Latitude

:0-E-

10 ~ :J <n <n Q)

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~ ____ ~~~~ __ L-______ L-______ LL~ 100

40°

Latitude

Figure 1 Zonal-mean temperature (0C) for the Southern Hemisphere on 19 May 1979. (a) From UMS, (b) from

SSU.


vertical temperature gradients are correspondingly smaller. In the middle and lower stratosphere, differences between the two fields are smaller, about 3 K, with SSU temperatures generally colder. Similar differences are present on other days in May (and in monthly-mean fields).

On the satellite TIROS-N, which provided data for analyses until June 1979, the top channel of the SSU radiometer (weighting function peaking near 1.5 mb) was inoperative, and HIRS and MSU radiometers were not carried. The vertical resolution of derived fields was impaired, and this must contribute to the above differences in temperature.

(a) LlMS

40

:0-E .s :. ~ 1: :l 0> 30 Ul

Ul 'a; ~ J: c..

20

100 20°5

Latitude

(b) SSU

80

40

E :. 1: 0> 30 'a; J:

20

k::::====:±=::::::::::===:d:::::::=...._---.l ___ L.-J 100 20°5 30° 50° 60°

Latitude

Figure 2 Zona1-mean geostrophic wind (ms- I ) for the Southem Hemisphere on 19 May 1979. (a) From LIMS,

(b) from SSU.


3.2 Zonal-mean Winds

Corresponding cross-sections of zonal-me an geostrophic wind are shown in Figure 2. The two fields show good agreement in the position of the maximum of the westerly jet (near 500 S at I mb), and weak easterly winds are present in both at 200 S in the lower stratosphere. The largest differences, of up to 12 ms - 1, are near 200 S at all altitudes. Differences are smaller at mid-latitudes (3 ms - 1 or less at 600 S). There is no consistent pattern in the differences between the two wind fields from one day to the next, except that, in May 1979, vertical shears tend to be greater in wind fields derived from UMS than in those from the SSU on TIROS-N (probably because of the missing top channel on this SSU).

3.3 Eliassen-Palm Fluxes

Cross-sections, from UMS and SSU data, of the (quasi-geostrophic) EliassenPalm flux divergence in the Southern Hemisphere on 19 May 1979 .are shown in Figure 3 (a scaled form of this quantity is actually plotted as explained in the caption). In the stratosphere, the two terms that constitute this divergence (see Eq. (2.2) in DUNKERTON et al., 1981) are frequently large and of opposite sign, so the divergence is prone to large errors. Indeed, on the day shown, there is no apparent qualitative, let alone quantitative, agreement between the two fields. The UMS field has convergence over a broad latitudinal band at middle latitudes, whereas the SSU field has divergence. It is likely that the SSU field is the more suspect of the two, for it shows little continuity from one day to the next around the chosen day; the continuity of the UMS field is better.

The serious discrepancies noted here between fields of E-P flux divergence are probably attributable to the poorer than normal vertical resolution of the SSU analyses in the first half of 1979. Afterwards, SSU analyses should generally be of much better quality (as found by GROSE and RODGERS, 1986), because of better instrument performance and additional data from the HIRS-2 and MSU radiometers. Even so, the vertical resolution of the best possible analyses from these instruments is poorer than from UMS. As most of the longitudinal variance in the stratosphere is in the longest zonal waves, which UMS analyses should be able to resolve, side-scanning in the SSU instrument does not prove to be a significant advantage for the calculation of E-P flux divergence, but it can be for calculations of synoptic maps of potential vorticity.

3.4 Isentropic Maps of Ertel's Potential Vorticity

Fields of Ertel's potential vorticity, Q, shown here are calculated using the following approximate expression:

Q ~ -ge, + f) ofJ/op

202

(b) SSU

40

E ~

L: Cl

"Qi 30 I

20

W. L. Grose and A. O'Neill

(a) LlMS

E ~

L: Cl 'Qi I

40

30

20

/ / J ) ." ... .",.."".., " - /""'- r- __

/ I -1-"" -,-- '-- -.,..,. -2 - __ -- __ ~_~-__ ,. ,-----:...--::;:, " '" -- - -- "' '\ - - -" '- 5 - - -- ) " .............. '" - - _ ... .?) I / ......................... --4--"/

" ........ ---3 -.,.; I "" --'-2- ,,/ ........ -1 ---20°5 30° 40°

Latitude

50° 60°

Latitude

Figure 3

PAGEOPH,

10

The convergence of the Eliassen-Palm Dux, scaled to give the zonal force per unit mass due to eddies, for the Southern Hemisphere on 19 May 1979. It is the quantity denoted as DF by DUNKERTON et al. (1981). Units: 10-5 ms- 2• (a) From UMS, (b) from SSU. Pecked lines indicate negative values

(convergence).


(a) UMS (potential vorticity)

900 W f--++--H----+-----++-+---j 900 E

0°

(b) SSU (potential vorticity)

900 W 1-""'-\-It+f'7"' .. ,f--:-"~HrJH--., OOOE

180°

(c) UMS (ozone)

900 W I---\-+++I---+----tf+t---i 900 E

180°

Figure 4 (a) LIMS and (b) SSU maps of modulus of Ertel's potential vorticity (see main text for approximate form used) on tbe 850 K isentropic surface for tbe Southern Hemisphere on 24 May 1979. Units: 10-4 Km2 kg- I S-I. (c) Ozone mixing ratio (ppmv) from LIMS on the 850 K surface on the

same day.


where , is the relative vorticity, / the Coriolis parameter, () potential temperature and p pressure. It is a highly differentiated quantity: basic fields must be differentiated to obtain approximate values for the horizontal wind components (using the geostrophic approximation), and then the winds must be differentiated to obtain relative vorticity. Errors in Q are thus liable to be large. In view of their potential value to studilts of dynamics and transport (McINTYRE and PALMER, 1983, 1984, 1985; HOSKINS et al., 1985; MILES and GROSE, 1986), the reliability of isentropic maps of Q needs to be assessed. The complexity of the retrieval method and of subsequent manipulation of data prec1ude a precise estimate of the errors involved. The best that can be done is to compare independently derived fields, as we do here for the middle atmosphere of the Southern Hemisphere.

Isentropic maps of Q on the 850 K surface (near 10 mb) for 24 May 1979 are shown in Figures 4(a) and 4(b). The UMS and SSU fields are in broad agreement, though there are noticeable differences. A tongue of high Q in the UMS field near 300 W has no counterpart in the SSU field. Generally, SSU maps of Q exhibit more longitudinal structure than do UMS maps. Some of this structure could be real, being on a scale that could be revealed by the good horizontal resolution afforded by side scanning on the SSU instrument (see CLOUGH et al., Figs. 2(a) and 10, for illustration). However, small-amplitude ripples, such as those in the top half of Figure 4(b) are probably artifacts of the methods of observation and derivation of gridded fields.

A feature both maps have in common is a large-scale extrusion of high Q into low latitudes near 180oE, and a localised minimum in Q adjacent to it near 90oE. Such a pattern is characteristic of the early stages of 'wave breaking', a process that may lead to an irreversible exchange of air between high and low latitudes (see McINTYRE and PALMER, 1984, for a detailed discussion of this concept). The ability to discern such behaviour from atmospheric data is crucial to a complete understanding of transport mechanisms (e.g., of ozone). Preliminary indications are that for the middle atmosphere of the Southern Hemisphere, a blurred view of the process can be gained on some occasions for large scales of motion in a deep layer of the atmosphere (though quantitative details would be unreliable). Corroboration comes from the ozone mixing ratio on the 850 K surface derived from UMS measurements for 24 May 1979 (Figure 4( c». There is a high degree of correlation between the UMS fields of Q and ozone. Other authors have also found such a correlation between satellite-derived fields of Q and quasi-conservative constituents in the middle and lower stratosphere (e.g., GROSE, 1984; LEOVY et al., 1985).

3.5 Influence 0/ Different Base Levels on Derived Quantities

In principle, basic retrieved fields from satellites (temperature for UMS; thickness for SSU) need be no less accurate in the Southern Hemisphere than they are in the Northern Hemisphere. Indeed the spatially uniform quality of the

Vol. 130, 1989 Comparison of Data for the Southern Hemisphere

(a) ECMWF base

(b) NMC base

40

E 30 "'-:E Cl ·iii I

10

30'

(c) UK Met. Office base

40

E 30 "':E Cl

~ 20

10

L-__ -

20'S 30' 40'

Latitude

Latitude

50' 60' 70' 80'

Latitude

Figure 5

100

~ :J

::l ~

100 Q.

90'

205

Zonal-mean geostrophic wind (ms- I ) for the Southern Hemisphere on 8 September 1985. Fields constructed using different base-level analyses of geopotential height at 100 mb: (a) ECMWF base level;

(b) NMC base level; (c) UKMO base level.


measurements is one of the main advantages of using satellite data in diagnostic studies. To calculate many quantities of dynamical interest, however, a field of geopotential height at a base level (usually in the lower stratosphere) is also needed. Herein lies the main shortcoming of derived quantities for the Southern Hemisphere: conventional observations of the troposphere and lower stratosphere (e.g.,

from radiosondes) are sparse. It is not our purpose here to judge the reliability of base level analyses made available by different meteorological centres. Rather, it is to illustrate the differences in derived quantities (zonal-mean wind, divergence of the Eliassen-Palm ftux, Q) that are produced in the stratosphere when data from one instrument-in this ca se the SSU-are used in conjunction with various base-level analyses of geopotential height at 100 mb. SSU thicknesses were tied to base-level analyses provided by ECMWF, NMC and UKMO. Geostrophic winds were then calculated and used in computing E-P ftux divergence and Q.

Three cross-sections of zonal-mean geostrophic wind on 8 September 1985 are shown in Figure 5. At 100 mb, the three fields differ by up to nearly 10 ms -I at high latitudes (the -10 contour near 80° is present only in the NMC analysis), the impact of which is noticeable up to the middle stratosphere. At middle and low latitudes, however, there is good agreement between the fields. These findings are typical for September 1985.

Three cross-sections of the E-P ftux divergence on 8 September 1985 are shown in Figure 6. Although the three fields all have divergence in the stratosphere at high latitudes and convergence at middle latitudes, there are significant differences. At high latitudes in the upper stratosphere, divergence with the ECMWF base is half as large as that with the others; while at 55°S there is a region of divergence with the NMC base but not with the others. Notice also that there are significant differences at high latitudes in the troposphere.

Three synoptic maps of Q on the 850 K isentropic surface on 24 September 1985 are shown in Figure 7. The fields are generally in good agreement. This result is only to be expected since derivatives of the thickness field (a field the three maps have in common) contribute most to the value of Q. At low latitudes, however, horizontal gradients of the thickness field become small, and those of the geopotential-height field at the base level contribute proportionally more to the value of Q. Moreover, gradients of Q are small at low latitudes, so a small difference between base-level analyses can make a big difference to an isopleth's position. Thus although the tongue of locally high Q near 1800 E appears on all three maps, it extends further westward for the ECMWF base.

KAROL Y (1987) has made a parallel study of the impact of base-level analyses on certain circulation statistics (including momentum and heat ftuxes, EliassenPalm ftuxes and their divergence) for the stratosphere of the Southern Hemisphere in September 1981. He finds, as we do, that the statistics that are most sensitive to the different base-level analyses are those that emphasize the shortest spatial scales through multiple differentiation of the geopotential-height field.

Vol. 130, 1989 Comparison of Data for the Southern Hemisphere

(al ECMWF

40

E ~ .c ~ .. I: 20

10 -~-

205 60'

Lalltude

(b) NMC

~ 30

.c '" 0; 20 I:

10

20·5 Lal,lude

(Cl UK Met Office

40

E 30 ~

.c CI 0; 20 I:

10

20'5

-~----• 30· 40" 50' 60' Lal,lude

Figure 6

70' 80·

70· 80·

10

D §. .. ~ ., ..

100 cl:

207

As for Figure 5 but for convergence of Eliassen-Pa1m fiux, scaled as in Figure 3. Units: 10- 5 ms- 2 .

Stippling indicates positive values (divergence).


0'

(a) ECMWF base

"---:;H7'1h'+----1 90'E

1800 0'

(b) NMC base

0'

(c) UK Met. Office base

Figure 7 Synoptic maps of modulus of Ertel's potential vorticity on the 850 K isentropic surface for the Southern Hemisphere on 24 September 1985. Units: 10-4 Km2 kg- I S-I. Fields constructed using different base-level analyses of geopotential-height at 100 mb: (a) ECMWF base; (b) NMC base;

(c) UKMO base.


4. Base Level Fields

The three base-level fields of geopotential height used in our comparison above are shown in Figure 8. Superficially, there is little difference between them (though note the difference of about 200 metres between geopotential heights near the centre of the vortex in the NMC and ECMWF analyses). Two distinct troughs near 900 W and 1800 Ware present on all three maps; otherwise the Bow is almost zonal. Slight difference in horizontal gradient may, however, be magnified when derived quantities are computed for the stratosphere.

Bigger differences are found in the temperature fields at 100 mb (not shown). Near the South Pole on the day shown, temperatures from ECMWF are about 10 K colder than those from either NMC or UKMO, so geopotential heights at the next analysed level up (50 mb) are lower over the pole in the ECMWF analysis. The inBuence of this discrepancy is spread in the vertical by vertical differentiation to obtain E-P Bux convergence and Q.

5. Concluding Remarks and Recommendations

5.1 General Comments

Overall, examination of the basic meteorological fields (temperatures, winds) derived from measurements by different satellites leads to similar conclusions to those reached in the PMP-I comparison of data for the Northern Hemisphere. While there is usually qualitative agreement between the different sets of fields, substantial quantitative differences are evident. Differences in magnitude and gradient are apparent in the temperature fields, which result in more pronounced differences in fields of derived winds, Ertel's potential vorticity, and (for the LIMSjSSU comparison especially) Eliassen-Palm Bux divergence.

It is clear from our study that the fidelity of the base-level analysis is of great importance in calculating derived quantities for the middle atmosphere, especially in the Southern Hemisphere. This was demonstrated by using a single set of satellite data (from an SSU) with base-level analyses obtained from three meteorological centres (ECMWF, NMC, UKMO). The Eliassen-Palm Bux divergence is particularly sensitive to the base-level analysis (though it can be more sensitive to the instrument used), as is Ertel's potential vorticity at low latitudes where horizontal gradients are weak (and most meridional transport by eddies takes place).

These findings are representative of the periods selected for the present study; they also emerged from the more extensive comparison of satellite data for the Southern Hemisphere made by participants in the Williamsburg workshop (see acknowledgements ).


0"

(a) ECMWF

0"

(b) NMC

'---f-ltl'-H-H-f-l 90" E

0"

(c) UK Met. Office

90"W 1-\----\,-+-\-\11+-...... --+1-: ++-I'HH-+---tt 90" E

180~

Figure 8 Base-level analyses of geopotential height (dam) at 100mb for the Southern Hemisphere on 8 September 1985. They are derived independently at three meteorological centres: (a) ECMWF, (b) NMC and

(c) UKMO.


5.2 Recommendations

On the basis of the experience that we have gained from this study and from the PMP-l and Williamsburg workshops, we feel it prudent to advise cautionin drawing inferences, particularly quantitative ones, from meteorological fields derived from satellite data. Such counsel is certainly apt for the Southern Hemisphere, where coverage of data from sources other that satellites is limited.

There are several techniques that may be used to evaluate the reliability of the information contained in the measurements: ( 1) Independent data sets (derived from different instruments and base-level

analyses) should, ideally, be used in parallel and examined for consistency. (2) The temporal continuity of derived fields is often useful in highlighting

problems with the data. (3) Consistency between zonal-mean meridional velocities inferred separately from

zonally averaged moment um and thermodynamic equations provides a powerful constraint (assuming unknown friction can be neglected).

(4) The conservation of potential vorticity over aperiod of a week or so in the middle stratosphere is an important objective check on the reliability of the analyses.

(5) A good correlation over short periods between so me quasi-conservative chemical species (whose concentrations are measured directly) and Ertel's potential vorticity (a highly derived quantity) is persuasive evidence that the data have at least qualitative value.

A comparative appraisal of the procedures used to construct the different base-level analyses for the Southern Hemisphere would be of value to students of the middle atmosphere. Such a task is beyond the scope of the average user of the data; those who produce the analyses are best placed to assess them.

Acknowledgements

Our paper draws from (and extends) the results obtained by the following scientists at the Williamsburg workshop: Mel Gelman, lohn Gille, Isamu Hirota, Matt Hitchman, David Karoly, Karin Labitzke, Tom Miles, Vicky Pope, Clive Rodgers and Masato Shiotani. We thank Tom Miles for providing Figure 4(c).

REFERENCES

CLOUGH, S. A., GRAHAME, N. S., and Ü'NEILL, A. (1985), Potential vorticity in the stratosphere derived using data Jrom satellites, Quart. J. Roy. Meteor. Soe. 111, 335-358.

DUNKERTON, T. Hsu, c.-P. F., and McINTYRE, M. E. (1981), Some Eulerian and Lagrangian diagnostics Jor a model stratospheric warming, J. Atmos. Sei. 38, 819-843.


GILLE, J. C. and RUSSELLL III, J. M. (1984), The limb infrared monitor of the stratosphere: Experiment description, performance and results, J. Geophys. Res. 89, 5125-5140.

GORDLEY, L. L., and RUSSELL III, J. M. (1981), Rapid inversion of limb radiance data using an emissivity growth approximation, Appl. Opt. 20, 807~813.

GROSE, W. L. (1984), Recent advances in understanding stratospheric dynamics and transport processes: Applications of satellite data to their interpretation, Adv. in Spaee Res. 4, 19~28.

GROSE, W. L., and RODGERS, C. D., eds. (1986), Coordinated study of the behavior of the middle atmosphere in winter: Monthly-mean comparisons of satellite and radiosonde data and derived quantities, Handbook of Midd1e Atmosphere Program, Vol. 21.

HAGGARD, K. V., REMSBERG, E. E., GROSE, W. L., RUSSELL III, J. M., MARSHALL, B. T., and LINGENFELSER, G. (1986), Description of data on the Nimbus-7 LIMS Map Archive Tape-Temperature and geopotential height, NASA Teehniea1 Paper 2553.

HOSKINS, 8. J., McINTYRE, M. E., and ROBERTSON, A. W. (1985), On the use and significance of isentropic potential vorticity maps, Quart. J. Roy. Meteor. Soe., 111, 877~946.

KAROLY, D. J. (1987), The impact of base-level analyses on stratospheric circulation statistics for the Southern Hemisphere, Pure Appl. Geophys. 130 (2/3), 181~194.

LEOVY, C. 8., SUN, C.-R., HITCHMAN, M. H., REMSBERG, E. E., RUSSELL, J. M., GORDLEY, L. L., GILLE, J. c., and LYJAK, L. V. (1985), Transport of ozone in the middle stratosphere: Evidence for planetary wave breaking, J. Atmos. Sei. 42, 230-244.

McINTYRE, M. E., and PALMER, T. N. (1983), Breaking planetary waves in the stratosphere, Nature 305, 593--600.

McINTYRE, M. E., and PALMER, T. N. (1984), The 'surf zone' in the stratosphere, J. Atmos. Terr. Phys. 46, 825~849.

McINTRYE, M. E., and PALMER, T. N. (1985), A note on the general concept ofwave breakingfor Rossby and gravity waves, Pure Appl. Geophys. 123, 964-975.

MILES, T., and GROSE, W. L. (1986), Transient medium-scale wave activity in the summer stratosphere, Bulletin Amer. Meteor. Soe. 67, 674--686.

O'NEILL, A., and GROSE, W. L., eds., Proeeedings ofIntemational Workshop, Williamsburg, Va., April, 1986.

RODGERS, C. D., ed. (1984), Report on the workshops on comparison of da ta and derived dynamical quantities during Northern Hemisphere winters (PMP-I winters), Handbook of Midd1e Atmosphere Program, Vol. 12.

PICK, D. R., and BROWNSCOMBE, J. L. (1981), Early results based on the stratospheric channels of TOVS on the TlROS-N series of operational satellites, Int. Coune. Sei. Unions, Comm. Spaee Res., Adv. Spaee Res. 1 (4), 247~260.

(Reeeived Deeember 10, 1987, revised/aeeepted May 6, 1988)


Some Comparisons between the Middle Atmosphere Dynamics of the Southern and Northern Hemispheres

DAVID G. ANDREWS 1

AbslraCI-Comparisons are drawn between certain middle atmosphere dynamical processes in the Southern Hemisphere and the Northern Hemisphere. Attention is focused on the zonal-mean climatological state, stationary waves, transient waves of various types, stratospheric sudden warmings and polar ozone minima. Observations of the similarities and differences between the hemispheres are mentioned, and ways in wh ich these comparisons may be used to enhance our dynamical knowledge of the whole middle atmosphere are discussed.

Key words: Middle atmosphere, dynamics, interhemispheric comparison.

1. Introduction

The middle atmosphere of the Southern Hemisphere has in the past received much less attention from dynamical meteorologists than its Northern Hemisphere counterpart. A major reason for this state of affairs has been the comparative lack of global-scale data for the Southern Hemisphere. However, with the advent of satellite measurements this imbalance has been greatly reduced. It is the purpose of the Middle Atmosphere of the Southern Hemisphere (MASH) pro gram to bring our understanding of the middle atmosphere of the Southern Hemisphere to a level comparable with that of the Northern Hemisphere.

There are several reasons for focusing on the Southern Hemisphere middle atmosphere. The most obvious are that it comprises half of the middle atmosphere and displays a number of phenomena that are not present, or are not so prominent, in the Northern Hemisphere. Moreover, to the extent that the hemispheres are independent (an assumption that must be used with caution), they can be regarded as two separate systems for testing our general understanding of middle atmosphere processes. Thus by comparing and contrasting the middle atmosphere in the Northern Hemisphere and Southern Hemisphere, we may expect to enhance our knowledge of the middle atmosphere as a whole.

I Meteorological Office Unit, Hooke Institute, Clarendon Laboratory, Parks Road, Oxford, OXl 3PU, U. K.

214 D. G. Andrews PAGEOPH,

Before discussing these issues, it is worth digressing briefty to consider the relationship between the two main tools of middle atmosphere study: observations and models.1t is important to recognise the difficulty, ifnot impossibility, ofinferring causal relationships between atmospheric processes solelyon the basis of observations, even if sophisticated diagnostics are used to process these data. Cause-andeffect mechanisms must be established by means of controlled experiments, and these cannot be performed on the large-scale atmosphere itself. Some hints may perhaps be conveyed by comparison of similar states at different times or in different hemispheres, but the only real opportunity for such experiments is afforded by models of the atmosphere. Ideally, one would wish to employ a whole hierarchy of models, ranging from simple (perhaps analytical) models through to the most complex general circulation models. Models are also needed for testing the interpretation and usefulness of diagnostics. A thorough understanding of causal mechanisms is not only of basic scientific importance but also a necessary foundation for the construction of reliable models for predicting the future behaviour of the middle atmosphere.

The first purpose of this paper is to draw some simple comparisons between the observed structure (mostly large-scale) of the middle atmosphere in the two hemispheres. The second aim is to provide a focus for some possible MASH-related projects by raising a few simple questions concerning the ways in which these comparisons may be studied and exploited.

2. Comparisons Between Observations 0/ the Two Hemispheres

a. Climatological Zonal Means

The most basic quantities that can usefully be compared between the two hemispheres are probably the elimatological zonal means. We here present the elimatological monthly zonal means of temperature T and geostrophic zonal wind ug compiled by BARNETT and CORNEY (1985) from five years of satellite data. We concentrate on the months of January, April, July and October. Note that the five-year averaging means that interesting features from individual years may be lost by being smoothed out.

Looking first at temperatures for the summer months (January, Southern Hemisphere; July, Northern Hemisphere) in Figure la, we see that there is a elose resemblance between the two hemispheres, with a cold equatorial tropopause (temperatures below 200 K), a warm, quasi-horizontal stratopause (peaking at over 280 K at the pole) and cold polar regions above 80 km altitude in each2• In winter, however, (July, Southern Hemisphere; January, Northern Hemisphere: Figure Ib) significant interhemispheric differences appear. While the stratopause tiIts upwards

2 J. J. Barnett (personal eommunieation, 1988) has pointed out that the similarity in the latter regions may be partly due to the c1imatology used in the temperature retrievals, whieh is symmetrie about the equator. At these low temperatures and pressures instrumental noise may be poor and c1imatology may be given high weight.

Vol. 130, 1989 Comparisons between Midd1e Atmosphere Dynamica1 Processes

0.01

2'0

0.1

" .ll E ..... CI! L.

260 ::J 111 III C» L.

n.. '0

'00

,ooo~1II 80S 70S 60S 50S 40S 30S 20S 'OS

Southern hemLsphere: Januory (a)

0.01

0.1

" .ll E

"" C» L.

260

2'O--_-=::::====~

210 200

290

230

ION 20N 30H 40N 50N 60N 70N 80N

Northern hemLsphere: July

210

215

80

70

r 0

60<0 I ~ , ~

50111 111 C ,

4O~ a ~

30 ~ c Cl. ~

20"

'0

o

80

70

7<'" 3

""

r o 60": ~ , ~

50 III III C ,

::J 111 III _---1" 40 ~ C» L.

n.. 10

a -~ 30

.... ~ c Cl. ~

20 ,... 100

l000~. 7< 3 v

'0

o 80S 70S 60S 50S 40S 30S 20S lOS ION 20N 10N 40N 50N 60N 70N 80N

(b) Southern hemLsphere: July Northern hemLsphere: January

Figure l(a, b)

0.01 -L-_---200 200 80

220 220 70

230 230 0.1 r

2iO 0 60 CD

250 I -U

260 ., 260

50 f)

~O I/) I/)

c 260

., 40

f)

,.... ...0 E

'-'

~ l. J I/)

250 250 0 2iO

....... ~

230 30 .... ~

I/)

~ l.

Cl. 10

220 c 0...

210 210___.. f)

20

) ,.... ,.-3 '-'

10

100

J~~li~~~~~~~!i!!1!1217Io 1000 o 80S 70S 60S 50S iOS 30S 20S lOS ION ZON 30N iON 50N 60N 70N 80N

( e) Sou~hern hem~sphere: Oc~ober Northern hem~sphere: AprLl

looo~1I 290 o 80S 70S 60S 50S iOS 30S 20S lOS ION ZON 30N iON 50N 'ON 70N 80N

(d) Sou~hern hem~sphere: Apr~l Nor~hern hemLsphere: Oc~ober

Figure 1 Monthly and zonally averaged temperature (K) at eorresponding seasons in the two hemispheres, based on a five-year climatology. (a) Summer, (b) winter, (e) spring, (d) autumn. (Adapted from BARNETT and

CORNEY, 1985.)

Vol. 130, 1989 Comparisons between Midd1e Atmosphere Dynamica1 Processes 217

towards the winter pole in both hemispheres, that in the Southern Hemisphere is a little higher in altitude and some 20 K warmer than that in the Northern Hemisphere. On the other hand the southern winter lower stratosphere is some 20 K cooler than the northern. In spring (Figure lc) the stratopause is fairly ftat, but noticeably warmer at the South Pole than at the North Pole. Moreover the zonal-mean temperature at about 40 km altitude is significantly cooler at 500 S than at the pole (BARNETT, 1974), while no such "cool collar" is observed in the Northern Hemisphere spring climatology. The temperatures in the two hemispheres are fairly similar in autumn (Figure Id) although the southern lower stratosphere is somewhat cooler (by about 4 K at 80° latitude and 30 mb) than the northern.

Comparable interhemispheric similarities and differences occur for the geostrophic zonal winds, displayed in Figure 2; this is of course to be expected, since the winds are obtained from the temperatures using the thermal wind relationship, together with a lower boundary condition. Thus the summer winds in Figure 2a are generally easterly (westward) in both hemispheres of the middle atmosphere above about 20 km (except in high southern latitudes). They both peak at just over 60 ms - I

at about 70 km altitude, and decrease above that level. On the other hand there are significant differences between the winter westerlies (Figure 2b), which reach 100 ms - I at about 50 km altitude and 42° in the Southern Hemisphere, but only about 60 ms - I at about 68 km and 35° in the Northern Hemisphere. Winds in spring are fairly weak, both easterly and westerly, in both hemispheres (Figure 2c), the main feature of note being a westerly jet in the southern lower stratosphere. Autumn winds (Figure 2d) are fairly symmetrie about the equator, and mostly westerly, although reaching somewhat larger magnitudes in the Southern Hemisphere.

One should of course be cautious about drawing general conclusions from this limited selection of data. For example, an examination of Barnett and Corney's dia grams shows that northern hemisphere winds in December are much stronger than in January, and quite similar to the southern hemisphere winds in June: it is interesting that the large mean-ftow decelerations found in the northern hemisphere upper stratosphere between December and January have no counterpart in the Southern Hemisphere. This fact was noted by HARTMANN (1985), drawing on data from GELLER et al. (1983) and from C. R. Mechoso.

b. Climatological Data that are not Zonally-averaged

A rather more complicated set of quantities that can be compared between hemispheres are climatological data that are not zonally-averaged, such as monthlymean maps. As an example, Figure 3a depicts monthly-mean maps of the 10 mb temperature field in winter (January, Northern Hemisphere; July, Southern Hemisphere). Significant differences appear: while the Northern Hemisphere map exhibits noticeable zonal asymmetries, with a minimum temperature of just below 210 K, the Southern Hemisphere chart is much more zonally-symmetric, with a lower central


80S 70S 60S 50S 40S 30S 20S lOS

(a) Southern hem~sphere: Januar~

0.01

0.1

10

100 ~...J..,l.-~-4-~ ........ --T'-..s....,--' 80S 70S 60S 50S 40S 30S 20S lOS

ION 20N 30N 40N 50N 60N 70N 80N

Northern hem~sphere: Jul~

ION 20N 30N 40N 50N .oN 70N 80N

Southern hem~sphere: Jul~ Northern hem~sphere: (b)

Figure 2(a, b)

80 r 0

CD 70 I

60

50

40

30

20

80

-0 , «I II! II! C , «I

0 -~ ... ~ C a.. «I

" " 3 'V

r o

CD 70 I

-0 , «I II!

60 II! C , «I

50 0 -~ .... 40 r

a.. «I

30 " " 3 'V

20

Vol. 130, 1989 Comparisons between Middle Atmosphere Dynamical Processes

0.1

.D E

~ L :J (/) (/)

(1/

L n..

10

219

80 r o

CD 70 I

" , I\l

60 ~ c , I\l

50 0 -C"" ... 40 f

0.. I\l

30 " 1<"" 3 '-"

20

80S 70S 60S 50S 40S 30S 20S lOS 1 ON 20N 30N 40N 50N 60N 70N 'ON

( c) Southern hem~sphere: Oetober Northern hem~sphere: Apr~l

0.01

20 1 4030 "'-I

0.1 ~I ,....

I .D E

'-'

~ L :J VI VI (1/

L n..

10

100

80S 70S 60S 50S 40S 30S 20S lOS 1 ON 20H 30H 40N 50N 60N 70H 80N

Southern hem~sphere: Apr~l Northern hem~sphere: Oe tob er ( d)

Figure 2

80 r o

CD 70 I

" , I\l VI

60 (/) c , I\l

50 0

30 "... 1<"" 3

20

As for Figure I, but showing geostrophic zonal winds in m s - I (eastward winds positive, westward winds negative). (a) Summer, (b) winter, (c) spring, (d) autumn. (Adapted [rom BARNETT and CORNEY,

1985.)

orlhern hemcsph"r,,: Januar\:!

(a)

SOIJLh2rn hem,sph"r2: Januar\:!

(b)

Figure 3 Polar stereographie maps of monthly averaged temperature (K) at IO mb (approximately 30 km altitude) at corresponding seasons in the two hemispheres: (a) winter, (b) summer. (Courtesy of 1.1. Barnett and

M. Corney, Department of Atmospheric Physics, Oxford University.)

value ( < 190 K) and correspondingly stronger latitudinal gradients. (These differences are consistent with those in Figure I b.) The summer charts in Figure 3b (July, Northern Hemisphere; January, Southern Hemisphere), on the other hand, are more similar and are both fairly zonally-symmetric. Similar features appear in the height fields of Figure 4: note the off-centered Northern Hemisphere westerly vortex in January and the stronger but more zonally-symmetric Southern Hemisphere westerly vortex in July.

Vol. 130, 1989 Comparisons between Middle Atmosphere Dynamical Processes 221

(al

(b)

Figure 4. As for Figure 3, but showing 10 mb geopotential height field (IIJ) /g (g = 9.8 m s - 2) in decametres. Arrows indicate direction of geostrophic flow. (a) Winter, (b) summer. (Courtesy of J. J. Barnett and M.

Corney, Department of Atmospheric Physics, Oxford University.)

A more quantitative (but not neeessarily more meaningful) way of representing the zonal asymmetries of the c1imatologieal data is to expand the monthly-mean data in zonal harmonies. Thus, denoting the c1imatologieal monthly mean of the geopotential $ by ($), and the zonal mean by an overbar, we ean write

($) = (<1» + L As(e/>, z)eos[sA + rt.s (e/>, z)] s ;,, 1

where As is the amplitude and rt.s the phase of the wavenumber S harmonie, A is longitude, e/> is latitude and z is a height eoordinate. The amplitudes and phases of these eomponents ean then be plotted in the meridional plane. Winter values


(0) Geopo~en~~ol he~9hl ompl~~ude wove number 1

0.01 80

.D E

Cl! L :J IJ) IJ)

ClI L

0...

,..... .D E

Cl! L :J IJ) IJ)

Cl! L

0...

0.1

10

100 ~~~~~~-r~--~,--+--r-~~~~T--r~

80S 70S 60S 50S ~OS 30S 20S lOS 0 ION 20N 30N ~ON 50N 60N 70N 80N

70

60

50

~O

30

20

Soulhern hem~sphere: Ju18 Northern hem~sphere: Jonuor8

wove number 2

80

70

0.1

60 16

50

~O

10

r 0

Cl) I

" , (:j IJ) IJ)

c: , (:j

0 -~ .... ~ c: Cl.. (:j

,....,

" 3

r o

Cl) I

" , (:j IJ)

IJ)

c: , (:j

o -~ ... ~ c: Cl.. (\)

30 ,....,

20

100

80S 70S 60S 50S ~OS 30S 20S lOS 0 ION 20N 30N ~ON SON 6bN 70N 80N

Southern hemLSphere: Ju18 Northern hemLSphere: Januar8

Figure 5

,;:-3

Amplitude (decametres) of the monthly-mean geopotential height field in winter for (a) wavenumber I and (b) wavenumber 2. (Adapted from BARNETT and CORNEY, 1985.)


(January, Northern Hemisphere; July, Southern Hemisphere) for the amplitudes of s = land 2 are shown in Figure 5. In the stratosphere, the northern hemisphere amplitudes tend to be stronger than those in the Southern Hemisphere, while the values are roughly comparable in the mesosphere. Summer amplitudes are much smaller in both hemispheres. Phase lines have a similar orientation in both hemispheres (although the phase gradients differ): those for s = 1 in winter are depicted in Figure 6.

As with the zonal-mean data, some important features of the interhemispheric differences may be missed because of the particular choice of months presented above. For example, HIROTA et al. (1983), using complete time-series, are able to examine the differing time-variations of geopotential height amplitudes in the winter stratospheres of the two hemispheres. While northern hemisphere values at 1 mb are generally large throughout the winter, the southern hemisphere values tend to maximise in early and late winter, with a relative minimum in midwinter: for further discussion see the paper by PLUMB (1989, this issue).

The climatological zonal asymmetries in January in the Northern Hemisphere are often regarded as due to the presence of stationary waves. This physical interpretation should be treated with caution, but nevertheless some progress can be made in modelling the zonal asymmetries using linear stationary-wave models: see section 3b.

GeopolenlLol heLghl phase (des- E) wave number 1

0.01 80 r 0

CO 70. -ci .,

0.1 (I;)

,... 330

.0

"'" E

(11

60 VJ C ., (I;)

ClI 0 ~

~~\ :J (11 (11

ClI ~

~~ a... 10

~ 100

210~

50 0 -~ ... 40 ~

c: a. (I;)

30 ,. 3 "V

20

80S 70S 60S 50S 40S 30S 20S lOS 0 ION 20N 30N 40N 50N 60N 70N 80N

Soulhern hemLsphere: Jul~ Norlhern hemLsphere: Jonuor~

Figure 6 Negative phase -lXI (degrees) of monthly-mean geopotential height for wavenumber I in winter.

(Adapted from BARNETT and CORNEY, 1985.)


c. Transient Planetary Waves

Examination of middle atmosphere data that are neither climatologically nor zonally averaged shows a great deal of transient, zonally-asymmetric activity. Some of this activity has been interpreted in terms of travelling disturbances with various time and space scales (see, e.g., SALBY, 1984). The most well-known travelling wave is the "five-day wave", which was first noted in tropospheric data and has also been detected in the middle atmosphere. This is a westward-travelling wave with period close to 5 days, whieh is roughly sinusoidal in the east-west direction with zonal wavenumber 1. Temperature and geopotential amplitudes are approximately symmetrie about the equator in the troposphere and lower stratosphere, but become more asymmetric in the upper stratosphere (being larger in the summer hemisphere). Another important westward-travelling disturbance, observed in radar and satellite data of the upper stratosphere and mesosphere, is the "two-day wave", of zonal wavenumber 3. This is mainly confined to the summer hemisphere, and tends to have larger amplitude in the Southern Hemisphere.

In addition to the 5-day and 2-day waves, several less prominent travelling modes have been identified, although in some cases only after careful time and space filtering of data. The Southern Hemisphere, having less stationary-wave activity than the Northern, can be a "cleaner" environment in whieh to see these travelling disturbances. One interesting example is the coherent "warm pool" found in satellite radiance data for the upper stratosphere by PRATA (1984), which encircles the South Pole several times, with aperiod of about 4 days. Another southern hemisphere case is the slowly eastward-travelling wavenumber 2 component noted by several authors (e.g., HARWOOD, 1975; MECHOSO et al., 1988), which has aperiod of 2-3 weeks. In neither of these two examples are the dynamies particularly weil understood at present.

A rather different type of transient process is the "breaking planetary wave". This name was given by McINTYRE and PALMER (1983, 1984, 1985) to large-scale, large-amplitude disturbances in which nonlinear advection leads to the rapid, irreversible distortion of air masses. Breaking planetary waves are quite weil depicted in quasi-horizontal isentropie maps of Ertel's potential vorticity (a quasiconservative tracer), where blobs of potential vorticity may be pulled out of the main stratospherie vortex and stretched into long, thin filaments. Such events appear to be quite common in the middle and upper stratosphere, where upwardpropagating quasi-stationary planetary waves attain large amplitudes, mainly because of the decreasing air density. Their non linear dynamics are not yet weil understood, and high-resolution numerical simulation will be an essential part of their study. (See JUCKES and McINTYRE, 1987 for arecent investigation.)

d. Stratospheric Sud den Warmings

Stratospheric sudden warmings are the most spectacular large-scale dynamical events to take place in the middle atmosphere; they occur in winter, and involve


rapid rises of temperature in the polar stratosphere. These temperature ehanges result in areversal of the latitudinal gradient of the zonal-mean temperature (at 10 mb and below, and poleward of 60° latitude, aeeording to the WMO definition of sudden warmings). They are also assoeiated with a deeeleration of the zonalme an westerly zonal wind in this region. If the winds reverse to beeome easterly, the warming is called "major"; if not, it is called "minor".

There is considerable interannual and interhemispherie variability in the oeeurrenee and morphology of sudden warmings. Major warmings oeeur on average in about one in two northern hemisphere winters, but have never been observed in the southern hemisphere winter. (They may therefore eomplieate the interpretation of the five-year c1imatology diseussed above, whieh inc1uded some years with northern hemisphere major warmings, and some without.) Strong minor warmings have been observed in both hemispheres; in the Southern Hemisphere they tend to be eonfined to the middle and upper stratosphere, whereas in the Northern Hemisphere they usually involve the whole stratosphere.

After some sudden warmings the polar temperature falls again and the zonal winds aecelerate, with the zonal-mean state reverting to roughly its previous form. Towards the end of winter, however, some sud den warmings lead directly into the "final warming", i.e., the ehange-over to summer eonditions of warmer polar temperatures and easterly zonal winds. An interhemispherie eomparison of the final warmings in 1982 is given by Y AMAZAKI (1987). He finds that the final warming in the Southern Hemisphere in Oetober is stronger and more rapid than that in the Northern Hemisphere at the end of March. The two events also differ in their detailed strueture and evolution.

e. Polar Ozone Distributions

It has been known for many years that there are signifieant disparities between the seasonal variations of ozone column amounts in the two hemispheres. For example, DOBsoN ( 1966) drew attention to the rather different annual variations at Halley Bay (75°S) and Resolute (75°N). Using agiobaI data set, DÜTSCH (l97\) noted maximum northern hemisphere column amounts of about 440 DU3 near the North Pole in spring and somewhat sm aller maximum southern hemisphere amounts (400 DU) in midlatitudes in spring, with a seeondary maximum (380 DU) near the South Pole in early summer. Minimum aretie values (300 DU) oeeurred in autumn and minimum antarctic values (280 DU) in midwinter.

These interhemispheric differences have reeently been aecentuated by the appearance of the "antaretie ozone hole", diseovered by F ARMAN et al. (1985) using ground-based measurements. When the ozone eolumn amount (as measured by the Total Ozone Mapping Spectrometer on the Nimbus 7 satellite) is averaged over four

3 The Dobson Unit (DU) equals 10 - 5 m of ozone at O°C and standard sea-level pressure.

years between 1978 and 1982 (see Figure 7), this phenomenon is manifested, albeit in smoothed-out form, by a deep spring minimum ( <240 DU) at 900 S that was not present in Dütsch's earlier data. This is in complete contrast to the northern polar spring maximum. On the other hand Figure 7 also shows that quite low values ( < 280 DU) occur in high latitudes of both hemispheres in autumn, before the onset of the polar night.

The increase in the ozone column during the northern hemisphere winter appears to be mainly due to tongues of ozone-rich air moving into the polar region from low latitudes at the time of large-amplitude "breaking planetary-wave" events. These tongues are clearly visible in the 10mb ozone mixing ratio data from the UMS (Limb Infrared Monitor of the Stratosphere) instrument on Nimbus 7, analysed by LEOVY et al. (1985). By contrast, it has been known since long before the appearance of the antarctic ozone hole that the south polar vortex in winter consists of a much more coherent air mass, wh ich is not penetrated by events of this type: see DOBSON (1963). (This interhemispheric difference is also manifested in the comparisons of the monthly-mean vortices discussed in Section 2b.) It seems, therefore, that meridional transport cannot significantly increase the antarctic ozone column in winter, and other mechanisms-whether chemical or dynamical-have the opportunity to deplete it instead. Only after the final warming, when the antarctic vortex breaks down, does significant poleward transport of ozone occur.

w o :::)

eo

30

I-- 0 i= :5

30

60

OOS~L-~---r-------r----~~~UU~~

JAN 1 APR 1 JUL1 OCT 1 JAN 1

Figure 7 Time-Iatitude section of the climatological zonal-mean ozone column (DU) for October 1978-September 1982 from the TOMS instrument, smoothed by the application of lO-day means. Gaps in the contours occur in the polar night, when no measurements are available. (From BOWMAN and

KRUEGER, 1985.)

Vol. 130, 1989 Comparisons between Midd1e Atmosphere Dynamical Processes 227

fOther Features for Comparison

There are several other areas in which interhemispheric comparison of data has scarcely begun: these include comparison of gravity-wave characteristics (as measured by radars and lidars, for example), atmospheric tides, and further aspects of tracer transport and interannual variability. There is a clear need for additional data and (perhaps more importantly) more extensive analysis of existing data sets.

3. Examination and Exploitation of the Interhemispheric Differences

a. The Climatological Zonal-mean State

A basic scientific question that provides a useful focus for discussion of the climatological zonal-mean state is "how is this state maintained?" A quick answer, which seems to be a reasonable first approximation to the truth, is that it is maintained by a competition between radiative and dynamical effects (e.g., FELS, 1985; ANDREWS, 1987). A "radiative spring" tries to puIl the zonal-mean state towards a hypothetical state of radiative balance (FELS, 1985; SHINE, 1987): this spring is opposed by dynamical processes, particularly rectified nonlinear eddy effects (expressed, roughly speaking, by the Eliassen-Palm ftux divergence). This dynamical driving manages to keep the observed zonal-mean state significantly different from the radiative state in the winter stratosphere and in the upper mesosphere, but not in the summer stratosphere or lower mesosphere. The relevant eddies are likely to be mainly planetary waves (stationary or breaking) in the winter stratosphere and breaking gravity waves (and perhaps tides, to a lesser extent) in the upper mesosphere. Gravity waves mayaiso playa role in the stratosphere.

In general, the hypothetical radiatively-determined state in the Southern Hemisphere is quite similar to that at the corresponding season in the Northern Hemisphere (K. P. Shine, personal communication, 1987); thus interhemispheric differences in the zonal-me an climatology must be mainly associated with differences in the eddy-induced forcing. In particular it seems likely that the differences in winter stratospheric temperatures, noted in Section 2a, are associated with the weaker southern hemisphere planetary waves, which are less able to keep temperatures weIl above the cold radiative value than are their stronger Northern Hemisphere counterparts. By contrast, it appears that the upper mesospheric gravity-wave forcing may be quite similar in the Northern Hemisphere and the Southern Hemisphere: see Section 3d.

Of course this simple picture of the radiative-dynamical interactions is incomplete in some respects: in particular, the eddy driving cannot be thought of as independent of the mean ftow, since in general the wave properties can be expected to be modified by the ftow through which they propagate. This implies a two-way interaction between eddies and mean state that leads to the possibility of subtle and

complex feedbacks, and also makes for difficulties in sorting out cause-and-effect relationships. An example of this kind of interactive process is studied by PLUMB

(1989, this issue) in a model designed to explore the interhemispheric differences in seasonal variation of the stationary waves noted in Section 2b.

A number of observational studies have been directed towards documenting interactions between the zonal-mean flow and the eddies in the middle atmosphere on various timescales. An example that concentrates particularly on the quite complicated interhemispheric differences in these processes is that of SHIOTANI and HIROTA (1985).

b. Planetary Waves

A large number of linear models have contributed to our understanding of the dynamics of planetary waves. The more complex models of this type specify zonal-mean background winds ü(</1, z) and temperatures 1'(</1, z) that bear a reasonable resemblance to climatology. In the ca se of stationary waves, orographic and thermal forcing is prescribed at the lower boundary. The generally somewhat weaker orographic forcing in the Southern Hemisphere may be one reason for the weaker stratospheric planetary waves there (another being the stronger zonal winds: see PLUMB, 1989). Explanations of the observed travelling waves are generally based on the existence of unforced normal modes of the linear equations (together with appropriate boundary conditions). Some of these explanations have been quite successful, and can account not only for the period but also for such secondary features as the difference in amplitude between summer and winter hemispheres noted in Section 2c. The observed waves mayaiso involve instabilities, although the linear theory can here only explain aperiod of growth be fore nonlinearities set in.

Arecent study of the possible nonlinear influence on the zonal-mean flow of a pulse of mesospheric 2-day wave activity was carried out by PLUMB et al. (1987);

their simple theory gives quite good agreement with radar observations of such an event. There is now an increasing need for further investigations of nonlinear processes associated with planetary waves, including the planetary-wave "breaking" mechanism and the nonlinear behaviour of unstable disturbances. The Southern Hemisphere provides some interesting examples, such as the possibility of instabilities growing and then perhaps equilibrating on radiatively-forced barotropically unstable flows in the polar upper stratosphere.

We can conclude from this subsection and the previous one that it may be necessary to seek joint explanations of interhemispheric differences in the climatological zonal flow and the planetary waves. This is in any case consistent with the fact that the "zonal mean, eddy" separation can be an artificial one, especially when the "eddies" are of large amplitude.

Vol. 130, 1989 Comparisons between Midd1e Atmosphere Dynamica1 Processes 229

c. The Dynamics of Sudden Warmings

Since the paper of MATSUNO (1971), a large body of theory has been developed to explain sudden warmings in terms of "wave, mean-flow interaction" mechanisms. It is suggested that planetary waves, propagating up from the troposphere, are focused into the polar cap in the stratosphere and, by rectified non linear effects, bring about rapid mean-flow changes there. It is not dear whether the infrequent occurrence of sudden warmings is due to the need for unusually large tropospheric forcing or to the requirement of an unusual configuration of the stratospheric me an state, perhaps resulting from earlier wave events.

This theory is partly based on "weakly nonlinear" arguments, and while it successfully accounts for certain aspects of observed and modelIed warmings it still cannot fully explain some features of major warmings and strong minor warmings, when the flow is highly distorted and the "waves" are strongly nonlinear. There is plenty of scope for observational and theoretical study, and here comparison between the hemispheres may be useful. For instance is the absence of major warmings in the Southern Hemisphere due mainly to the stronger winter westerlies there (which would need to decelerate more than the weaker northern hemisphere westerlies in order to reverse) or to weaker tropospheric forcing of planetary waves; or are both of these elements inextricably linked in any case?

d. The Large-scale Effects of Gravity Waves

It was mentioned in Section 3a that departures from radiative balance in the upper mesosphere are thought to be mainly due to breaking gravity waves. Much research on breaking gravity waves has been carried out in recent years, following the paper of LINDZEN (1981), but their fully nonlinear mechanics when amplitudes reach "saturation" values are still far from well-understood. In complex processes like this, every avenue of research should be explored, and diagnostic studies of the observed atmosphere, in conjunction with conceptual and quantitative models, may well be of value. For example an indirect estimate, based on satellite data, of the eddy-forcing required to maintain the current dimatology of the mesosphere may help us to better und erstand the large-scale effects of breaking gravity waves. My colleagues Drs. K. P. Shine and C. J. Marks are currently investigating this possibility (see SHINE, 1989).

An interesting point in this regard was made by Dr. R. A. Plumb at the Adelaide MASH workshop: the dose similarity at all seasons (except perhaps in winter) between the two halves of the upper mesosphere in Figure I suggests (if the data and current theory are to be believed) that the gravity-wave forcing of the mean flow is very similar in the two hemispheres. This is despite the probable differences in magnitudes of the generation mechanisms for the waves at lower levels, and the differing environments through which the waves have propagated to reach the


upper mesosphere. The comparison may be giving us valuable clues to the gravity wave saturation mechanisms and the resultant driving ofthe mean ftow by the waves.

e. Polar Vortices

Even though the primary cause of the observed long-term depletion of antarctic ozone seems likely to be the increase of man-made chlorine compounds in the atmosphere (e.g., PvLE and FARMAN, 1987), a full understanding of the process will require a clearer picture of the dynamical state of the antarctic stratosphere under which the chemical destruction mechanisms occur. As noted in Section 2e, the south polar winter vortex is much less disturbed by planetary-wave events than its northern counterpart. This is presumably partly related to the comparative weakness of the southern hemisphere planetary-wave activity. (Further possible reasons for the resilience of the antarctic stratospheric vortex are discussed by JUCKES and McINTYRE ( 1987).) Moreover, the same dynamical processes allow the "chemical containment vessel" formed by the vortex to be much colder than the northern winter stratosphere (see Section 3a), and this may enhance the effectiveness of certain ozone-destruction mechanisms, such as heterogeneous chemical reactions on polar stratospheric cloud particles.

4. Conclusion

This paper has been more concerned with ralSlng questions and suggesting avenues for future research than supplying any definitive answers. It has pointed out some areas in which comparisons between the two hemispheres may perhaps be exploited to extend our understanding of the middle atmosphere as a whole. These comparisons have of course to be put into the context of the methods used for atmospheric study, involving a careful combination of observational data and theoretical modelling. An important use of models is to test hypotheses, and it is possible that the observed differences between the two hemispheres may help provide sharper hypotheses for models to test.

One caveat that must be borne in mind, however, is that the Northern and Southern Hemispheres are not totally independent. A further important topic for future research is the investigation of the extent to which the two are coupled, for example by cross-equatorial wave propagation and interhemispheric transport of tracers.

Acknowledgements

This paper draws heavily on other people's ideas. In particular, I wish to thank C. 1. Marks, A. O'Neill, K. P. Shine and especially R. A. Plumb for helpful

Vol. 130, 1989 Comparisons between Midd1e Atmosphere Dynamiea1 Proeesses 231

suggestions, and H. Cattle, R. S. Harwood and I. N. James for some constructive comments on an earlier version of the manuscript. J. J. Barnett and M. Corney kindly provided the majority of the diagrams. I am most grateful to the MASH Organizing Committee and Monash University for providing travel funds that enabled me to attend the Adelaide Workshop.

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Soe. 113, 603--633. SHINE, K. P. (1989) Sources and sinks 0/ zonal momentum in the middle atmosphere diagnosed using the

diabatic circulation, Quart. J. Roy. Met. Soc. 115, to appear. SHIOTANI, M., and HIROTA, I. (1985), Planetary wave-mean jlow interaction in the stratosphere: A

comparison between Northern and Southern Hemispheres, Quart. J. Roy. Met. Soe. 111, 309-334. Y AMAZAKI, K. (1987), Observations 0/ the stratospheric final warmings in the two hemispheres, J. Met.

Soc. Japan 65, 51-65.

(Received Oetober 13, 1987, revised February 29, 1988, aecepted March 3, 1988)

PAGEOPH, Vol. 130, Nos. 2/3 (1989) 0033-4553/89/030233-10$\.50 + 0.20/0 © 1989 Birkhäuser Verlag, Basel

On the Seasonal Cycle of Stratospheric Planetary Waves

R. ALAN PLUMB1,2

Abstract-Quasi-stationary planetary waves exhibit different seasonal behaviour in the two winter stratospheres. Whereas, in a c1imatological sense, wave amplitudes are large throughout northern winter, in the Southern Hemisphere there is a c1imatological minimum in midwinter. It is suggested here that the southern hemisphere behaviour is basically linear, the midwinter minimum arising from the opacity of the strong westerlies of southern midwinter to stationary wave propagation. On the other hand, it is further suggested that, in the northern hemisphere winter, the westerlies are prevented from becoming so strong (in a c1imatological sense) by the action of the waves themselves on the mean state and that the penetration of large-scale waves into the midwinter northern stratosphere thus depends on a nonlinear feedback process. Preliminary tests of this hypothesis are conducted, using a highly truncated beta-plane model of the stratospheric flow.

Key words: Planetary waves, stratospheric circulation, wave, mean-flow interaction.

1. Introduction

The well-defined seasonal eycle of quasi-stationary waves in the northem

hemisphere stratosphere-the waves being strong throughout the winter half-year,

typieally from Oetober to the final warming in April, but essentially absent through

the summer months-is usually interpreted as a simple eonsequenee of the CHAR

NEy-DRAZIN (1961) eriterion goveming the propagation of sueh waves. Aeeording

to this eriterion (see, e.g., HOLTON (1975) for a diseussion) vertieal propagation is

permitted in a uniform mean wind U on a beta-plane provided

( 1)

the eritieal veloeity Uc being

(2)

where (k, l) are the zonal and meridional eomponents of wavenumber, f is the

Coriolis parameter, N is the buoyaney frequeney and H the seale height. Upward

1 CSIRO Division of Atmospheric Research, Aspendale 3195, Australia. 2 Present Address: M.l.T., Cambridge, MA 02139, U.S.A.

234 R. Alan Plumb PAGEOPH,

propagation is therefore forbidden in easterlies and in strong westerlies unless the wavenumber is sufficiently small to make Ue exceed U. While extensions to and modifications of these simple rules are necessary to take account of spherical geometry and meridional wind shear (MATSUNO, 1970) and of wave refraction in the meridional plane (KAROLY and HOSKINS, 1982), the Charney-Drazin criterion lies at the heart of our qualitative understanding of the seasonal wave climatology. Thus it is conventional to regard the presence of large-scale planetary waves in the wintertime northern stratosphere as a simple consequence of the transparency of westerly flow to large-scale waves.

Evidence that such an interpretation may be incomplete is provided by southern hemisphere observations. The seasonal cycle of the quasi-stationary, large-scale planetary waves is there rather different; wave amplitudes are large in early winter (April/May) but weak in midwinter (July/August), strengthening again in September until the final warming in late October or November (HIROTA et al. , 1983; MECHOSO et al., 1985). Results of HIROTA et al. (1983) for the stationary wave I amplitude at the 1 hPa level during 1979-81 are reproduced here as Figure 1; stationary wave 2 shows similar behaviour. Figure 2 shows the equivalent plot of the climatological cycle (for the 12 year period 1972-83) of stationary wave 1 at 300 hPa; while there is a weak maximum at 600 S in September-October, this is only about 20 percent larger than midwinter amplitudes. The much more dramatic midwinter collapse and spring time amplification of stationary wave amplitudes in

1mb 80 80

60 60

40 40

w 20 20 0 ::J

(a) :: 0 0 t-

S -20

-40

-GO

-80

J A

Figure I Latitude-time section of amplitude (geopotential, m) at I hPa of the monthly-mean wave of zonal

wavenumber I, Sep. 1979-May 1981. (After HIROTA et al., 1983.)

Vol. 130, 1989 On the Seasona1 Cyc1e of Stratospheric Planetary Waves 235

WAVE 1 AMPLITUDE (GPM) 300hPa

-20 L L 5 9

L 7 IiQ~

<:~ LU L Cl => iD~ ~IiQ _____ r-r- 40 :)

~-eo~ <> 6l H H V,,96 80 116 'O~

-80 ~l ~-:~ ------ --JRN RfR JUL 0CT JRN

Figure 2 Annual cyc1e of stationary wave I amplitude (geopotential, m) in the Southern Hemisphere at 300 hPa. Values represent the c1imatological monthly-mean wave averaged over the period 1972-1983, from

Australian Bureau of Meteorology analyses. (Data provided in this form by D. J. Karoly.)

the southern stratosphere may not, therefore, be merely a reflection of similar behaviour in tropospheric forcing.

An alternative explanation is that the stratospheric behaviour must result from variability in wave propagation or transmission. In fact the midwinter collapse of the waves, though quite unlike what happens in northern winter, can be interpreted in terms of a transmission criterion such as (2) if it is recognised that the stratospheric westerlies are much stronger in the southern hemisphere winter than in northern winter (e.g., HARTMANN, 1976; HIROTA et al., 1983) and if it is supposed that the midwinter westerlies in the Southern Hemisphere are simply too strong to permit transmission of even the largest scale waves. Thus the southern hemisphere observations may be rationalized on the basis that transmission is allowed in the moderate westerlies of early and late winter but prevented in the strong midwinter westerlies and, of course, in the summer easterlies.

This raises the question of why the midwinter wind regimes of the two hemispheres are so different. The differences in wind c1imatology are consistent with differences in temperature structure, the southern polar night being substantially colder (and therefore closer to radiative equilibrium) than the polar night in the Northern Hemisphere. Departures from radiative equilibrium arise primarily from the effects of wave transport (e.g., WMO, 1986, Chapter 6, and the discussion by Andrews in this issue) and therefore the differences in zonal wind climatology between the two winter hemispheres probably arise from the differences in the


intensity of wave transport, the waves being substantially weaker in southern winter than in northern winter.

These arguments suggest a feedback mechanism may be occurring whereby the penetration of planetary waves into the northern winter stratosphere is to some extent dependent on the effects of those same waves3 in limiting the strength of the midwinter westerlies. This is the basic hypothesis of this paper, which is tested using the simplest type of stratospheric planetary wave model that incorporates the effects of wave-induced modification of the mean flow.

2. Model Formulation

The model used for this investigation is a severely truncated beta-plane model for the evolution of mean wind and a single planetary wave. This kind of model was introduced by GEISLER (1974) and HOLTON and MASS (1976) for studies of stratospheric warmings; the reader is referred to the latter reference for details.

The system considered is a beta-plane of width 6000 km centred on 600 S and extending from the earth's surface at z = 0 to an upper boundary at z = 80 km. The prediction equations for wave and mean flow are

(3)

and

:t [:~] = - : y22 [0/x' q'] + ~ :z [ap ~2 :z (u - u.)] ( 4)

where ljJ and q are geostrophic streamfunction and potential vorticity and u the zonal wind. The overbar denotes a zonal mean and (') adeparture therefrom. The Coriolis parameter is f, while p(z) and N(z) are respectively the mean density and buoyancy frequency. The wave and mean flow relax toward radiative equilibrium at a rate a(z); ue(z, t) is a "radiative equilibrium" wind, i.e., the mean zonal wind in thermal wind balance with radiative equilibrium temperatures.

The zonal mean wind is defined as

U = U1(z, t)sin ~ y

and the planetary wave geopotential height perturbation ep' = fljJ'/g as

ep' = Re[ $(z, t)e ikx sin i y 1 3 It will be noted later that there mayaiso be a contribution from gravity waves.

(5)

(6)

Vol. 130, 1989 On the Seasona1 Cyc1e of Stratospheric P1anetary Waves 237

terms ofmeridional wavenumber greater than niL are neglected. The wave is forced by specifying = <1>0 on z = O. The radiative cooling rate IX increases linearly from (20 day)-I at (and below) 10 km to (2 day) -I at and above 40 km. The mean wind is specified at z = O.

It is not the intention of these ca1culations to generate a realistic simulation of the winter stratosphere; to do so would of course require a much more sophisticated model. Rather, the present model is used to perform some highly idealized ca1culations to investigate the dependence of the seasonal behaviour of planetary waves on the forcing amplitudes. In this spirit, the surface amplitude <1>0 of the wave is assumed to be constant in time while üe is specified to vary seasonally as:

(7)

where

Ue =5+3Z ms- I, z<7.5km

= 27.5 ms-t, 7.5< z < 10 km

= 27.5 - 100 sin (~::) sin n(zl~OlO) ms-t, 10 < z < 60 km

= 27.5 - 100 sin 2nt) (I yr

ms- I, z > 60 km, (8)

where Z is in km and where t = 0 corresponds to vernal equinox. Thus the assumed radiative equilibrium profile is independent of season below 10 km but increases with z in the stratosphere from 27.5 ms- I at z = 10 km to -72.5 ms- I at t = 91 days (summer solstice) and 127.5 ms- I at t = 274 days (winter solstice) at 60 km.

3. Model Results

The time evolution of the mean zonal wind and planetary wave geopotential height for wavenumber I forcing of <1>0 = I mare shown in Figure 3. At this forcing amplitude the wave-induced mean flow changes are negligible; the mean winds are almost identical to the specified equilibrium winds (with a slight time lag) and the wave behaviour is therefore completely linear. As the stratospheric westerlies set in following autumnal equinox (day 183) the stratospheric wave amplitude grows rapidly but then decreases in midwinter (by a factor ranging from about 1.3 in the lower stratosphere to about 2 at and above the stratopause). In late winter, however, as the westerlies begin to weaken again, the wave grows to amplitudes comparable with those attained in early winter before collapsing at the final warming as the stratospheric westerlies become easterlies. Through the second and subsequent winters (not shown here) almost identical behaviour was seen.

238

( a)

(b)

70

60

:iSO ::.::: '-"'10 f-

~ 30 w I20

R. Alan Plumb

M S EX PT lYOl

10

O~~====~~====~~==~ o

70

60

"'""50 ~ :::.:::: '-"''10 f-

~ 30 w I20

10

0 0

250 TIME (DAY)

500

WAVE AMPUTUDE GPM L ~H~"r-.-,,~~~~--~

9 78

L

250 TIME (DAY)

Figure 3

500

PAGEOPH,

Time-height plots of (a) mean zonal wind U (ms- I ) and (b) wave amplitude cp' (units: 0.1 m) for wavenumber I with forcing amplitude <110 = I m. Day 0 corresponds to vernal equinox. (See text for

details.)

Since the forcing amplitude is held constant, this behaviour is symptomatic of the system response rather than the forcing. In order to test whether the reamplification through late winter could be a manifestation of oscillatory behaviour following the early winter transience, the experiment was rerun with the equilibrium wind profile specified as before until winter solstice (day 274) and then held constant at the midwinter value. The early winter behaviour was found to be the same, of course, followed by amidwinter collapse; subsequently the amplitude was alm ost steady with no secondary amplification. Therefore it appears that the late

Vol. 130, 1989 On the Seasonal Cycle of Stratospheric Planetary Waves 239

winter amplification is a response to the changing mean wind profile and that la te winter conditions are more favourable than those of midwinter to wave propagation into and through the stratosphere.

Increasing <1>0 up to 30 m makes little difference to this behaviour; the mean wind changes remain relatively small and the only significant change to the wave is an increase in amplitude. For larger forcing amplitude, however, more significant, qualitative, changes occur. The wintertime mean zonal winds become substantially reduced and, in consequence, the wave propagation characteristics differ from the weakly-forced experiments. The differences become more dramatic for still larger <1>0; at <1>0 = 60 m (Figure 4) the westerlies have been reduced to a maximum of about 50 ms - 1 in midwinter and, as a result, the midwinter minimum in wave

(al

(b)

70

60

~ 50 ~ ~ ~40 I-

i§ 30 w I20

JO

70

60

SESO ~ '--''l0 I-

~30 LU :::r: 20

10 'J

- EXPT IY60

250

TIME (DAY)

WAVE AMPLITUDE GPM) l

1 l

2 2~611

~J EXPT 1Y60

l 3

500

OJ-__ ~l~~~l~ __________ ~l~ ____________ ~ .;) " o 250

TIME (DAY)

Figure 4 As Figure 3, except for <IIo =60m. Units (a) ms- 1 (b) 10m.

500

amplitudes no longer occurs-on the contrary, the evolution of wave amplitude through the winter is such that there is for this case a single, midwinter, maximum.

The changing evolution of wave amplitude at 50 km through the winter, as a function of forcing amplitude, is illustrated in Figure 5a; the double peak is clearly visible for <1>0 < 30 m, as is its disappearance at larger values. Also shown, in Figure

(a)

(b)

2000

;1600 a.. (!)

~ 1200 :J f--1 800 a.. ~ «

400

500

~ 400 a.. (!)

w o 300 :J f--1

~ 200 «

100

60

-I 00 0 I 00 200

DAYS FROM WINTER SOLSTICE

O~~~~ __ L-~~~~~~ -200 -100 0 100 200

DAYS FROM WINTER SOLSTICE Figure 5.

Time series through winter of wave amplitude (m) at z = 50 km. (a) Zonal wavenumber I; (b) zonal wavenumber 2. Labels on curves are forcing amplitudes cllo (in m).

Vol. 130, 1989 On the Seasona1 Cyc1e of Stratospheric P1anetary Waves 241

5b, is a similar plot for wavenumber 2. This shows similar characteristics; in fact the midwinter collapse of wave amplitude is even more marked [note from (2) that the critical velocity Ue decreases with increasing k]. The double peak of winter wave amplitude disappears at rather smaller forcing amplitudes (<1>0 = 20 m), although the vertical Eliassen-Palm flux at this value is similar to that at which the midwinter minimum disappears in the wavenumber I case (which is perhaps not surprising, since the requirement seems to be that there be substantial reduction of the mean zonal wind). It is also worth noting from these figures that the "final warming"when the wave amplitudes collapse and the mean zonal wind reverses at the end of winter-occurs earlier at the larger forcing amplitudes.

4. Discussion

In interpretation of these results, it must be borne in mind that the model used for these experiments is of course a very crude simplification of the real stratosphere. It does allow some feedback between wave and mean flow-an essential requirement since this is at the heart of the hypothesized mechanism-but many of the effects acting on stratospheric planetary waves are absent. For example, the waves in the truncated model must propagate purely in the vertical direction and are dissipated by simple Newtonian cooling whereas real planetary waves may (and do) propagate meridionally and dissipate at least in part by breaking in low-tomiddle latitudes (McINTYRE and PALMER, 1983). In fact, the confinement of wave activity by the side walls in this model probably causes an enhancement of wave, mean-flow feedback effects. Nevertheless, these experiments have qualitatively reproduced the kind of seasonal behaviour observed in the two hemispheres, at different forcing amplitudes. There are so me significant shortcomings of the r~

sults-e.g., the double-peaked wintertime behaviour at small amplitude is not very evident in the lower stratosphere-and, of course, the quantitative aspects of the present results should not be taken too seriously. It is desirable that experiments such as these be conducted in more complete models in order to confirm the qualitative nature of the present results and to give quantitative criteria for the transition from double-peak to single-peak winter behaviour, whose significance can then be assessed by comparison with the real situation.

The present results suggest that the southern hemisphere wintertime cycle is indicative of essentially linear behaviour of the quasi-stationary waves, in that their propagation characteristics are determined by zonal winds wh ich are little affected by the waves' presence. If these winds are such as to inhibit vertical propagation in midwinter (as was found to be the case in these experiments) wave amplitudes have separate maxima in early and late winter, when the westerlies are weaker. Since the "radiative equilibrium" winds in northern winter should differ little from those in southern winter the present results suggest that the Northern Hemisphere, where the tropospheric forcing of quasi-stationary waves is larger, is in the "large-amplitude"


regime of the present experiments. On this interpretation, the absence of a midwinter minimum in the climatology of northern hemisphere quasi-stationary waves arises from nonlinear effects of the kind described here, whereby the wave propagation in midwinter is enabled as a result of the reduction of the mean westerlies by the waves themselves. (There may perhaps be contributions from other sources, such as gravity waves, in reducing the westerlies but this is difficult to assess, given the incompleteness of our understanding of the role of gravity waves in the general circulation of the stratosphere.) Overall, the conclusion, albeit tentative, of the present study is that the conventional explanation of the northern hemisphere cycle in amplitude of the quasi-stationary planetary waves as a simple consequence of linear propagation characteristics, while correct to a point, may be incomplete.

Acknowledgements

The ideas explored in this paper arose in part from comments made by Mark Schoeberl (on possible feedbacks of the kind discussed here), Jerry Mahlman (on the behaviour of planetary waves in stratospheric general circulation models of moderate resolution) and by Michiya Uryu in a paper presented at the First Symposium of the IAP, Beijing, in August 1986. I am also grateful to David Karoly for discussions and for extracting, and the Australian Bureau of Meteorology for providing, the data presented in Figure I.

REFERENCES

CHARNEY, J. G., and P. G. DRAZIN (1961), Propagation 0/ planetary-scale disturbances /rom the lower in the upper atmosphere, J. Geophys. Res. 66, 86-109.

GEISLER, J. E. (1974), A numerical model 0/ the sudden stratospheric warming mechanism, J. Geophys. Res. 79, 4989-4999.

HARTMANN, D. L. (1976), The dynamical climatology 0/ the stratosphere in the Southern Hemisphere during late winter 1973, J. Atmos. Sei. 33, 1789-1802.

HIROTA, I., T. HIROOKA, and M. SHIOTANI (1983), Upper stratospheric circulation in the two hemispheres observed by satellites, Quart. J. Roy. Meteor. Soe. /09, 443-454.

HOLTON, J. R., The Dynamic Meteorology o/the Stratosphere and Mesosphere (Ameriean Meteorologieal Soeiety, Boston, 1975) 216 pp.

HOLTON, J. R., and C. MASS (1976), Stratospheric vacillation cycles, J. Atmos. Sci. 33,2218-2225. KAROLY, D. J., and B. J. HOSKINS (1982), Three dimensional propagation o/planetary waves, J. Meteor.

Soc. Japan 60, 109-123. MATSUNO, T. (1970), Vertical propagation 0/ stationary planetary waves in the winter northern hemi

sphere, J. Atmos. Sci. 27, 871-883. McINTYRE, M. E., and T. N. PALMER (1983), Breaking planetary waves in the stratosphere, Nature 305,

593-600. MECHOSO, C. R., D. L. HARTMANN, and J. D. FARRARA (1985), Climatology and interannual variability

0/ wave, mean-j/ow interaction in the Southern Hemisphere, J. Atmos. Sei. 42, 2189-2206. WMO (1986), Atmospheric Ozone 1985, Global Ozone Research and Monitoring Project-Report No.

16; World Meteoro1ogica1 Organization, Geneva.

(Received February 7, 1988, revised/accepted May 23, 1988)


Body Force Circulations in a Compressible Atmosphere: Key Concepts

TIMOTHY J. DUNKERTON1

AbslraCI-The body force circulation problem of Eliassen is extended to spherical geometry and a quasi-compressible atmosphere using the zonally symmetric tidal theory. The concept of body force circulation is generalized to include the effects of mechanical friction and Newtonian cooling. This viewpoint is conceptually advantageous when the circulation is driven by body forces against radiative relaxation. The resulting linear theory is qualitatively useful in middle atmosphere applications, including the equatorial momentum source for which an analytic solution has not been given previously. Further generalizations of the theory are possible by including dynamical and photochemical feedback effects.

Key words: Mean meridional circulation, zonally symmetric tidal theory.

1. Introduction

It is a well-known property of rotating, stratified fluids that the response of a balanced, axisymmetric flow to external forcing excites a mean meridional circulation. This circulation is required to maintain balance, and generally opposes the forcing (Lenz' law). The induced circulation then has a twofold effect, locally reducing the impact of the forcing, and causing a nonlocal response outside the source region in such a way as to maintain thermal wind balance everywhere.

a. Eliassen' s Circulation

The classic illustration was provided by ELIASSEN (1951), who derived an elliptic equation for the mean meridional streamfunction of the form

V2x = oF + oQ oz oy (1.1)

where ~F and Q are appropriately normalized measures of body force and diabatic heating. The circulation induced by a point source is derived from the Green's

I Northwest Research Associates, Inc., Bellevue, WA 98009, U.S.A.

244 T. J. Dunkerton PAGEOPH,

function appropriate to the geometry and boundary conditions of the problem. The semi-infinite domain has G oc Inlx - xol plus an "image charge" beneath the surface. The response to a body force (heat source) is given by the vertical (latitudinal) derivative of the Green's function. With the point source distant from the surface, the induced mean meridional circulation has the well-known double-cell structure. Its effect is nonlocal inasmuch as the function Inlx - xol and its first derivatives are of broad spatial extent relative to the point source b(x - xo).

b. Middle Atmosphere Applications

Considerable progress has been made in the literature to generalize Eliassen's circulation to a spherical, quasi-compressible2 atmosphere. LEOVY (1964) calculated the diabatic circulation induced by radiative heating in the middle atmosphere. An early attempt to explain the quasi-bien ni al oscillation invoked a diabatically-driven mean meridional circulation (DICKINSON, 1968). MATSUNO and NAKAMURA (1979) determined the body force circulation induced by a vertically-propagating, steady, conservative Rossby wave encountering its critical level in a beta-plane channel. Their model provided a paradigm of the Eulerian and (nondivergent) Lagrangian mean meridional circulations during a sudden stratospheric warming. PLUMB (1982) returned to the sphere and showed that the diabatic circulation due to the warming would extend into the opposite hemisphere, in agreement with observations. In contrast, the diabatic circulation due to the tropical quasi-biennial oscillation probably would not extend to polar latitudes. Finally, GARCIA (1987) generalized Leovy's problem to include body forces, retaining unequal coefficients of mechanical friction (~M) and Newtonian cooling (~T)'

All of these studies have emphasized, among other things, the nonlocal character and effect of the induced mean meridional circulation.

c. Transformed Eulerian Mean Formulation

In the transformed Eulerian mean (TEM) formulation, the relevant "body force" per unit mass is the Eliassen-Palm flux divergence factor

V·F DF =---

poa cos () ( 1.2)

where F is the Eliassen-Palm flux, Po = Ps exp - z / His basic state density, a is earth radius, and () is latitude (DUNKERTON et al., 1981). Two important advantages of TEM are (I) DF is zero for linear, steady, conservative waves (ANDREws and

2 Eliassen's model was formulated with pressure as the vertical coordinate, but the more recent papers have helped to elucidate the effects of quasi-compressibility.

Vol. 130, 1989 Body Force Circulations in a Compressible Atmosphere 245

McINTYRE, 1976), and (2) the residual eddy fluxes in the thermodynamic equation are small in the quasi-geostrophic limit (DUNKERTON, 1980).

One dis advantage of TEM in log-pressure coordinates-that the residual vertical velocity is nonzero even for adiabatic motion-is overcome with isentropic coordinates (TUNG, 1982, 1986), in which vertical velocity equals diabatic heating. However, the isentropic density may not always have a simple variation as in a quasi-compressible (quasi-Boussinesq) system like the log-pressure co ordinate TEM.

d. Outline

In this paper, analytical properties of Eliassen's equation in a spherical, quasicompressible atmosphere will be reviewed. The governing equation will be extended, as in GARCIA (1987), to include mechanical friction and Newtonian cooling (Seetion 2). The linear problem is separable; we therefore consider the latitudinal and vertical structure equations in Sections 3 and 4, respectively. The special case of an equatorial momentum source is also discussed (Section 4f). Further generalizations to include dynamical and photochemical feedbacks are suggested in Section 4g.

2. Governing Equations

a. Linearized Mean Flow

The linearized mean flow is governed by the equations

fü = -fv

ePZI + N 2w* = Q - cxr<Pz

1 0 _* II 1 0 - * 0 ---v cos u +--Pow = cos e oy Po oz

(2.1a)

(2.lb)

(2.1c)

(2.ld)

where ü is the zonal me an wind, 5* and w* are residual meridional and vertical velocities, eP is geopotential, fis the Coriolis parameter 20 sin e, and N is static stability.

It is assumed that the mean flow is linear in the sense that the shear terms and ePzz are sm all (LEOVY, 1964). There might be some quantitative error in this assumption. For example, DUNKERTON (1988) compared streamfunction solutions with and without shear and found errors approaching 50%. However, the insights gained from the linear theory are nevertheless worthwhile. Note that no assumption of linear waves has been made. The complete streamfunction equation, including nonlinear advection terms, is given in the Appendix.

The eontinuity equation (2.1 d) leads to the definition of a residual mean meridional streamfunetion

( 0 1) -v* eos () = - oz - H X *

oi* w* eos () = oy.

b. Nondimensionalization

The following definitions are helpful:

JI. = sin ()

f=20JI.

Z=zjH

R=(~:ay HDF

F= 20

H 2Q Q = 402a

(2.le)

(2.11)

(2.2a)

(2.2b)

(2.2e)

(2.2d)

(2.2e)

(2.21)

so long as the atmosphere is quasi-eompressible (H< 00), rotating (0 # 0) and spherieal (variable 8). Statie stability enters the problem via R. Fand Q have streamfunetion units here (m2 S-I).

c. Elliptic Streamfunction Equation

Following LEOVY (1964) and GARCIA (1987), substitution of a harmonie time dependenee exp iwt yields (replaeing i* with X)

(~ _ 1) OX + R(iW + (XM) I - JI.2 02X = Jl7 oF + (iW + (XM) 1 - JI.2 oQ. oZ oZ iw + (XT JI.2 OJI.2 JI. oZ iw + (XT JI.2 OJI.

(2.3)

Boundary eonditions are X( ± 1, Z) == 0 at the poles. At the top and bottom boundaries X may not neeessarily be zero due to the vertieal component of Eliassen-Palm flux (EDMON et al., 1980). However, an optional boundary layer may be inserted at the surfaee, implying singular D F there.

With (XM = (Xn (2.3) is independent of wand reduces to Eq. (4.4) of DUNKERTON (1988). The vertical veloeity equation proportional to o(2.3)joJI. is the zonally symmetrie Laplaee tidal equation (GARCIA, 1987, Eq. 2) under the eondition (2.1b) whieh evidently requires Iwi ~ 120JI.1.

Vol. 130, 1989 Body Force Circu1ations in a Compressib1e Atmosphere 247

The properties of Eliassen's equation are retained in (2.3): (a) the equation is elliptic, (b) the aspect ratio is R 1/2 , (c) the body force is differentiated with respect to height, and (d) the diabatic heating is differentiated with respect to latitude. As a consequence of (c), the vertically-averaged body force induces a mean flow acceleration. Similarly, because of (d), the latitudinally-averaged diabatic heating produces a me an temperature rise. Both tendencies result from the inability of a mean circulation to cancel the external sources of heat and momentum.

3. Latitudinal Structure Equation

a. Separation of Variables

Separation of (2.3) proceeds using the set of orthogonal eigenfunctions '1n:

where

1- J-l2 --2- '1~ == f.n'1n

J-l

'1n( ± I) == O.

(3.1)

(3.2)

(3.3)

The '1n eigenfunctions are simply related to the zonally symmetrie Hough modes (see below) which form a complete set according to HüLL (1979, his case 4). It is assumed for the moment that the external sources satisfy (3.1); the special ca se of an equatorial momentum source is examined in Section 4f.

b. Eigenfunctions and Eigenvalues

Figure la shows the first 12 eigenfunctions and Table I gives the corresponding eigenvalues, obtained by solving (3.2) with the tridiagonal algorithm and a shooting method (AJ-l = 0.001). Orthonormal functions are shown, i.e.,

fl ('1~)2dJ-l == I (3.4)

along with the structure functions for body force (Figure I b) and diabatic heating (Figure Ic):

~'1n y'1-J-l

and '1~,

respectively, where '1~ are the zonally symmetrie Hough modes (FLATTERY, 1967;

248 T. J. Dunkerton

a 0.5,---------------------------------,

5

9

0.0 11

7

3

-0.51---.--.---.--.--.---r--'---r--.--~

0.0 0.2 0.4 f..L 0.6 0.8 1.0

0.5,---------------------------------,

0.0

-0.51---.--.---r--.--.r--.--.---.--.--~

0.0 0.2 0.4 0.6 f..L

Figure l(a)

0.8 1.0

PAGEOPH,

LONGUET-HIGGINS, 1968; PLUMB, 1982; GARCIA, 1987). In Table I, note that t n < 0 by virtue of (3.2). The convention here is that odd (even) n are symmetrie (antisymmetrie) in X about the equator. The eigenfunctions are relatively smooth near the equator, varying more rapidly near the poles (on the sine latitude grid). This is particularly true of the body force structure functions (Figure I b), implying that a local source at high latitudes projects more efficiently onto the gravest eigenfunctions than a mid-Iatitude source.

Vol. 130, 1989 Body Force Circulations in a Compressible Atmosphere

b 0.5,-----------------------------------,

-0.5~--r-_,---.--_r--~--._-.--_.--.-__1

0.0 0.2 0.4 0.6 0.8 1.0

0.5,-----------------------------------,

4

-0.51---,--.,--.---,--,---.--.---,---.--1 0.0 0.2 0.4 J1 0.6 0.8 1.0

Figure I(b)

c. Projection 0/ Body Force Profiles

In general,

fl P, Fn(Z) = -(n ~ 'lnF(P" Z) dp,.

_1y'1_p,2

249

(3.5)

To illustrate the remark just made, Figure 2 shows the projection of a local body force onto the first 12 structure functions for two cases, a high-Iatitude and mid-Iatitude source.

250 T. J. Dunkerton

c 3.0,_----------------------------------,

o. O-t--..... ~E==-_

-3.04---~~r_~--_.--,_--._~r__.---r~

0.0 0.2 0.4 P. 0.6 0.8 1.0

3.0,_----------------------------------,

2

0.0

4

-3.0;---~--r__.--_r--,_--~~r__.---r~

0.0 0.2 0.4

Figure I(c)

Figure I

0.6 0.8 1.0

PAGEOPH,

Eigenfunctions of the latitudinal structure equation, and related structure functions for body force and diabatic heating.

As will be shown in the next section, higher eigenfunctions decay more rapidly in the vertical. This result is intuitively consistent since the "Rossby height" (/oL/N) is proportional to the Coriolis parameter, i.e., the distance from the equator, and the meridional scale L. However, the concept of Rossby height should not be used carelessly in a spherical, quasi-compressible atmosphere. Different vertical scales pertain above and below the source, as discussed below (PLUMB, 1982).


Table I

Eigenvalues and related vertical scales (in scale heights) of the first 12 eigenfunetions for R = .02276.

n -fn Je;I( +) Je;I(_)

I 8.127 .862 -6.27 2 12.54 .812 -4.32 3 35.42 .655 -1.90 4 44.73 .615 -1.60 5 82.38 .511 -1.04 6 96.62 .484 -0.939 7 149.1 .415 -0.710 8 168.2 .397 -0.658 9 235.5 .349 -0.535

10 259.6 .335 -0.505 11 341.6 .300 -0.429 12 370.7 .290 -0.409

3

2 a

0

-1

-2

-3 0 2 3 4 5 6 7 8 9 10 11 12 13

n

3

2 b

0 ------------- -------------- --------

-1

-2

-3 0 2 3 4 5 6 7 8 9 10 11 12 13

n

Figure 2 Projection of high-Iatitude and mid-Iatitude body force profiles (4.1 0) onto the first 12 structure

functions. (a) JlI = .75, Jlo = .25, (b) JlI = .50, Jlo = .25.


d. Pairing of Adjaeent Eigenfunetions

The pairing of adjacent eigen va lues in Table 1 (e.g., n = 1,2) suggests a reason for the cancellation of adjacent eigenfunctions in one hemisphere when the two are added together. This cancellation is particularly strong for the body force structure functions, as shown in Figure 3 of DUNKERTON (1988). As a result, it is straightforward to estimate the cross-equatorial penetration of the streamfunction when the body force profile is confined to high latitudes of one hemisphere. Similar cancellation of the heat source functions was noted by PLUMB (1982). For further discussion see FLATTERY (1967) and LONGUET-HIGGINS (1968).

4. Vertical Structure Equation

a. Upward and Downward Vertical Deeay Scales

The vertical structure equation resulting from (2.3), (3.1), and (3.2) is

[(a~ -1) a~ +R G:: ::) En}n = F~ + EnG: ::: )Qn ( 4.1)

as derived by previous authors. The homogeneous problem (rhs = 0) admits solutions of the form

(4.2)

where

A = ~ + {R iw + r:t. M IE I ~}1/2 n 2- . + n+4 IW r:t. T

( 4.3)

(MATSUNO and NAKAMURA, 1979; PLUMB, 1982; GARCIA, 1987; DUNKERTON, 1988). Values of )on are shown in Table I for R = .02276 and r:t. M = r:t. T . Upward-decaying solutions have a much larger vertical decay scale than the downward-decaying solutions (PLUMB, 1982). This asymmetry is exaggerated when w is small and r:t. M ~ r:t. T (GARCIA, 1987).

b. Shallow Souree

Equation (4.1) admits analytic solutions in special cases. For example, if the forcing decays exponentially away from some level Zc, the inhomogeneous part is easily obtained. Unfortunately, when boundary conditions are taken into account, the coefficients require inversion of a 4 x 4 matrix. If the boundaries are at ± 00 the order is reduced to 2 x 2. A simpler case like that of MATSUNO and NAKAMURA (1979) is to examine the effect of a shallow source

( 4.4)

Vol. 130, 1989 Body Force Circu1ations in a Compressib1e Atmosphere

Defining g' == X (dropping the subscript n), gives

g" -g'- RIE:lg =F.

Substituting g == G exp Z' /2 simplifies (4.5) to

where, if IXM = IX n

The solution is

Z' G" - NG = F exp --

2

{Gm exp - AZ' Z' > 0

G-Gm exp+ AZ' Z' <0

253

(4.5)

(4.6)

(4.7)

(4.8)

with Gm determined by integration across the delta-function. The functions G decay at an equal rate away from the source, but when the weight factor exp Z' /2 is inserted, the upper solution decays much more slowly (cf, Table 1). Thus, the derivative of g is smaller above the source, making the streamfunction amplitude smaller there. It is perhaps remarkable that the time-dependent problem exhibits this tendency for downward control, a property more readily seen in the steadystate ca se as noted by McINTYRE (1987). The lower cell carries most of the mass; the mass flux ratio between upper and lower cells is (A - 1/2)/(A + 1/2). Note, however, that the meridional velo city is larger in the upper cello

c. Some Examples

Putting these results together it may be said that the body force circulation of Eliassen retains its qualitative character in a spherical, compressible atmosphere, but is quantitatively distorted in a rather complicated way: the circulation cells are no longer symmetrie. The asymmetry depends on the latitude and meridional extent of the forcing, the proximity to the surface, the aspect ratio R 1/2, and the effects of mechanical friction and Newtonian cooling. Regarding the latter, note that when w is smalI, the effective static stability is

2 _IXM 2 Neff=-N. IX T

(4.9)

For illustration, a body force profile was used in Figure 3 of the form

D F = Df~ exp - {(~ :O~IY + (z ~oZIY} ( 4.lOa)

D F = IOms- 1 day-I rn

(4. lOb)


a

z

25

20

15

10

5

0 ".5 0 .5

b

30

200

25

0

20

15

10

5

04--,-,-,r-r-,-,--,-,--r-r-,-,--,-,--r ".5 o .5

Figure 3( a, b)

Vol. 130, 1989 Body Force Circulations in a Compressib1e Atmosphere 255

c

5

0 -.5 0 I-' .5

d 30

z

25 200

20

0

15

10

5

04--r-.--.-.-.--r~-,--r-.-~-r-.-,~ -.5 o I-' .5

Figure 3( c,d)

Figure 3 Body force circulations for the simple cases discussed in Section 4c.

256 T. 1. Dunkerton PAGEOPH,

with boundary conditions X(O) = 0, X'( 42 km) = 0, and N = .02 S-I. The four cases shown correspond to w = 0, Z 1 = 15 km, Zo = 2 km, and

3a. 111=·75 110 = .25 rt. M =rt.T

3b. 111 = .75 110 = .25 rt.M = .2rt. T

3c. 111 = .50 110=·10 rt. M =rt. T (4.lOc)

3d. 111 = .75 110 = .25 rt. M = 5rt. T

The asymmetry in the circulation cells is most evident in Figure 3b, and least prominent in Figures 3c, d. The lower cell is strongest in each case, quite apart from the influence of the lower boundary. In the limit N~ff -+ 0, the mass flux ratio between upper and lower cells approaches zero.

In all of these examples the imaginary part of the solution is zero. In the general ca se of nonzero wand nonidentical rt. M , rt. T the solution is complex. One interesting time-dependent solution is the "diffusive" regime of DICKINSON (1968) relevant near the equator.

d. ARemark on Terminology

In referring to Figures 3a-d as "body force" circulations it should be recalled that the effects of mechanical friction and Newtonian cooling have been incorporated on the Ihs of (2.3) and (4.1). One may then define a generalized body force circulation that represents the response of an atmosphere to an applied force and the restoring effects of mechanical friction and radiative relaxation. In the middle atmosphere, it has been frequently noted that the diagnostic (diabatic) residual circulation of DUNKERTON (1978) owes its existence to the decelerating effect of planetary and gravity waves (e.g., MAHLMAN et al., 1984). Thus, the concept of a generalized body force circulation makes sense in this context, in which wavedriving opposes radiative relaxation.

e. Inviscid, Steady-state Limit

If w == 0 and mechanical friction is excIuded (rt. M == 0), (4.1) reduces to a first-order equation (cf, 2.1a). Consequently, two boundary conditions overdetermine the solution. Instead, in the time average,

fpox* /: = iCG

Dfpo cos e dz' + nonlinear terms (4.11)

as implied by (2.la, e). The constraint on the time-averaged DF in the linear ca se was noted above. McINTYRE (1987) observes that the integral is strongly convergent in its upper limit due to constraints imposed by wavebreaking processes. The steady-state solution can be viewed as a limiting ca se w -+ 0 provided that the two vertical boundary conditions of the second-order problem are chosen to be compatible with the first-order solution when w == o.

f Equatoria/ Momentum Source

As noted by PLUMB (1982), an equatorial moment um souree eannot be represen ted by the expansion (3.1). To examine the effeet of a near-equatorial source, it suffiees to eonstruet body force profiles that satisfy (3.1) but are nevertheless of finite amplitude at some sm all distanee off the equator. Profiles like this ean easily be eonstrueted by harmonie expansion of a funetion that does not satisfy (3.1). One partieularly simple funetion is ~ (eosine latitude). Figure 4a shows the projeetion of this funetion 3 onto the symmetrie body force strueture funetions of the truneated series n = 2, 4, 6 ... 100. At large n, the eigenvalues are found to be closely approximated by the WKB result (2n = _n 2n2. The eoeffieients Fn also inerease with n, approximately like n 1/3, at least to n = 100. The eosine funetion is adequately resolved by the first 100 strueture funetions only outside of about 1J11 = 0.1 (~5° latitude). There is evidenee of the overshooting "Gibbs phenomenon" near this latitude. The behavior is as if we were trying to reeonstruet the diseontinuous funetion everywhere equal to eosine latitude exeept at the equator. Clearly the near-equatorial souree distributes its effeet over a wide range of eigenfunetions, in aeeord with the remarks of Seetion 3e; this implies a more rapid deeay of the streamfunetion in the vertieal, and a more symmetrie pattern.

For the shallow Matsuno-Nakamura source, the behavior above and below Z' = 0 ean be elueidated starting from (4.8), noting first that Gmn = - Fmn /2An (reinserting the harmonie subseript n). Henee

Fmn {G - An )expG - An )z'}z' > 0 (4.12)

Xn = - 2An G+ An)eXpG+ An )Z' Z' < O·

The total streamfunetion is then given by (3.1). Going a step further, the residual vertieal velocity is

8X I" Fmn { } w*a = - = -- 1.... - •.. Yf~(J1). 8J1 2 n An

( 4.13)

For the eosine funetion of Figure 4a, it is diffieult to evaluate (4.13) near the origin beeause the produet FmnYf~(O) inereases (albeit very slowly) with inereasing n, at least to n = 100. There is, then, no evidenee of eonvergenee at J1 == 0 in the limit Z' -+ O. If we do not take this limit, the infinite series solution apparently does

eonverge, on aeeount of the exponential term in (4.12). Figure 4b shows the vertieal velocity profiles at Z' = ± 0.2, 0.3, and 0.5. Most of the fine strueture due to the highest eigenfunetions has deeayed away; adding higher terms to the series would change the total by only a small amount. The latitudinal seale of the streamfunetion

3 Note that any body force can be represented by a linear combination of the eosine function and a function satisfying (3.1).

258 T. J. Dunkerton

1.5~----------------------------------~

a F

1 .0-r---t--4--L

0.5

-n = 2-100

o . 0 -- .. -- ------- --- ---- -- --------- ------- ---. --------- ----------- -- -- -- --- ------

-0.5~--~--,_--,_--,_--~--~--~--r_-r_~

0.0 0.2 0.4 0.6 0.8 1.0

8.0~--------------------------------~

b

4.0

0.0

Z = 0.2

-4.0-1--~

-8.0~--~--,_--,_--,_--~--~--~--r_-r_~

0.0 0.2 0.4 Jl

Figure 4

0.6 0.8 1.0

PAGEOPH,

(a) Representation of an equatorial body foree (eosine latitude) by the first 100 strueture furiCiions (aetually the first 50 symmetrie strueture funetions). (b) Solution for vertieal ve10eity above and below

the souree level.

expands receding from the source, in agreement with the fact that higher eigenfunctions decay more rapidly in the vertical. The streamfunction exhibits the familiar quadrupole or "butterfly" pattern (not shown). We note in passing that the vertical symmetry of this pattern is destroyed by Newtonian cooling; the diabatically-driven circulation has been discussed, e.g., by DICKINSON (1968), PLUMB and BELL

(1982), and DUNKERTON (1985).

Regarding equatorial convergence, it should be kept in mind that (i) all forcings of geophysical interest are of finite amplitude, encompassing a broad range of nonzero frequencies, and (ii) the quasi-geostrophic assumption breaks down within the latitude band 1J.l1 < 10"1 where w == 200". A uniformly convergent solution can be obtained, for example, in the case of a finite-amplitude, broken-line exponential forcing cited at the beginning of Section 4b (not shown). Similarly, R. Garcia (personal communication, 1987) obtained a numerically convergent solution for the Gaussian F-profile. Concerning geostrophic balance, the necessary modification to (3.2) is

( 4.14)

Dispersion curves were shown in FLATTERY (1967) and LONGUET-HIGGINS (1968). The eigenvalues listed in Table I agree with their limiting values when i. < 0 and 0" .... O. Flattery notes that the equation (4.14) can be transformed into the spheroidal wave equation. With a little effort, the first five eigenvalues can be located in Table 21.1 of ASRAMOWITZ and STEGUN (1970). As 0" moves away from zero, the eigenvalues bend back from their limiting values more rapidly with increasing n (Flattery's Fig. 1). The gravest modes, on the other hand, are less affected by nonzero 0" until (J approaches I.

The situation changes dramatically for nonzero zonal wavenumbers. The limiting values disappear as the dispersion curves are split in two, with an eastwardpropagating branch going back to i. = - 00, and a westward-propagating branch crossing the (J-axis to form the rotational dass, i. > O.

Of course, all zonal wavenumbers induding s = 0 also admit a gravitational dass with positive i.. These modes are oscillatory in time, having a vanishingly small vertical wavelength as 0" .... O. A specific example may help to place the importance of these modes in perspective for very low frequency forcings. If w = 2n/month and N = .02 S -1, then the gravest mode has a vertical wavelength of about 80 m, and the inertial latitudes are about 10 off the equator! It is expected, then, that a much deeper momentum source would not excite this mode very efficiently. On the other hand, a shallow source would necessarily lead to radiation of zonally symmetric inertia-gravity waves in the equatorial waveguide.

Finally we note that, in addition to the breakdown of geostrophic balance, the assumption of linear mean ftow is violated near the equator by the presence of cross-equatorial shear in the latitude band f(f - üy ) < 0, admitting inertially unstable modes (DuNKERToN, 1981, 1983; BOYD and CHRISTIDIS, 1982).

g. Dynamical and Photochemical Feedbacks

Further generalizations of the linear theory are possible and will be mentioned here. These are motivated by the consideration that the source terms on the rhs of


(2.3) may still depend on the streamfunction solution. For instance, D F depends on the zonal wind field and its shears. Symbolically we may write

oD Dp(ü) = Dp(üo) + (ü - üo) oüF + ... ( 4.15)

and include the linear term on the lhs of (2.3). [Note that a negative relaxation is possible-e.g., easterly DF increases as westerlies are decelerated as in the LINDZEN

and HOLTON (1968) theory of the quasi-biennial oscillation.] Similarly, the radiative equilibrium temperature may depend on constituents advected by the mean meridional circulation, and the rate of variation

can also be brought over to the lhs of (2.3). Further discussion of these feedbacks is outside the scope of this paper, and both merit additional investigation.

5. Conclusion

The body force circulation problem of ELIASSEN (1951) may be generalized in several ways, including the effects of spherical geometry (via the zonally symmetric tidal theory), atmospheric compressibility, mechanical friction, Newtonian cooling, and additional feedback effects. The problem is more complicated, but qualitatively similar. The response of the mean meridional circulation depends on several factors including the latitude and meridional extent of the body force. These determine the projection onto the latitudinal structure functions which, together with boundary conditions, determine the upward and downward decay of the solution. The lower circulation cell is generally stronger, the asymmetry being greatest when the forcing projects primarily onto low-order modes having the largest disparity in decay rates (Table I). The same effect is achieved by relatively fast Newtonian cooling with small mechanical friction.

The linear theory has quantitative limitations4, but the insights obtained with it are nevertheless useful. The generalized body force circulation plays an important role in atmospheric dynamics. By considering as many feedbacks as possible on the lhs of (2.3), we are able to unify the body force circulation problem to include all time scales for which the balance assumption is applicable.

4 In finite-amplitude time-dependent applications, the linear system violates the conservation laws of angular momentum and potential temperature. Two examples are the Hadley circulation (SCHNEIDER, 1977; HELD and Hou, 1980) and the semiannual oscillation (HOLTON and WEHRBEIN, 1980; DELISI and DUNKERTON, 1988), both in the tropics.

Vol. 130, 1989 Body Foree Cireulations in a Compressible Atmosphere 261

Acknowledgements

This research was supported by the National Aeronautics and Space Administration, Contract NASW-4230, and by the National Science Foundation, Grant ATM-8616983.

Appendix

A second-order streamfunction equation can be derived from the zonal mean equations when non linear advection terms are included, provided that the gradient wind approximation is replaced by the geostrophic approximation:

( ODF 00.*) = cos e f Tz + oy . (Al)

Under most geophysical conditions (Al) is elliptic (HOLTON, 1975). An obvious exception is when the fluid is centrifugally or statically unstable. From the numerical solutions that have been given in the literature, it appears that local regions of hyperbolicity can admit unstable modes without significantly affecting the stable modes that exist when such regions are absent (DUNKERTON, 1989).

REFERENCES

ABRAMOWITZ, M., and I. A. STEGUN, Handbook of Mathematical Functions (National Bureau of Standards, Washington D.C. 1970) 1046 pp.

ANDREWS, D. G., and M. E. McINTYRE (1976), Planetary waves in horizontal and vertical shear: The generalized E1iassen-Palm relation and the mean zonal acceleration, J. Atmos. Sei. 33, 2031-2048.

BOYD, J. P., and Z. D. CHRISTIDIS (1982), Low wavenumber instability on the equatorial beta-plane, Geophys. Res. Lett., 9, 769-772.

DELISI, D. P., and T. J. DUNKERTON (1988), Seasonal variation of the semiannual oscillaton, J. Atmos. Sei., 10 appear.

DICKINSON, R. E. (1968), On the excitation and propagation of zonal winds in an atmosphere with Nell'tonian cooling, J. Atmos. Sei. 25, 269-279.

DUNKERTON, T. J. (1978), On the mean meridional mass motions of the stratosphere and mesosphere, J. Atmos. Sei. 35, 2325-2333.

DUNKERTON, T. J. (1980), A Lagrangian mean theory ofwave, mean-jlow interaction with applications to nonacceleration and its breakdown, Rev. Geophys. Space Phys. 18, 387-400.

DUNKERTON, T. J. (1981), On the inertial stability of the equatorial middle atmosphere, J. Atmos. Sei. 38, 2354-2364.

DUNKERTON, T. J. (1983), A nonsymmetrie equatorial inertial instabi/ity, J. Atmos. Sei. 40,807-813.


DUNKERTON, T. J. (1985), A two-dimensional model of the quasi-biennial oseil/ation, J. Atmos. Sei. 42, 1151-1160.

DUNKERTON, T. J. (1988), Body force eireulation and the Antaretie ozone minimum, J. Atmos. Sei. 45, 427-438.

DUNKERTON, T. J. (1989), Nonlinear Hadley eireulation driven by asymmetrie differential heating. J. Atmos. Sei., to appear.

DUNKERTON, T. J., c.-P. F. Hsu, and M. E. McINTYRE (1981), Some Eulerian and Lagrangian diagnostics for a model stratospheric warming, J. Atmos. Sei. 38, 819-843.

EDMON, H. J., B. J. HOSKINS, and M. E. McINTYRE (1980), Eliassen-Palm cross seetions for the Iroposphere, J. Atmos. Sei. 37, 2600-2616.

ELiASSEN, A. (1951), Siow thermally or friclionally controlled meridional erieulation in a circular vortex, Astrophys. Norv. 5, 19-60.

FLATTERY, T. W. (1967), Hough Funclions, Teehnieal Report No. 21, Dept. of Geophysieal Seiences, University of Chieago, 175 pp.

GARClA, R. R. (1987), On the mean meridional circulation of the middle atmosphere, J. Atmos. Sei. 44, 3599-3609.

HELD, I. M., and A. Y. Hou (1980), Nonlinear axially symmetrie eireulations in a nearly inviseid atmosphere, J. Atmos. Sei. 37, 515-533.

HOLL, P. (1979), The completeness of the orthogonal system of the Hough funetions. Translated by B. Haurwitz from Nachrichten der Akademie der Wissenschaften in Göttingen, 11. MathematischPhysikalische Klasse Jahrgang 1970, No. 7., 159-168.

HOLTON, J. R., The Dynamic Meteorology of the Stralosphere and Mesosphere (Amer. Meteor. Soe., 1975),319 pp.

HOLTON, J. R., and W. M. WEHRBEIN, (1980), A numerical model 0/ the zonal mean eireulation 0/ the middle alm().\phere, Pure and Appl. Geophys. 118, 284-306.

LEOVY, C. B. (1964), Simple models ollhermally driven mesospheric circulations, J. Atmos. Sei. 21, 327 341.

LINDZEN, R. S., and J. R. HOLTON (1968), A theory o/Ihe quasi-biennial oscil/ation, J. Atmos. Sei. 25, 1095-1107.

LONGUET-HIGGINS, M. S. (1968), The eigen/unctions of Laplace's lidal equations over a sphere, Phi I. Trans. Roy. Soe. London 262, 511-607.

MAHLMAN, J. D., D. G. ANDREWS, D. L. HARTMANN, T. MATSUNO, and R. G. MURGATROYD, Tramport of trace constituents in the stratosphere, in Dynamics 0/ the Middle Atmosphere (1. R. Holton and T. Matsuno, eds.) (Terra Scientific 1984) pp. 387-416.

MATSUNO, T., and K. NAKAMURA (1979), The Eulerian and Lagrangian mean meridional eireulations in the stratosphere al the lime of a sudden warming, J. Atmos. Sei. 36, 640--654.

MclNTYRE, M. E. (1987), Dynamies and tracer transport in the middle atmosphere: An overview ofsome recent del'elopments, Tramport Processes in the Middle Atmosphere, (NATO Workshop Proeeedings, Eriee) G. Visconti, cd.

PUJMB, R. A. (1982), Zonally symmetrie Hough modes and meridional eirculations in the middle atmosphere, J. Atmos. Sei. 39, 983-991.

PLlJMB, R. A., and R. C. BELL (1982) A model of the quasi-biennial oscillation on an equatorial heIa-plane, Quant. J. Roy. Meteor. Soe. /08, 335-352.

SCHNEIDER, E. K. (1977), Axially symmetrie steady-state models 0/ the basic state for instahility and climate studie.I·. Part 11: Nonlinear calculations, J. Atmos. Sei. 34, 280--297.

TUNG, K. K. (1982), On the /Wo-dimensional transport of stratospheric traee gases in isentropic ('()ordinates, J. Atmos. Sei. 39, 2330 2355.

TUNG, K. K. (1986), Nongeostrophic theory of zonally averaged cireulation. Part I: Formulation, J. Atmos. Sei. 43, 2600.

(Rcceived September I, 1987, revised/accepted January 18, 1988)

PAGEOPH, Vol. 130, Nos. 2/3 (1989) 0033--4553/89/030263-13$1.50 + 0.20/0 © 1989 Birkhäuser Verlag, Basel

Satellite Data Analysis of Ozone Differences in the Northern and Southern Hemispheres*

MARVIN A. GELLERI, MAO FAO Wu l and ERIC NASH2

Abstract-Four years of SBUV ozone data and NOAA/NMC temperature data are analyzed for the relations between the annual total ozone behaviour in the Northern and Southern Hemispheres and the transport of ozone by planetary waves. It is found that the interhemispheric differences in the annual variation of total ozone are well explained by the interhemispheric differences in the planetary waves and the resulting ozone transports. The annual variation of the ozone transports by the stationary waves is found to control the ozone behavior in both hemispheres. Both the day-to-day and the interannual variation in total ozone are found to be strongly related to the corresponding variability of the planetary waves.

Key words: Ozone, planetary waves, interhemispheric variations, Southern Hemisphere behavior.

1. Introduction

It is well-known that both the Northern and Southern Hemispheres show similar patterns in the annual variation of total ozone but with systematie differenees in the timing, loeation, and magnitude of specifie features (see, for example, DUETSCH, 1971). As an example of this, the top panel of Figure 1 shows the variation in total ozone as observed by the SBUV instrument on the Nimbus 7 satellite for the period Deeember 1, 1978 to November 30, 1979. These data are taken from the NOAA/ NMC analysis of the SBUV data. The SBUV instrument measures ozone by means of baekseattered solar radiation, so no data is available during the polar night. Also, no ozone data is derived from SBUV poleward of 80 degrees latitude at any time of the year. Thus, the "ozone values" poleward of the dashed lines in the top panel of Figure 1 were obtained by the NOAA/NMC analysis proeedure through extrapolation from observed values while the ozone values equatorward of the dashed lines are those that have been derived direetly from satellite measurements.

I NASA Goddard Space Flight Center, Greenbelt, Maryland, United States. 2 NASA Goddard Space Flight Center and Applied Research Corporation, Landover, Maryland,

United States. * Contribution Number 46 of the Stratospheric General Circulation with Chemistry Project at

NASA/GSFC.

264 M. A. Geiler er al. PAGEOPH,

Z 60

.30 LU 0 :J 250

I- 0 I-<{ ...,;

z Z ID 0:: 0:: tr r > < <1: w < < < < -) -) t.- U (5 u "') "') t.. ::;, ~ ~ ~ (/) 0 7

~ tC ~ lfl 0 v ,- tC r lfl 0 iIl 0 v cn '" (r. n !C N r-. N .... tC ~ "l ~ n ~ r I') ~ "1 r r'1 ~ N C\ N ~ N N N

RMS WAVE AMP' ITUDC 90~~-~--~--~---L--~--~--~--L-__ ~ __ ~-~~

Z 60 o

lJ..,

o :J

.30

r- 0 I-<{ ...J

-.30

lfl- 60 o

.o~ __

~ ~ _~'iO' ') 0-'00 16°-r2öo-~- "")) . .,0 ~~)_ ::=::: ~_ / ~_ IN

- 90 .... , --,,----~---,--_.,,--..___r-- T

U Z ID tr tr r Z J W < w < ~ < ~ ) 0" L..::;' <)-) 1

Figure

o )

< ~

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o

Top-Variation of SBUV-measured totalozone (in Dobson Units) throughout the period December I, 1978, to November 30, 1979. Bottom- Variation of the wavenumber one rms wave amplitude (in units of geopotential meters) at 100 mbar for the period December I. 1978 to November 30, 1979. From

GELLER and Wu (1987).

In Figure 1, the maximum values in total ozone appear during thc la te

winter-spring seasons at high latitudes in both hemispheres, The Northern Hemisphere maximum in total ozone is larger, occurs earlier, and is at highcr latitudes than is the ca se for the total ozonc maximum in the Southern Hemisphere. In

Vol. 130, 1989 Satellite Data Analysis of Ozone Differences 265

Figure 1, the Northern Hemisphere ozone maximum of 464 Dobson units occurs weil before the time of equinox while the Southern Hemisphere maximum of 398 Dobson units occurs weil after the time of equinox. The Northern Hemisphere ozone maximum also occurs at higher latitudes (poleward of 70 degrees) while the Southern Hemisphere maximum occurs at about 60 degrees. Of course, the exact timing, latitude of occurrence, and magnitude of the ozone maxima vary from year to year, but the systematic interhemispheric differences described here are seen consistently.

Figure I was shown by GELLER and Wu (1987) to argue that the different annual variation in total ozone in the Northern and Southern Hemispheres is a consequence of the annual variations of the planetary wave behavior in both hemispheres. For instance, the Northern Hemisphere planetary waves have larger amplitudes than those in the Southern Hemisphere. The planetary waves in the Northern Hemisphere reach their maximum amplitudes before the time of the vernal equinox while the Southern Hemisphere planetary waves reach their maximum amplitudes after the autumnal equinox. Also, the maximum planetary wave amplitudes occur at higher latitudes in the Northern Hemisphere than in the Southern Hemisphere. A similar picture of the differing seasonal marches of planetary wave one in the Northern and Southern Hemispheres is seen in Figure 8 of HIROTA et al. (1983) and also in the power spectral density results shown in Figure 5 of HIROTA (1976). Both of these results are for the 1 mbar level, however.

It is the purpose of this paper to better understand and further document the relations between the annual variation of total ozone and planetary waves in the Northern and Southern Hemispheres.

2. Annual Variations in Total Ozone

Figure 2 shows the variation of the monthly averaged zonal mean total ozone values at 60 degrees latitude in both the Northern and Southern Hemispheres for the period November 1978 to September 1982. The ozone values at 60 degrees latitude are shown to examine more closely the nature of the high latitude variations of total ozone at a latitude that is always equatorward of the terminator so that we are always dealing with observed rather than with extrapolated ozone values. In Figure 2, we have shifted the Northern Hemisphere ozone values forward by six months so that the interhemispheric differences can be seen most easily. As before, one sees that the Northern Hemisphere ozone maximum occurs earlier than does the Southern Hemisphere maximum and that the amplitude of the total ozone variation in the Northern Hemisphere significantly exceeds that in the Southern Hemisphere. It is also seen that during approximately a six month period (MayOctober in the Northern Hemisphere and November-April in the Southern Hemisphere) the Northern and Southern Hemisphere variations in total ozone almost overlay one another. Referring back to the bottom panel in Figure I, it is

266

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Variation of monthly and zonally averaged totalozone at 600 N and 600 S for the period November 1978 to September 1982. The bold curve is for 600 N and the thin curve is for 60oS. Note that the curve for 600 N is advanced by six months relative to the curve for 60oS. The top scale is for the 600 S curve while

the bottom curve is for the 600 N curve.

seen that during these periods the planetary wave amplitudes are very small at 100 mb. If these small planetary wave amplitudes are taken to indicate that dynamics effects are unimportant, then we may conclude that variations in total ozone are largely under solar photochemical control, which is approximately the same in bath hemispheres, during these periods. Another feature that is seen clearly in Figure 2 is that the total ozone variations at 60 degrees N are quite symmetric, with the total ozone smoothly rising from September to March and then decreasing smoothly again. In comparison to this, the Southern Hemisphere ozone is seen to build during the period March-July, with a slight decrease being seen from July to August, then rapidly rising to its maximum in October, and then decreasing smoothly back to its March minimum.

This behavior is seen even more clearly in Figure 3 in which d03/dt is plotted. These values of d03/dt were computed by taking centered differences of the monthly mean ozone values. Again, the six month advanced Northern Hemisphere values are plotted over the Southern Hemisphere values. The Northern Hemisphere d03/dt shows maximum rates of ozone decrease during the May-June period and maximum rates of ozone increase during the December-February period. In comparison, the Southern Hemisphere d03/dt shows more of a semiannual behavior with maximum rates of ozone decrease in December, maximum rates of ozone increase in September, with a secondary maximum in d03/dt occurring around May. Again referring back to the bottom panel of Figure 1, one sees that the maximum positive values of d03/dt are found during the periods when the planetary

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wave amplitudes are the highest. Also, the contrast between the annual behavior of d03/dt in the Northem Hemisphere with its semiannual behavior in the Southem Hemisphere is consistent with the annual behavior of planetary wave number one (responsible for most of the transport) in the Northem Hemisphere and its semiannual behavior in the Southem Hemisphere that was pointed out by GELLER and Wu (1987).

3. Ozone Transport by Planetary Waves

Wu et al. (1985, 1987) have used satellite observations of stratospheric temperatures and ozone to ex amine the nature of stratospheric ozone transport. They carried out these analyses in an Eulerian framework. Their analyses indicated that, during the winter season, mean poleward motions provide the principal means for ozone to be transported from the tropics to middle latitudes. In middle latitudes, mean vertical motions were found to transport ozone downward, and in high latitudes a net poleward flux of ozone was found to result from a large poleward flux of ozone by planetary wave motions together with a slightly less but largely compensating equatorward flux of ozone from the mean meridional motions. This overall picture is very consistent with the noninteraction concepts of ANDREws and McINTYRE (1978).

Given the results of Wu et al. (1985, 1987), we will examine the planetary wave fluxes of ozone in an effort to better understand the nature of the annual variations in ozone at high latitudes since these planetary wave fluxes of ozone are believed to

268 M. A. Geiler el al. PAGEOPH,

be the driving influences for the observed ozone behavior. As is weIl known (see MAHLMAN et al., 1984), meridional transports of constituents owe their existence to eddy motions in two ways. Firstly, eddy motions provide the accelerative or decelerative effects which are required for the existence of the diabatic circulation, and secondly these eddy motions directly drive compensating meridional fluxes as is implied by the noninteraction theorem (ANDREws and McINTYRE, 1978). MILLER et al. (1977) did an early observational study that nicely illustrated these compensating effects.

In our analysis, we separate the eddy fluxes of ozone into stationary and transient components. Since transient waves are thought to playa greater role in the Southern Hemisphere than in the Northern Hemisphere (see HIROTA et al., 1983, and GELLER and Wu, 1987, for example), it is possible that the stationary and transient eddies may exert different amounts of control on the Northern and Southern Hemispheres' annual ozone variation.

Figure 4 shows the monthly mean ozone flux divergences for the twelve months December 1978 to November 1979 due to total eddy motions. Since these calculations have utilized SBUV ozone values, they are confined to the altitude range where measured ozone values are available, between 30 mbar and 0.4 mbar. It should be mentioned that the high latitude regions of Figure 4 were obtained using extrapolated ozone amounts since none are observed poleward of the terminator. We believe the overall divergence/convergence patterns to be real though, since they are dominated by the planetary wave structure. We do not have as much confidence in the quantitative values though. This is not believed to be serious for two reasons. First, the exact quantitative values of the planetary wave flux divergences are largely compensated by the divergences from the mean meridional motions so that the net divergence is only a small fraction of the planetary wave flux divergence. Secondly, in this paper, we are only interested in qualitative features such as during what months are the convergences the largest.

Note that the largest high latitude ozone flux convergences (negative divergenees) in the Northern Hemisphere are seen during the months of NovemberMarch which is seen from Figure 2 to be the period when the ozone at 60 degrees N increases from its minimum to its maximum. This is also seen to be consistent with the period during which d0 3/dt has its largest positive values, as is seen in Figure 3. In the Southern Hemisphere, the largest ozone flux convergences are seen during the months of September and October with weak convergences also seen in May. This is also very consistent with the periods of maximum positive d03/dt seen in Figure 3. Thus, our picture of our buildup in total ozone being controlled by the planetary wave transport of ozone is supported by these results.

Figure 5 shows the separate contributions to the ozone flux divergences from the standing and transient eddies for the months January, April, July and October 1979. In the Northern Hemisphere, one sees that the standing eddies domina te in January, and littIe is seen in April, July, and October. In the Southern Hemisphere, one sees

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that the standing and transient eddy divergences are of the same order of importance in October with Httle being seen in January, April, and July. (Note that eastward traveling wave two has been seen to be quite large in the July Southern Hemisphere, see HARWOOD, (1975), GELLER and Wu, (1987), for example, but this wave does not appear to contribute significantly to the poleward transport of ozone.) These results indicate that, by and large, the annual variation in the total

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ozone is being determined in both hemispheres by the standing eddies. One reason why this is so is seen in Figure 6.

Figure 6 shows the vertical flux of standing and transient wave energy integrated between 40 and 87.5 degrees latitude in both the Northern and Southern Hemispheres as a function of altitude and month for the four years of the present analysis. These curves were calculated using the formulae from ELIASSEN and PALM

(1961). One sees that the standing wave energy in the Northern Hemisphere troposphere is much greater than that in the Southern Hemisphere. One also sees that the transient waves are much larger in the Southern Hemisphere troposphere than in the Northern Hemisphere. The standing waves are seen to penetrate higher into the stratosphere in both hemispheres, however. This is consistent with the dominant role of the standing planetary waves in determining the annual variation of total ozone in both hemispheres.

4. Day-to-Day and Year-to-Year Variations

Figure 7 shows plots of the vertical energy flux through 30 mbar integrated between 40 and 87.5 degrees of latitude and the poleward ozone transport across the 50 degree latitude circle at 30 mbar in both the Northern and Southern Hemispheres. These plots are for the periods December I through March 31 in the Northern Hemisphere and for JUDe 1 through October 31 in the Southern Hemisphere for each of the four years of our analysis (except where our NOAA SBUV ozone analysis cuts off on September 27, 1982). These periods have been chosen since they are the periods when the planetary wave activity is high and the total ozone values at high latitudes are increasing toward their maximum value (see Figure 1). The vertical energy fluxes are seen to be very highly correlated with the poleward ozone transports during these periods. In fact, for the Northern Hemisphere, these correlation coefficients are calculated to be 0.561 for Dec 78-Mar 79, 0.681 for Dec 79-Mar 80,0.850 for Dec 80-Mar 81, and 0.623 for Dec 81-Mar 82. In the Southern Hemisphere, they are calculated to be 0.528 for lun 79-0ct 79, 0.788 for lun 80-0ct 80, 0.525 for lun 81-0ct 81, and 0.756 for lun 82-Sep 82. These correlation coefficients are all found to be statistically significant at the 99.7% level. Thus, there can be no question that the day-to-day changes in ozone transport are controlled by waves that are forced in the troposphere and propagate upward to the stratosphere.

Given the clear association between the day-to-day changes in ozone and planetary wave activity, we may ask whether any similarly clear association can be found between year-to-year variations in total ozone and year-to-year variations in planetary wave activity. Looking at Figure 2, for example, we see that the October total ozone at 60 S is about 20 Dobson units greater in 1979 than in 1980 and 1981. Also, the March total ozone at 60 N is about 10 Dobson units greater in 1980 than

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31, 1981 , SH; and (h) June I, 1982-October 31, 1982, SH.

274 M. A. Geiler et al. PAGEOPH,

in 1979 and 1982 which are, in turn, about 10 Dobson units greater than in 1981. When we integrate the ozone transport curves shown in Figure 7, we find that the integrated transport of ozone at 30 mbar across 50 S for the months of September and October are 4.31 ppmv in 1979, 3.18 ppmv in 1980, and 3.88 ppmv in 1981. The integrated ozone transports for the months of February and March across 50 N are 3.80 ppmv in 1979,4.20 ppmv in 1980, 1.99 ppmv in 1981, and 3.95 ppmv in 1982. Thus, the integrated transports are largest in years when the ozone maximum is the largest and smallest when the ozone maximum values are the smallest. This association between the year-to-year ozone values and the planetary wave ftuxes is not as obvious as the association between the day-to-day values, but nevertheless there is a dear indication that year-to-year variations in total ozone amounts are related to year-to-year variations in ozone transports and that the ozone transport is controlled by year-to-year variations in the wave activity emanating out of the troposphere. SHIOTANI and GILLE (1987) have reached similar condusions.

5. Summary of Results

The preceding analysis has shown that the poleward eddy transport of ozone to high latitudes is a maximum in late Fall and early Winter in the Northern Hemisphere whereas in the Southern Hemisphere the poleward eddy transport to high latitudes has its principal maximum in the Spring with a lesser maximum in the Fall. These results are very consistent with the observed total ozone variations in both hemispheres. It is seen that there is a buildup in total ozone at high latitudes that is associated with the increasing poleward ozone transport that accompanies the increasing planetary waves that reach their maximum amplitudes in early to mid-winter in the Northern Hemisphere and during the Spring in the Southern Hemisphere. The different nature of the variations of the planetary waves in the Northern and Southern Hemispheres is due to the very different continent-ocean and orography distributions in the two hemispheres. The greater level of planetary wave activity in the Northern Hemisphere is also the underlying cause for the presence of more ozone in the Northern Hemisphere than in the Southern Hemisphere on an annually integrated basis. The results of our observational analysis of the annual ozone behaviour is very consistent with the picture put forth by ROOD (1983).

The transient wave activity is seen to be greater in the Southern Hemisphere troposphere than in the Northern Hemisphere, and the stationary wave activity is seen to be greater in the Northern Hemisphere troposphere than in the Southern Hemisphere. The annual variation of the ozone transport is seen to be controlled mainly by the stationary waves in both hemispheres, however. This is seen to be consistent with the fact that the stationary waves penetrate the stratosphere with greater amplitude than do the transient waves in both hemispheres.


An excellent day-to-day correlation between planetary wave activity (as measured by the vertical energy flux) and poleward ozone transport is seen indicating that daily ozone changes are controlled by wave disturbances that have their source in the troposphere and propagate into the stratosphere. This of course, is already very well-known through the c1assic work of DOBSON et al. (1929), for example. Furthermore, the year-to-year differences in wave activity appear to control the year-to-year variations in total ozone at the high latitudes ofboth hemispheres. Thus, in the real atmosphere year-to-year ozone variations are controlled by year-to-year changes in the ozone transport together with changes in photochemical factors such as solar ultraviolet ftux and the concentrations of anthropogenically produced trace gases that catalyze ozone destruction. It is, of course, very important not to confuse ozone changes that have their cause in naturally occurring changes in tropospheric dynamics with the search for anthropogenically produced ozone changes.

REFERENCES

ANDREWS, D. G., and M. E. McINTYRE (1978), Generalized Eliassen-Palm and Charney-Drazin Theorems for Waves on Axisymmetric Mean Flows in Compressible Atmospheres, J. Atmos. Sei. 33, 2031-2048.

DUETSCH, H. U., Photochemistry of atmospheric ozone, in Advances in Geophysics, 15, (Academic Press, 1971) pp. 219-322.

DOBSON, G. M. B., D. N. HARRISON, and J. LAWRENCE (1929), Measurement ofthe Amount ofOzone in the Earth's Atmosphere and fts Relation to Other Geophysical Conditions, Proc. Roy. Soc. London A122,456-486.

ELIASSEN, A., and E. PALM (1961), On the Transfer of Energy in Stationary Mountain Waves, Geophys. Pub. 22(3), 1-23.

GELLER, M. A., and M.-F. Wu, Troposphere-Stratosphere General Circulation Statistics, Transport Processes in the Middle Atmosphere (eds. G. Visconti and R. Garcia) (D. Reide1 Publishing Company, Dordrecht 1987) pp. 3-17.

HARWOOD, R. S. (1975), The Temperature Strueture of the Southern Hemisphere Stratosphere August-Oetober 1971, Q. J. Roy. Met. Soc. 101, 75-91.

HIROTA, I. (1976), Seasonal Variation of Planetary Waves in the Stratosphere Observed by the Nimbus 5 SCR, Q. J. Roy. Met. Soc. 102, 757-770.

HIROTA, 1., T. HIROOKA, and M. SHIOTANI (1983), Upper Stratospherie Cireulations in the Two Hemispheres Observed by Satellites, Q. J. Roy. Met. Soc. 109, 443-454.

MAHLMAN, J. D., D. L. HARTMANN, T. MATSUNO, J. R. MURGATROYD, and J. F. NOXON, Transport of trace eonstituents in the stratosphere, in Dynamies of the Middle Atmosphere (eds. J. R. Holton and T. Matsuno) (Terrapub., Tokyo 1984) pp. 387-416.

MILLER, A. J., R. M. NAGATANI, K. B. LABITZKE, E. KLINKER, K. ROSE, and D. F HEATH (1977), Stratospherie Ozone Transport Transport During the Mid-winter Warming of Deeember 1970 - January 1971, Proe. Joint Symp. Atmos. Ozone, Dresden, German Dem. Rep., 135-148.

RooD, R.B. (1983), Transport and the Seasonal Variation of Ozone, Pure Appl. Geophys. 121, 1049-1064. SHIOTANI, M., and J. C. GILLE (1987), Dynamieal Faetors Affeeting Ozone Mixing Ratios in the Antaretie

Lower Stratosphere, J. Geophys. Res. 92, 9811-9824. Wu, M.-F., M. A. GELLER, J. G. OLSON, A. J. MILLER, and R. M. NAGATANI (1985), Computations

of Ozone Transport Using Nimbus 7 Solar Baekseatter Ultraviolet and NOAAjNational Metrological Center Data, J. Geophys. Res. 90, 5745-5755.

Wu, M.-F., M. A. GELLER, J. G. OLSON, and E. M. LARSON (1987), A study of the GlobalOzone Transport and the Role of Planetary Waves Using Satellite Data, J. Geophys. Res. 92, 3081-3097.

(Received September 14, 1987, revisedjaccepted March 9, 1988)


Further Evidence of Normal Mode Rossby Waves

TOSHIHIKO HIROOKA 1•2 and ISAMU HIROTA 1

Abstract-Further observational evidence of normal mode Rossby waves with higher meridional mode numbers is presented with the aid of global data from the troposphere to the stratosphere over the period November 1979 through April 1986.

It is shown, without using an apriori assumption of meridional structure, that the third antisymmetric modes of zonal wavenumbers land 2, i.e., (1,4) and (2,4) modes, substantially exist in the real atmosphere. These modes are, however, easily influenced by the nonuniform background fie1d even in the equinoctial season; amplitude submaxima near the equator are apt to be dubious in the upper stratosphere so that the prototype meridional structure becomes obscure. The period of the ( 1,4) mode often falls into that of the (1,3) mode, about 16 days. Hence, these two modes cannot be c1assified simply by their periods, but the separation is made by their meridional structure.

An appearance calendar of various modes is also presented for the analysis period. It is found that each mode appears irregularly throughout the year and that the year-to-year variation is fairly large.

Key words: Normal mode Rossby waves, third antisymmetric modes, 16-day waves, west ward traveling waves.

Introduction

Normal mode Rossby waves are originally defined as free wave solutions of

linearized equations for the motionless and isothermal atmosphere on a rotating

sphere. Eaeh mode is represented by an ordered pair of integers (s, n - s), where s

is the zonal wavenumber and n is an index of meridional strueture relating to the

subseripts of Hough funetions (see LONGUET-HIGGINS, 1968). For the geopotential

disturbanee, the meridional strueture is symmetrie with respeet to the equator when

n - s is odd, and antisymmetrie when it is even. The vertical structure is that of a

Lamb wave type.

On the other hand, it is well-known that the real atmosphere with nonisothermal

and nonresting strueture will influenee the waves in their strueture as well as period.

In his numerical model, SAuIY(1981) showed that the effeets of nonuniform basic

field become large with inereasing sand n, especially in the solstitial upper

I Geophysical Institute, Kyoto University, Kyoto 606. Japan. 2 Present affiliation: Meteorological College, Kashiwa 277, Japan.

278 T. Hirooka and I. Hirota PAGEOPH,

atmosphere, so that the higher degree mo des are localized in the winter hemisphere. However, in the troposphere, where the spatial and seasonal variations in the zonal mean field are rather smalI, the waves reserve almost symmetrie structure of the magnitude of amplitudes in the two hemispheres throughout the year.

In recent years, various evidence for the existence of normal mode Rossby waves in the real atmosphere has been presented by many investigators (see reviews by MADDEN, 1979; SALBY, 1984). There still remains, however, a problem concerning the higher degree modes of s = 1: Westward traveling waves with aperiod of 10--20 days have been called 16-day waves after MADDEN (1978). He showed statistically that the waves are similar to the theoretical (1,3) mode, although he used northern hemispheric data only. Hence, the 16-day wave often means the (1,3) mode in a narrow sense. AHLQUIST (1982) projected global tropospheric data onto the basically symmetrie normal modes and found no conspicuous spectral peak for the ( 1,3) mode component.

MADDEN and LABITZKE (1981), SMITH (1985) and DALEY and WILLIAMSON (1985) investigated the notable westward traveling wave with aperiod of 19 days prior to the stratospheric sudden warming of January 1979. MADDEN and LABITZKE suggested that the wave could be identified with the (1,3) mode, on the basis of northern hemispheric data up to 10 mb, while SMITH and DALEY and WILLIAMSON, from global data sets, could not show the evidence of global mode even in the troposphere.

HIROTA and HIROOKA (1984) and HIROOKA and HIROTA (1985) (hereafter, HH84 and HH85, respectively) studied various modes of I ~ n - s ~ 3 of the s = 1 and 2 components without using an apriori assumption of meridional structure, for the global da ta of 100 mb and above. They showed that the (1,3) mode certainly exists and that such a higher degree mode is localized in the winter stratosphere in contrast to the lower degree modes, i.e., the (1,1) and (2,1) modes, wh ich appear with global structure even in the solstitial upper stratosphere. They also reported that the wave with an antisymmettic structure similar to the (1,2) mode sometimes travels with aperiod of near 15 days which is dose to the dominant period of the (1,3) mode.

Therefore, it cannot be said that the westward traveling waves of 10--20 days have been sufficiently understood. Thus, it will be of interest to darify the detailed structure of such longer period traveling waves. In this study, we present some new evidence of higher degree Rossby modes together with a "calendar" of the appearance of various modes, including the lower degree modes.

2. Data and Method of Analysis

Two sources of data are used in this study: (a) global stratospheric geopotential height data at 20, 10, 5, 2 and I mb levels produced by the British Meteorological

Vol. 130, 1989 Evidence of Normal Mode Rossby Waves 279

Offiee (BMO) and (b) global tropospherie and lower stratospheric geopotenti al height data at 850, 500, 300, 200, 100 and 50 mb levels analyzed by the National Meteorologieal Center (NMC). The data set (a) is originally obtained from radianee measurement by the Stratospherie Sounding Units (SSUs) on board TIROS-N/NOAA se ries satellites, eombined with the NMC 100 mb height data.

Both data are at 1200 GMT and arranged to 5° x 5° latitude-longitude grid spaeing. The analysis period is November 1979 through April 1986. Missing data in time series are linearly interpolated.

The proeedure of the analyses is as follows: First, the geopotential height fie1d is deeomposed to zonal Fourier harmonies for eaeh latitude. In order to study the normal mode Rossby waves, we filter the wave eomponents of some speeified period bands. The primary proeess is a spaee-time speetral analysis (HAYASHI, 1977, 1981) to seek the dominant period band in the wave speetra by applying the Maximum Entropy Method (MEM) to the Fourier eoeffieients. Next, we filter out eastward traveling portions using the Fourier trans form (HAYASHI, 1971), beeause the normal mode Rossby waves essentially travel westward. Finally, numerical bandpass filters are used to separate the dominant period eomponents. Thus, we ean obtain the westward traveling eomponents of some specified periods. (See HH84 and HH85 for more detail.)

The wave strueture is investigated for eaeh period band to judge whether the eomponent is a modal one or not, in terms of the meridional and vertieal distribution of the wave amplitude and phase.

3. Third Antisymmetrie Modes of s = 1 and 2

In this seetion, we present the evidenee of the third anti symmetrie Rossby normal modes of s = 1 and 2, i.e., the (1,4) and (2,4) modes. For the (1,4) mode, VENNE (personal eommunieation) suggested the existenee of this mode by the teehnique of eomplex-valued prineipal eomponent analysis, but our report gives the first c1ear evidenee of the third anti symmetrie modes.

Aeeording to c1assieal tidal theory assuming an isothermal and motionless atmosphere under adiabatie eonditions, the westward traveling periods of the (1,4) and (2,4) modes are 17.5 and 11.5 days, respeetive1y. However, these mo des are eonsidered to be easily influeneed by the nonuniform atmosphere beeause of their slow traveling speeds, so that we investigate the wave strueture for the eomponents filtered between westward periods of 12.0 and 24.0 days. It is antieipated that we eannot c1early separate these modes from the seeond symmetrie modes, i.e., the ( 1 ,3) and (2,3) modes, simply by their periods, beeause this period band is overlapped for both anti symmetrie and symmetrie modes. This is also the ease for the separation from long-period variations of quasi-stationary foreed waves.


Nevertheless, the mode identification is possible by the wave structure. Such overlapping of modal frequencies is also discussed in SALBY (1981).

Generally, the higher degree modes are more easily found in the equinoctial season than in the solstitial season, because the background field is relatively uniform on agiobai scale. Hence, we have first investigated the (1,4) mode for the equinoctial season. Here, among obtained typical cases, we present an example of the period March through April in 1981.

Figure I shows the MEM power spectra of the s = 1 component at 75°N, and 1 and 200 mb over three months from 1 March to 31 May 1981. In this case, the notable two peaks are seen near 9 and 17 days in the westward traveling regime. The 9-day peak is due to the (1,2) mode, i.e., lO-day wave, as already reported in HH85. On the other hand, the 17-day peak had been classified as that of the (1,3) mode following the former classification, i.e., the so-called 16-day wave, based on its period. However, the meridional wave structure contributed to this 17-day peak has an antisymmetric structure, so that this wave was incorrectly judged as a lO-day wave in HH85. Here, we investigate this wave in detail, especially for the tropospheric structure, by using the filtered components between westward 12.0 and 24.0 days.

Figure 2a shows a latitude-height section of the filtered wave amplitude and locations of the nodes determined by the phase structure on 28 March 1981. Figure 2b illustrates the amplitude structure miltiplied by J p /1000 in the same frame as in Figure 2a, where pis each pressure value (mb). This weighted amplitude is roughly

>-. 0

-0

N

E

>-..... V)

z w CI

10 7

10 6

10 5

J 0 4

J 03

Power Spectra eWN-I ,7S 0 N) ( 1 Mor.-31 Moy.1981 I

3 4 WESTWARD

6 15 .. 15 6 PER I OO( doys I

Figure 1

2

MEM power srectral density of s = 1 wave component at 7SON for the period 1 March through 31 May 1981. Solid line denotes the spectrum at 1 mb, and dashed li ne at 200 mb.

Vol. 130, 1989

2

..0 5 E

-' 10 w > 20 w ..J

W 0: 50 :::> V) V) 100 w er:: 0.. 200

300 500

850

( a)

2

..0 5 E

-' 10 w > 20 w ..J

w er:: 50 :::> V) V) 100 w 0:

0.. 200 300 500 850

(h)

Evidence of Normal Mode Rossby Waves

. .

1,4) Wove Ampl i tude (28 War. 1981 I

, ",,' ,~"", ,_ ......

I I , I I I + , , " '.'

-80 -60 -40 -20 0 20 LATITUOE

40 60

Weighted ( 1 ,4) Wove Amplitude (2Blotar.19811

. , , . , ,

,.' ,

. I I

'-, " '-'

-80 -60 -40 -20 0 20 40 60 LATITUDE

Figure 2

80

281

. 500

45

40

35 E

30 -'"

25 ~ :::> I-

20 -I-

-' 15 <

10 100

5

o

100

45

40 80

35 E

30 -'" 60 W 25 0 :::> I-

20 40 I-..J

15 <

10 20

5

0

(a) Latitude-height section of the s = I west ward traveling wave amplitude between 12.0 and 24.0 days on 28 March 1981. (b) As in (a) except for the amplitude values multiplied by Jp /lOOO, where pis pressure (mb). The contour interval is 25 m in (a) and 5 m in (b). Dashed lines denote the nodal lines.

Signs + and - indicate the relative phase structure.

considered to be in proportion to the square root of the energy density. From these figures, it is seen that nodal lines lie near 50oN, 50oS, and in the tropical latitudes. Large amplitude maxima are found near 700 N and 700 S and submaxima are near 400 N and 40oS. The weighted amplitude has the maxima in the troposphere and decays with height, which indicates the wave is external. From these features and their correspondence with the classical structure, the wave is identified as the (1,4) mode.

Submaxima near the equator disappear in the stratosphere and the (1,4) mode structure becomes obscure, although the antisymmetric structure is still preserved. Because of their reduced amplitudes, it might be concluded that the wave in the upper stratosphere is a (1,2) mode. From the connection between the lower and upper atmosphere, it is natural to consider that the stratospheric wave is the (1,4) mode. The longer-period (1,2) mode of about 15 days reported in HH85 now should be revised as a manifestation of the (1,4) mode.

Figure 3 illustrates the meridional structure and time evolution of the wave at 100 mb over April 1981. From the figure, we can clearly see the almost antisymmetric structure with three nodes between the two poles during the first half of the month. The kink near the equator may be due mainly to the error resulting from the small amplitude of the wave.

On the other hand, in the solstitial season, the (1,4) wave is largely localized in the winter hemisphere in the stratosphere, whereas in the troposphere the wave certainly has its counterpart in the summer hemisphere. Figure 4 is the same as Figure 2b except for the wave on 21 December 1983 when the mode is in the mature stage. In this case, apower spectral peak can be seen near westward 20 days, in the

100mb (1,4) Wave

150

E 100

w 50 Cl :=) 0 I-

....J -SO Cl.. ~ -100 <

-150 -80 -60 -40 -20 0 20 40

LATITUDE

Figure 3

60 80

30 25

20 '0"-15 "-~

Three-dimensional plot of the 100 mb (1,4) mode amplitude versus latitude and time for April 1981.

Vol. 130, 1989

2

.D 5 E

...J 10 UJ > 20 UJ ...J

UJ a: 50 ::::> <I)

~ 100 a: Q" 200

300 500

850 -80

Evidence of Nonna1 Mode Rossby Waves

Weighted (1,4) Wove Ampl itude ( 2 I Oec. 1983 I

Figure 4

\00

45

40 80

35 E

30 ~ 60

25 ~ :::>

20 ~ 40 .... ...J

15 <

10

5

20

o

As in Figure 2b except for the amplitude on 21 December 1981.

283

troposphere of both hemispheres and in the stratosphere of the Northern Hemisphere. While the wave resembles the classical (1,4) mode strueture up to 100 mb, we eannot see the wave eomponent in the summer stratosphere where the easterlies are very strong. This asymmetry is the same as that of other higher degree modes (see HH85).

Looking at the wave strueture of the troposphere in detail, we find that the nodes exist near 50oN, 300 N and 500 S. The loeation ofthe eentral node (300N), whieh must be on the equator in ease of the prototype (1,4) mode, is eonsidered due not only to the error resulting from the small amplitude but also to the asymmetrie zonal wind field in the two hemispheres. The wave amplitude also shows a large asymmetry with a faetor of about 2 with larger value in the winter hemisphere. Anyhow, the overall strueture is similar to the prototype strueture.

In his numerieal model, SALBY (1981) showed that the higher degree mo des have global strueture with symmetrie magnitude of amplitude in the troposphere even for the solstitial eondition. On the other hand, DALEY and WILLIAMSON (1985) presented, as for the ca se of January 1979, that higher degree modes, e.g., the (1,3) and (1,4) modes, have the asymmetrie eharaeter even in the troposphere, although the phase strueture is global. DALEY and WILLIAMSON eonsidered that the distinetion with respeet to the (1,3) mode from SALBY'S theoretieal predietion is attributed to the different background wind field used in their models. Our present study indieates, in harmony with the DALEY and WILLIAMSON'S results, that the asymmetry between the two hemispheres is a general eharaeter in the solstitial troposphere.

284

2

..0 5 E

....J 10 UJ > 20 UJ ....J

UJ er 50 => c/)

~ 100 er 0.. 200

300

500

850

T. Hirooka and 1. Hirota

Weighted (2,4) Wove Ampl itude ( 15 1,10 r . 1980 I

" , ,

-80 -60 -40 -20 0 20 40 60 80 LATITUOE

Figure 5

PAGEOPH,

100

45

40 80

35 E

30 -" 60

25 ~ :::0 >-

40 20 -... ....J

15 <

10 20

5

0

As in Figure 2b except for s = 2 amplitude between west ward 12.0 and 24.0 days on 15 March 1980.

The (2,4) mode has been also observed in our study. This is the s = 2 analogue of the (1,4) mode. For this mode, the submaxima near the equator are apt to be dubious as weil as the (1,4) mode, even in the equinoctial season. Since the (2,4) mode has a very slow traveling speed, say 8 m sec - I in the midlatitude (45°) with aperiod of about 20 days, this is also affected by the non uniform atmosphere. Figure 5 shows an example of the appearance in March 1980. In this case, the mode structure is c1early seen up to the middle stratosphere. Of course, this mode is localized in the winter hemisphere in the solstitial stratosphere.

4. Appearance Calendar 0/ Various Modes

In addition to the third antisymmetric modes reported in Section 3, we have also investigated other modes of I :-0; n - s :-0; 3 of the s = 1 and 2 components and obtained c1ear evidence of (2,2) and (2,3) mo des (not shown here); the existence of these was less convincing in the analyses performed in HH85, because the height coverage of the data was limited only to the stratosphere.

Next, we have made a "calendar" of the appearance of various modes. The bandwidth of the filters used for each mode is given in Table I. Since the modes are generally predominant in the stratosphere, it is suitable to define the appearance period as the duration of large amplitude at the upper stratosphere (I mb). The critical value of amplitude is 100 m for the (1,2), ( 1,3) and ( 1,4) modes and 50 m for

Vol. 130, 1989 Evidence of Normal Mode Rossby Waves

Table I

Bandwidth (days) of the band-pass filters used to separate each mode component.

s=1 s=2

4.8-fl.3 3.6-4.4

n -s

2 3 & 4

7.5-12.0 6.7-10.0

12.0-24.0 12.0-24.0

285

other modes in middle and high latitudes at I mb. In practice, for a global mode, the appearance period is picked up when the amplitude exceeds each critical value in either Northern or Southern Hemisphere. As for the localized mode in the winter hemisphere, it is confirmed that the global structure is observed in the troposphere and the traveling components are coherent between the stratosphere and troposphere. For such a case, the appearance period is defined as the duration while the amplitude exceeds each critical value in the winter stratosphere.

The resultant diagram is shown in Figure 6 for the six years from January 1980 to December 1985. In this calendar, also presented are the large amplitude periods of quasi-stationary (Q-st.) waves of s = land 2, the I mb zonal mean geostrophic wind regime at 500 N and 50oS, and the periods of northern hemispheric sudden warmings. The quasi-stationary waves are defined as components of the period longer than 30 days; the threshold value of 30 days is due to the fact that the power spectral peaks of the stationary waves are generally isolated from other ones as seen in Figure I. The critical amplitude is 200 m for s = land 100 m for s = 2 in middle and high latitudes at 1mb. The period of sudden warmings corresponds to the zonal mean easterlies at I mb and 800 N.

Inspection of this figure reveals that the mo des appear irregularly throughout the year and that the year-to-year variation is remarkable. Every mode will persist for about one month; AHLQUIST (1985) reported that the lifetime is about 20 days on the average.

As regards the relationship to the quasi-stationary waves, each mode coexists very often with the quasi-stationary waves of the same zonal wavenumber, suggesting that zonal wind vacillations occur due to the interference of the two (MADDEN, 1983; HIROOKA, 1986; SALBY and GARCIA, 1987b). Moreover, as was reported in HH85, the modes often become active prior to the stratospheric sudden warmings. In such a case, basically the same interference phenomenon will occur, although the nonlinear wave-wave interaction must be considered because of the large amplitude of the two waves. In order to thoroughly understand the dynamics of the sudden warming, we must clarify the behavior of the normal mode Rossby waves in such a condition.

286

s-I Q-st.NH s-2 Q-st.NH

5-1 Q-st.SH s-2 Q-sLSH

11 0 1) ( 2 0 ( )

( 1 02 ) ( 2 0 2 ) ( 10 3 ) ( 2 0 3 )

(Ion ( 2 0 n

SO'N WINDS 50'S WINDS

WARMINGS

s-I Q-st.NH s-2 Q-st.NH

0-1 Q-.t. SH s-2 Q-.t.sH

(1 0 1) ( 2. ( )

( 1.2 ) ( 2 0 2 )

( 1 0 3) ( 2 0 3 )

I I 0 ~ )

( 2 0 ~ )

SO'N WINDS 50'5 WINDS

WARMINGS

s-I Q-st.NH 5-2 Q-st .NH

s-1 Q-.t.SH .-2 Q-st.SH

(( 0 I ) ( 2 0 ( )

I I 02 ) ( 2 0 2 )

I 10 3 ) ( 2 0 3 )

( I 0 ~ )

( 2 0 ~ )

50'N WINDS 50'5 WINDS

WARMINGS

T. Hirooka and I. Hirota

APPEARANCE CALENDAR

-e-.*...-•• -.t.-

--.-. ••• -e-. • ... . • ____ ...... -e- _

--- . ..... ---- .... ___ • .-e-.. W------E-------W--- ---E--------W --E------W----

PAGEOPH o

•

FMAMJJASONDJFMAMJJASOND \980 \98\

...

• -e ••• .. --.-. -e- --e

-Ar -e- ... 6- .. -e-___ .... ..--11-

-----. ....

•

• ... W ---E-------W------E---·----) -------W -- E --- W----

FMAMJJASOND \983

-----... _ •• •• --11-

............ ... A ... .... -Ao--~--.110-

...... -e-- • .. . •

•

-- . ...... ..o.-e- . ... ...

... ___ -A.-

....... ___ -..6.-

-W------E-- ----w ---E-------I

---W----- --E- - - W----

FMAMJJASONDJFMAMJJASOND \984 \985

Figure 6 Appearance calendar of various normal mode Rossby waves and quasi-stationary waves at 1mb, along with the change of the I mb zonal mean geostrophic wind regime at SOnN and SOGS and the periods of stratospheric sudden warmings of the Northern Hemisphere. For the critical values of amplitude used in determining these periods, see the text. The circles denote waves with global meridional structures at 1mb. Thc squares and triangles denote waves localized in the Northern and Southern Hemisphere, rcspectively. The center of each mark indicates the date of the maximum amplitude. For the wind regime,

Wand E denote westerlies and easterlies, respectively.

Vol. 130, 1989 Evidence of Normal Mode Rossby Waves 287

Quite recently, SALBY and GARCIA (l987a), GARCIA and SALBY (1987) and DA SILVA and LINDZEN (1987) have investigated the forcing mechanism of the normal mode Rossby waves by using numerical models. The former two treated unsteady tropical heating due to the cumulus convection as the forcing source, whereas the latter emphasized the forcing mechanism associated with temporal changes of the zonal winds in the tropics. From this point of view, this calendar is very interesting, and further studies on the forcing mechanism are needed to elucidate the condition for the appearance of normal modes.

5. Summary

Throughout the present study, the existence of the (1,4) and (2,4) modes have been clearly shown on a global basis. These modes are easily influenced by the background atmospheric field and the amplitude submaxima at low latitudes often become dubious with height. The (1,4) mode has the traveling period overlapped with that of the (1,3) mode, and is considered to be a portion of the so-called 16-day wave.

Including the modes presented in HH84 and HH85, we have investigated the eight modes of I ~ n - s ~ 4 of the s = land 2 components. In the present study, we have found the westward traveling waves not only in the upper stratosphere, which are often localized in the winter hemisphere, but also in the lower atmosphere, and completed the appearance calendar of the eight identified modes.

Under the solstitial condition, meridional structures of higher degree modes are substantially asymmetric with respect to the equator even in the troposphere, which is probably due to the effect of the asymmetry of background field. In this regard, the analysis simply using the Hough function decomposition would not be suitable even for the troposphere as weIl as the stratosphere. It should be again emphasized that our method does not apriori assume the meridional wave structure but the mode identification is made after finding the characteristc wave structure in the two hemispheres.

We have confined our analyses to the s = 1 and 2 components, since the planetary waves of s = 1 and 2 are gene rally predominant in the upper stratosphere. It is considered that the normal mode Rossby waves of larger zonal wavenumber is fairly small, except the (3,0) mode wh ich is one of the most likely candidates of the 2-day wind oscillation observed in the mesosphere (see SALBY, 1984). As to the existence of s = 1 and 2 modes of n - s > 4, the possibility is also very small and the separation from the slowly-varying, forced stationary waves is difficult because of their longer periods. In the troposphere, however, other normal modes with larger sand n possibly exist, as shown by AHLQUIST (1982, 1985) and LINDZEN el al. ( 1984).

We have not reached the full understanding of the dynamics of normal mode


Rossby waves, and therefore further studies are needed from both theoretical and observational aspects.

Acknowledgements

We are grateful to Dr. Murry L. Salby and an anonymous reviewer for providing helpful comments on the earlier version of this paper.

The computations were carried out on the F ACOM M382jVP200 computer at the Data Processing Center of Kyoto University. This work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture of Japan.

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Vol. 130, 1989 Evidenee of Normal Mode Rossby Waves 289

SALBY, M. L. (1984), Survery ofplanelary-scale Iraveling waves: The slale of Iheory and observalions, Rev. Geophys. Spaee Phys. 22, 209-236.

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(Reeeived August 8, 1987, revised/aeeepted January 15, 1988)


Monthly Mean Winds in the Mesosphere at 44S and 78S

G. J. FRASER'

Abstract-A medium frequeney partial-refleetion spaeed-antenna wind radar was installed at Seott Base (78S) on Ross Island, Antaretiea, in November 1982. Results from this radar for the period Deeember 1982 to Oetober 1984 inclusive are eompared with simultaneous measurements made with a similar radar at Christehureh (44S), N. Z. Monthly mean zonal winds measured at 80 km are eompared with reeent models for the Southern Hemisphere middle atmosphere. There is a general agreement with the models but there is evidenee that the Christehureh winter flow was atypieal in 1983.

Key words: Mesosphere, high latitude, Southern Hemisphere, partial reflection radar, winds.

1. Introduction

Since the initial mesospheric wind observations at Scott Base (78S, l67E) (FRASER, I 984a), the observations have continued and monthly mean wind components for the period from December 1982, to October, 1984, are presented below. Simultaneous mean winds from the Christchurch (44S, 173E) radar are presented for comparison. Both installations are medium-frequency (MF) partial-reflection spaced-antenna wind radars. The recent availability of models (BARNETT and CORNEY, 1985; KOSHELKOV, 1985) for zonal winds in the Southern Hemisphere middle atmosphere enable the Scott Base and Christchurch wind measurements to be compared indirectly (through the models) with long-term mean winds measured at other latitudes and longitudes, and by different methods.

The principles of the medium frequency partial reflection spaced antenna wind technique have been described elsewhere (FRASER, 1984b). BRIGGS (1984) describes the full correlation analysis of the radar data to estimate the wind velocity. VINCENT (1984) has reviewed the application of the method to mesospheric dynamics.

The Christchurch MF radar has been in almost continuous operation since 1978. In November 1982 a temporary MF radar was installed at Scott Base. The

I Physies Department, University of Canterbury, Christehurch, New Zealand.

292 G. J. Fraser PAGEOPH,

Table I

Medium frequency partial-reflection spaced-antenna wind radars (as of January 1987).

Location

Frequency Basic antenna unit

Transmitting array

Receiving arrays

Receiving triangle Shape Side lengths

Transmitters Pulse width" Peak power output Pulse repetition period

Christchurch, N.Z. 43.8°S, 172.8°E 2.4 MHz two },./2 folded dipoles )./2 spacing (broadside) four units (2 x 2) linear polarisation one unit linear polarisation righ t -angled

2}", 2},., 2.8}"

25 J1.s (4 km) 80kW 256ms

Receivers (one for each antenna) Superheterodyne single conversion Intermediate frequency 455 kHz Bandwidth 60 kHz Detector Video Dynamic range

active diode linear or logarithmic -60dB

A / D converters (one channel for each receiver) Minimum sampling interval I km Resolution 12 bits External storage 960 words

Computer DEC Micro PDP-II

Scott Base, Ross Island 77.8°S, 166.rE 2.9 MHz I},. circumference horizontal tri angular loop one unit linear polarisation one unit linear polarisation approx. equilateral

1.2)., 1.2}", 1.3}"

40 J1.s (6 km) 60kW 256ms

double conversion 4 MHz, 545 kHz 80 kHz active diode linear or logarithmic -60dB

I km 8 bits 512 words

DEC PRO-350

"Full width to half-power, measured at receiver output. The equivalent range in km is also given.

Christehureh radar in its various stages of development has been previously

deseribed by FRASER (1965,1968), FRASER and KOCHANSKI (1970) and SMITH

(1981), and the Seott Base radar by FRASER (1984a). The temporary radar at

Seott Base was replaeed by a permanent, but similar, installation in January 1987.

Details of the new Seott Base radar and the eurrent Christehureh radar are given in

Table 1. The temporary Seott Base radar reeorded data on a limited sehedule (onee an

hour) and over a limited height range (67 to 97 km in 2 km steps) from late

November 1982 until early November 1984.

Vol. 130, 1989 Monthly Mean Winds in the Mesosphere 293

2. Measurement Technique

The partial reflection echoes arise from irregularities in the atmospheric refractive index. Free electrons make the only significant contribution to the refractive index at medium frequencies. At middle latitudes the day/night variation in solar photon flux will cause a variation in the echo power through the variation in electron production rate. At polar latitudes in summer the variation in solar zenith angle is small with a consequent small variation in echo rate. In polar latitudes electrons are produced at all times of the year by incoming solar particles.

The probability of estimating a wind vector from the received echoes depends on the signal-to-noise ratio. For example VINCENT (1984) shows that the probability of a successful wind measurement at Adelaide in early winter is 60--70 percent (around mid-day, at heights of 70--90 km).

The number of wind measurements per hour varies with the time of day. If mean values are calculated with each observation being given equal weight, the result may be biased by the winds occurring at the time of the most frequent measurements. The bias will depend on the relative distribution of measurements through the hours of the day, rather than the actual number of measurements. If there is any significant bias it will be due to the solar tidal winds because the sun is also the dominant source of ionisation.

The relative distribution of measurements is illustrated in Figures I to 4, expressed as a percentage of the total number of wind measurements. If the measurements were uniformly distributed over 15 heights and 24 hours, the fraction present in a 7-hour interval at one height would be 1.9 percent ((is) x (iI)).

Figures land 2 illustrate this diurnal variation at Christchurch in mid-winter and mid-summer. The "day" interval is defined as the seven hours centred on local noon and "night" as the seven hours centred on local midnight. In winter there is clearly little tidal bias above 80 km whereas in summer there may be bias up to 90 km. A reasonably frequent aural assessment of the Christchurch radar receiver output indicates that the lower nighttime data rate in summer is due mainly to excessive noise from distant thunderstorms.

In contrast, the Scott Base data rate in Figures 3 and 4 shows the lack of distinction between "day" and "night", expected because of the small change in solar zenith angle. However, Figure 3 shows that even during the polar night there was still a diurnal contribution due to variations in particle influx below 76 km, in 1983-84.

The data rate loss below 80 km at Christchurch is exaggerated because the system in use from 1978-86 did not correct the autocorrelation functions for high-frequency noise and interference (e.g., GOLDSTEIN, 1951), a procedure generally known as "de-spiking". This has resulted in the loss of data with a low signal-to-noise ratio which would have been usable if de-spiked, as in the Seott Base

and new Christchurch radars.

294

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G. J. Fraser

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Figure I

PAGEOPH,

Comparison of the day/night relative measurement distribution at Christehureh for winter (June, 1983/4). The solid li ne is for daytime, averaged over the 7 hours eentred on loeal noon. The dashed line is for nighttime, averaged over the 7 hours eentred on loeal midnight. The expeeted rate for a uniform

distribution over 15 heights and 7/24 of a day is \.9 percent.

100

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Figure 2

5

Comparison ofthe day/night relative measurement distribution at Christehureh for summer (Deeember, 1982/3). (Curve identifieation as in Fig. \.)

Vol. 130, 1989

100

90

BO

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'Monthly Mean Winds in the Mesosphere

~ ... ", .. , r

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2 3 4 5 PERCENTAGE OF TOTAL NUMBER OF OBSERVATIONS

Figure 3

295

Comparison of the "day(night" relative measurement distribution at Scott Base for winter (lune, 1983(4). (Curve identification as in Fig. 1.)

90

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PERCENTAGE OF TOTAL NUMBER OF OBSERVATIONS

Figure 4 Comparison of the "day(night" relative measurement distribution at Scott Base for summer (December,

1982(3). (Curve identification as in Fig. 1.)

296 G. 1. Fraser PAGEOPH,

An attempt has been made to reduce the diurnal bias due to the variable number of data points per hour by calculating hourly me an winds and then using equal weights for the hourly means in calculating the monthly mean. This will reduce diurnal bias but introduce a diurnal variation in variance of the means.

3. Zonal Winds

The observations at Scott Base and Christchurch can be compared with the zonal wind models published by KOSHELKOV (1985) and BARNETT and CORNEY (1985). There are three limitations in such a comparison: (a) The observations represent only one longitude region ('" 170E) in the hemi

sphere. (b) The observations cover only a two-year interval and one of those years (1983)

has an atypical winter circulation at Christchurch, and (c) The latitude limit for the models is 70S whereas Scott Base is at 78S.

Long-term measurements of winds in the meteor zone (PORTNYAGIN, 1986) show that the longitudinal variability of the me an zonal wind (about 7 ms-I) is much less than the interannual variability. MANSON et al. (1987) compare individuallocations with zonal means and conclude that, especially in summer, stationary waves should not be an important factor.

KOSHELKOY'S model is derived from observations made by different techniques over many years at various longitudes and latitudes. He estimates the uncertainty to be about 10 ms - I in the mesosphere.

BARNETT and CORNEY derived the geostrophic winds of their model from a combination of satellite radiance measurements above 30 mb (20-24 km) and radiosonde da ta below. They estimate the uncertainty to be a few ms -I below 60 km but greater at higher altitudes due to forcing by tides and gravity waves.

Evidence of inaccuracies arising from use of the geostrophic approximation has been presented by ELSON (1986) and BOYILLE (1987). ELSON inferred the circulation in the late northern winter (February and March 1979) from UMS radiance data. BOYILLE used a general circulation model for January to compare the true winds produced by the model with those deduced from the geopotential height using the geostrophic approximations. Both studies indicate the geostrophic wind can exceed the true wind by more than 10 ms - I around 50 km, at latitudes of 50°-70°. Gravity wave drag and other sources of ageostrophy have also been discussed by MANSON et al. (1987).

As the upper limit of the models is 80 km, Scott Base and Christchurch wind observations for this height have been selected for comparison. There may therefore be some bias due to imcomplete cancellation of the diurnal tide in the summer months at Christchurch. KOSHELKOY'S data is given for 80 km, and values for 80 km from the BARNETT and CORNEY model were calculated by linear interpola-


tion. The Scott Base data is for 81 km, but with a pulse width equivalent to 6 km, the I km difference is not significant. However, a much larger and unavoidable discrepancy arises because the models have an upper latitude limit of 70S, whereas Scott Base is at 78S, and might therefore be expected to have somewhat smaller mean zonal winds than the models.

In the 80 km data presented here the number of individual measurements contributing to each mean value is - 300-500 at Scott Base and -100-400 at Christchurch. The standard deviation of individual observations about the monthly mean is typically 20-40 ms I or less. This is small compared with the interannual variation evident in this data, the longer-term variations reported by PORTNY AGIN (1986), the uncertainties estimated by KOSHELKOV (1985) for his model, and the ageostrophic error (BARNETT and CORNEY, 1985).

Scott Base (78S)

Despite the difference In latitude, the winter zonal winds (Figure 5(a) have amplitudes not too different from KOSHELKOV'S model (Figure 5(c» for 70S and the model and both observation years show an autumn transition in April. However, the spring transition occurs earlier at Scott Base and the late winter circulation is generally much weaker. The one complete summer at Scott Base has a maximum zonal wind in January, compared with December in the model.

The observed winter zonal wind and KOSHELKOV'S model both show a weaker flow than that predicted by the BARNETT and CORNEY model (Figure 5( d». This is consistent with the possible errors in using the geostrophic approximation. It is, however, also consistent with the difference in latitude of the observations.

Both models showaspring transition around October but the transition at Scott Base is one or two months earlier.

Christchurch (44S)

The observed zonal wind amplitudes (Figure 6(a» are in better agreement with the 50S (Figures 6(c) and (d» models than the 40S models, except for the weak zonal flow in winter 1983. The autumn reversal occurs in March similar to the 50S KOSHELKOV model and the 50S and 40S BARNETT and CORNEY models. The 40S KOSHELKOV model shows a much earlier transition in January. The Christchurch spring reversal in November is about a month later than all four models which show a transition in October.

A notable difficulty in comparing the Christchurch observations with either model is the much weaker winter circulation in 1983. Comparisons with Christchurch observations in 1978/80 (SMITH, 1981; MANsoN et al., 1985) indicate that the 1983 winter was atypical. Further evidence of the unusual circulation is the northward (equatorward) meridional wind throughout the winter, compared with

298

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G. J. Fraser

a

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Figure 5

MAMJJAS

1984

PAGEOPH,

(a) Mean monthly zonal and (b) meridional wind speeds (in ms- 1 at 81 km for Scott Base (78S), December 1982 to October 1984. (c) Model zonal wind speeds from rocket observations for 80 km at 70S (KOSHELKOV, 1985). (d) Model zonal wind speeds from satellite radiance measurements for 80 km at

70S (BARNETT and CORNEY, 1985).

Vol. 130, 1989

50

-50

50

-' ... z ::: 0 :::

Ir UJ X

-50

50

U> 0 .... + U> 0

0 In

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Monthly Mean Winds in the Mesosphere

a

b

Figure 6

299

(a) Mean monthly zonal and (b) meridional wind speeds (in ms- I ) at 80 km for Christchurch (44S), December 1982 to October 1984. (c) Model zonal wind speeds from rocket observations for 80 km at 40S (dashed line) and 50S (solid line) (KOSHELKOV, 1985). (d) Model zonal wind speeds from satellite radiance measurements for 80 km at 40S (dashed line) and 50S (solid line) (BARNETT and CORNEY,

1985).

300 G. J. Fraser PAGEOPH,

southward (poleward) flow in 1984 and 1978/80. The same radar and data-processing methods were used at Christchurch from 1978 to 1986 so the differences are not instrumental. MANSON et al. comment on the year to year variations becoming apparent at Adelaide (35S) and Saskatoon (52N) as data from an increasing number of years become available. Further analysis of the Christchurch observations is clearly necessary to determine an adequate climatology and assess the frequency of disturbances such as that in the 1983 winter. The latter, with its reduced zonal flow and equatorward meridional flow bears so me resemblance to the mesospheric circulation patterns associated with stratospheric warmings (SMITH et al., 1983) but the time scale of the disturbance is months, rather than days, and the measurements are only time means at one longitude.

4. Meridional Winds

The meridional wind at Scott Base (Figure 5(b» at 81 km is northward (equatorward) except for abrief poleward movement in summer.

As mentioned above, the meridional flow at Christchurch in winter 1983 (Figure 6(b» is not comparable with other years, which show a southward (poleward) flow from February to October. The latter is also consistent with other observations from the global radar wind network (MANSON et al., 1987).

5. Conclusion

Although the Scott Base zonal and meridional winds are similar in both years, and similar to other measurements at altitudes of 80-100 km at Mawson Base (68S, 63E) (MACLEOD and VINCENT, 1985), the Christchurch winter circulation was unusual in 1983. It is apparent that the 1983-84 period is unlikely to be representative of the long-term mean zonal circulation and further studies of the 1978-86 winds are essential. Limited data will shortly be available for 1985 at Scott Base (with a maximum altitude of 85 km and a height sampling interval of 4 km) and the new radars have a much wider height range (50-105 km), more frequent sampling and a reduced height sampling interval of 1 km (although the height resolution, determined by the pulse width, remains the same). This will provide both improved estimates of the mean circulation and more detailed information on deviations from the mean.

6. Acknowledgements

Financial support has been provided by the University of Canterbury and the New Zealand University Grants Committee. Logistic and operational support for the Scott Base radar is provided by the Antarctic Division of the N.Z. Department of Scientific and Industrial Research.


REFERENCES

BARNETT, J. J., and CORNEY, M. (1985), Middle Atmosphere Reference Model Derived from Satellite Data. Handbook for Middle Atmosphere Program, 16(eds. Labitzke, K., Barnett, J. J. and Edwards, B. SCOSTEP Seeretariat).

BOVILLE, B. A. (1987), The Validity of the Geostrophic Approximation in the Winter Stratosphere and Troposphere, J. Atmos. Sei. 44, 443-457.

BRIGGS, B. H. (1984), The Analysis of Spaced Sensor Records by Correlation Techniques. Handbook for Middle Atmosphere Program, 13 (ed. Vineent, R. A. SCOSTEP Seeretariat).

ELSON, L. S. (1986), Ageostrophic Motions in the Stratosphere from Sate//ite Observations, J. Atmos. Sei. 43, 409-418.

FRASER, G. J. (1965), The Measurement of Atmospheric Winds at Altitudes of 64-110 km Using Ground-based Radio Equipment, J. Atmos. Sei. 22, 217-218.

FRASER, G. J. (1968), Seasonal Variation of Southern Hemisphere Mid-Iatitude Winds at Altitudes of 7()'-100km, J. Atmos. Terr. Phys. 30, 707 719.

FRASER, G. J. (1984a), Summer Circulation in the Antarctic Middle Atmosphere, J. Atmos. Terr. Phys. 46, 143-6.

FRASER, G. J. (1984b), Partial Rejlection Spaced Antenna Wind Measurements. Handbook for Middle Atmosphere Pro gram, 13 (ed. Vineent, R. A. SCOSTEP Seeretariat).

FRASER, G. T., and KOCHANSKI, A. (1970), lonospheric Driflsfrom 64-IOOkm al Bird/ings Flat, Ann. de Geophys. 26, 675-687.

GOLDSTEIN, H. (1951), The Fluctuations of Clutter Echoes. Propagation of Short Radio Waves (ed. Kerr, D. E., MeGraw-Hill).

KOSHELKOV, Yu. P. (1985), Ohserved Winds and Temperatures in the Southern Hemisphere. Handbook for Middle Atmosphere Pro gram, 16 (eds. Labitzke, K., Barnett, J. J. and Edwards, 8. SCOSTEP Seeretariat).

MACLEOD, R., and VINCENT, R. A. (1985), Observations of Winds in the Antarctic Summer Mesosphere Using the Spaced Antenna Technique, J. Atmos. Terr. Phy. 47, 567-574.

MANSON, A. H., MEEK, C. E., MASSEBEUF, M., FELLOUS, J. L., ELFORD, W. G., VINCENT, R. A., CRAIG, R. L., ROPER, R. G., AVERY, S., BALSLEY, B. 8., FRASER, G. T., SMITH, M. J., CLARK, R. R., KATO, S., TSUDA, T., and EBEL, A. (1985), Mean Winds of the Mesosphere and Lower Thermosphere (60-110km): A Global Distribution from Radar Systems (MF, Meteor, VHF), Adv. Spaee Res. 5, 135-44.

MANSON, A. H., MEEK, c.E., MASSEBEUF, M., FELLOUS, J. L., ELFORD, W. G., VINCENT, R. A., CRAIG, R. L., ROPER, R. G., AVERY, S., BALSLEY, B. 8., FRASER, G. J., SMITH, M. J., CLARK, R. R., KATO, S., and TSUDA, T. (1987), Mean Winds of the Upper Middle Atmosphere (70-ll0km)from the Global Radar Network: Comparisons with CIRO(72), and New Rocket and Sate//ite Data, Adv. Spaee Res. (in press). Also available as Atmospherie Dynamies Group Report No. 3, Institute of Spaee and Atmospherie Studies, University of Saekatehewan, Saskatoon, Canada.

PORTNYAGIN, Yu. I. (1986), The C/imatic Wind Regions in the Lower Thermospherefrom Meteor Radar Observations, J. Atmos. Terr. Phys. 48, 1099-1109.

SMITH, M. J. (1981), Upper Atmosphere Circulation and Wave Motion, Ph.D. Thesis, Physies Department, University of Canterbury, Christehureh, N.Z.

SMITH, M. J., GREGORY, J. B., MANSON, A. H., MEEK, C. E., SCHMINDER, R., KÜRSCHNER, D., and LABITZKE, K. (1983), Responses of the Upper Middle Atmosphere (60-ll0 km) /0 the Stratwarms of the Four pre-MAP Winters (1978/9-1981/2), Adv. Spaee Res. 2, 173-176.

VINCENT, R. A. (1984). MF/HF Radar Measurements of the Dynamics of the Mesopause Region-A Review, J. J. Atmos. Terr. Phys. 46, 961 974.

(Reeeived September 9, 1987, revised/aeeepted February 18, 1988)


Radar Observations of Prevailing Winds and Waves in the Southern Hemisphere Mesosphere and Lower Thermosphere

A. PHlLLlPS land R. A. VINCENT2

Abstract-HF radar stations (utilizing the spaced-antenna partial-reflection technique) located at Adelaide (35°S, 138°E) and Mawson Station (67°S, 63°E) have observed horizontal mesospheric winds continuously since mid-1984. Observations in the period 1984--87 are compared with the Northern Hemisphere [Iatitude conjugate] stations of Kyoto (35°N, 136°E) and Poker Flat (65°N, 147°W), and with satellite-derived circulation models. Particular reference is made to the equinoctial changeovers in zonal flow and to the temporal and altitude variations in the planetary wave activity at Mawson and Adelaide.

Key words: Mean circulation, planetary waves, mesosphere, Southern Hemisphere.

I. Introduction

It is now recognised that there are significant differences between the me an circulations of the middle atmosphere in the Northern and Southern Hemispheres as shown, for example, by recent climatologies and models of the prevailing winds based on satellite and rocket borne temperature measurements (BARNETT and CORNEY, 1985; KOSHELKOV, 1985; GROVES, 1985). The winds in these models, which are derived using the geostrophic approximation, extend up heights near 80 km. Winds in the upper middle atmosphere (60--100 km) can be found directly using radar techniques and such observations are particularly valuable because, although they are restricted to one location, they have better time and height resolution than the satellite measurements. In this paper we report wind measurements made with partial reflection radars operating at Adelaide (35°S, 138°E), Australia and Mawson Station (67°S, 63°E) in the Antarctic. These radars have been operating continuously since November 1983 at Adelaide and since June 1984 at Mawson. Here we discuss the mean circulation and planetary wave activity in the

I Mawson Institute for Antarctic Research, University of Adelaide, G.P.O. Box 498, Adelaide, South Australia, 5001.

2Department of Physics and Mathematical Physics, University of Adelaide, G.P.O. Box 498, Adelaide, South Australia, 500 I.

304 A. Phillips and R. A. Vincent PAGEOPH,

upper mesosphere and lower thermosphere and compare with earlier, less extensive measurements made at these two locations, and with the recent model winds for the Southern Hemisphere. Comparisons are also made with recent observations made at similar latitude stations in the Northern Hemisphere.

2. Observations

At Adelaide, the observations ex te nd from heights near 65 km up to 100 km altitude with a 24-hour coverage at heights above about 78-80 km and between 8 to 12 hour (daytime) coverage at heights near 70 km (VINCENT, 1984). The Mawson system is less sensitive and consequently the height coverage varies between about ~ 75-80 km up to 108 km. However, ionization associated with auroral precipitation means that wind measurements often can be made over a fuH 24-hour period at the lower heights, although there is some seasonal variation in echo strengths which reduces the amount of useful data at the lower heights in summer.

2./ Zonal Winds

Figure 1 shows the zonal mean (or EW) circulation at Adelaide constructed from 3 years of continuous data. The rms differences between the years (on a monthly basis) vary between 2 and 10 ms - " values which may be taken as a measure of the interannual variability in the EW component. This time-height cross-section is very similar to that in MANSON et al. (1985) which was made from observations taken at Adelaide during the period 1978-1983 (although the data in MANSON et al. cover a longer period than that shown in Figure 1, they are from an assemblage of observational campaigns ranging from a few days to a few weeks in duration). The only significant difference between the present and earlier results (1978-83) is that the zonal f10w is somewhat more westward at heights above 95 km in winter during the period 1984-1987. Otherwise the zonal f10w is relatively constant during the decade between 1978 and 1987.

A time-height cross-section of the zonal f10w at Mawson is shown in Figure 2. ft is apparent that the zonal mean circulation in winter at Mawson is considerably weaker than at Adelaide and that the summer westward f10w extends to slightly higher altitudes at Mawson. Again, the interannual variability on a monthly basis is about 5 ms - '.

One interesting difference in the temporal behavior of the zonal winds concerns the relative timing and rapidity of the reversals of the f10w at the two sites. The

change over from the summer to winter circulation commences at both locations at

about the end of February with the zero wind contour descending rapidly. Similarly, the reversal of the zonal winds in spring proceeds systematicaHy at Adelaide with the zero-wind contour descending at a steady rate of about 10 km per

Vol. 130, 1989 Southern Hemispheric Winds and Waves 305

110r-------------------------------------------,

E .x -I-:x: l!)

W :x:

Figure 1 Contours of zonal mean wind at Adelaide in ms - I constructed from 3 years of continuous data. Periods

of westward (easterly) flow are indicated by shading.

110~--------------r/~~~I~~~~----------------~ -,./

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1984-87 3 VEAR AVERAGE Figure 2

Contours of zonal mean wind at Mawson in ms - I constructed from 3.5 years of continuous data. Shading as for Ade\aide.

306 A. Phillips and R. A. Vincent

15 111 17 11 11 2021 2223 24 25 28 27 21 28 30 311 2 3 4 5 8 7 8 8 10 11 OCTOBER NOVEKIIEll (1986)

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Figure 3

PAGEOPH,

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Spring transition at Mawson. Arrows represent unfiltered mean daily winds.

month. The springtime reversal at Mawson however, occurs much more rapidly than indicated in Figure 2 because it is constructed from monthly averages which tends to disguise the suddenness of the reversal. Figure 3 illustrates more vividly the spring transition, with individual vectors indicating the direction and strength of the me an wind at each height on a daily basis in the period October 15 to November 19,1985. During the first weeks ofOctober, the winds are variable from day to day, probably reftecting propagation of planetary wave activity from below. However, in the third week of October, the variability gives way to a strong westward ftow with the transition occurring alm ost simultaneously at all heights.

2.2 The Meridional Winds

The three-year meridional mean (or 'NS') winds, are shown in Figures 4 and 5. The rms monthly deviations are about 2-5 ms - I so that, on a proportional basis, the meridional winds are more variable than the zonal winds. At Adelaide the NS ftow is essentially poleward in all seasons except summer at heights be10w about 85-90 km and equatorward at heights above this level. Only in mid-summer does an equatorward ftow penetrate downward into the mesosphere. The meridional winds appear to behave in a less systematic manner at Mawson and in general they are also weaker than at Adelaide. One feature which is common at both locations is the 'jet' like structure which occurs in mid-summer at or just above the height at which the EW winds reverse. Equatorward winds reach peak values of about 10 ms - I

about 2 weeks after the solstice.

110r-------------------------------------------~

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1985-1987 - 3 YEAR AVERAGE Figure 4

Contours of meridional mean wind at Adelaide in ms - I. Regions of southward or poleward (negative) flow are denoted by shading.

100

E ~ -~ 90 <.!> iii J:

80

1984-87 3 YEAR AVERAGE Figure 5

As for Figure 4 but for Mawson.


Values in excess of 5 ms - 1 in magnitude are also observed at heights near 80 km or below in February-March and in August to October at Adelaide. As previously noted, echoes are observed for periods of less than 24 hours at these heights and so it is possible that incomplete averaging of the diurnal tide might contaminate these results, especially as the diurnal tide attains its largest amplitudes at the equinoxes (VINCENT et al., 1988). These authors show that at the equinoxes at 80 km, the time of maximum northward diurnal wind occurs near midnight with amplitudes of about 10-20 ms - I. At Adelaide, the incomplete sampling at night at heights below 78 km, causes a tendency for the diurnal tide to produce a net negative bias. Estimates of the possible bias made by extrapolating downward the phase and amplitudes measured near 80 km to heights near 75 km suggests that the diurnal tide produces a southward (negative) bias of about 2 ms - I. While significant, this bias cannot account for the values of - 10 ms - 1 observed in August to October at 75 km.

Similar tidal bias effects may be expected for the zonal winds, although they will not be proportionately as large because of the greater magnitudes of the prevailing zonal winds. The phases of the zonal component of the tide are such that it is estimated to produce a net westward bias of less than 5 ms - 1 at heights near 75 km during the period between March and September i.e., the incomplete averaging of the diurnal tide causes the strength of the eastward (westerly) winds to be slightly underestimated during the winter.

2.3 Planetary Waves

The prevailing winds often exhibit significant changes on a day by day basis, especially in winter, behavior which suggests the presence of large-scale travelling or quasi-stationary wave activity. In order to investigate how this activity varies as a function of season and altitude, the data were band-pass filtered such that fluctuations with periods less than about 2 days and longer than about 30 days were removed. Defining u and v as the zonal and meridional prevailing wind and u' and v' as perturbations from mean, time-height contour plots of the mean square amplitudes (U'2 + V'2), provide a convenient measure of wave activity. Figures 6 and 7 show the mean square amplitudes for Adelaide and Mawson, respectively, for the years 1985 and 1986.

At Adelaide, most activity is concentrated in the lower and middle mesosphere, with peak values being reached near 70 km in mid-winter. A subsidiary maximum also appears in autumn (March/April) 1985. The maximum rms amplitudes are about 25 ms - 1 but it should be noted that the filtering process suppresses contributions of the quasi-2-day wave which is a well-known feature of the mesopause region at Adelaide in mid-January (CRAIG and ELFORD, 1981; PLUMB et al., 1987). Amplitudes greater than 50 ms - 1 are observed with this wave.

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The lower sensitivity of the Mawson radar makes it more difticult to study the planetary waves at heights below 75-80 km than at Adelaide, especially in summer. However, Figure 7 suggests that again the wave activity peaks in mid-winter but that the amplitudes are sm aller at the high latitude site. Some interannual variability is evident, with larger amplitudes occurring in 1986 than in 1985. These results should be treated with caution because of the relatively low sensitivity of the Mawson radar and more data will be required to elucidate clear seasonal effects at the lower heights.

Ionospheric differences mean that the Mawson radar can probe 10 km higher than the Adelaide system. It is apparent from Figure 7 that the wave amplitudes grow with altitude and reach their maximum values of about 400 m2s ~- 2 in late winter. It is possible that these disturbances are not associated with meteorological activity in the lower atmosphere but may be associated with auroral generated disturbances in the lower thermosphere. Mawson station is in the auroral region and strong local heating by particle precipitation (associated with intense solar events) can cause disturbances which persist for several days.

Examination of the individual fluctuations in u and v shows that at Adelaide the zonal perturbations te nd to be larger by factors of about 1.5 to 2 on average at heights below 80-85 km, while the meridional fluctuations tend to dominate above 90 km. Calculation of the u'v' covariances shows that only in June/July do the zonal and meridional perturbations show significant correlation (Figure 8). At Mawson, the u'v' covariances (not shown) are small and not very significant; at Adelaide are almost invariably negative in sign. This means that usually a north~ ward perturbation is associated with a westward perturbation and a southward perturbation with an eastward perturbation.

3. Discussion

The Middle Atmosphere Pro gram (MAP) has been the stimulus for a number of radar studies of the circulation of the middle atmosphere. Of particular interest for the height region above 80 km have been the me an wind observations made with the meteor radar located at Kyoto (35°N, 136°E) which is at a geographically conjugate location to Adelaide. Mean wind observations for the period 1983-1985 were recently presented by TSUDA et al. (1987). Similarly, a sequence of mean wind observations made in the period 1980 to 1984 using meteor techniques with the Poker Flat (65°N, 147°W) radar has been given by TETENBAUM et al. (1986) and this sequence is very suitable for comparing with the Mawson data. For heights below 80 km, our observations can be compared with the new wind models derived from satellite and rocket data (e.g., BARNETT and CORNEY, 1985; GROVES, 1985). The Kyoto observations (TSUDA et al., 1987) show a predominantly eastward circulation at all heights in the 82-106 km region and there is little evidence of the


upper part of the westward (easterly) cell which is so apparent at Adelaide in summer at heights below 85 km (Figure 1). TSUDA el al. comment that the zonal winds may be rather poorly determined at the lowest heights of observation because of the relatively low meteor rates at these heights. The eastward flow maximizes at Kyoto in July with values of about 30 ms -, at heights near 95 km. The situation is similar at Adelaide although the winds are more constant above 95 km at this location. The meridional circulations at each si te show many similarities. As noted above, the meridional flow is mainly equatorward at heights above about 85 km at Adelaide and there is a similar tendency for equatorward flow at Kyoto at most times of the year. TSUDA el al. report that the equatorward winds maximize in July-August with speeds of about 10 ms -, at heights between 90 and 95 km. The height of the peak meridional flow therefore occurs at a somewhat higher altitude than at Adelaide and at a slightly later time in summer but the peak velocities are of about the same magnitude at the two locations.

The winds at Mawson may be compared with the first sequence of observations made with the PR radar at that site in January 1981 (MACLEOD and VINCENT, 1985) and the PR measurements reported for Scott Base (78°S, l70U E) by FRASER (1984). There is excellent agreement, especially in the magnitude and direction of the meridional 'jet'. With regard to Northern Hemisphere observations, a 10ng sequence of wind measurements has been given by TETENBAUM el al. (1986) for Poker Flat (65°N, 14TW). Figures 9 and 10 show comparisons of the zonal and meridional winds observed at Mawson in the period 1984 to 1986 and at Poker Flat for the years 1983 to 1984 (note that the zonal winds at Mawson have been shifted by 6 months for ease of comparison). There are interesting similarities and differences. The zonal circulation exhibits reversals in February at Poker Flat, behavior associated with minor stratospheric warmings in these years. As noted above however, the spring time reversal at Mawson is very abrupt and appears to occur a little later in spring than at Poker Flat. The summer-time winds show very similar patterns at both sites.

TETENBAUM el al. (1986) note that the meridional winds at Poker Flat showed less year to year consistency than the zonal winds and Figure 10 shows that significant interannual variability is also evident at Mawson in this wind component. Perhaps the most consistent feature at both locations is the summer 'jet' wh ich peaks at, or just above, 90 km with peak equatorward velocities of 10 ms - '. Interestingly, the meridional shears are such that v becomes poleward at heights below about 85 km. Although the magnitude of the summer meridional winds are the same as the mid-Iatitude values, it should be noted that the Coriolis torques (given by fl, where f is the Coriolis parameter) are 1.6 times larger at the high latitudes. This implies that the gravity wave body-forces, which are thought to drive the meridional circulation (e.g., LINDZEN, 1981), are also correspondingly larger at 65-70° latitude (about 115 ms - , day -, compared to 70 ms- , day -, at

35° latitude).


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shifted by 6 months for ease of comparison).

Recently, satellite measurements have provided better models of the zonal circulation in the Southern Hemisphere middle atmosphere. BARNETT and CORNEY

(1985) produced latitude versus height cross-sections of the monthly zonally averaged mean geostrophic winds derived from temperatures measured remotely by satellites between 1973 and 1978. There is also an extensive collection of more directly measured winds and temperatures in the Southern Hemisphere which have provided the base for specific Southern Hemisphere model by KOSHELKOV (1985). GROVES (1985) combined both rocket and satellite temperature observations to genera te winds using the geostrophic equation. These models have upper limits at about 80 km so that they partly overlap the radar winds discussed here. Table 1 shows the monthly mean winds at a height of 70 km from the above models compared with the Adelaide radar winds. The last column shows the me an difference between the respective model winds and the corresponding monthly

Vol. 130, 1989 Southern Hemispheric Winds and Waves

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315

values at Adelaide. The best agreement is with the BARNETT and CORNEY (1985) and KOSHELKOV (1985) models. The GROVES (1985) model gives zonal winds which are, on the average, 10 ms' 1 more eastward (westerly) than the radar winds.

Considering the interannual variability inherent in the radar winds (between

4-13 ms - I at 70 km) and the estimated uncertainties in the satellite mesospheric

winds of about 10-20 ms - I (BARNETT and CORNEY, 1985) and the estimated

Table I

Comparison 0/ monthly mean zonal winds (ms - I) at a height 0/70 km observed at Adelaide (A) with model results/rom BARNETT and CORNEY (1985) (B), GROVES (1985) (G) and KOSHELKOV (1985) (K). The last

column (DU) is the monthly difference between the model and radar winds.

J F M A M J J A S 0 N D DU

A -53 -25 20 44 63 66 62 66 45 12 -25 -53 B -58 -30 20 44 70 75 60 58 45 5 -30 -50 -I G -44 -15 23 60 81 87 70 62 51 20 -18 -36 10 K -40 -li 17 43 64 70 67 63 46 -I -29 -43 2

316 A. PhiIIips and R. A. Vincent PAGEOPH,

uncertainty of 10 ms - 1 quoted by KOSHELKOV (1985), the agreement may be considered exceIlent. Nevertheless, there may be some systematic differences which are discussed below.

Table 2 shows a similar comparison between the model zonal winds and the Mawson winds at a height of 80 km. Here the discrepancies between the radar winds and the models are considerably larger than for Adelaide; the differences are especially significant in winter.

These comparisons must however, be treated with some caution because the model winds are zonal means whereas the radar observations are confined to a single location and were made in a later epoch than the satellite measurements. However, it is clear that, while the model and radar winds agree weIl for most of the year, the models show larger eastward (westerly) winds in mid-winter (especiaIly at the latitude of Mawson). It was noted in Section 2.1 that incomplete removal of the diurnal tide could cause the strength of the zonal winds at Adelaide to be underestimated by a few ms - 1 at most, so this factor cannot account for all of the systematic difference. While it is possible that some other (as yet unresolved) factor may be causing the radars to slightly underestimate the winds, it seems that it only operates in mid-winter since there is excellent agreement at other times of the year. Furthermore, it is not due to the fact that the radars are incapable of measuring large wind speeds since it is not uncommon for zonal wind speeds in excess of 100 ms - 1 to be measured for several days at a time at Adelaide in mid-winter during the passage of planetary waves.

It is noticeable that the largest discrepancy occurs between the radars and the models of BARNETT and CORNEY (1985) and GROVES (1985). The characteristic of these models is that the winds are derived by applying the geostrophic approximation to the rocket and satellite measured temperatures and radiances. Recently, BOVILLE (1987), for example, has pointed out that the geostrophic winds can significantly exceed the true winds in the winter upper stratosphere where the curvature of the streamlines is large due to the presence of waves. It is possible therefore, that the radar and model wind differences which are apparent in mid-winter are caused by overstimated model winds; as noted in Section 2.3, it is in

Table 2

Comparison o(monthly mean zonal winds (ms - I)at a height 01 80 km observed at Mawson (M) with model resultslrom BARNETT and CORNEr (1985) (B), GROVES (1985) (G) and KosHELKov (/985) (K). The last

column (DU) is the mean mOn/hly difference between the model and radar winds.

J F M A M J J A S 0 N D DU

M -20 -14 -10 10 10 10 10 10 10 4 -20 -21 B -15 -16 10 10 31 41 40 38 10 3 -10 -20 13 G -22 -4 II II 31 46 47 52 21 4 -12 -23 15 K -29 -26 -17 0 12 4 14 13 5 -9 -30 -36 -7


this period that the planetary waves in the lower mesosphere attain their largest amplitudes at Adelaide, so that the flow curvature will be largest, at least locally. Further intercomparisons are required to resolve these discrepancies.

The large planetary wave activity which is observed in JunejJuly at Adelaide is consistent with the analysis of the circulation of the upper stratosphere in the Southern Hemsiphere by HARTMANN (1976) and HIROTA et al. (1983). They found that transient planetary waves of wavenumber 2 and periods of the order 10 days exhibit a change in their 10cation during winter, following the latitudinal march of the co re of the stratospheric westerly jet which attains its most equatorward position near 40 0 S in June and July. The upper limit of the observations was near 50 km altitude, so our observations show that the wave amplitudes maximize at some height below 70 km (Figure 6). The rapid decrease in amplitude with height between 70 km and 80 km is probably due to gravity wave drag effects (MIYAHARA, 1985). The negative u'v' fluxes (Figure 8) are also consistent with what is known about the waves since they correspond to an equatorward Eliassen-Palm flux (proportional to -u'v') which is characteristic of waves in the Southern Hemisphere mid-winter (SHIOTANI and HIROTA, 1985). In their height-Iatitude analysis of the variations of the zonal wind and wave activity with time, SHIOTANI and HIROTA (1985) showed that in late winter the jet shifts poleward and downward and that quasi-stationary wavenumber I activity is enhanced. This may account for the relatively small long period wave activity noted at Mawson since the radar is only sensitive to the travelling wave components and to variations in the position of the quasi-stationary wave. Improvements to sensitivity of the Mawson radar are required to study winds and waves at heights below 75-80 km.

Acknowledgements

This research was supported by the Australian Research Grants Scheme and by the Australian Antarctic Division. One of us (AP) was in receipt of an Australian Commonwealth Postgraduate Scholarship.

REFERENCES

BARNETT, J. J., and CORNEY, M. (1985), Middle atmosphere reference model derived from satellite data, Handbook for MAP 16, 47-85.

BOVILLE, A. B. (1987), The l'alidity or the geostrophic approximation in the winter stratosphere and troposphere, J. Geoph. Res. 44, 443-457.

CRAIG, R. L., and ELFORD, W. G. (\981), Observations of the quasi 2-day wave near 90km altitude at Adelaide (35S), J. Atmos. Terr. Phys. 43, 1051-1056.

FRASER, G. J. (\ 984), Summer circulation in the Antarctic middle atmosphere, J. Atmos. Terr. Phys. 46, 143146.

GROVES, G. V. (1985), Aglobai reference atmosphere from 18 to 80km, U.S. Air Force Surveys in Geophysics 448, 128 AFGL-TR-85-0129.

318 A. Phillips and R. A. Vineent PAGEOPH,

HARTMANN, D. L. (1976), The structure 0/ the stratosphere in the Southern Hemisphere during late winter 1973 as observed by satellite, J. Atmos. Sei. 33, 1141-1154.

HIROTA, I., HIROOKA, T., and SHIOTANI, M. (1983), Upper stratospheric circulations in the two hemispheres observed by satellites, Roy. Meteorol. Soe. Q. J. 109, 443--454.

KOSHELKOV, Yu. P. (1985), Observed winds and temperatures in the Southern Hemisphere, Handbook for MAP 16, 15-35.

LINDZEN, R. S. (1981), Turbulence and stress owing to gravity wave and tidal breakdown, J. Geoph. Res. 86, 9707-9714.

MACLEOD, R., and VINCENT, R. A. (1985), Observations in the Antarctic summer mesophere using the spaced antenna technique, J. Atmos. Terr. Phys. 47, 567-574.

MANSON et al. (1985), Mean winds o/the upper middle atmosphere (60--100 km): A global distribution 0/ radar systems, Handbook for MAP 16, 239-268.

MIY AHARA, S. ( 1985), Suppression 0/ stationary gravity waves by internal gravity waves in the mesosphere, J. Atmos. Sei. 42, 100--107.

PLUMB, R. A., VINCENT, R. A., and CRAIG, R. L. (1987), The quasi-two-day wave event 0/ January 1984 and its impact on the mean mesopheric circulation, J. Atmos. Sei. 44, 3030--3036.

SHIOTANI, M., and HIROTA, I. (1985), Planetary wave-mean f10w interaction in the stratosphere; A comparison between Northern and Southern Hemispheres, Roy. Meteorol. Soe. Q. J. 111, 309-335.

TETENBAUM, 0., AVERY, S. K., and RIDDLE, A. C. (1986), Observations o/mean winds and tides in the upper mesosphere during 1980--1984, using the Poker F1at, Alaska, MST radar as a meteor radar, J. Geoph. Res. 91, 14539-14556.

TSUDA, T., NAKAMURA, T., and KATO, S. (1987), Mean winds observed by the Kyoto meteor radar in 1983-1985, J. Atmos. Terr. Phys. 49, 461--466.

VINCENT, R. A. (1984), MF(HF radar measurements 0/ the dynamics 0/ the mesopause region-A review, J. Atmos. Terr. Phys. 46, 961-974.

VINCENT, R. A., TSUDA, T., and KATO, S. (1988), A comparative study o/mesopheric solar tides observed at Adelaide and Kyoto, J. Geoph. Res. 93, 669-708.

(Reeeived 16th December, 1987, revised(aeeepted 27th April, 1988)


Comparison of Geostrophic and Nonlinear Balanced Winds from LIMS Data and Implications for Derived Dynamical Quantities

T. MILES I and W. L. GROSE I

Abstract-Nimbus 7 UMS geopotential height data are utilized to infer the rotational wind distribution in the Northern Hemisphere stratosphere and lower mesosphere during aperiod of substantial wave-mean tlow interaction in January, 1979. Rotational winds are derived from the application of a successive relaxation numerical procedure which incorporates the spherical polar coordinate iterative algorithm of PAEGLE and TOMLINSON (1975) for the nondivergent nonlinear balance equation. Optimum convergence of the numerical solutions is found to occur when under-relaxation is utilized. The UMS height analyses were also latitudinally smoothed and constrained to obey the ellipticity criterion for spherical coordinates. The balanced winds are compared with geostrophically derived values and with in situ radiosonde reports for 100 mb to 10 mb over Berlin.

From a localized perspective, the Berlin-UMS comparison indicates that radiosonde and balanced wind vectors exhibit somewhat doser agreement in direction than is associated with the geostrophic estimates. However, substantial quantitative differences between radiosonde, balanced, and geostrophic wind speeds are also evident, suggesting that caution should be exercised in the local application of derived winds, as for example in the quantitative interpretation of trajectories derived from satellite height analyses during periods of enhanced stratospheric wave activity.

On a longitudinally averaged basis, balanced zonal-mean wind speeds are typically 20% weaker than geostrophic values in polar latitudes, and as much as 50% weaker in tropical and midlatitude regions. Meridional balanced wind velocities, at a given longitude, are generally within ± 10% of geostrophic values. Although these alterations in horizontal wind components result in only modest differences between balanced and geostrophic meridional eddy heat tluxes, a more substantial change appears in the meridional eddy momentum tlux analysis. The corresponding patterns of Eliassen-Palm tlux divergence are found to be somewhat more (less) intense for the balanced wind case in the stratosphere (lower mesosphere) in polar latitudes.

Key words: Geostrophic, balanced, winds, stratosphere, UMS, radiosonde.

1. Introduction

Since the commencement of diagnostic studies of the planetary-scale stratospheric circulation from satellite observing systems some two decades aga (e.g., KENNEDY and NORDBERG, 1967), the conventional approach to inferring horizon-

I Atmospheric Sciences Division, NASA Langley Research Center, Hampton, Virginia 23665, U.S.A.

320 T. Miles and W. L. Grose PAGEOPH,

tal motions has centered on the application of the thermal wind concept in which satellite temperature or thickness gradients are coupled to a synoptic reference level geopotential height analysis, thereby enabling zonal and meridional geostrophic wind components to be computed at stratospheric levels. Such observational studies have greatly expanded our knowledge of middle atmosphere dynamics, with key progress made in radiosonde-void Southern Hemisphere regions. While not all dynamical investigations require knowledge of wind patterns (e.g., spectral analysis of radiance waves), such information is the starting point for virtually all observational studies involving the evaluation of eddy transport properties and interaction with the mean circulation.

Intercomparison of Southern Hemisphere Eliassen-Palm (EP) diagnostics, and other dynamical quantities inferred from satellite (SSU and UMS) thickness data, have been reported at arecent workshop held in Williamsburg, Virginia, in 1986 (GROSE and O'NEILL, 1989) on the Midd1e Atmosphere of the Southern Hemisphere (MASH), uti1izing reference height information from NMC, ECMWF, Melbourne, and zonally averaged rocketsonde c1imatological analyses. Geostrophic winds have been incorporated in these calculations. On the basis of model studies, ROBINSON (1986) and BOVILLE (1987) have hypothesized that the specification of geostrophic winds may create spurious satellite-derived EP flux diagnostics in the polar winter stratosphere. Robinson conc1uded that there are "significant shortcomings in the application of the divergence of the quasi-geostrophic Eliassen-Palm flux as a diagnostic of wave-mean flow interactions in the stratosphere." Boville states: "the errors associated with the quasi-geostrophic approximations are so large that it is questionable whether one may reasonably make the common assumption that the winter stratospheric circulation is nearly in geostrophic balance." These model investigations, however, are not without 1imitations. The Robinson analysis restricts attention to steady linear motion, whereas Boville's diagnostic evaluation of the EP flux divergence suffers from large residuals in the model momentum balance. ELSON (1986) and RANDEL (1987) have provided observational evidence which suggests that departures from geostrophic equilibrium may indeed playa significant role in 1arge-scale stratospheric dynamical processes during winter. In the present study, Nimbus 7 UMS height data is used to examine Robinson's hypothesis concerning the potential importance of ageostrophic processes on satellite-derived quantities such as the EP flux divergence. [Note that Robinson's conc1usions focus on the importance of nondivergent ageostrophic winds.]

While the use of geostrophic wind balance has facilitated the development of an invaluable body of theoretical work on extratropical middle atmosphere dynamics, the approximations involved in utilizing this form of balance from the full equations of motion may, for certain atmospheric circulation regimes, be rather inappropriate. In particular, the stratospheric wintertime polar-night jet stream is associated with, by tropospheric standards, quite large velocity gradients, such that forces in addition to the Coriolis and pressure gradient forces assume added importance. Whether one can accurately calculate these ageostrophic contributions from,

Vol. 130, 1989 Comparison of Geostrophic and Balanced Winds 321

ultimately, asynoptic satellite radiance information is, however, open to question in light of the probable uncertainties of the satellite measurements, retrieval, and synoptic mapping-let alone approximations associated with the ensuing numerical analysis. The UMS height data has been used to generate iterative solutions of the nondivergent horizontal wind field from the non linear balance equation. These "balanced" winds have been compared with the standard geostrophic estimates, as weil as with in situ radiosonde wind reports. A stringent test of this hypothesis, however, dictated use of the Northern Hemisphere UMS data, because the Southern Hemisphere data suffer from limited polar coverage (to 64°S), relatively poor-quality base height information (e.g., paucity of radiosonde data and less accurate forecast guess-fields), and generally small amplitude wave disturbances over the duration of the UMS experiment.

2. Data

The derivation of balanced and geostrophic winds in this study is made using the Nimbus 7 UMS height analyses genera ted from NMC 50-mb reference height analyses and UMS temperature data synoptically mapped to 12 UTC, which incorporates ascending plus descending orbital temperature information. The UMS temperature analyses used herein are for the 100, 70, 50, 30, 16, 10, 7, 5, 3, 2, 1.5, 1.0, 0.7, 0.5, 0.4, 0.2, 0.1, and 0.05 mb levels. The vertical resolution of the UMS orbital temperature profiles is ~ 2.5 km; i.e., the UMS instrument can, at best, vertically resolve a temperature disturbance with half-wavelength of 2.5 km and amplitude of 2 K, for a signal-to-noise ratio of two (REMSBERG and RUSSELL, 1987). However, in the present study, because mapped temperature fields at adjacent pressure levels are used, rather than the orbital profile data, the relevant vertical resolution is somewhat degraded to about 3-4 km. Gridded temperature and height analyses are provided at 4' intervals from 64°S to 84°N, and in the present study, data from the Equator to 84"N is used. The reader is referred to GILLE and RUSSELL (1984) for details of the UMS experiment.

Validation of the UMS balanced winds is made via comparison with radiosonde wind reports for 12 UTC at Berlin (Tempelhof Airport). These data, obtained using the standard GMD tracking system, are representative of a mean wind over about al-km layer (GROSE et al., 1988). For the present study, the 100, 50, 30, and 10 mb reports are utilized and a 1-2-1 time smoothing is applied to the daily Berlin winds.

3. Balanced Wind Analysis

The form of the balance equation used in the present study is that appropriate for the nondivergent horizontal motion, which may be expressed in spherical polar

322

coordinates as:

where

T. Miles and W. L. Grose

vtt/>t/J = [vtt/> + ADV + BETA + ACC] If = FA.t/>

ADV=2[ ov ~_~ ou ] a cos 4> OA. a 04> a 04> a cos 4> OA.

BETA = uof a 04>

ACC = (1 + tan 4> o~ ) [u 2 + v2]!a 2

ot/J u=---

a 04>

ot/J v=----

a cos 4> oÄ

PAGEOPH,

(1)

(2)

(3)

( 4)

(5)

( 6)

and t/J is the stream function for nondivergent horizontal motion, = gz is the geopotential, f = 2Q sin 4> is the Coriolis parameter, 4> and A. denote latitude and

longitude, a is the Earth's mean radius, and u, v represent zonal and meridional

rotational wind components. Following the approach of PAEGLE and TOMLlNSON (1975), solutions for the

rotational winds are obtained iteratively in spherical coordinates. The source function in (1) is estimated from geostrophic winds initially, or from the latest stream function gradients on subsequent iterations via inversion of V2t/J. Convergen ce of this numerical solution yields the final estimate for u, v. A linear solution is determined as the guess for generating the nonlinear iterations. Complications associated with divergence of the above numerical process are addressed by PAEGLE and TOMLlNsoN (1975), IVERSEN and NORDENG (1982), and BULSMA and HOOGENDOORN (1983). These studies indicate that the potential for obtaining satisfactory convergent solutions is considerably enhanced if und er-relaxation is

incorporated into the iterative method and the geopotential distribution is con

strained to obey the ellipticity criterion appropriate for (1).

The finite difference analogue of (1) applied in the present study is a successive relaxation technique used to obtain a solution fOT the stream function at iterative step v + I (ANDERSON et al., 1984):

./, ~ + I = r [(./, ~ + ./, ~ + I ) + r (./, ~ + ./, v + I ) 'I' I .. t/> I 'I' I. + I.t/> 'I' I. - I.t/> 2 'I' '-.t/> + I 'I' A.t/> - I

where

r I = W 12( I + y 2 cos2 4» with w the successive relaxation parameter for the

Poisson inversion and the grid aspect ratio y = bÄ/b4>

Vol. 130, 1989 Comparison of Geostrophic and Balanced Winds

r 2 = y2 COS2 4J r 3 = b4Jy2[COS2 4J/( 1+ a)tan 4J - sin 4J cos 4J1I2 r 4 = (a cos 4J bAV/(1 + a)

and a is the Paegle-Tomlinson under-relaxation parameter.

323

Equation (7) is applied to the UMS 10° x 4° A., 4J grid which is illustrated in Figure 1. For initial conditions, we define

from 00N-84°N with geostrophic winds specified at interior grid points. At 4°N the non linear advection term is set to zero and geostrophic winds are set equal to the values at 8°N. Boundary values are required for ot/l /o4J at OON and 84°N; at OON the value is also set equal to the geostrophic value at 8°N, while a value of 0.9 x ugeo was applied at 84°N, as suggested from the model simulations of BOVILLE ( 1987).

Prior to the application of (7) to all 18 UMS pressure levels, aseries of numerical tests were performed at 100, 10, I, and 0.1 mb for January 14, 1979, to assess the convergence of the balanced wind solutions for a range of relaxation parameters (e.g., w = 0 --+ 2 and a = 0 --+ 1) and application of smoothing to the UMS height data. Optimum convergence was found to occur at all pressure levels only when (1) the heights were smoothed 1-2-1 in latitude from 00N-84°N,

(2) under-relaxation was used-namely, a = 0.3 and w = 0.6, and (3) the height distribution was modified at each iteration step to conform with the ellipticity criterion (see below). The omission of latitudinal smoothing resulted in divergent

80.

I , , , , ,I , .,' '.

°tv '. JSoE'

I!l old '" estimate I tor interior x new '" estimate grid points ..... - updating sequence

Figure I Successive relaxation grid configuration.

solutions at virtually all pressure levels. An initial application of the 1-2-1 operator three times (i.e., at v = 1) was found to represent a level of smoothing which, while allowing for acceptable convergence, did not completely remove horizontal wind shear structure related to flow departures from geostrophy, e.g., related to the ADV and ACCEL terms in (2) and (4). [The geostrophic solution also incorporates latitudinal smoothing.] The solution convergence for the stream function and relative vorticity was monitored through computation of I(",H 1 - "'V);.,,,, 1 = b'" and I(V2", v + 1 - P + I);.,,,, 1 = I: after each iteration. For optimum convergence, values of b'" < 1 % of "'~.'" and an uncertainty in relative vorticity, 1:, generally < 10% of the UMS geostrophic relative vorticity resulted. Values of I: approaching 50% or larger, however, occurred in flow regions immediately adjacent to the northern boundary at 84°N and numerical solutions in these arctic regions were regarded as containing large uncertainties. Balanced wind results are, therefore, described for the domain 8°N-noN. Over the 18 pressure levels and analysis period of January 14--20 considered in this study, satisfactory convergence was achieved using 4(10) iterations for the linear (nonlinear) solutions of equation (7). The values selected for IX and w (0.3 and 0.6) were found to result in the most rapid convergence and minimum vorticity error. The sensitivity of the stream function solution convergence to values of w is shown in Table 1 for the lO-mb level on January 14. Values of b'" (for 4°N-800N) vs. v are shown for two cases, w = 0.6 and 1.8, the latter approximately the theoretical optimum value for w for the UMS grid mesh (ANDERSON et al., 1984). It can be seen that under-relaxation results in convergent solutions for the nonlinear balance equation.

The third requirement for achieving meaningful numerical solutions is to ensure that the UMS height distribution obeys an elliptic criterion for (1). In spherical polar coordinates the appropriate criterion for the nondivergent balance equation (HOUGHTON, 1968) is:

(8)

If (8) is not obeyed at the start of each iteration, then the UMS height distribution in (1) is modified such that:

(9)

Violations were found to occur primarily in anticyclonic (clockwise) flow regions in tropical latitudes, but were more widespread if smoothing was not applied to the UMS heights and over-relaxation was used for (7). Modifications which were applied to the UMS height data in extratropical latitudes using (9) generally did not exceed ~ 10% of the geostrophic relative vorticity or, equivalently, result in a decrease of less than 10 m in height at centers of anticyclonic vorticity. In effect, these alterations are designed to bring the UMS mass field into balance with the


Table I

Stream /unction Solution Convergence, by" 0/ Nondivergent Nonlinear Balance Equation at 10 mb-Iteration Step vs. Relaxation Parameter.

v w =0.6 w = 1.8

119· 315· 5 23 158

10 12 157 15 11 157

• Initial value of stream function - 24000 m2s - I.

325

rotational wind field. The occurrence of nonelliptic regions in the Tropics may arise, in part, from errors in the 50 mb reference-level NMC height analysis, amplified by /-1 in the Laplacian term in (8).

4. Comparison 0/ LIMS and Radiosonde Winds

The UMS balanced winds were analyzed for the interval January 14-20, 1979, during which substantial variations in extratropical zonal-mean wind and EP ftux divergence occurred (GROSE, 1984). The synoptic pattern in the middle stratosphere at this time featured a triangularly shaped polar vortex somewhat offset from the North Pole with the development of an Aleutian anticyclone (Figure 2). Over Europe, a trough propagates from west to east resulting in a veering of wind direction from SW to NW.

The daily variation in the 10 mb horizontal wind speed and direction over Berlin is shown in Figure 3a based on the derived UMS geostrophic and balanced analysis and the in situ balloon measurements. The radiosonde (RAOB) wind speed decreases from 47 to 31 mls from January 14-17 while veering in direction from 230° to 270°. Thereafter, the RAOB speed increases to 40 m/s from a northwesterly direction. On a daily basis, quantitative differences of order 5-10 m/s are seen between the UMS and RAOB wind speeds. The time variation in speed for both the geostrophic and balanced analysis appears to lag behind that shown for the RAOB data during the trough passage over Europe (January 16-18). Wind directions for the three methods of wind analysis differ by approximately 10°-30°, although on occasion (January 18-20), the balanced wind values are quite similar to the RAOB information.

The corresponding time-mean wind comparison is displayed in Figure 3b, including results for 100, 50, and 30 mb. The UMS and RAOB wind speeds are generally in close qualitative agreement, e.g., in terms of vertical shear, and the balance wind directions agree more c1ose1y with in situ data at 30 and 50 mb. The

14,1

,79

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I ~\ \

H\

/ / ,QV~H

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Fig

ure

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MS

Nor

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pher

e ge

opot

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17, a

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~ E c w 00 geo w •.. , Cl. 40 CIl -\

· · · .. ' ." • 35 • • • • • • • . : ,--_ ... ..... 30

i 'tI

Z

~ 28 o w !!: c

220;---r--,~~---r--~~ 14 15 16 17 18 19 20

JANUARY 1979

Figure 3a

327

time-mean balanced wind speeds at 30 and 10 mb tend to be somewhat weaker than indicated for RAOB. Using a larger sampie of RAOB measurements (for JanuaryFebruary 1979) over Berlin, GROSE el al. (1988) show that the UMS geostrophic wind speeds are often in quantitative agreement with in situ values (Figure 3c). Discrepancies in time-lag evident at the lO-mb level in Figure 3a may signify the influence of transience errors inherent in the Kalman-filtering of satellite thickness information restricted to six zonal wave components. Such problems appear to arise during intervals of high frequency oscillations (periods < 1 week), albeit of modest amplitude, such as the localized trough passage over Europe cited herein.

328

.D E w a: ::J I/) I/)

~ 50 D..


January 14-20

" ." I: ." I: I: I: I: I : I : I : , ~ I \ , .. , " I .. ~ ••••• geo

00 1 ..... 00

0 •

PAGEOPH,

(B)

... 100'~--L-~~--____ r-____ ~~ ____ ~ __ ~f __ -r ____ ~ ____ ~ __ ~~_·~·~~

o 10 20 30 40 270 300 330 360 030

SPEED, m/s DIRECTION, deg

100

(CI

80

., 60 i": "- .. E

raob ',;', 0

'" '" Q. VI

40

20

10mb "

0 1 10 19 28 37 46 55 64

TIME. doys

Figure 3b,c

Figure 3 Comparison of UMS and radiosonde horizontal wind over Berlin (52°N, 13°E) for 12 UTC: (a) Time evolution of wind speed and direction at IO mb for radiosonde (solid), UMS geostrophic (dotted), and UMS nonlinear balanced'(dashed); (b) As in (a), but for time averaged values; and (c) Time evolution of 10 mb wind speed for radiosonde (dotted) and UMS geostrophic (solid) data from January I

(day I) to February 28 (day 59), 1979.

Vol. 130, 1989 Cornparison of Geostrophic and Balanced Winds 329

5. Geostrophic and Balanced Diagnostics

The period of analysis considered, January 14-20, 1979, represents an interval of enhanced extratropical planetary wave activity with the geopotential height amplitude of zonal wavenumber 1 increasing from 800 m to 1600 m at 2 mb, 600 N between January 15-18, 1979. Geostrophic (ug , vg) and nonlinear balanced (Ub' Vb)

wind components have been used to calculate latitude-height distributions for several zonally averaged quantities: zonal wind, Ü, meridional eddy flux of heat and momentum, v'e' and u'v', quasi-geostrophic EP flux, F = a cos 4J( -u'v',fv'e'jep ),

and the EP flux divergence (EPFD), V . F (a cos 4J) -I, where e is potential temperature and the subscript p denotes differentiation with respect to pressure. As proposed by ROBINSON (1986), F is utilized herein for computation of both the geostrophic and balanced EPFD distributions, although strict1y the latter should be derived from expressions based on the (nondivergent) primitive equations (e.g., ANDREWS, 1987). Results are described below primarily for January 18 which is representative of the period of pronounced wave-mean flow interaction in the stratosphere and lower mesosphere.

A. Horizontal Wind and Vorticity Analysis

Meridional cross-sections for üg and Üb for January 18 extending from 50 mb to 0.1 mb (~21-65 km) and 8°N to nON are shown in Figures 4a and 4b. The nonlinear balanced analysis exhibits a negative bias compared to geostrophic values which increases with altitude, particularly in subtropical and middle latitudes. Stratospheric balanced wind speeds are typically 10--20% weaker than the geostrophic estimates in middle and polar latitudes, while in the lower mesosphere, differences approach 25-50% between 300 N and 600 N. The wind speed differences at stratospheric levels are similar to those reported in previous observational investigations (e.g., RANDEL, 1987).

Root-mean-square (RMS) differences for ug - Ub and vg - Vb (note Vb = 0), evaluated at 10° longitude increments and zonally averaged are presented in Table 2 for 50, 10, 1, and 0.1 mb levels and selected latitudes for January 18. Zonal wind differences increase with altitude and maximum RMS values occur in subtropical latitudes. In contrast, differences between geostrophic and balanced meridional wind speeds are smaller in magnitude with the largest values occurring in the sub-Tropics at 1 mb and 0.1 mb, and typically are about ± 10--30% of the local value of vg •

It is instructive to consider the relative importance of terms in the nonlinear balance equation (1) which influence the geostrophic-rotational wind differences cited above. Contributions from the four source terms in (1) for January 18 are presented for zonally averaged and localized cases in Tables 3 and 4, respectively. The zonally averaged vorticity analysis is described for the same range of pressure

330

E '"

... o :l ... ;: ...J ~

20

GEOSTROPHIC ij

BALANCE ij


32 44

LA TlTUDE • dog N •

LATITUDE • dog N.

Figure 4

PAGEOPH,

.0

~ w

2 a: :l (/) (/) w a: Q.

56

(Al

(B)

Zonally averaged distribution of zonal wind (ms- I ) derived from (a) geostrophic and (b) nonlinear balanced formulation for January 18, 1979.

levels and latitudes as in Table 2. The balanced zonal wind solutions in low latitudes are seen to arise primarily from inclusion of the BETA source term, whereas in extratropical regions the remaining ageostrophic source terms ass urne added importance. Although substantial differences exist between geostrophic and balanced va lues of absolute vorticity in low latitudes (where the irrotational wind may be important), extratropical values differ typically by ± 10%.

The relative importance of terms in (1) is found to change quite noticeably when diagnosed on a local basis. Values of these vorticity terms, along with geostrophic


Table 2

Zonally Averaged RMS Difference Between Geostrophic and Balanced Zonal and Meridional Winds (mr')for January 18, 1979.

8°N 24°N 400 N 56°N 72°N

0.1 mb 22.1 3 \.4 22.2 14.1 9.8 1mb 7.6 17.8 16.8 14.2 7.1

10mb 4.7 4.1 4.0 8.3 3.9 50mb 4.2 \.4 2.0 3.4 I.I

0.1 mb I3.1 7.5 4.9 5.6 5.3 1mb 8.5 5.9 3.1 3.8 5.0

10mb 2.5 \.8 2.6 3.6 3.2 50mb \.0 \.2 \.2 1.2 0.8

Table 3

Zonally Averaged Vorticity Analysis (10- 6 r ') for January 18, 1979.

8°N 24°N 400 N 56°N 72°N

(V2(f1)lf 0.1 mb -23 -45 26 21 28 1mb 9 -31 -5 14 41

10mb 15 -8 -21 7 27 50mb -3 -5 -9 6 10

f 20 59 94 121 139

BETAlf 0.1 mb 20 17 9 3 I 1mb -15 7 8 5 2

10mb -20 -I 4 5 2 50mb I 2 3 2 I

ACCELlf 0.1 mh I 4 -I -2 I 1mb 0 I 2 0 -2

10mb 0 0 2 I -I 50mb 0 0 0 0

ADVlf 0.1 mb 0 I -I 0 -3 1mb 0 0 0 -2 -3

10mb 0 0 0 -I -3 50mb -0 -0 I -I -2

V21/1 0.1 mb -2 -23 33 22 27 1mb -6 -23 5 17 38

10mb -5 -9 -15 12 25 50mb -2 -3 -4 7 9

331


Table 4

Loeal Analysis of Vortieity (10- 6 s -1) and Horizontal Wind Veloeity (ms -1) for January 18, 1979.

0.1 mb, 28°N Imb,60o N 10 mb, 600 N

OOE 1800 E 1200 E 3()()OE 1800 E 3()()OE

(V 2CJJ)/f -53 -24 27 72 -26 73 f 69 69 126 126 126 126

BETA/f 21 19 7 3 3 4 ACCEL/f 7 3 I -4 7 -4

ADV/f 7 -I -9 -0 -7

V2t/1 -18 -I 34 62 -16 66 ug 116 79 95 54 39 49 uB 70 65 78 37 34 43 vg 18 -11 44 -21 38 13

VB 21 -10 40 -22 44 12

and balanced wind speeds, are presented in Table 4 at grid points which are located in selected narrow jet stream regions in the middle-upper stratosphere and lower mesosphere (Figure 5). An example in which all three ageostrophic source terms influence the balanced wind solution is shown for 0.1 mb at 28°N, OOE, where the value of Ub (70 ms-I) on the equatorward flank of the subtropical jet core is 46 ms - I weaker than ug • In constrast, at 28°N, 180oE, the percentage difference in ug - Ub is sm aller and largely arises from the linear BETA source term. As evident in the zonally averaged analysis in Table 3, the localized values of absolute vorticity at 0.1 mb, 28°N for the balanced wind field are larger than those for the geostrophic solution as a consequence of a reduction in the magnitude of negative (anticyclonic) values of relative vorticity. In the upper stratosphere (l mb), the balanced wind solution in the vicinity of the polar-night Siberian jet stream trough at 60oN, l200E is essentially linear due to the BETA contribution, when::as within the Canadian jet stream trough at 60oN, 300oE, the balanced solution for U is strongly nonlinear with nonlinear advection processes substantially larger than the BETA or ACCEL source terms. At the 10-mb level, the Aleutian anticyclone is somewhat better defined and the vorticity budget for 60oN, 1800 E (in the northwest quadrant of the anticyclone) reveals the importance of meridional variations in U and v via the ACCEL source term, plus the secondary role of the BETA source term, in creating ageostrophic departures in both the U and v velocity components (both being similar in magnitude in this sector). Over Canada, the balanced solution for 60oN, 3000 E is, as observed for 1 mb, strongly nonlinear in the vicinity of the polar jet stream trough, as can be surmised from a visual inspection of the geopotential height maps in Figure 5.

The above analysis, therefore, indicates the importance of non linear balanceboth in the stratospheric polar-night jet stream and mesospheric subtropical jet core

Vol. 130, 1989 Comparison of Geostrophic and Ba1anced Winds 333

regions. The quantitative similarity between geostrophic and balanced absolute vorticity values presented in Tables 3 and 4 for extratropical regions suggests that the spatial variability of the ageostrophic source terms is of a sufficiently large scale with respect to the UMS grid interval used for two-dimensional differentiation of u and v (aside from the increasing magnitude of planetary vorticity with latitude). Potential vorticity diagnostics generated from a three-dimensional general circulation model simulation of a Northern Hemisphere mid-winter stratospheric sud den warming (BLACKSHEAR et al., 1987) provide independent evidence of the similarity between geostrophic and primitive equation derivations of vorticity in extratropical regions. During a spontaneous January warming event, the model zonal wavenumber one component attained an amplitude of ~ 2500 m at 2 mb, 70oN. The model 850 K potential vorticity distribution during this warming event is shown in Figure 6, based on (1) a geostrophic calculation from the model geopotential height distribution and (2) direct calculation from the prognostic vorticity distribution (induding divergent motions). The model comparison underlines the interpretation applied above to the UMS analysis: name\y, the generally dose agreement between geostrophic and (nondivergent) primitive equation vorticity distributions in extratropical regions. In subtropical regions, however, both the UMS data and the model-generated diagnostics suggest that somewhat larger disagreements may arise (e.g., near 900 E in Figure 6).

A

Figure 5a

334 T. Miles and W. L. Grose

OE

Figure 5b,c

Figure 5

PAGEOPH,

1mb

B

10mb

c

UMS Northern Hemisphere geopotential height distribution for January 18, 1979, at (a) 0.1 mb, (b) 1mb, and (cl 10 mb. Contour interval is 0.2 gpkm.


OE

OE

Figure 6 Northern Hemisphere distribution of potential vorticity (10- 5 S-l) on 850 K surface determined (a) geostrophically from model height field and (b) direct1y from model (prognostic) vorticity equation.

B. Zonally Averaged Eddy Flux Quantities

In this section, the impact of ageostrophic u and v motions on several zonally averaged eddy flux diagnostics is presented. The meridional eddy heat flux distributions for geostrophic and nonlinear balanced equations are presented in Figures 7a and 7b, respectively. As this diagnostic does not depend on the zonal wind component, only modest differences (± 10-20%) are found between geostrophic

336

E .:.t.

&.I c ::;) ... i= ...J

'"

E .:.t.

&.I C ::;) ... i= ...J

'"


64.5.--.-,.--,--,·

21.0 a'-~'---'---- :-':-_1_....JL'---::-'~...l.----..J'--.l...L--'-L--'.L_""'--..J.."""--L-....L---'

GEOSTROPHIC Y'T' LA TlTUDE • dag N.

64.5

21.0 a=--'--L--::':--=""""-:'=--L

BALANCE Y'T'

LATITUDE • dag N.

Figure 7 As Fig. 4, hut for meridional eddy heat flux (K ms- I ).

(A)

(B)

PAGEOPH,

.c E W I%: ::;) fI) fI) W I%: Cl.

.c E -W I%:

2 ::;) fI) fI) W I%: Cl.

and balanced analyses. Both distributions are marked by a maximum centered near the polar stratopause, and a secondary maximum is suggested in the mid-Iatitude mesosphere. Balanced heat fluxes tend to be weaker than geostrophic va lues in the lower stratosphere in the 48°N-64°N latitude band, but stronger in extratropical mesospheric regions. Note that, in general, because the vertical gradient of the eddy

E ~ .a

E .... W c 2 a:: :::> ::J l- r/)

;:: r/)

~ w

-< a:: Q.

10

GEOSTROPHIC u'v' (A)

LA TlTUDE • deg N.

53,2

E ~ .a

E .... ui c 43,5 2 a:: :::> ::J l- r/)

;:: r/)

~ w

-< a:: Cl.

56 68

BALANCE U'V' (B) LATITUDE • deg N.

Figure 8 As Fig. 4, but for meridional eddy momentum flux (m2 s - 2).

heat f1ux is also quite similar in these two analyses, the vertical component of the EPFD analysis will exhibit an analogous behavior. Exceptions to this occur in the lower stratosphere near 56°N and the mesosphere between 44° and 52'N.

The corresponding set of geostrophic and balanced eddy moment um /lux analyses is shown in Figures 8a and 8b. Because this diagnostic depends on both u

and v components, a more noticeable impact is observed. In tropical latitudes (i.e., 8°N) of the upper stratosphere and mesosphere, the geostrophic momentum flux is marked by a large positive bias in accord with the RMS differences noted in Section 5A. In particular, the meridional gradient of u'v' is quite substantial for the tropical geostrophic solution which, as will be discussed below, will create a large anomaly in the EPFD analysis in this region. On a qualitative basis, both geostrophic and balanced extratropical eddy momentum flux distributions are characterized by maxima located in the polar upper stratosphere and mid-Iatitude mesosphere. Both analyses also indicate a region of negative flux in the polar mesosphere. On a quantitative basis, however, the balanced flux values are sm aller and exhibit somewhat sharper meridional gradients in the polar stratosphere from 68°N-72°N and in the suotropical and mid-Iatitude mesosphere, where the geostrophic momentum flux pattern exhibits a broader meridional scale (e.g., between 200 N and 48°N).

The geostrophic and balanced EPFD distributions for Janaury 18 are displayed in Figures 9a and 9b. The analyses in tropical regions of the upper stratosphere and mesosphere are markedly different, reflecting the anomalous geostrophic

E .><

--- .. __ ...... _- .. _--

32.2

GEOSTROPHIC EPFO

--.

, ,

., , , , , ,

, , ,

" , -... ---

, ," " " , ... .... .. , -.... : : \. ., " "', ....... ,..,../ "

' ........... ,.. ...... .",) ~ -----

'- .. ~.. ... ....

(A) LA T1TUOE • dog N.

Figure 9a

D

2 E W a: ::;)

'" '" w a: 0..

1(\

Vol. 130, 1989

E '"

Comparison of Geostrophic and Balanced Winds

8 20

BALANCE EPFD

32 44

LATITUDE • dog N.

Figure 9b

Figure 9

56 68

(B)

As Fig. 4, but for Eliassen-Palm f1ux divergence (10- 5 ms- 2).

.c E w a: :> ll! w CI: ~

339

momentum flux distribution. In extratropical regions, in contrast, geostrophic and balanced EPFD patterns are in dose qualitative agreement. Both analyses indicate a region of convergence in the subtropical mesosphere and the polar latitude dipole reversal between stratospheric and mesospheric levels is also similarly captured in the two analyses. On a grid-point quantitative basis, however, quite large percentage differences are evident as shown in Table 5. Perhaps the most interesting difference occurs at 72°N where the balanced positive EPFD values substantially exceed those for the geostrophic solution in the stratosphere. In contrast, in the polar mesosphere, the balanced EPFD values tend to be smaller than the geostrophic values. At 44(N and 56°N, both analyses are quantitatively similar in the middle upper stratosphere, but in the lower stratosphere at 56°N, the magnitude of convergence is considerably larger for the balanced solution, reflecting differences in the vertical gradient of v'W. The meridional gradient of the EPFD in the extratropical mesosphere is quite substantial in both analyses and, therefore, a re1ative1y small


Table 5

Geostrophic and Ba/anced E-P F/ux Divergence (lO-5 mr2)for January 18, 1979

200 N 32°N 44°N 56°N nON

GEO BAL GEO BAL GEO BAL GEO BAL GEO BAL

0.1 mb -5.3 1.7 -21.0 -18.9 -1.4 0.3 48.0 47.8 -24.5 12.8 0.4 mb -5.1 -1.4 -30.1 -22.5 -2.7 -18.2 27.8 9.1 -100.0 -79.8 2mb -1.7 -1.3 -8.1 -4.6 -10.1 -9.8 -22.8 -32.1 13.1 22.7 7mb -1.5 -0.4 -2.4 -1.6 -6.4 -6.5 -22.2 -25.0 -2.5 3.2

50mb 0.3 -0.2 -1.7 -0.5 0.3 0.9 -0.5 -2.2 2.8 6.1

shift in latitude of the balanced EPFO analysis can lead to quite a large percentage difference between geostrophic and balanced EPFO grid-point values.

The EPFO comparison, therefore, indicates that while certain details of the extratropical EPFO pattern are altered in the balanced analysis, the high-latitude stratospheric dipole configuration is not removed but, rather, is slightly intensified in the balanced case. These findings were also evident on other dates analyzed during mid-January. To illustrate the temporal agreement between geostrophic and

PRESSURE = 10mb LATITUDE = 60· N

------ fv· 1 • ----- V·F(acOScI>f o ---0:- aü/at

balance geostrophic

~.--------------------------,

N 'CI)

E '" '0 ,....

20

-20

\ ~

\

\. \-" ~\,~ e' ", \

• I V \ \' \,.J \ I , I '~ \(

•

January 1979

Figure 10 Time evolution of terms in transformed momentum equation for 10 mb, 6OoN.


balanced values along the mid-stratospheric polar-night jet core axis, the zonally averaged momentum budget at 10 mb, 600 N is presented in Figure 10, showing both geostrophic and balanced EPFD values for January 14-20. The increased level of wave-mean ftow interaction which occurred during this period is depicted in a quantitatively similar pattern in the geostrophic and balanced analyses.

6. Conclusion

Comparison of satellite-derived geostrophic and nonlinear balanced horizontal wind analyses during January 1979 has indicated a substantial positive geostrophic bias for the zonal component in the middle-upper stratosphere and mesosphere, which approaches 60-70% of the nonlinear balanced wind values in subtropical and mid-latitudes at 0.1 mb. Smaller differences are found for the meridional wind solutions. The importance of nonlinear advection processes in causing these ageostrophic differences is stressed for both polar and subtropical regions.

On a zonally averaged basis, the balanced solutions result in generally weaker eddy momentum ftux, which is found to lead to alterations in the EPFD distribution. However, these changes do not result in severe changes on a large-scale basis or in terms of temporal variations. The polar EPFD dipole configuration observed in the stratosphere and mesosphere is, qualitatively, quite similar in the geostrophic and balanced cases-in contrast to the model studies of ROBINSON (1986) and BOVILLE (1987). Extratropical distributions of absolute vorticity based on UMS geostrophic and balanced winds also exhibit a substantial level of agreement in accord with CLOUGH et al. (1985).

Comparison of balanced winds with in situ radiosonde measurements reveals quite substantial differences at 10 mb on a daily basis, although agreement in terms of direction tends to improve somewhat as the NMC 50 mb base-level is approached. Although this 7-day comparison with ground-truth measurements is of a somewhat limited nature, the fact that the dosest agreement between satellite and in situ winds occurs at 50 mb suggests that the accuracy of satellite ageostrophic corrections, e.g., at 10 mb, is ultimately constrained by uncertainties in the UMS temperature (thickness) fields related to aspects of retrieval, resolution (e.g., measurement geometry), and KaIman filtering. Of course, a dilemma in attempting to ascertain the true ageostrophic contribution is that the uncertainty in the radiosonde observations during strong wintertime ftow is probably similar in magnitude to the true ageostrophic wind components. Nevertheless, the lack of agreement between radiosonde and balanced winds during January 14-20 at 10 mb suggests that caution should be exercised in using derived winds on a local basis, as for example in the quantitative interpretation of stratospheric air parcel trajectories derived from satellite height analyses.


7. Acknowledgments

We wish to thank Michael McIntyre and Ellis Remsberg for useful discussions, Karin Labitzke for providing the Berlin radiosonde information, Gretchen Lingenfelser for graphics assistance, and Sheila D. Johnson for typing the manuscript.

REFERENCES

ANDERSON, D. A., J. C. TANNEHILL, and R. H. PLETCHER, Computational Fluid Mechanics and Heat Transfer (MeGraw-Hill 1984) 599 pp.

ANDREWS, D. G. (1987), On the interpretation of the Eliassen-Palm j1ux divergence, Quart. J. Roy. Meteor. Soe. 113, 323-338.

BIJLSMA, S. J., and R. J. HOOGENDOORN (1983), A convergence analysis of a numerical method for solving the balance equation, Mon. Weath. Rev. 111, 997-1001.

BLACKSHEAR, W. T., W. L. GROSE, and R. E. TURNER (1987), Simulated sudden stratospheric warming; synoptic evolution, Quart J. Roy. Meteor. Soe. 113, 815-846.

BOVILLE, B. A. (1987), The validity of the geostrophic approximation in the winter stratosphere and troposphere, J. Atmos. Sei. 44, 443-457.

CLOUGH, S. A., N. S. GRAHAME, and A. O'NEILL (1985), Potential vorticity in the stratosphere derived using da ta from satellites, Quart. J. Roy. Meteor. Soe. 111, 335-358.

ELSON, L. E. (1986), Ageostrophic motions in the stratosphere from satellite observations, J. Atmos. Sei. 43, 409-418.

GILLE, J. c., and J. M. RUSSELL III (1984), The Iimb infrared monitor of the stratosphere: Experiment description, performance, and results, J. Geophys. Res. 89, 5125-5140.

GROSE, W. L. (1984), Recent advances in understanding stratospheric dynamics and transport processes: Application of satellite data to their interpretation, Adv. Spaee Res. 4, 19-28.

GROSE, W. L., T. MILES, K. LABITZKE, and E. PANTZKE (1988), Comparison of LIMS temperatures and geostrophie winds with Bertin radiosonde temperature and wind measurements, J. Geophys. Res. 93, 11217-11226.

GROSE, W. L., and A. O'NEILL (1989), Comparison of data and derived quantities for the middle atmosphere of the Southern Hemisphere, Pure Appl. Geophys. 130, 2/3, 195-212.

HOUGHTON, D. D. (1968), Derivation of the elliptic eondition for the balance equation in spherical coordinates, J. Atmos. Sei. 25, 927-928.

IVERSEN, T., and T. E. NORDENG (1982), A convergent method for solving the balance equation, Mon. Wea. Rev. 110, 1347-1353.

KENNEDY, J. S., and W. NORDBERG (1967), Circulation features of the stratosphere derived from radiometrie temperature measurements with the TlROS VII satellite, J. Atmos. Sei. 24, 711-719.

PAEGLE, J., and E. M. TOMLINSON (1975), Solution of the balance equation by Fourier transform and Gauss elimination, Mon. Wea. Rev. 103, 528-535.

RANDEL, W. J. (1987), The evaluation of winds from geopotential height data in the stratosphere, J. Atmos. Sei. 44, 3097-3120.

REMSBERG, E. E. and 1. M. RUSSELL III, The near global distributions of middle atmospheric H20 and N02 measured by the Nimbus 7. LIMS experiment, in Transport Processes in the Middle Atmosphere (eds. G. Visconti and R. Gareia) (Reidel 1987) pp. 87-102.

ROBINSON, W. A. (1986), The apptication of the quasi-geostrophic Eliassen-Palm j1ux to the analysis of stratospherie data, J. Atmos. Sei. 43, 1017-1023.

(Reeeived Deeember 7, 1987, revised May 3, 1988, aeeepted May 8, 1988)


A Review of Gravity Wave Saturation Processes, Effects, and Variability in the Middle Atmosphere

DAVID C. FRITTS1

Abstract-This paper provides a review of our current understanding of the processes responsible for gravity wave saturation as weil as the principal effects and variability of saturation in the lower and middle atmosphere. We discuss the theoretical and observational evidence for linear and nonlinear saturation processes and examine the consequences of saturation for wave amplitude limits, momentum and energy ftuxes, the diffusion of heat and constituents, and the establishment of a near-universal vertical wavenumber spectrum. Recent studies of gravity wave variability are reviewed and are seen to provide insights into the significant causes of wave variability throughout the atmosphere.

Key words: Gravity waves, saturation, middle atmosphere dynamies, turbulence, diffusion, momenturn ftuxes.

1. Introduction

Internal gravity waves were first reeognized to play an important role in the middle atmosphere hy HINES (1960). Sinee that time, their influenee on the largeand small-seale dynamics of the middle atmosphere has heeome inereasing apparent. Principal among gravity wave effeets, perhaps, are the vertical transport of horizontal momentum and the eomplex wave and turbulenee interaetions by whieh gravity waves are saturated. Also eertain to he signifieant in terms of their middle atmosphere effeets is the ohserved temporal and geographie variability of the wave speetrum.

Gravity wave momentum fluxes aet to aeeeierate or deeeierate the large-seale flow at levels where the waves are transient or dissipating (BRETHERTON, 1969; CHUNCHUZOV, 1971; HIN ES, 1972; LILLY, 1972). This has signifieant eonsequenees for the me an eireulation and the thermal and eonstituent struetures in the mesosphere and lower thermosphere, where gravity wave drag is the major eontributor to the reversal of the vertieal shear of the mean zonal wind and to the resulting mean meridional cireulation and reversal of the meridional temperature gradient

I Geophysical Institute and Department of Physics, University of Alaska, Fairbanks, AK 99775-0800, U.S.A.

344 David C. Fritts PAGEOPH,

near the mesopause (HOUGHTON, 1978; LINDZEN, 1981; HOLTON, 1982; DUNKERTON, 1982). These theoretical results have received recent confirmation from a variety of observational studies in the mesosphere that revealed the strength of the mean meridional circulation and the magnitude of the gravity wave momentum flux divergence (NASTROM et al., 1982; VINCENT and REID, 1983; SMITH and LYJAK, 1985; FRITTS and VINCENT, 1987; REID and VINCENT, 1987a; LABITZKE et al., 1987). At lower levels, despite an early recognition of the importance of the momentum flux due to mountain wave activity (LONG, 1955; BRETHERTON, 1969; NEWTON, 1971; LILLY and KENNEDY, 1973) a broader appreciation ofits effects on the large-scale circulation of the 10wer stratosphere did not emerge until more recently (LINDZEN, 1985; PALMER et al., 1986; TANAKA, 1986; McFARLANE, 1987).

Wave saturation processes likewise are important as they act in concert with wave sources and filtering to determine the spectrum of middle atmosphere motions and their effects at small- and meso-scales. Initial attempts to understand these processes focused on the conditions necessary for the 10cal instability of an essentially linear wave field (HODGES, 1967; HINES, 1971), referred to in this paper as a "linear" instability, and were successful in explaining, at least crude1y, the observed limit on wave amplitudes. These linear instabilities will be distinguished from "nonlinear" instabilities, such as wave-wave and wave vortical-mode interactions, that require a knowledge of the global wave field, though we must recognize that both instabilities are inherently nonlinear in that they effect an exchange of energy between different scales andjor types of motions. The apparent success of linear theory has prompted its use in the parameterization of gravity wave effects (LINDZEN, 1981, 1984; HOLTON, 1982, 1983; HOLTON and ZHU, 1984; GARCIA and SOLOMOM, 1985; PALMER et al., 1986; RIND et al., 1988), the deve10pment ofmore complete spectral descriptions of the saturated wave fie1d and its effects (DEWAN and GOOD, 1986; SMITH et al., 1987; FRITTS et al., 1988a; V ANZANDT and FRITTS, 1989), and further study of the time scales and likely modes of linear instability (HINES, 1988).

Other theoretical studies have addressed the effects of nonlinear interactions within the atmospheric internal wave field (MIED, 1976; KLOSTERMEYER, 1982; WEINSTOCK, 1982, 1985; YEH and LIU, 1981, 1985; FRITTS, 1985; INHESTER, 1987; DUNKERTON, 1987; DONG and YEH, 1988) and the implications of wave dissipation and turbulence generation for heat and constituent transports (WALTERSCHEID, 1981; WEINSTOCK, 1983; SCHOEBERL et al., 1983; CHAO and SCHOEBERL, 1984; FRITTS and DUNKERTON, 1985; STROBEL et al., 1985, 1987; Coyand FRITTS, 1988). Observational studies, on the other hand, have attempted to identify the processes responsible for wave field saturation and provide evidence of their effects (see FRITTS and RASTOGI, 1985, for references; TSUDA et al., 1985; REID et al., 1987; FRITTS et al., 1988b).

Vol. 130, 1989 Gravity Wave Saturation Processes 345

Finally, a number of reeent observational and theoretieal studies have revealed eonsiderable temporal and geographie variability of the gravity wave speetrum and its effeets in the middle atmosphere. This includes variations in wave energy densities (MEEK et al., 1985a; VINCENT and FRITTS, 1987), momentum fluxes (VINCENT and REID, 1983; FRITTS and VINCENT, 1987; REID and VINCENT, 1987a; FRITTS et al., 1989), turbulenee intensities (HOCKING, 1987; WATKINS et al., 1988),

and eonstituent eoneentrations (THOMAS et al., 1984) on time seales ranging from minutes or hours to a year. Theoretieal studies suggest that sueh variability may arise in response to variable sourees and/or filtering by mean or low frequeney planetary, tidal, or gravity wave motions (DUNKERTON and BUTCHART, 1984; MIYAHARA et al., 1986; FRITTS and VINCENT, 1987; NA STROM et al., 1987). Onee aehieved, sueh variability mayaiso eontribute to the foreing of other motions in regions of wave dissipation on eomparable temporal and geographie seales (SCHOEBERL and STROBEL, 1984; HOLTON, 1984).

As noted above, we have made eonsiderable progress in reeent years in understanding the proeesses affeeting gravity wave propagation and saturation as well as the possible eauses and effeets of gravity wave variability in the middle atmosphere. Our purposes in this review are to summarize these reeent advanees and endeavor to identify those areas in whieh signifieant uneertainties remain. For eonvenienee, we will not review all of the early eontributions to the field, but instead will refer the interested reader to the previous reviews of gravity wave saturation and saturation proeesses by FRITTS (1984) and FRITTS and RASTOGI (1985). Also of relevanee to nonlinear wave-wave interaetions in the oeean is the review by MULLER et al. (1986).

We will begin by reviewing our eurrent understanding of the proeesses thought to eontribute to gravity wave saturation in Seetion 2. These include linear instability meehanisms and nonlinear wave-wave and wave-vortieal mode interaetions. Both theoretieal studies and available atmospherie and laboratory observations suggest that linear instability proeesses may provide the most likely limits on gravity wave amplitudes. Nonlinear interaetions may, nevertheless, be important in determining the evolution and effeets of the overall wave speetrum. The implieations of saturation for gravity wave momentum and energy transports and for turbulent diffusion will be examined in Seetion 3. Consistent with theoretieal expeetations, the dominant wave fluxes appear to be assoeiated with wave motions with high intrinsie frequeneies and phase speeds. Also observed is a vertieal wavenumber speetrum with a nearly universal amplitude at high wavenumbers that is eonsistent with that predieted by linear saturation theory. Reeent indieations of the temporal and geographie variability of the gravity wave speetrum are reviewed in Seetion 4. This speetral variability implies eonsiderable variability in the signifieant gravity wave

sourees and/or filtering eonditions as well as in their middle atmosphere effeets. The eonclusions are presented in Seetion 5.


2. Saturation Theories and Observations

Observations of wind and temperature fluctuations in the middle atmosphere, now widely attributed to internal gravity waves, have shown both the amplitudes and the vertical wavelengths to increase with height, but more slowly than implied by the decrease in density in the absence of dissipation (see FRITTS, 1984). Also apparent in the data is a tendency for the velocity shears and the temperature gradients to be bounded, with representative values being near that required to achieve local convective (or static) instability. A number of theories have been advanced to explain either the apparent amplitude limits or the evolution of and interactions within the motion spectrum. These range from linear studies of the gravity wave amplitudes and time scales required for convective or dynamical instability to nonlinear studies of the resonant and nonresonant interactions among gravity waves or between gravity waves and other modes ofmotion. Several authors have also suggested that the motion spectrum may be largely a manifestation of quasi-geostrophic (quasi-two-dimensional) turbulence. This interpretation, however, appears to be contradicted by some of the observation al data discussed in this paper. Our purpose in this section is to review the theories pertaining to gravity wave saturation, with emphasis on work subsequent to the review by FRITTS

( 1984).

a. Linear Saturation Theory

Linear theory was first used to address gravity wave instability and turbulence production by HODGES (1967, 1969) assuming a vertical convective instability of the wave field. This leads to a threshold for wave instability that is independent of wave frequency given by

(I)

or

u' = c - ü, (2)

where () and u are potential temperature and horizontal velocity in the direction of wave propagation, primes and overbars denote the usual perturbation and mean quantities, subscripts denote differentiation, and c is the horizontal phase speed of the wave motion. The assumption implicit in this theory is that any wave amplitude in excess of the threshold value will lead to instability and the production of turbulence that acts to prevent further growth of the wave amplitude.

More recently, it was suggested by FRITTS (1984) and shown by DUNKERTON

(1984) and FRITTS and RASTOGI (1985) that wave motions can be dynamically unstable (as measured along a vertical axis) at substantially smaller wave amplitudes for intrinsic frequencies near the inertial frequency, OJ '" f, due to the

transverse shear in the velocity field of such motions. The threshold amplitude assuming a minimum Richardson number of 1/4 is given by (FRITTS et al., 1988a)

u' ()~ 2(1 -[210)2) 1/2

(c - ü) = {Jz = 1 + (1 -[210)2)1/2' (3)

This threshold is shown as a function of 11m in Figure l. It must be noted here,

however, that while the amplitude required for instability (scaled by the intrinsic phase speed) falls to zero at f, the vertical shear of the velocity field at the threshold amplitude actually increases to a value of u~ = 2N due to the increase in the vertical wavenumber as 0) approaches/(FRITTs et al., 1988a). Thus, it is important to keep in mi nd what measure of wave amplitude is being used in assessing the conditions for wave instability.

The linear theory was generalized by HINES (1971) and more completely by HINES (1987), for the case of convective instability, to account for possible slantwise instability along a path of arbitrary orientation. Hines examined both the threshold for instability for various growth rates and the axis of maximum instability and concluded that slantwise static instability (SSI), of which the vertical convective instability considered by HODGES (1967) is a special ca se, is the more likely mode of instability. The amplitudes inferred by HIN ES (1988) for vertical and maximum slantwise instability are shown for various growth rates in Figure 2. What is significant here is that, under the assumptions made, slantwise instability is always dominant, with the axis of maximum instability more nearly horizontal than

1.0 ----------------

.8

.2

o~--~----~--~----~--~ o .2 .4 f/w

Figure 1

.6 .8 1.0

Norrnalized wave amplitude required for dynamical instability (Ri < 1/4) as a function of I/w, assum ing a vertical stability axis. The wave amplitude required for convective instability is shown by a

dashed line.

348

1.4

1.2

1.0

0.8

David C. Fritts

U; /

I /

/

"

, ß ..... ,

,12 2 , /

/ I

, ,

--:=;.-_"<.-..9_-

0.6P------__

0.4

0.2

~ __ ~~--~~--_L----~----~w/N 0.2 0.4 0.6 0.8 1.0

Figure 2

PAGEOPH,

Normalized wave amplitude required for SSI (solid) and VSI (dashed) for various growth rates, ß, normalized by wave frequency as a function of w IN. In all cases, SSI is predicted at smaller amplitudes

than VSI.

vertical for reasonable growth rates or turbulence lifetimes. These results imply a more anisotropie turbulence spectrum than anticipated in the classicallinear theory and may provide a ready means of excitation at small scales of the vortical mode (quasi-two-dimensional turbulence with essentially vertical vorticity) in the atmosphere, thought to be important by some authors (GAGE, 1979; LILL Y, 1983). This extension of the linear theory also provides for a means of estimating instability growth rates based on observed saturated wave amplitudes and suggests, if the theory can be applied reasonably to a spectrum of superposed gravity wave motions, that growth rates are comparable to intrinsic wave frequencies.

b. Nonlinear Interactions

In contrast to the linear saturation theories discussed above, non linear interactions, in general, do not re!y on a threshold wave amplitude for energy exchange, but simply opera te more efficiently for (or among) waves of large amplitudes. These interactions are of two types. Resonant interactions require an (approximate) quantization of total wavenumber and intrinsic frequency such that the sum or

Val. 130, 1989 Gravity Wave Saturation Processes 349

difference for an interacting pair must equal that of the third wave, k] ± kz = k3 and w] ± w 2 = w 3 • Resonant interaction theory is also most appropriate for waves of sm all amplitudes, a condition that is of dubious relevance to middle atmosphere gravity waves. Nonresonant or off-resonant interactions, on the other hand, become more significant at large wave amplitudes, may involve other wave components, and are poorly approximated by weak (resonant) interaction theory. For a more detailed discussion of nonlinear interactions among gravity waves in an oceanic context, the reader is referred to the review by MULLER et al. (1986). Our objective he re is to summarize what is currently understood about the role of nonlinear interactions in amiddIe atmosphere context.

As in the ocean, much of our knowledge of nonlinear interactions among gravity waves in the atmosphere has co me from application of weak, or resonant, interaction theory. This followed closely the early work of HASSELMANN (1967) and McCoMAs and BRETHERTON (1977), who first identified the three dominant resonant interaction triads: induced diffusion, elastic scattering, and the parametric subharmonic instability. These are the interactions that permit an efficient energy exchange while simultaneously satisfying the resonance conditions and the gravity wave dispersion relation. Of these, induced diffusion amounts to a random walk of the wavenumber in response to a smalI, near-vertically oriented, wavenumber motion with low intrinsic frequency. Elastic scattering involves an interaction between a high-frequency wave motion and a low-frequency motion with approximately half the vertical scale and drives this component of the wave spectrum towards an equilibration of upward and down ward propagating waves. Of the three interactions, the parametric subharmonic instability (PSI) is alm ost certain to be the most relevant in terms of effecting a transfer of energy in the atmosphere to smaller scales of motion. The PSI involves the decay of a large-scale motion of low frequency via excitation of upward and downward propagating motions at primarily smaller vertical scales and approximately half the parent wave frequency.

These interactions have been considered in an atmospheric context by YEH and LIU (1981, 1985) and found to be of potential significance in the decay of wave motions under various circumstances. Elastic scattering was found to operate efficiently for motions with small scales and relatively high frequencies, whereas induced diffusion was found to have small interaction times for either very small horizontal or vertical scales. The PSI, on the other hand, operates most efficiently on waves with relatively low intrinsic frequencies and sm all scales. These results imply that such interactions should be important for motions with small vertical wavelengths but relatively less significant for the more energetic wave motions with larger vertical wavelengths.

More recently, INHESTER (1987), DUNKERToN (1987), and DONG and YEH (1988) have considered further the implications of such interactions. Wave packet localization and nonuniform stratification were found by INHESTER (1987) to lead to threshold PSI amplitudes and smaller interaction rates. DUNKERTON (1987)


addressed the effects of the PSI on the momentum flux of the wave field and concluded, in accordance with the study by FRITTS (1985), that nonlinearity serves to reduce the momentum flux through excitation of other wave motions but fails to prevent the attainment of linearly unstable wave amplitudes. DONG and YEH ( 1988) considered both resonant and nonresonant interactions among gravity waves and between gravity waves and acoustic and vortical modes of motion. They concluded that gravity wave-acoustic wave interactions are unlikely to be significant, but that the nonresonant interaction of a gravity wave and two vortical modes would occur above a threshold wave amplitude of u' = 21/2 (c - ü). This could prove to be an efficient me ans of transferring energy from the gravity wave field to the vortical mode, but it is uncertain how frequently it could operate as the threshold amplitude is above that required for linear wave instability and mean wave amplitudes observed in the atmosphere (see above and Section 3).

Other recent studies have attempted to address the relative importance of competing amplitude-limiting mechanisms within the gravity wave field. WEINSTOCK (1985) suggested that the buoyancy sub range theory of LUMLEY (1964) could be used as an appropriate framework within which to understand the high wavenumber portion of atmospheric vertical wavenumber spectra, which are seen to have a near universal amplitude and a slope near - 3 (DEWAN et al., 1984; SMITH et al., 1987; FRITTS et al., 1988a). If appropriate, this would imply a range of vertical wavenumbers over which gravity wave interactions are strong and rapid.

To address the relative importance of linear wave field instabilities and nonlinear interactions for vertical wavelengths appropriate to the middle atmosphere, FRITTS (1985) performed numerical simulations of gravity wave propagation and saturation under the influence of convective adjustment and fully nonlinearity. The results of these experiments suggest that while nonlinear interactions are able to restrain wave amplitudes to some degree, they are unable to prevent the occurrence of wave amplitudes sufficient to induce linear convective or dynamical instabilities within the wave field. Fritts concluded, therefore, that nonlinear wave-wave interactions were not the principal mechanism for limiting wave amplitudes at large vertical scales, but rather that gravity wave saturation at these scales must involve a rapid cascade of energy into turbulence. This does not imply, however, that the saturation mechanism is linear-which it demonstrably is not-but only that linear theory provides a reasonable guide to the wave amplitudes at which such processes become significant.

c. Observations oi Wave Saturation

There have been relatively few detailed studies to date of the processes and effects of gravity wave saturation in the atmosphere due to observational constraints. Perhaps the best known of these is in association with downslope wind storms occasionally observed in the lee of major mountain barriers (LILLY and


KENNEDY, 1973; LILLY, 1978). Aircraft observations during such events reveal a large-amplitude wave structure with intense turbulence occurring where the largescale wave field is convectively unstable. Observations of gravity wave instability and turbulence generation in the laboratory were reviewed by FRITIS (1984) and FRITTS and RASTOGI (1985) and likewise suggest that instability associated with large-amplitude wave motions is consistent with expectations of linear theory.

More recently, several studies have addressed the association of atmospheric turbulence with gravity wave structure using radar, balloon, and rocket velocity and temperature data in the stratosphere and mesosphere. TSUDA et al. (1985) used Arecibo UHF radar data to examine the correlation between echo power and wind shear and found a maximum correlation at a lag of ~ 500 m, in good agreement with predictions of linear theory (FRITTS and RASTOGI, 1985) for the dominant wave scales of Az ~ 2 km. SIDI and BARAT (1986) and COT and BARAT (1986) used high-resolution balloon data to examine the inertia-gravity wave oscillations and their associated turbulence in the stratosphere. It was found. that turbulence layers occurred preferentially near wind maxima (see Figure 3) rather than in regions of maximum shear, due to the occurrence of minimum static stability at the level of maximum shear in the (smaller) transverse component of the horizontal velocity field, again consistent with linear theory (see FRITIS and RASTOGI, 1985). Such layers also generally were associated with small positive Richardson numbers, suggestive of a dynamical instability of the low-frequency wave field.

A study using the MST radar and rocket-derived wind and temperature fields at Poker Flat, Alaska, by FRITTS et al. (1988b) provided evidence of the wave amplitudes and processes leading to wave saturation and turbulence production in

28000

E

'" 0 :J .... ~ -' ~ 27000

o 2 6

LIGHT

LIGHT

lIGltl

LIGHT

8

MAGNITUDE f)F lHE RELATIVE WIND (m.· I)

Figure 3

10

Correlation of wind magnitude with occurrence of c1ear air turbulence observed with a high-resolution balloon. Note that instability appears at maxima of the wind rather than the wind shear.


the mesosphere and lower thermosphere. The horizontal velocity field obtained during one phase of this experiment is shown in Figure 4 and reveals the presence of a large-scale, low-frequency wave motion that caused the velocity vector to rotate clockwise with increasing time and height. This velocity field, together with the associated temperature field obtained using a rocket probe, was used to infer the structure, direction of propagation, and phase of maximum instability of the dominant wave motion. The radar signal-to-noise (S jN), which provides a strong indication of the location and intensity of turbulence, was likewise found to be weH correlated with the phase of maximum instability (see Figure 5). As in the stratospheric studies described above, these observations suggest a dynamical instability of the low-frequency wave motion and turbulence that was localized and strongly concentrated at that phase of the wave motion anticipated to be most unstable on the basis of linear theory (see FRITTS and RASTOGI, 1985). Also

.I::

.Q"l (l)

I 84

POKER FLAT MST RADAR 15 June 1983

HORIZONTAL WIND VECTORS (15 Minute Averaged Value)

SOmls

/

80~~~~~~~~~~~~~~~~~~~ o 4 8 12 16 20 24

Local Time

Figure 4 Horizontal wind vectors showing the large-scale wind field during the STATE experiment at Poker Flat

in lune 1983. Note the dominant motion with aperiod near 7 hrs.

Vol. 130, 1989

j: 85 <!l LU J:

Gravity Wave Saturation Processes

S/N 15 JUNE

-- 20 db --- 10 db .......... 0 db

80~--~--~--~L---~ __ -L __ ~ __ ~

10 12 14 16 18 20 22 24

lOCAl TIME (hr)

Figure 5

353

Signal-to-noise (SjN) for the last 14 hours of the velocity data shown in Figure 4. The slanted lines show the inferred position of the most unstable phase of the dominant wave motion and exhibit an excellent

correspondence with the occurrence of large SjN.

observed at smaller scales near the locations of maximum instability were wave motions exceeding nominal saturated amplitudes that were suggested to have been generated in situ via wave-wave or wave-turbulence interactions. Other evidence of possible wave excitation via the PSI was reported by KLOSTERMEYER (1984).

The implications of these results for the gravity wave spectrum in the middle atmosphere are several. First, at large vertical scales, at wh ich most of the gravity wave energy resides, wave propagation appears to be reasonably described by linear or weakly nonlinear theory because of the long interaction times and the inability of nonlinear wave-wave interactions to restrain wave amplitudes effectively. Once wave motions achieve (linearly) unstable amplitudes, however, nonlinearity must playamajor part in the generation of turbulence and the excitation of additional (smaller-scale) wave motions. This turbulence and small-scale wave generation appears to be largely localized within the wave field and to coincide with the most unstable phase of the large-scale wave field anticipated using linear theory. At smaller vertical scales, where interaction times are predicted to be shorter and wave scales are closer to the buoyancy ::cale, L b, estimated to be '" 13 and 500-1000 m in the lower stratosphere and mesosphere, respectively, by HOCKING (1983) and WEINSTOCK (1985), nonlinear interactions are likely to playamore fundamental role in the evolution of and the energy exchange within the wave/turbulence spectrum. These conclusions are also consistent with the observational results discussed in the following section.


3. Implications of Gravity Wave Saturation

a. Energy and Momentum Fluxes and Divergence

Observations of gravity wave structure cited in the previous section suggest that wave amplitudes are limited by saturation processes to values generally c0l!-sistent with eqs. (I) and (2). Assuming this to be true for all wave motions, we can infer that portion of the wave spectrum that contributes preferentially to the vertical fluxes of momentum and energy. For wave motions with intrinsic frequencies such that.f ~ w 2 ~ N 2, these fluxes may be written approximately as

-,-, w ( -)2 uw~-c-u

N ( 4)

and

w 3 (5) c E ~ - (c - u) gz N .

Thus, gravity wave moment um and energy fluxes should be dominated by those motions with high intrinsic frequencies and large horizontal phase speeds (or vertical wavelengths). At frequencies w ~ f, these fluxes are reduced even furt her due to the reduction of the vertical wavenumber (and of the vertical group velocity) by rotational effects.

Gravity wave saturation results in the convergence of momentum and energy fluxes, causing a net deceleration of the zonal mean flow and a turbulent heating of the environment. The magnitude of the drag can be inferred from the strength of the observed mean meridional circulation (NASTROM et al., 1982), from satellite estimates of the momentum budget or geostrophic wind (SMITH and LYJAK, 1985; LABITZKE et al., 1987), or from direct measurements of the momentum flux convergence using radar techniques (VINCENT and REID, 1983; FRITTS and VINCENT, 1987; REID and VINCENT, 1987a; AVERY and BALSLEY, 1989). All of these techniques suggest a zonal drag of ~ 20-100 mjsjday in the mesosphere and 10wer thermosphere, consistent with that required to explain the observed circulation and thermal structure of this region. Observations in the lower stratosphere by FRITTS et al. (1989) suggest a zonal drag of ~ 1-2 mjsjday and appear consistent with expectations based on models of the general circulation (PALMER et al., 1986; McF ARLANE, 1987).

Finally, several studies have revealed that the dominant moment um flux is associated with wave motions with high intrinsic frequencies. FRITTS and VINCENT (1987) found ~ 70% of the moment um flux and divergence in the mesosphere and

lower thermosphere at Adelaide to be associated with waves with periods less than Ihr during an 8-day period in June 1984 (see Figure 6), consistent with the inferences above and the more quantitative estimate by FRITTS (1984). A similar

Vol. 130, 1989 Gravity Wave Saturation Processes

ZONAL MOMENTUM FLUXES JUNE 9-17 100,-----------------------,

t-I '2

90

w BO I

70

-- 8mm-lhr

~ - Bmln -8hr

- Bmln -24hr ~

/' ::------

'~

-:/ \, ~

~',,~ '~ //

~-------~----------

-6 - \ - 4 - J - 2

U'W' Im 2s- 2 }

Figure 6

355

Mean zonal moment um !lux profiles for three ranges of gravity wave periods during an 8-day observation in Adelaide in lune 1984.

conclusion was reaehed by REID and VINCENT (1987a). Likewise, FRITTS el al. (1989) inferred that most of the momentum Bux in the 10wer stratosphere during a 6-day observation was due to wave motions with high intrinsie frequeneies, despite its appearanee at lower observed frequeneies.

b. Heat and Constituent Fluxes

The observational and theoretieal studies of wave interaetion and dissipation ei ted earlier suggest that the most likely meehanism of wave saturation is via a loeal instability of the wave field resulting in the loeal generation of turbulenee. The resulting turbulenee appears to be most intense in that portion of the wave field where the statie stability is small or negative, shown sehematieally by the shaded region in Figure 7. CHAO and SCHOEBERL (1984) suggested that this should lead to a redueed dissipation of the wave in the thermal field and a Prandtl number greater than I. An additional eonsequenee of this is that the turbulenee will aet on thermal and eonstituent gradients that are potentially mueh smaller that mean gradients and thus eause a sm aller net diffusion than if the turbulenee were distributed uniformly. These ideas were quantified by FRITTS and DUNKERTON (1985) and COY and FRITTS (1988), who derived the dependenee of the Prandtl number on wave amplitude and the distribution of turbulenee. The net effeet of this proeess is that turbulenee may aet strongly to dissipate wave energy, yet only weakly to diffuse

356 David C. Fritts

x

Figure 7

>0 oz

PAGEOPH,

Schematic of the occurrence of turbulence due to an unstable gravity wave. The shaded region is convectively unstable and is a region in which strong turbulence will cause only a small diffusion.

heat and constituents. Subsequent studies by STROBEL et al. (1985) and STROBEL et

al. ( 1987) have addressed the consequences of various levels of turbulent diffusion for the thermal and constituent profiles and served to confirm these theoretical predictions, suggesting Pr - 3-10.

c. A Saturated Gravity Wave Spectrum

Another result of gravity wave saturation that has potentially significant im pli cations in the lower and middle atmosphere is the attainment of a near-universal spectral amplitude at large vertical wavenumbers due to wave superposition and wave field instability. DEWAN and GOOD (1986) argued that dynamicalor convective instabilities of the wave field should cause the saturated power spectral density of horizontal velocity to vary as Fu(m) - bN21m 3, where b is a constant and N and mare the Brunt-Väisälä frequency and the vertical wavenumber. By integrating the contributions to the variance of potential temperature gradient over all wavenumbers, SMITH et al. (1987) inferred a coefficient b - 1/6 for a spectrum of waves at marginal saturated amplitudes. The resulting saturated power spectral densities for velocity

and normalized temperature (T' I T) due to hydrostatic wave motions, assuming a frequency spectrum for total wave energy of the form cu - P with p = 5/3, are

and

I N 2

F~(m) ~ 6 m3 ( 6)

(7)


These saturated spectral amplitudes are in excellent agreement with the observations of ENDLICH et al. (1969), DEW AN et al. (1984), SMITH et al. (1987), FRITTS et al. (l988a), and SmI et al. (1988). The average velocity and normalized temperature spectra obtained by FRITTS et al. (1988a) are shown in Figure 8 and reveal a dose correspondence between the observed and predicted amplitudes and slopes at high vertical wavenumbers.

At low vertical wavenumbers, the atmospheric motion spectrum departs from saturated amplitudes (SMITH et al., 1987; FRITTS and CHOU, 1987; SmI et al., 1988) and appears generally consistent with the form assumed appropriate for the ocean (GARRETT and MUNK, 1972, 1975; DESAUBIES, 1976). As noted by VANZANDT and FRITTS (1989), however, it is necessary to have a positive slope of Fu(m) at low wavenumbers in order to insure that the vertical flux of wave action remains finite. A form consistent with atmospheric observations is

(8)

where s is the asymptotic slope at sm all m. The departure of the vertical wavenumber spectrum from saturated amplitudes at small m also can account for the growth of wave energy (per unit mass) with height (SMITH et al., 1987). These authors noted that wave growth at small m with amplitude limits at large m would lead to a slower than exponential growth of wave energy and a growth of the dominant vertical scale (a reduction of m*) with increasing height, results that generally are consistent with observed increases of wave seal es and energies with height (BALSLEY and CARTER, 1982; FRITTS, 1984; BALSLEY and GARELLO, 1985). The more gradual than exponential growth of wave energy with height also implies a smooth increase with height of both the turbulent diffusion and the momentum flux convergence arising from gravity wave saturation and invalidates the notion of a wave breaking level based on monochromatic wave theory.

Despite the apparent utility of the saturated spectrum concept, there are reasons to believe that the gravity wave spectrum may undergo systematic changes in response to variations in the environment that depart from normal growth with height at sm all m. This can be seen by noting that the saturated momentum flux for individual wave motion given by eg. (4) depends on both ü(z) and N(z). As a result, wave motions that experience areduction in the intrinsic phase speed (e - ü) will dissipate preferentially while those that experience an increase in (e - ü) will grow with height. This results in a filtering of the gravity wave spectrum (LINDZEN, 1981, 1985) and also may account for much of the geographie, seasonal, and short-term variability observed in a variety of observational and numerical studies (MEEK et al., 1985a; MIYAHARA et al., 1986; FRITTS and VINCENT, 1987; VINCENT and FRITTS, 1987; REm and VINCENT, 1987a). Likewise, wave motions that

encounter an increase in N should experience enhanced saturation and a reduction in the vertical energy and momentum fluxes. These arguments were guantified by


lOS --~---- uP ! i

a -;-U i I I ,. 10'

U g /

,. " ~ (ij Ir.' ~ .! ;;; ,. z .. 0- 0 u; I ,. Z w "

::: I 0 a: .. ,.

~ " a: .. z w

10" - - -10 • I 10·l

10 q 11 , 10 2

WAvENUMBER (CYC/M) WAVENUMBEFI (CYC/MJ

2.0 ----- SO-IO" - - -- - .. I e C .qC;.tO Fi d

E .q!'1 · 10·"

...

(\ lS-IO &

E 0- I 1 ", - 10 b ~ I z :" I r ;-; -10 •

/ z 0

~ ' IO () " >-

" 1 'j ~Ia b a: w Z I _10 6

"" w

,. I 5'10

o l 0 I 1 10 1 10 • 10 1

WAVENUMBER (CYC/M) WAVENUMBER (CYC/M)

Figure 8 Mean power spectral densities a) of eastward plus northward radial velocity and b) of normalized temperature at 5- 12.5 (--), 12.5-20.5 (--), and 20.5- 30 (- - -) km heights measured at the MU observatory. The long dashed Iines show the predicted saturated spectral amplitudes for the 12.5-20.5 km height range. Shown in c) and d) are the corresponding area-preserving spectra. Note the excellent

agreement with the predicted amplitudes at high wavenumbers in the stratosphere.

V ANZANDT and FRITTS (1989) and appear to account for the needed wave drag and enhanced radar eehoes near the tropopause (LARSEN and ROTTGER, 1982; PALMER et al., 1986; TANAKA, 1986; T. TSUDA, private eommunication, 1986) and the highlatitude summer mesopause (BALSLEY et al., 1983; FRITTS et al. , 1988b). The saturated spectrum and its variations with height and environment may, therefore, provide a eonvenient framework within whieh to deve10p a useful parameterization of gravity wave drag and diffusion in the lower and middle atmosphere.

4. Gravity Wave Variability

Gravity waves have been known for many years to produee fluetuations in temperature, density, ve1oeity, eonstituent coneentrations, and emission intensities. Yet it has only been in the last few years that the extent of the geographie and


temporal variability of the gravity wave speetrum and its effeets have begun to be reeognized. The purposes of this seetion are to review some of the enormous variability and to present evidenee of some of the major sourees of this variability in the lower and middle atmosphere. For eonvenienee, we will emphasize here the studies performed foIlowing the review by FRITTS (1984).

As deseribed in the previous seetion, observations suggest that the atmospherie gravity wave speetrum exhibits eonsiderable universality of amplitude at large m due to saturation proeesses (VANZANDT, 1982, 1985; DEwAN and GOOD, 1986; SMITH et al., 1987; FRITTS et al., 1988a). There are many reasons to expeet, however, that the wavenumber and frequeney eomposition and the degree of anisotropy of the wave speetrum may vary eonsiderably with time and loeation. This variability must arise in part in response to geographie and temporal variations in the strengths of the important gravity wave souree meehanisms. But equaIly important, perhaps, are the interaetions of gravity waves with and their filtering by the variable environments through whieh they must propagate.

An exeeIlent example of the geographie variability of a signifieant souree of gravity wave motions and of the effects of filtering of those motions by the atmospherie wind field is the numerieal study by MIYAHARA et al. (1986) using the GFDL "SKYHI" model. These authors found that the direet simulation of gravity waves excited by eonveetion in a high-resolution GeM eould aeeount, if erudely, for the principal effeets of gravity waves anticipated from previous theoretical, parametrie, and observational studies. In partieular, the modulation of eonveetive aetivity in the troposphere was seen to impose signifieant geographie variability on the momentum flux distribution at low latitudes in the summer hemisphere (see Figure 9a) due to the propagation of (artificiaIly) long waves out of the equatorial region. Likewise, gravity waves exeited by eonveetion at middle and high latitudes in the winter hemisphere were found to be strongly filtered by loeal wind profiles modulated by large-seale planetary waves (see Figure 9b), resulting in a momentum flux distribution at greater heights that exhibited maxima (opposing the flow) above zones of large zonal wind speed. Thus, modeling studies ean provide important insights into gravity wave variability that may be diffieult or impossible to obtain using observational teehniques.

Another example of geographie variability of the motion speetrum attributed here to gravity waves is provided by the observational study using GASP data by NASTROM et al. (1987). The principal finding in this study was a pronouneed enhaneement of the amplitude of the motion speetrum (inereases in velocity and temperature varianee of - 2-3) at horizontal seales of -4-80 km over rough terrain (the western U.S.) relative to the eastern Pacifie and the east-eentral V.S. Even larger speetral amplitudes were observed by LILL Y and LESTER (1974) in close proximity to major topography. Larger speetral amplitudes over topography imply as weIl higher intrinsic phase speeds and the potential for substantially larger momentum fluxes than over smooth terrain, as diseussed by NASTROM et al. (1987).

360

(a)

(b)

David C. Fritts

_u'w,t (lO-5ms l mb sec l ) at .03mb 26 JAN.-14 FEB. N.P . .,-----'------'-------------~

w Cl

S.P.

N.P.

~ EG. i= ::s

S.P.

-0.2

o -0.2

o

0 90 180 270 360

LONGITUDE

t -1 IT (m sec ) at 03mb 26 JAN -14 FEB - ~cqo- J

~"~ ~~ 30 V 60

2iP -' 40 ..::::::;

C' 50:"-30 _20__ ~ =-- ---10-

0 10

20 -30 40 50

-60 70

70 SO

30_ 10

o 90 180 270 360

LONGITUDE

Figure 9

PAGEOPH,

Time-mean of a) the momentum flux in pressure coordinates and b) the zonal mean flow at 0.03 mb (-70 km) computed by the GFDL "SKYHI" model. The momentum flux exhibits three maxima in the Southern Hemisphere resulting from the equatorial convective hot spots. The modulation of the flux in

the Northern Hemisphere is due to filtering by the planetary wave field.

Thus, there is evidenee that topography may eontribute substantially to the exeitation of the gravity wave speetrum and to the geographie variability of gravity wave effeets in the lower and middle atmosphere. Other sourees, sueh as wind shear,


convection, and geostrophic adjustment, are also likely to be important and to contribute to geographie variability (as noted in the study by MIY AHARA et al., 1986), but are less quantified at this time.

Temporal variability of the gravity wave spectrum is likewise considerable and is apparent on a wide range of scales. Seasonal trends are evident in long-term climatologies (MEEK et al., 1985a; VINCENT and FRITTS, 1987), with maximum gravity wave energies occurring in summer and winter and minima near equinoxes. These seasonal variations appear to be more pronounced for waves with higher frequencies due, perhaps, to the more nearly horizontal propagation of waves at low intrinsic frequencies and their smaller sensitivity to filtering by the local mean flow. The equinoctal minima also appear to be well correlated with the transitions from winter westerlies to summer easterlies, providing further evidence of the importance of filtering processes in shaping the gravity wave spectrum at greater heights. Similar trends have been proposed to account for seasonal variations of 0 3 at mesospheric heights due to induced variations in the turbulent transports of other chemically active species by THOMAS et al. (1984). This suggestion has received some support from a long-term study of turbulence intensities by HOCKING (1987).

Variations in gravity wave energies and momentum fluxes on planetary wave time scales have also been noted in a number of studies. Gravity waveenergy variations with periods of 5~ I 0 days are present in the mesospheric climatologies that are available (MEEK et al., 1985a; VINCENT and FRITTS, 1987) and appear to correspond closely to the time scales of variations in the observed zonal and meridional winds due to planetary waves. Similar variations are observed in the time series of vertical and oblique velocities obtained by various radars in the troposphere and lower stratosphere (ECKLUND et al., 1982; GAGE and BALSLEY, 1984; ECKLUND et al., 1986; FRITTS and CHOU, 1987) and likewise imply a strong modulation of gravity wave sources or filtering conditions by planetary wave activity. The study by ECKLUND er al. (1982) found that the vertical velocity variance was correlated strongly with the strength of the 500 mb zonal wind (see Figure 10), suggesting that the wind shear may play a significant role in the excitation of gravity waves with a high intrinsic frequencies (and momentum fluxes).

There is also considerable evidence of gravity wave and turbulence variability on time scales of a day or less. Recently, FRITTS and VINCENT (1987) and REID and VINCENT (1987a) observed significant fluctuations of wave energies and momentum fluxes in the mesosphere and lower thermosphere, due apparently to modulation of the wave spectrum by the diurnal and semi-diurnal tidal motions. This effect was found to be very significant when the tidal amplitudes were large and to cause large diurnal variations in the induced drag at a particular phase of the diurnal tidal oscillation. Momentum fluxes computed in 8-hr blocks by FRITTS and VINCENT (1987) at various heights during a 3-day period with large tidal amplitudes are shown in Figure 11. The large negative fluxes near 0000 L T coincide with those times during which the tidal shears reversed the zonal mean shear and permitted

362 David C. Fritts

Pla leville Radar Verllcal WindS

2O.2'm .. . -~_ . ....... " ~- -- I~·-"-"·· ·,,- ,.'.'-

(a)

19.0km --- --- ---- ~----_ ... - ~ .. ,. ..... ' ~--...."

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16.6'm

~a,m

~6km

10

N on

N' E

'" u c: 0

~ ~ ü .Q :J; 0

~ ~

~t!"F .. ' ~ .......... ---

=:::=-~:.......- -~ :~~ ~,(:~,f . ::~:~,. =~""'"Y'l ,1,,'

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~. ,. ,'I " ',,~I, 'i>( ' ~ ,I. ,,' ( I .. ' .., ~~

',.. ,lt ' .., ,,- 'I;'. +". I,;. ., ,rr. Iof (t ",,,

12 13 14 I~

500 mb lanal Wind 024 Average Varlance 01 15.4 and 178 km

0.20 016 0.12 0.08 ooq 0

500 mb lonal Wmd Averoge Varlance 01 10.6 and 13.0 km

0.24 0.20 0.16 012 0.08 0.04 0

Q32 0.28 500 mb Zonal W",d

024 Average VOrlance 01 5.8 and 8.2 km

020 0.16 0.12 0.08 0.04 0

25 20 15 10 5 0 5 on ,

E

"0

25 i!l 0. Vl

20 "0

15 c:

~ 10 Ci 5

c: 0

N 0 .0

-5 E

8 lI'l

25 20 15 10 5 0

MARCH 10 12 14 16 ARCH 30 (b) Doy

Figure IO

PAGEOPH,

2m/, .... Up'lllDld

Variability of the vertical velocity observed at the Platteville VHF radar (a) and the correlation between vertical velocity variance and the zonal mean wind at 500 mb at three heights (b).


812

789

14 00

1S 00 16 00

Figure 11 Momentum flux estimates in 8-hr blocks at 2-km intervals for a 3-day period during June 1984 in Adelaide. Note the large diurnal modulation and the down ward phase progression of the fluctuations.

westward propagating wave motions to experience preferential growth with height at lower levels. Tidal influences on gravity wave-induced diffusion have been

suggested to be important in accounting for diurnal variations in 0 3 observed by the Solar Mesosphere Explorer (SME) satellite by BJARNASON et al. (1987). Other

recent studies of the relation between gravity waves and turbulence (e.g., RUSTER,

1984; KLOSTERMEYER and RUSTER, 1984; THRANE et al., 1985; TSUDA et al., 1985; Y AMAMOTO et al., 1987; ROTTGER, 1987; FRITTS et al., 1988b) have revealed

significant modulation of turbulence intensities by the local wave environment on

time scales characteristic of the dominant wave motions.

Another uniquc vicw of gravity wave variability in the mesosphere is provided

by recently available space shuttle re-entry data. The density fluctuations inferred

during two re-entries along virtually identical low-Iatitude ( '" 20°) tracks are shown

in Figure 12 (R. Blanchard, private communication, 1986). These data vary in

altitude from 80-60 km along a ",4000 km path and thus comprise a nearly

horizontal view of the atmospheric motion field. What is particularly striking is the

364

. 10

.05

'<4 '~ 0 .0

-. 05

-. 10 0

10

.05

,~ a..: 00

-. 05

- 10

0

,I~ ,1, ~

"I'

David C. Fritts

1000 2000

Distance (Km)

T

3000 4000

1000 2000 3000 4000

Distance (Km)

Figure 12

PAGEOPH,

Density fluctuations inferred between 80 and 60 km for two space shuttle re-entries over the central Pacific. Note the differences in wave amplitudes and scales between the two.

very different character of the two tracks, which exhibit very different horizontal scales and wave amplitudes. Despite the obvious differences, however, horizontal wavelengths generally are consistent with estimates using radar and other techniques (VINCENT and RElD, 1983; MEEK et al., 1985b; RElD, 1986; RElD and

VINCENT, 1987b) and support the claim that high-frequency, smaJI horizontal scale motions must play an important role in the dynamics of the middle atmosphere (FRITTS, 1984; FRITTS and VINCENT, 1987).


Variations in gravity wave energies and fluxes are observed on short time scales in the lower atmosphere as weil. These arise, no doubt, from episodic or transient wave sources such as wind shear or convective activity and may give rise to a pulsing of wave energy or momentum fluxes. A good example is the moment um flux data obtained by FRITTS et al. ( 1989) using the MU radar shown in Figure 13. This figure illustrates the momentum flux during a 6-day observation calculated using the technique of VINCENT and REID (1983) every 30° (or 45°) of azimuth from north ( top) to south (bottom), averaged between 10 and 19 km, and subjected to a I-hr running average. The resulting data exhibit considerable consistency between adjacent azimuths and reveal significant short-term variability of the moment um flux in the lower stratosphere. Characteristic periods range from ~ 2-20 hours and suggest, as noted above, that high-frequency, small horizontal scale motions must also playa significant role in the transport of energy and momentum in the lower stratosphere.

1q

12

10 C\I ~

rn .... ~

x 8 ::J -' LI..

::Ii ::J 6 I-Z w ::Ii 0 ~ q

2

20 qO 60 80

TIME (HR)

Figure 13

100 120 HO 160

Momentum fluxes inferred with the MU radar at 30° or 45° azimuth increments from north (top) to south (bottom) during a 6-day period in March 1986. Note the good consistency between adjacent

azimuths and the high degree of short-term variability in the fluxes.

5. Conclusions

We have reviewed in this paper the processes thought to lead to gravity wave saturation as weIl as their principal effects and variability in the lower and middle atmosphere. Current theory and observations largely support the view that gravity wave saturation occurs primarily via linear wave field instabilities that ~t locally to dissipate wave energy and produce turbulence. Gravity wave saturation and turbulence generation are nevertheless highly nonlinear and complex processes and will require considerable additional study to achieve a detailed understanding. Nonlinear wave-wave and wave-vortical mode interactions, in contrast, act globally throughout the wave field and appear not to limit wave amplitudes effectively or prevent the occurrence of linear wave field instabilities, except perhaps at sm all vertical scales (Az < I km in the mesosphere). Such nonlinear interactions may, however, effect significant energy exchanges between different scales under certain conditions.

The principal effects of gravity wave saturation are wave amplitude limits generally consistent with linear theory and convergence of wave energy and momentum fluxes. The momentum and energy fluxes and divergences are associated primarily with waves with high intrinsic frequencies and phase speeds because of their larger amplitudes and vertical group velocities. The momentum flux divergence resulting from gravity wave saturation plays a significant role in driving the large-scale circulation of the lower and middle atmosphere, being largely responsible for the closure of the mesospheric jets and the mean meridional circulation in the mesosphere and lower thermosphere. Similar effects are also now believed to be important in the lower atmosphere, where gravity wave drag is thought to be responsible for the small zonal winds and mean poleward drifts near the tropopause.

The convergence of energy flux due to gravity wave saturation leads to turbulence and heating, with turbulence motions likely contributing to the excitation of additional gravity waves and vortical modes as weIl. The turbulence also contributes to the vertical diffusion of heat and constitutents, but likely does not have as great an effect as originally thought due to its occurrence primarily in regions of the wave field that have the smallest static stability.

The spatial and temporal variability of the gravity wave spectrum now appears to be enormous and is only beginning to be fully appreciated. This variability is due in part to the geographic distribution and temporal modulation of the primary gravity wave sources in the lower atmosphere. At greater heights, there appears to be a significant modulation of wave energy and momentum fluxes due to atmospheric filtering conditions as well. Yet our knowledge of gravity wave variability is meager at the present time. Understanding this variability and its effects on the lower and middle atmosphere will likely be one of the exciting challenges in the years ahead.

Vol. 130, 1989 Gravity Wave Saturation Proeesses 367

Acknowledgments

Support for this review was provided by the Division of Atmospheric Sciences of the National Science Foundation under Grant ATM 8404017 and by the SOlO/IST and managed by the Office of Naval Research under contract NOOOl4-86-K --0661.

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(Received Ju1y 27, 1987, revised/aecepted Deeember 16, 1987)


Theory of Internal Gravity Wave Saturation

TIMOTHY J. DUNKERTON 1

Abstract-Gravity wave saturation is an important process affecting the transport and deposition of momentum, heat, and constituents in the earth's atmosphere. This paper informally discusses several saturation mechanisms and their effects, inc1uding convection, Kelvin-Helmholtz instability, vortical mode instability, parametric subharmonic instability, and mean flow interaction. Convective saturation is emphasized. The parameterization of convective adjustment is discussed and a few remarks are made concerning the effects of turbulence localization on the convective saturation process. Several outstanding problems in saturation theory are identified that could be addressed with observational, numerical, and laboratory studies.

Key words: Internal gravity waves, nonlinear instability, transport.

1. Introduction

Recognition of internal gravity waves as an essential ingredient in the atmospheric general circulation has, within the last decade, stimulated a large number of theoretical attempts to parameterize the two major effects of these waves-momenturn flux deposition and turbulent diffusion-for incorporation in large-scale general circulation models. While there is not yet any consensus on how to do this, there is nearly universal agreement that gravity wave saturation is, in some sense, very significant in enhancing these two effects.

Closer inspection reveals the term "saturation" being used in at least two ways: (I) with respect to the limiting amplitude for a near-monochromatic wave or an organized, nonrandom superposition of waves (as over local topography) or (2) with reference to the entire spectrum of waves, interacting nonlinearly. The first meaning can be defined precisely in specific cases, but is limited to grossly simplified spectra. The second meaning appears to be more universal in scope, but is difficult to quantify theoretically, and requires a statistical approach. Consequently, there has been considerable progress in ( I), some of which will be reviewed in the present paper, while (2) remains elusive, except as a linear, statistical variant of (I).

I Northwest Research Associates, Inc., P.O. Box 3027, Bellevue, WA 98009, U.S.A.

374 Timothy J. Dunkerton PAGEOPH,

Much of the difficulty in developing a general theory of nonlinear saturation is due to the imprecision of this concept. By definition, the term "saturation" places a limit on the amount of something an object can hold, like a sponge which, when saturated, cannot have liquid added to it without, at the same time, giving up the same amount someplace else. In practice, the usefulness of "saturation" in nonlinear waves derives from the speed of the nonlinear saturation mechanisms relative to the other time scales involved. In the ca se of local convection, for instance, the instability occurs rapidly enough for saturation to be a viable concept. However, this is not true of nonlinear interactions in general. Some of these are too slow to operate in comparison to the time scales for wave excitation, propagation, and breakdown. With respect to these slower mechanisms, the spectrum is flexible, and does not "saturate" quickly enough.

It might be objected that, if we only waited longer, a saturated spectrum would emerge due to the combined effects of dispersion, breaking, and all nonlinear interactions. There is a basic problem with this idea, however. If we desire a realistic parameterization of heat and momentum transport, the (hypothetical) non linear saturation theory would need to produce an accurate estimate of these transports when averaged over many discrete wave events-i.e., those times when the spectrum is least saturated in the nonlinear sense and (very possibly) transporting the greatest amount of heat and momentum! An accurate estimate is unlikely, however, as a simple example demonstrates. The irreversible deposition of momentum due to a sequence of vertically propagating gravity wave packets differs in its vertical distribution from that due to a single disturbance forced continuously, even when the time-averaged momentum flux at the lower boundary is the same. The difference is greatest when all nonlinear interactions are taken into eonsideration.

Further development and applieation of a general nonlinear saturation theory must await a better understanding of the atmospherie gravity wave speetrum and the nonlinear interaetions important within it. A more traetable task at present is to foeus our attention on the saturation meehanisms that are relatively weIl understood and require a simplified view of the gravity wave speetrum. These meehanisms include eonveetion, Kelvin-Helmholtz instability, vortieal mode instability, parametrie subharmonie instability, and mean flow interaetion (Seetions 3-6 and 3d, respeetively). It will be shown that eonvection is the most important of these in the sense that, for nonrotating hydrostatic waves, none of the other mechanisms ean prevent the initial evolution to a eonveetively unstable state in a smoothly-varying quasi-compressible atmosphere. Emphasis is given to the parameterization of eonveetive adjustment, and so me effects of turbulenee localization are reviewed. A summary and outlook on gravity wave saturation theory is given in the final seetion.

Many of the observational aspects of gravity wave saturation were reviewed by FRITTS (1984) and FRITTS and RASTOGI ( 1985). The present paper will eonfine itself to the theory of gravity wave saturation and the identification of outstanding problems that could be addressed without observational, numerical, and laboratory studies.

Vol. 130, !989 Theory of Interna! Gravity Wave Saturation 375

2. Governing Equations and Wave Action Law

For hydrostatic motion in log-pressure coordinates (HOLTON, 1975), a suitable set of governing equations is

Ut + UUx + v(uy - f) + WUz + tPx = - X

Vt + u(vx + f) + vVy + wVz + tPy = - y

~t + u~x + V~y + w(N2 + ~z) = - Q

1 Ux + vy + -(Pow)z = 0

Po

(2.1a)

(2.1b)

(2.1c)

(2.1d)

(2.1e)

where u, v, and ware zonal, meridional, and vertical velocity, ~ is a buoyancy variable proportional to the deviation from horizontally-averaged temperature, tP is geopotential, and N 2 is the Brunt-Väisälä frequency squared. Spatial position is denoted by x, y, z (longitude, latitude, and height, respectively), and t is time. The Coriolis parameter f is taken to be constant, and arbitrary body forces X, Y and thermodynamic source Q are allowed on the rhs of (2.1a-c). This set is essentially the same as that used by ANDREws and McINTYRE (1976) except for the exponential basic state density profile introduced in (2.1d), Po = Ps exp-zjH. Generalizations to the nonhydrostatie, fully compressible, spherieal case are not warranted here.

An important quadratic conservation law proceeding from (2.1a-e) is the so-called wave action law

o --1----ot [~~(ut - frf') + '1~v'] + ('1~tP')y + Po (PoCtP')z + ~~X' + '1~Y' + Cq' = 0 (2.2)

obtained by introducing the field variables

Dt~' == ut == U' + r/'uy + C'uz (2.3a)

(2.3b)

(2.3c)

(2.3d)

of which the first three are linearized displacements, the primes denoting departures from the zonally symmetrie state. This conservation law is formally nonlinear if the source terms are modified to include tripie correlations (ANDREWS and McINTYRE, 1976). Those authors also noted the central role of (2.2) as a stepping-stone to the generalized Eliassen-Palm theorem. In the present context we will instead utilize (2.2) as a wave amplitude equation. This procedure is essentially equivalent, e.g., to that of LINDZEN (1971) and HOLTON (1975) in describing slow variations of


equatorial wave amplitudes. In my experience the significance of ANDREWS and McINTYRE'S derivation of (2.2) lies mainly in its generality and direct physical relation to the Lagrangian conservation laws, such as the Kelvin and Bjerknes circulation theorems. Note that, by virtue of the orthogonality of zonal Fourier components, a wave action law of the form (2.2) applies to each component individually.

3. Convective Instability

The most widely discussed mechanism of gravity wave saturation in recent literature is the amplitude-limiting effect due to convection in regions of overturned isentropic surfaces. Gravity waves owe their existence to the restoring effect of the mean state's stable stratification, but when the amplitude of these waves grows to a critical value, the isentropic surfaces become locally vertical. In a frame of reference moving with the wave, the fluid is stationary at this point, except for a small upward velocity component (for hydrostatic waves having upward group velocity); the perturbation horizontal velocity is equal and opposite to the me an flow seen by the observer. As the wave amplitude grows beyond this critical value, the fluid becomes statically unstable. It is most common to consider plane waves, in wh ich the regions of instability align themselves parallel to the phase fronts. Note, incidentally, that the amplitude threshold for rapidly-growing convection in hydrostatic (but not nonhydrostatic) waves is nearly the same for vertical and slantwise instability (HINES, 1988); therefore it suffices to use the traditional ÜRLANSKI and BRYAN (1969) criterion as a convective threshold in this limit.

Local convective instability in internal gravity waves has not been as widely documented in atmospheric observations as, for example, the breakdown of KelvinHelmholtz (KH) instabilities, but its existence is indisputable based upon laboratory and numerical evidence. Convective turbulence has also been associated with the breakdown of topographically-induced resonances and hydraulic jumps. Perhaps the strongest argument for convective breakdown of superadiabatic gravity waves comes from the corresponding breakdown of Kelvin-Helmholtz instabilities which, unlike plane gravity waves in a low-shear environment, are able to "roll up" and achieve significant superadiabaticity before convection has time to develop. Since convection nevertheless develops and halts further roll-up of the KH disturbance (as observed) the gravity wave, that slowly slides a slab of "heavier" fluid over "lighter" fluid, is much more susceptible to convective breakdown.

This much is obvious, but what is not so obvious are (1) the effect of convective instability on the amplitude growth of the gravity wave, (2) the nature of the resultant turbulent mixing, particularly of heat and constituents, (3) the form of the convective instability, and its effect on the nonlinear evolution of the spectrum, and (4) the degree to which the me an flow can change in response to convective

Vol. 130, 1989 Theory of Interna1 Gravity Wave Saturation 377

breakdown and other nonlinear effects. The remainder of this section will be structured around these four questions.

a. Convective Adjustment

This concept was popularized a long time ago in the context of global circulation modeling, to correct for the destabilizing effect of radiative heating in the troposphere. Since then, it has appeared from time to time in the context of internal gravity waves and tides. Most current interest in convective adjustment sterns from LINDZEN (1981), who laid out the basic theoretical concepts in a cogent way, and placed the problem squarely in the context of the mesospheric momentum budget, where it assurnes its greatest importance.

As the title of LINDZEN'S paper suggests, the convective adjustment or "saturation" hypothesis for internal gravity waves is built on two main ideas: that convection (I) prevents amplitude growth beyond the point of overturning, resulting in stress divergence, and (2) is adequately parameterized in terms of second-order vertical eddy viscosity and diffusivity. Moreover, the hypo thesis was originally designed for near-monochromatic disturbances. First, the linear, steady, conservative gravity wave sets up a (density-weighted) moment um flux constant in height (EUASSEN and PALM, 1960; ANDREWS and McINTYRE, 1976; cf. Section 2b) and induces no mean flow acceleration. In a quasi-compressible atmosphere with no shear, or approaching the critical level, there is amplitude growth with increasing height, causing isentropic overturning at some "breaking" level Zb' Above this level, wherever the calculated amplitude exceeds the threshold for overturning, the convective adjustment hypo thesis requires that the amplitude be restricted to its neutrally stable value. Consequently, the moment um flux in the neutral region is divergent, and the mean flow is subject to a nonzero body force. Second, associated with the neutralized wave is a turbulent viscosity and diffusivity, assumed equal, which are exactly enough to account for the cessation of amplitude growth with height.

We may quantify these relationships with complex wavenumbers (LINDZEN, 1981) or in a different, but equivalent, way using the approximate form of the wave action law (2.2)

aA I a 2 - + - - PoW A = -(v + K)m A at Po az g (3.1)

where

(3.2)

is the wave action density for a two-dimensional, hydrostatic, nonrotating, linear


gravity wave (having equipartition of kinetic and available potential energies), and

kc 2

w=g N (3.3)

is the vertical group velocity. In the usual notation k, m, C, N, Po, v, and K denote horizontal and vertical wavenumber, intrinsic phase speed, Brunt-Väisälä frequency, basic state density, viscosity, and diffusivity. Throughout this discussion it will be assumed that N is a constant and that Po = Ps exp - z/H. Also, the quantity kA will frequently be used in place of A since it has the same units as C = c - ü, ü being the mean flow speed.

The approximate wave action law (3.1) makes several important assumptions: (1) the waves are nearly steady and nearly conservative, propagating on a slowlyvarying mean flow; (2) the slowly-varyingness extends to the damping coefficients themselves; (3) the damping process is modeled in terms of conventional second-order mixing, in the vertical direction only (appropriate for hydrostatic waves); and (4) the damping coefficients are independent of the horizontal direction (x). That is to say, the viscous and diffusive damping of the wave field is accomplished on all phases of the wave at exactly the same rate. Moreover, as it is simplest to assume v = K, it follows directly that in the saturated (neutralized) region where

1 kc 3

Bsat = kA sat Wg = 2 N (3.4)

is the saturated momentum flux u'w', the required turbulent viscosity for steady waves is

(LINDZEN, 1981).

v = kc4 [~_ 3üz ]

2N3 H ü-c (3.5)

To illustrate LINDZEN'S parameterization we consider a single wave approaching its critical level in a quasi-compressible atmosphere with shear, shown in Figure 1 (Case 1). The wave action amplitude kA grows slightly faster than exponential with increasing height, due to the decrease in intrinsic phase speed, until the breaking altitude is reached. Thereafter, the amplitude is simply ! C up to the critical level.

The mean flow acceleration (including a viscous contribution) and eddy viscosity coefficeint, shown in Figure 1 b, have the characteristic sudden onset and maximum amplitude at the breaking level, with rapid decrease above this point (DUNKERTON, 1982). The decrease is more evident in the viscosity, due to its stronger fourth-power dependence on C. The reason this quantity maximizes at the breaking level in this case is twofold. First, the intrinsic phase speed is largest at the on set of breaking, so that the vertical wavenumber m (proportional to C -I) is smallest here. To achieve the same viscous dissipation rate (vm 2) the eddy viscosity

30

~ 3

0 ]

3

0

\ a

b J

c km

\ , ,

20-1

IIA

·, 2

0

20

, \(

1

\ \ u

t V

-1

P

r eff

\ 10

-1

kA

\

\ 10

1

0

J I

I J

I J

I I

I j

I I

I I

I I

I I

I I

I I

-30

-1

5

0 15

3

0

-40

0

-20

0

0 2

00

0

.0

0.6

1

.2

1.8

2

.4

-1

ms

1d

ay

-1

m

2s-

1 m

s

Fig

ure

Com

pari

son

of

LIN

DZ

EN

(19

81)

grav

ity

wav

ebre

akin

g pa

ram

eter

izat

ion

(I)

wit

h a

mod

ifie

d sc

hem

e ba

sed

on t

urbu

lenc

e lo

cali

zati

on (

11).

(a)

Mea

n fi

ow a

nd

wav

e ac

tion

am

plit

ude

kA;

(b)

mea

n fi

ow a

ccel

erat

ion

(sol

id)

and

eddy

vis

cosi

ty (

dot-

dash

); (

c) e

ffec

tive

inve

rse

turb

ulen

t P

rand

tl n

umbe

r. W

ave

para

met

ers

are

c =

0 a

nd k

= 2

7[/5

0 km

; N

= .

02 s

-'.

<: ?- w

P

\0

00

\0

-l ::r '" 0 .... '<

0 .., [ '" .... ::s e:. 0 .... po :'i. -< ~

po < '" rJ> po S .... ~

ö'

::s W

-...J

\0


coefficient must maximize at this point. Second, the vertical group velocity (Wg)

varies like c2, so to maintain the required vertical damping scale (Wg /vm 2) the eddy viscosity must be further increased by a factor of c2 , bringing the total dependence to c4 •

It has been noted in the literature, whenever this parameterization is applied, that the breaking altitude can be regarded as somewhat fuzzy due to either the effect of intermittency or a nonlinear cascade. Thus, in numerical models it is common to add some kind of exponential tail below the breaking level that provides for a more smoothly-varying onset of body force and eddy viscosity. However, we may note that the amplitude-limiting assumption discussed above is overly restrictive, and if relaxed somewhat, can smooth these profiles without recourse to intermittency or nonlinearity arguments (however valid they may be). This point was implicit in the numerical results of FRITTS and DUNKERTON (1984) in which convective adjustment was applied locally, rather than uniformly, in the superadiabatic regions of the wave field. We observed slightly larger primary wave amplitudes than allowed by LINDZEN (1981), by about 20%. Since that time I have run a few linear cases, without mean flow acceleration or shear, and found somewhat larger excess amplitudes, by about 50%. An example is shown in Figure 2, using the DUNKERTON and FRITTS (1984) model with the local conveetive adjustment deseribed in that paper. Wave parameters were taken to be c = 40 ms-t, k = 2n/50 km, and Iw'(O)1 = 3.0 ms- 1• The perturbation zonal veloeity of the primary wave was found to exeeed the value for a neutral sine wave. The reason for this is simply that eonveetive adjustment acts only near the superadiabatie region, and not at a distanee kx = n downstream, so that the projection of the neutralized total wave field on the primary wave harmonie exeeeds unity. Equivalently, there is no restrietion on the speed of air pareels opposite the direction of intrinsic phase propagation, under the loeal eonveetive adjustment hypothesis.

The effeet of the loeal thermodynamie adjustment can be approximated by a simpler one-dimensional model of the potential temperature field,

()' = (I- ~ sin(kx + mz + ... ) "m

(3.6)

shown in Figure 3. The dashed li ne indieates the superadiabatie wave before adjustment. The resultant field after adjustment has a projection on the primary harmonie greater than I, with maximum possible amplitude equal to 2 (somewhat larger than in Figure 2-possibly due to vorticity mixing used in the time-dependent code). Of course, in the sawtooth limit, many higher harmonies are required to represent the adjusted field, but if we are not too far in exeess of a = 1 to begin with, these higher harmonies are smalI, and make only a negligible contribution to seeond-order quantities. In physieal spaee, the loeal adjustment is aeting on a small portion of the wave field, and eannot automatieally restriet the amplitude. of the primary harmonie to unity (SCHOEBERL, 1988). This tends to reduee the eddy

Vol. 130, 1989 Theory of Interna1 Gravity Wave Saturation

u~ 1.0~-------------.--------------~

0.8

0.6

0.4

0.2

c

O.O;-,-~~.-~~~~-.~-r-r-r~'

-100 -50 o -I

ms

Figure 2

50 100

381

Horizontal perturbation velocity for the primary wave in a numerical experiment using the convective adjustment scheme of DUNKERTON and FRITTS (1984). Bar at right indicates breaking region. On 1eft

axis Zo = 80 km.

viscosity and mean flow acceleration at the breaking level, as seen in the next section. Before showing this, it is instructive to consider the other major effect of local adjustment: an increase in the effective turbulent Prandtl number for the mean state.

b. Heat and Constituent Transport

The most important insight thus far derived from local convective adjustment is that the turbulent transport of heat and constituents can be significantly less than implied by the assumption K = v i= v(x) (CHAO and SCHOEBERL, 1984; FRITTS and DUNKERTON, 1985; COY and FRITTS, 1988). If it is assumed that mixing occurs primarily in the regions of overturning, the net effect of turbulence is reduced relative to the ca se where turbulence acts on a constituent field undisturbed by large-amplitude waves (or turbulence not positively correlated with superadiabaticity).

2.0,-----------------------~------------------------,

1.5

1.0

0.5

o

", ,,-

/ .",'

/ ,/ / ,/

1/ /

...... 1/ . I' ·i/· .. 1/ ....

1/ ........ v 1/ ....

1/ ". 1/ ..... .

i .......... . i ' .

. i ........ .

kx

Figure 3

'" ..........

Simple model of eonveetive adjustment for a monoehromatie wave (solid) and its projeetion on the first harmonie (dot-dash) for an input amplitude 1.5 (dimensionless). Short dashes indieate the strueture funetion assumed for loealized eddy viseosity, falling to I/e at the edge of the region affected by

convective adjustment.

This result was developed most thoroughly by COY and FRITTS (1988), and I will mere1y highlight their conclusions and pi ace them in the context of the wave action law to see how the eddy viscosity is affected. The perturbation equations for momentum and potential temperature may be written as

u; + üu'. + <p~ = vu~z + O(/la) + O(a 2)

8; + ü8'. + w'8z = v8~z + v~~z + O(/la) + O(a 2 )

(3.7a)

(3.7b)

where a and /l are nondimensional measures of wave amplitude and slowly-varyingness, with /l assumed small. [COY and FRITTS (1988) note that some of the O(a 2)

terms are required for physical consistency; I will bring this contribution into the final result later.] The fundamental assumption on the rhs of (3.7a, b) is to introduce an x-dependent eddy viscosity, assumed locally equal to the x-dependent eddy diffusivity:

v = v(x) = K(X) = K. (3.8)

Writing

v' = vf'(x) (3.9)

Vol. 130, 1989 Theory of Internal Gravity Wave Saturation 383

where f is a nondimensional structure function, the wave action law for steady waves then assurnes the form

Defining

we then have

(VI) k V [-2 (J~2 (JIF] VZ - H WgA = - e u~ +~ + z •

F(J~ aß == - T.

z

(~ -~) kWA = -2kAvm 2(l- ß/a) vz H g

(3.10)

(3.11)

(3.12)

with the rhs identical to before except for the factor in parenthesis. The same result was derived in the case of no shear by COY and FRITTS (1988) using the wave energy equation.

It may now be assumed that eddy viscosity is required in the breaking region to retard the wave amplitude as in Figure 3. More generally, we might allow any degree of superadiabaticity a > 1. Neglecting quadratic contributions from higher harmonics, the required viscosity is

_ 1 kc4 [ 1 3üz 2 va] v=(I-ßla)- - ---_ ---- . 2N3 H u - c a vz (3.13)

According to (3.13) there is competition between the effect of 10calization, that requires high er average viscosity to achieve the same amount of damping, and wave growth (az > 0), that calls for less viscosity. It is desirable to relate these two effects in a one-to-one manner. I have done this in Figure 1 using the same localization function of FRITTS and DUNKERTON (1985)

[1 + cos(kx + ... )]n

v(x) = vo 2 (3.14a)

with the index n defined such that the structure function f falls to l/e of its maximum value at the point where kXm = a sin(kxm ) in Figure 3, as also illustrated in that figure. Thus,

n - 1 = In [ 1 + c~s kXm 1 (3.14b)

It is seen from Figure I (Case 11) that the impact on the Lindzen parameterization

is to initially decrease the eddy viscosity and mean flow acceleration near the level of breaking, with a compensating increase in acceleration at higher levels and a slight increase in eddy viscosity due to localization. The wave amplitude, determined by applying the adjustment of Figure 3 to the nondivergent momentum flux profile,


is allowed to grow slightly larger than before. The effect of this modification is more dramatic in a compressible atmosphere without shear (SCHOEBERL, 1988).

COY and FRITTS (1988) discussed generalizations of the structure function f Their effect will depend also on the possible correlation of Vi and u~ which will modify the average contribution coming from the rhs of the momentum equation (3.7a). Such a modification will be required to assess the effect of local dynamical instability, for instance.

Localization not only alters the amplitude growth and required viscosity; it has a potentially significant effect on the heat and constituent transport. In particular, the effective eddy diffusivity of the mean state does not equal the zonally-averaged eddy diffusivity. Instead, as shown by COY and FRITTS (1988),

(3.15)

where y is a small number coming from some triple-correlation terms neglected by FRITTS and DUNKERTON (1985). (We alternately considered the effect ofhorizontal diffusion, that makes a contribution similar to y.) The effective inverse turbulent Prandtl number is illustrated in Figure lc for that same case. This number is indeed small near the breaking height, but grows to near '" 3 at higher levels, because a has been allowed to exceed 1.

In summary, the effect of turbulence localization in convectively unstable gravity waves is to modify the wave growth, eddy viscosity, and turbulent Prandtl number. While this modification can be significant, the case for large turbulent Prandtl number should not be overstated. The magnitudes of mean flow acceleration, viscosity, and diffusivity remain quantitatively "Iarge" in the modified parameterization scheme.

c. Form of the Instability

Much of what is known about the form of local instability in near-monochromatic gravity waves has come from a laboratory experiment described by Koop and MCGEE (1986). The instability appears as aseries of rolling motions in the unstable region between phase fronts of the primary wave. Their aspect ratio is near unity (in x, z). The dominant motions appear to be two-dimensional on the shadograph, but a three-dimensional cascade could very well be consistent with the laboratory observations. Their effect on the primary wave has not been thoroughly investigated in the laboratory. The ongoing stratified, nonrotating round-tank experiment at Northwest Research Associates directed by my colleague, Dr. D. P. Delisi, has also generated rolling motions in gravity wave criticallayers, with similar character, but their detailed structure and long-term effects remain to be diagnosed (DELISI and DUNKERTON, this issue).

Little is known from numerical studies either, although this area is being vigorously pursued by a few investigators. Walterscheid (personal communication,

Vol. 130, !989 Theory of Interna! Gravity Wave Saturation 385

1987) has observed local convective instabilities in a fully compressible two-dimensional numerical simulation. Studies of this sort are generally frustrated by resolution and time-stepping requirements as the turbulent cascade develops. Thus the long-term effects of the instability remain elusive. Progress is currently being made, however, and significant new results could very weIl be achieved in the near future for the two-dimensional case.

These simulations may be adequate to explore the initial mechanism and effect of two-dimensional gravity wave breakdown. UItimately, three-dimensional turbulence will be realized, of course. This point was also made by KLAAssENand PELTIER (1985) in their linear stability analysis of a background state distorted by finite-amplitude, overturned KH disturbances. Indeed, those authors remarked that the longitudinally symmetric instabilities may have the largest linear growth rates. Their suggestion contrasts with the laboratory observations of locally unstable gravity waves. Whether this is due to an intrinsic difference between KH and gravity wave breakdown, or is in some way related to the distribution of energy initially present in the spectrum, remains to be determined. It is possible that the quasi-twodimensional character of the rolling motions, along with their spatial scale, is derived from the primary wave itself. The dominant turbulent motions may then be determined by the vertical scale of the primary wave, regardless of what the maximum linear growth rates are. It is difficult to test this conjecture in the laboratory because the effects of molecular viscosity are feit not far below the scale of the dominant turbulent motions. The question can only be addressed with larger tank facilities andjor higher resolution numerical simulations. Of these, only the laboratory is suitable for the fully three-dimensional investigation, given current computing capabilities.

As mentioned above, the three-dimensionallinear stability of Kelvin-Helmholtz waves was examined theoretically using an eigenvalue technique by KLAASSEN and PELTIER (1985). A two-dimensional version of their method may be suitable for comparison to numerical simulations. The linear stability of a distorted basic state can be described by the equations

u; + Uu~ + u'U~ + Wu~ + w'Uz + 4J~ = 0

e; + U(},~ + u'0x + we~ + w'0 z = 0

(3.16a)

( 3.l6b)

where the primes now denote adeparture from the distorted basic state (U, W,0). If the disturbances vary rapidlyon the scale of the primary wave, and have aspect ratio near unity, so that in a hydrostatic primary wave the vertical advection terms proportional to Ware small, then the disturbance equations (3.16a, b) reduce to the hydrostatic equations for gravity waves, but with negative Brunt-Väisälä frequency squared. (One can easily generalize to nonhydrostatic disturbances.) The most unstable disturbances are found at largest zonal wavenumber k, apart from viscous damping, analogous to the instability of a density interface (TURNER, 1979, p. 94).


Further investigation will be necessary to solve the stability problem (3.16) and reconcile its solution with the laboratory observations. That is outside the scope of this paper. From all indications, however, the unstable growth rates favor sm all horizontal scales, suggesting that the breakdown of an inviscid gravity wave will produce chaos and not organized, rolling motions.

d. Mean Flow Interaction

For most practical applications to date, the convective adjustment procedure has been utilized in a steady-state framework. Time-dependence of the wave field is ignored in using (3.1). As DUNKERTON (1982) noted, however, it is easy to incorporate transience in the slowly-varying formulation, and solve for the required eddy viscosity. A further modification is to incorporate self-acceleration (COY, 1983; FRITTS and DUNKERTON, 1984), but this effect is oflimited importance because the mean flow is gene rally driven by a combination of opposing body forces. In addition to self-acceleration there might be "self-deceleration" brought about by a reduction of N in the breaking region.

The most important conclusion of DUNKERTON (1982) was that the mean flow acceleration, due to transience, enhances breakdown of the primary wave. When acting alone, the near-monochromatic wave drives the mean flow towards its phase speed and, in effect, tries to create a critical layer where one may not have been present initially. In that paper I relied on the quasi-linear, slowly-varying formulation, and, within the context of that approximation, demonstrated that the critical layer would descend with time, without interruption, or until encountering the lower boundary.

It is not too provocative to ask whether this result is correct. There is no general answer yet, but a couple of issues need to be raised. First, the slowly-varying assumption is viola ted by the slowly-varying solution due to the formation of a step (or "shock") in the me an velocity field (and very likely potential temperature as well) (DUNKERTON, 1982). Thus, partial reflection is inevitable if the forcing continues long enough (DUNKERTON and FRITTS, 1984), and, if the reflected component is contained from below, resonance becomes possible. In this ca se the form of the convectively unstable gravity wave field will be changed, and the mean flow acceleration temporarily restrained, in the vicinity of the mean flow discontinuity. Second, the forced wave will und ergo parametric subharmonic instability, which will limit the rate at which its action can be transmitted upwards to the descending critical layer (DUNKERTON, 1987). This mechanism will be discussed in Section 6 below.

Having outlined theoretically the nature and effect of convective instability in internal gravity waves, attention will now be directed at three competing instability mechanisms. It will be shown that although all of these mechanisms may have some role to play in gravity wave saturation, for high-frequency hydrostatic waves none of them can prevent the initial evolution to a convectively unstable state except under very special circumstances.

Vol. 130, 1989 Theory of Interna! Gravity Wave Saturation 387

4. Kelvin-Helmholtz Instability

The Kelvin-Helmholtz (KH) instability belongs to a broader class of dynamical instabilities on a parallel shear ftow, for which a necessary but not sufficient condition for instability is

Ri< 1/4 ( 4.la)

where Ri is the Richardson number of the mean state

( 4.lb)

It is important, of course, not to confuse dynamical instability of a parallel, i.e., zonally symmetrie, ftow with dynamical instability in general. Indeed, HASSELMANN (1967) demonstrated some time ago that any gravity wave is unstable to two other gravity waves through the weakly nonlinear resonant triad interaction. The condition (4.la) is obviously irrelevant in the general case. Thus, in the remainder of this section, attention will be restrieted to the special limit in whieh a horizontal spatial and temporal scale separation can be made between the unstable primary wave and its local instabilities, so that these instabilities can be thought to grow on a "locally parallel" ftow. In other words, the stability of the distorted basic state at any phase of the primary wave will be examined as if the ftow were everywhere horizontal and zonally symmetrie, having the velocity and static stability profile at that point.

As is well-known, the monochromatic, nonrotating primary wave in zero shear cannot satisfy (4.la) locally unless Ri < O. In reality there is both mean shear and rotation. Therefore it is worthwhile to briefly recall how both affect the criterion (4.1a) as applied to the monochromatie wave.

a. Local KH Instability in Inertia-Gravity Waves

For simplicity consider the inertia-gravity wave with zonal horizontal wavevector orientation and write

u' = ca sin 

where is wave phase. The local Richardson number in zero mean shear is

As = n /2 its value is

l-a Ri(n/2) = (0- 2 - 1) -2-

a

(4.2)

(4.3)

(4.4)


where a == w/f Ri is minimum at this phase for values less than 1/4, satisfying (4.la) (although for higher values the minimum gene rally appears elsewhere). Thus for Rimin = 1/4, the necessary relation is

2 .25a 2

a -1=-I-a

( 4.5)

(DUNKERTON, 1984; FRITTS and RASTOGI, 1985). Alternately we may write a = a,(a), and the "dynamically saturated" wave action density is

(4.6)

using the equipartition law as modified by rotation (DUNKERTON, 1984). The local KR instability grows on the vertical shear of the transverse velocity component which maximizes at the local minimum of BV frequency.

From ( 4.5) it appears that the waves must be close to circularly polarized (a -+ I) before a clear distinction can be made between the thresholds of local KR and convective instability. Of course, there do exist observations of near-inertial waves in this category which, moreover, appear to have regions of local instability possibly due to KR (BARAT, 1983). But these observations form only a limited subset of all gravity waves, and for most high-frequency waves approaching the criticallayer, the local KR instability seems unlikely unless the incident wave amplitude is quite small.

b. Effect of Mean Wind Shear

The same conclusion follows in the ca se of a nonrotating wave in mean shear, but for a different reason. In this ca se

( 4.7)

Defining J1 == !ü=!/N (inverse square-root Richardson number of the mean state), it follows approximately that for Rimin = 1/4,

I 2 (I - a) ~ - J1 2 . ( 4.8)

In the case J1 small (large mean Richardson number), the threshold amplitude is virtually unity (convective threshold). A significant reduction in the threshold requires a mean Richardson number near 1.

In summary, the effects of rotation and mean wind shear can, under special conditions, allow the local criterion (4.la) to be met well before the convective instability threshold. In such cases, as noted in the previous section, the effect of the


local instability on turbulent mixing might be significantly different than if local convection alone were occurring. Saturation due to local KR instability might also occur. But for high-frequency waves (0" ~ 1) in a low-shear environment (J1. ~ 1), considered important in the mesospheric momentum budget (FRITIS, 1984), such effects are unlikely*.

5. Vortical Mode Instability

It has been suggested that vortical mode instability (VMI) may saturate the primary gravity wave, although it cannot act prior to convective breakdown (DONG and YEH, 1988). Those authors investigated the weakly nonlinear triad interactions among acoustic, gravity, and vortical waves, extending a previous study (YEH and LIU, 1981). The vortical "mode" is characterized by horizontal motion, nondivergent but not irrotational in the horizontal plane. Unlike the other two modes, the vortical motions have a nonzero vertical component of vorticity. Their possible importance in geophysical flows was discussed by RILEY et al. (1981), LILL Y (1983), M ULLER et al. (1986), and GAGE and NASTROM (1986), among others.

It should be kept in mind that the generation of a vertical component of vorticity is subject to the constraint that potential vorticity

~a' V(J

p

is conserved following the motion if the fluid is conservative. Gravity waves do not carry potential vorticity. While they can cause rearrangement of potential vorticity between isentropic surfaces, the conservation law disallows production. (When two gravity waves cross, a vertical component of vorticity is produced, but no potential vorticity is involved.) Apparently, growth of the vertical vorticity component in a breaking gravity wave would come at the expense of the stratification, if at all, unless dissipation were present. In the rotating case, on the other hand, potential vorticity is initially present, and the growth of stratified vortical motions seems possible. The relevant instability criterion for an inertia-gravity wave remains to be worked out.

* Loeal Kelvin-Helmholtz instability will rapidly lead to overturning and, henee, eonveetion. As a result, it may be diffieult to determine whether the unstable rolling motions observed in the laboratory are due to eonveetion or KH instability. In general, the outbreak of loeal KH instability implies mixing and stress divergenee below the eonveetive instability threshold. The proeess might be labeled eonveetive saturation provided that it is understood that KH aets as a mediator without whieh saturation would have oeeurred only at larger amplitude. Seeond, turbulence loealization applies in the ease of loeal KH, albeit with different quantitative implieations.


6. Parametrie Subharmonie Instability

One of the more intriguing suggestions in the literature is that nonlinear wave-wave interactions (resonant or nonresonant) may saturate the gravity wave apart from local instabilities such as convection and Kelvin-Helmholtz instability (YEH and LIU, 1981; WEINSTOCK, 1982). A possible saturation mechanism in this category is the parametric subharmonic instability (MIED, 1976; KLOSTERMEYER, 1982). The primary gravity wave is unstable to two secondary waves having approximately half the intrinsic frequency. The parametric subharmonic instability (PSI) may be likened to the instability of a pendulum oscillated up and down at twice its natural frequency. In the ca se of gravity waves the direction of gravity relative to the isentropic surfaces oscillates with time as these surfaces are rotated back and forth by the primary wave (MCCOMAS and BRETHERTON, 1977).

The PSI has been omitted from consideration in the "eikonal saturation" model of gravity wave propagation currently in vogue (DUNKERTON, 1987). Fortunately, there is some justification for this. It is relatively easy to show that in a compressible atmosphere, the upward propagating primary wave will gene rally not be affected by the PSI before reaching high altitudes and undergoing convective breakdown. Four reasons may be adduced in support of this conclusion. First, the PSI is a weak instability operating on a time scale roughly like

A 2 wT ~ lu'/el ( 6.1)

which amounts to a "Iong" time when the primary wave IS weil below the convective instability threshold. Second, the time scale (6.1) has reference to the initial growth of secondary waves, and not to the decay of the primary wave. Thus, considering only exponential growth with a constant rate, the decay of the primary wave can be postponed indefinitely by propagating it into a clean initial state. Third, it is an inherent property of the PSI to transfer wave action into waves of about half the intrinsic frequency of the primary wave. These secondary waves have slower vertical group velocity.

6)2 w=

g Nk (6.2)

(hydrostatic limit) unless we are near the BV cutoff frequency to begin with (ISRAHIM, 1987). Traditionally the secondary waves have been thought to in'lolve small horizontal scales, but the results of YEH and LIU ( 1981) indicate a significant, and possibly dominant, transfer of action to secondary waves of about twice the horizontal wavelength (a result also demonstrated numerically in DUNKERTON, 1987). In this ca se the secondary waves have about half the vertical group velocity of the primary wave, and therefore cannot keep up with it. Fourth, more generally, for resonant interactions to be effective in the context of dispersive wave packets,


the triad components must maintain some degree of overlap--a criterion not easily satisfied in shear or with highly transient wave packets. The stabilizing effect of dispersion was illustrated by means of a simple example in BENNEY and NEWELL (1967; quoted by Ibrahim).

Despite these inherent limitations, the PSI might play an essential role in some

cases of gravity wave saturation. It reminds us that gravity waves are not imQ1ortal;

spike relaxation will occur in a disturbed spectrum due to nonlinear instability even

when dispersion and/or convective saturation are unimportant (FREDERIKSEN and BELL, 1984; MULLER el al., 1986; DUNKERTON, 1987; MOBBS, 1987). The result will be a chaotic mix of subharmonics tending towards horizontal motion and local convective instability (or other instabilities expected when w --+ f). Irreversible mean flow accelerations and turbulent mixing resulting from these end-product instabilities can, for practical purposes, be attributed to the irreversible nature of the PSI itself (McEwAN and ROBINSON, 1975).

When the primary wave continues to be forced from below for indefinitely long

times, there will be competition between the influx of wave action and nonlinear

decay. A heuristic approach to describe the decay process might utilize the time scale of (6.1):

I 0 I --poWA=-Ar- + ... Po oz g

(6.3)

together with other saturation restraints, if appropriate. I hasten to point out that (6.3) has not been tested in terms of the more complete Boltzmann equation. According to (6.3), vertical propagation is favored for waves with vertical wavelength comparable to or greater than the density scale height. Conversely, waves with large mH are attenuated before reaching the convective threshold. The example previously

used in Figure 1 was recalculated using (6.3) and is shown in Figure 4. The broadening of the mean flow acceleration seen he re is analogous to that of WEINSTOCK (1982) but was obtained with a somewhat simpler parameterization.

The frictional damping used in (6.3) is extreme, since it does not accurately describe the initial breakdown of the primary wave which, as noted above, can be delayed indefinitely by making the initial state undisturbed, i.e., without resonating partners. Highly transient packets are largely unaffected by the PSI; hence, the damping rate should be made time-dependent. In shear, the PSI mechansim will be less effective. Thus, in general, the damping parameterized by (6.3) will need to be

reduced to a more modest level to accurately capture the effect of nonlinear decay. Another issue is the effectiveness of the PSI in convectively unstable waves.

Convection obviously implies a broad spectrum, particularly at high wavenumbers,

out of which resonating partners could grow. On the other hand, convection would

presumably disrupt the PSI, like a pendulum violently jerked up and down. In the

latter case the effect of the PSI would be to erode the primary wave from below, i.e., beneath the convective breaking height Zb'

392 Timothy J. Dunkerton

30~--------~----~r---------~ \ . \ km

\

25 \

\

20

15

10

5

\. '.

.\ !\ ! \ ! \ u ! \

\ \ \ \ \

O;-.--r-r-r~-.~~~r-r-r-+-~

-40 o 20

Figure 4

PAGEOPH,

Mean flow acceleration for the wave of Figure I but with the simple PSI parameterization (6.3).

7. Summary and Outlook

The theory of internal gravity wave saturation discussed here has emphasized convective instability as a mechanism of saturation. Following the traditional approach, I have used a simplified view of the spectrum-an ensemble of nearmonochromatic waves-as a foundation for discussion. A novel aspect of Section 3 was the self-consistent determination of stress divergence and turbulent mixing based on a simple model of turbulence localization (COY and FRITTS, 1988; SCHOEBERL, 1988). This modified parameterization represents a slight improvement, but in common with the scheme of LINDZEN (1981), the picture of convective saturation in near-monochromatic waves remains decidedly violent, with quantitatively "Iarge" me an flow accelerations, eddy viscosity, and diffusivity. There is probably nothing wrong with the parameterization in this respect, since the exact nonlinear evolution would have similar character under the same circumstances, at least in the early stages of breakdown.


There are, to be sure, many unsettled issues in gravity wave saturation still to be explored. Without going into detail, our discussion will conclude with a broadbrush summary of these issues, and an outlook on the methods that might be used to explore them.

a. Hypothetical Nature of Convective "Saturation"

The importance of convective breakdown in near-monochromatic waves cannot be disputed. However, much is still unknown about the form and the effects of convection in internal gravity waves. The convective saturation hypo thesis tends to ignore the form as irrelevant, and makes several assumptions about the effects, e.g., the degree of turbulence localization, limiting wave amplitude, and magnitude of mixing coefficients. Suitable laboratory and numerical studies must now be devised to test for these effects and the accuracy of the parameterization. Of these, only the laboratory is adequate for the three-dimensional problem, given current computing capabilities.

b. More Realistic Gravity Wave and Mean Flow Spectrum

It might be objected that the emphasis given to convective saturation is a direct consequence of the near-monochromatic assumption. Similarly, the example of gravity wave transport cited in the Introduction as a poor candidate for nonlinear saturation theory might in itself be too unrealistic to be of importance.

Although I do not agree with this objection, there is no doubt that a more realistic spectrum must be studied be fore any parameterization scheme can be accepted. There are many interesting issues arising from our consideration of a more realistic spectrum. To summarize a few, there is (1) the instability of primary waves due to resonating partners in the background state (YEH and LIU, 1985); (2) the reflection or scattering of waves due to low-frequency background shear content (MOBBS, 1987); (3) the relative importance of criticallayers and caustics as loci of gravity wave breakdown (BROUTMAN, 1984) (part of a more general assessment of WKB accuracy); (4) the isolation of quasi-linear or nonlinear mechanisms responsible for selective transmission and polarization of gravity waves (DUNKERTON and BUTCHART, 1984), (5) the effect of superposition on gravity wave interactions, including local convective instability (SMITH et al., 1987); (6) the in situ excitation of low-frequency waves by gravity wave breaking (ZHU and HOLTON, 1987); and (perhaps most important) (7) testing the relative importance of dispersion and nonlinearity in gravity wave transport (as a function of wave scale, frequency, background conditions, etc.).

Hopefully, observations will provide knowledge of the spectrum for use in theoretical, numerical and laboratory studies of these issues. Undoubtedly the variability of the spectrum is at least as important as the time-averaged statistics,


particularly for small m where most of the transport is occurring. I would suggest the use of the Monte-Carlo technique as a means for investigating this variability theoretically, numerically, and experimentally. This method has been used successfully (FLATTE et al., 1985) and deserves to be extended to include nonlinear interactions and a more realistic model of convective saturation.

c. Three-dimensional Modeling with Rotation

The convective breakdown of gravity waves is a three-dimensional turbulent phenomenon. Inclusion of rotation suggests that dynamical instability mechanisms mayaiso enter the saturation process. However, the three-dimensionality remains.

Numerical models are presently able to simulate 3-D stratified flow only in a coarse-grained manner, emphasizing the transfer of energy between the gravest resolvable harmonics. Although not without its own limitations, the laboratory currently provides the optimal means of investigating 3-D waves and turbulence. Two immediate problems for experimental study are (1) gravity wave critical layer interactions, emphasizing convective breakdown and nonlinear reflection, and (2) gravity wave, vortical flow interactions and the decay of stratified turbulence. To my knowledge, no one has constructed a rotating stratified facility with gravity waves specifically in mind; this, too, would be useful since the instability criteria are substantially modified by rotation.

d. Long-term Effects

The other aspect in which the laboratory excels is the simulation of gravity waves over long time intervals. To be sure, most facilities have had problems in this regard, suffering from mixed layer growth due to external driving (KATO and PHILLIPS (1969), end-wall surges in the tilt-tank (THORPE, 1981), and internat mixing due to shear generation (Koop and MCGEE, 1986). Fortunately, some progress in overcoming these problems has been made with a nonrotating, stratified annulus (DELISI and DUNKERTON, this issue), an enlarged and improved version of a facility used by PLUMB and McEw AN (1978) in their laboratory analog of the quasi-biennial oscillation. Among other things, it has been shown that the long-term effects of critical layer breaking can be simulated in this facility, including the three-dimensional mechanism of break down itself. The annulus of this size ('" 6' outer diameter), or larger, has a usefully large parameter range over which the effects of unstable breaking can be analyzed and compared to other saturation mechanisms, particularly the PSI and mean flow modification.

e. "Event-oriented" Observational Network

Although I promised not to say anything about observations, it is worthwhile to note the potential value of observational studies for testing gravity wave saturation


mechanisms. A current observation al priority is to construct a worldwide climatology of gravity waves and momentum transport. This is important, but by itself cannot resolve ambiguities in determining saturation mechanisms from singlestation observations. There is also a danger in relying on time-averaged statistics when, in fact, the nature and effects of gravity wave saturation might be identified from the time evolution of the spectrum (particularly on "active" days). A strong emphasis in future observational studies should therefore be given to the establishment of local networks, possibly including novel high-resolution sampling methods in the horizontal, and the analysis of sp€;ctral evolution as a function of time.

A cknowledgments

Comments by D. P. DeJisi, D. C. Fritts, M. E. McIntyre, and J. J. Riley were heJpful in revising this paper. This research was supported by the Air Force Office of Scientific Research under Contract F49620-86-C-0026, and by the National Aeronautics and Space Administration under Contract NASW~230.

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the mean jiow, Ann. Geophysieae 5, 197-208.

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SMITH, S. A., D. C. FRITIS, and T. E. VANZANDT (1987), Evidence for a saturated spectrum of atmospheric gravity waves, J. Atmos. Sei. 44, 1404---1410.

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(Received July 21, 1987, revised February I, 1988, accepted February 4, 1988)


A Theory of Enhanced Saturation of the Gravity Wave Spectrum Due to Increases in Atmospheric Stability

THOMAS E. V ANZANDT 1 and DAVID C. FRITTS2

Abstract-In this paper we consider a vertical wavenumber spectrum of vertically propagating gravity waves impinging on a rapid increase in atmospheric stability. If the high-wavenumber range is saturated below the increase, as is usually observed, then the compression of vertical scales as the waves enter a region of higher stability results in that range becoming supersaturated, that is, the spectral amplitude becomes larger than the saturation limit. The supersaturated wave energy must then dissipate in a vertical distance of the order of a wave1ength, resulting in an enhanced turbulent energy dissipation rate. If the wave spectrum is azimuthally anisotropic, the dissipation also results in an enhanced vertical divergence of the vertical fiux of horizontal momentum and enhanced wave drag in the same region. Estimates of the enhanced dissipation rates and radar refiectivities appear to be consistent with the enhancements observed near the high-Iatitude summer meso pause. Estimates of the enhanced mean fiow acceleration appear to be consistent with the wave drag that is needed near the tropopause and the high-Iatitude summer mesopause in large-scale models of the atmosphere. Thus, this process may playa significant role in determining the global effects of gravity waves on the large-scale circulation.

Key words: Gravity waves, saturation, wave breaking, energy dissipation, moment um fiux, mean fiow acceleration.

J. Introduction

Internal gravity waves are now recognized to playa significant role in establish

ing the large-scale circulation and structure of the lower and middle atmosphere.

Their effects include, among others, a reduction of the me an zonal velocity in the

lower stratosphere leading to mean poleward motions at these heights (PALMER et al., 1986; T ANAKA, 1986), the revers al of the vertical shear of the mean zonal wind

in the mesosphere and a corresponding reversal of the mean meridional temperature

gradient near the mesopause (LINDZEN, 1981; HOLTON, 1982; DUNKERTON, 1982; VINCENT and REID, 1983; MIY AHARA et al., 1986; FRITTS and VINCENT, 1987),

I Aeronomy Laboratory, National Oceanic and Atmospheric Administration, Boulder, Colorado 80303-3328, U.S.A.

2 Geophysical Institute and Department of Physics, University of Alaska, Fairbanks, Alaska 99775-0800, U.S.A.

400 T. E. VanZandt and D. C. Fritts PAGEOPH,

and the turbulent diffusion of heat and constituents throughout regions of wave dissipation (SCHOEBERL et al., 1983; CHAO and SCHOEBERL, 1984; THOMAS et al., 1984; FRITTS and DUNKERTON, 1985; STROBEL et al., 1985).

The recognition of the important role played by gravity waves has motivated a number of attempts to develop suitable parameterizations of their sources, distribution, and effects in large-scale atmospheric models (e.g., HOLTON, 1983; GARCIA and SOLOMON, 1985; PALMER et al., 1986; TANAKA, 1986; MIYAHARA et al., 1986; McF ARLANE, 1987). These attempts have met with considerable qualitative success in approximating the averaged effects of such motions. The parameterizations achieve conditions of wave saturation, with resulting dissipation, drag and induced diffusion, principally as a result of wave amplitude growth with height due to the decreasing atmospheric density or the interaction of waves with a shear flow.

In this paper we consider another gravity wave process that can produce significant enhancements of dissipation, drag, and diffusion in certain regions of the atmosphere. This process involves the response of the vertical wavenumber spectrum of vertically propagating gravity waves impinging on a rapid increase in atmospheric stability, such as at the tropopause and at the high-Iatitude summer mesopause. As motivations for this study we note that (1) this process results in enhanced wave drag in the lower stratosphere where additional drag is required to bring large-scale circulation models into agreement with the observed circulation, and (2) MST radars observe large enhancements of the radar reflectivity near the high-Iatitude summer mesopause (ECKLUND and BALSLEY, 1981; CZECHOWSKY and RüsTER, 1985). These increases are likely due in part to enhanced turbulence energies at the scales to which the radars are sensitive.

BALSLEY et al. (1983) attributed the strong VHF radar echoes at the high-la titude summer mesopause to the compression of vertical wavelengths of gravity waves in the very stable region just above the mesopause, leading to an increased tendency for shear instability of the waves. Recently it has come to be understood that convective instability usually takes precedence over shear instability (FRITTS and RASTOGI, 1985) and that the high-wavenumber range of the gravity wave spectrum is saturated at all or most heights (DEWAN and GOOD, 1986; SMITH et al., 1987). In this paper we have taken advantage of these new insights to develop the basic idea of BALSLEY et al. (1983) into a model from which the resulting enhancements in dissipation and mean flow acceleration can be estimated. This model may provide a useful basis for a more comprehensive and physical parameterization of gravity wave effects on the general circulation.

We begin in Section 2 by reviewing the implications of WKB scaling of gravity waves. In Section 3 we develop a model vertical wavenumber spectrum of gravity wave motions that is consistent with recent observations of the vertical wavenumber spectrum, with the theoretical saturated spectrum at large vertical wavenumbers, and with the requirement of a finite vertical flux of wave action or wave energy. This canonical spectrum is used throughout the following sections of the paper. In

Vol. 130, 1989 Saturation of the Gravity Wave Spectrum 401

Section 4 we present the theory of enhanced saturation and illustrate the etfects of an increase in the buoyancy frequency on the total wave energy and the characteristic vertical wavenumber of the wave motions. The etfects of enhanced saturation on the vertical Buxes of energy and momentum and the resulting enhancements of energy dissipation rate e and mean Bow acceleration are discussed in Section 5. The conclusions of this study and suggestions for experiments that could test and help refine the enhanced saturation theory are presented in Section 6.

2. WKB Scaling 0/ Gravity Wave Energy

Adetermination of the variations of wave energy density for conservative motions due to changes in the environment can be developed in several ways. We can either require the vertical Bux of wave action (or of momentum) to be invariant for steady, conservative motions (BRETHERTON and GARRETT, 1969; ANDREWS and McINTYRE, 1976; BOYD, 1976), or we can determine the wave energy from the form of the wave motions appropriate for a general sheared and stratified Bow (BOOKER and BRETHERTON, 1967). Both approaches yield the same result. Following the former, we assume hydrostatic motions, a constant mean velocity, and slowly varying stability. Then the WKB gravity wave dispersion relation is

kN m = - W{)~2 (1)

where k and mare the horizontal and vertical wavenumbers, w is the intrinsic frequency,jand N are the inertial and buoyancy frequencies, and ()+ = I ± Ujw) 2.

We have assumed here that k and w > 0, so that m < 0 for a wave propagating upward and eastward. In this approximation k and ware independent of aItitude for a single wave, so that m oc N. The gravity wave action Bux is then

(2)

where cgz is the vertical group velocity, Po is the background atmospheric density, and Eis the total (kinetic plus potential) gravity wave energy density per unit mass. Thus, for a constant wave action Bux the energy density per unit mass E must vary as

N m Eoc-oc-.

Po Po (3)

That is, the energy per unit mass Evaries in response to changes in N as weIl as to the decrease of the mean atmospheric density Po with height. Which etfect dominates variations of E will depend on the relative changes of N and Po.


Equation (2) holds even in the presence of reflection, since the reflected component merely reduces S A below the height of reflection. Equation ( I) holds for all waves except that the sign of m is reversed for the reflected component, while Eq. (3) holds only for the transmitted component. The effect of reflection will be considered further at the end of Section 5a.

3. Model Spectra

a. Canonical Gravity Wave Spectra

It has been known for many years that in the lower atmosphere the shapes of the observed spectra of atmospheric mesoscale velocities and temperatures as functions of k, m, and ware insensitive to the geophysical parameters obtained when the data were taken. Recently it has been found that the spectral shapes in the mesosphere and lower thermosphere are very similar to those in the lower atmosphere (BALSLEY and CARTER, 1982; VINCENT, 1984). It has also been pointed out that in the lower atmosphere the amplitudes, as weil as the shapes, of these spectra are similarly insensitive (V ANZANDT, 1982) and that the amplitude of the m spectra at large m is only a weak function of altitude (V ANZANDT, 1985; SMITH et al., 1987).

Following a suggestion by DEWAN (1979), V ANZANDT (1982) showed that the spectra are consistent with the gravity wave dispersion relation by fitting the GARRETT and MUNK (1972, 1975) oceanic gravity wave spectral model to the atmospheric spectra. The GARRETT and MUNK (1975) model for the total energy, from wh ich the spectrum of a component of velocity or of the temperature versus k, m, or w can be derived, is

A(/l) F(m,w) =E-B(w)

m. ( 4)

where E is the total (kinetic plus potential) energy, A(/l) is the model vertical wavenumber spectrum as a function of /l = m/m., where m and /l are now assumed > 0, m. is a characteristic vertical wavenumber, and B(w) is the model frequency spectrum. This model assumes, as a first approximation, that the dependence of the spectrum on m and w is separable.

The observed frequency spectra can be approximated by negative powers of w, so that Garrett and Munk expressed B(w) as

(5)

normalized so that J1 B(w) dw = I. Garrett and Munk fitted the oceanic frequency spectra with p = 2, and VanZandt fitted the atmospheric spectra with p = 5/3, a nominal, long-term average value.


The observed vertical wavenumber spectra at large m can be described by negative powers of m, so A(/1) was expressed by GARRETT and MUNK (1975) and DESAUBIES (1976), respectively as

(6a)

and

CD C t. n AD(/1) = 1 + /11' D = ~ sm t (6b)

where the constants normalize SO' A(/1) d/1 to unity. In Figure la, log (AG(/1)/CG) and log (A D(/1)/CD ) are plotted versus log /1. With a positive value of t the model A(/1) approach C at small /1 and are asymptotic to C//11 at large /1. GARRETT and MUNK (1975) found that the observed oceanic spectra could be fitted with t = 2.5. V ANZANDT (1982) fitted the observed lower atmospheric spectra with t = 2.4, but recent observations of atmospheric vertical wavenumber spectra show that t is elose to 3 (DEwAN et al., 1984; SMITH et al., 1987; FRITTS and CHOU, 1987). Also, as we discuss later, there is theoretical support for a limiting slope of t = 3. Therefore, expressions with t = 3 as weIl as with a general t will be given throughout this paper.

However, the constant energy density at small /1 of AD(/1) and AG(/1) leads to unrealistic vertical ftuxes of wave action or energy. The energy ftux is given by

100 iN E 100 A(/1) iN SE = dm dw pocgzF(m, w) = Po - d/1-- dw wLB(w). o IJ m. 0 /1 IJ

(7)

Then with t = 3, for example, the /1 integral of A D(/1) is -(l/3)ln(1 + 1//13)1~ =

(1j3)ln(1 + I/Jl~J As JlL decreases toward 0, the integral increases toward 00. Of course, a lower limit of 0 is not physical, but even with a lower limit of 0.1, which is consistent with the approximations of gravity wave theory in the lower atmosphere, the ratio of vertical energy ftux to total energy is large and most of the ftux comes from near /1u half from between 0.1 and 0.32. A more realistic ftux is obtained by modifying the A(Jl) by multiplying them by /1s with s > 0 to obtain

(8a)

and

C =--smn -- . s+t. (S+I) MD n s + t (8b)

Since these functions vary as /1s when /1 ~ I, they permit the convenience of setting /1L equal to O.

The value of s is uncertain, but some recent observed spectra increase at small

u , , < , ~

u , , " , , ~

--

-, "

--------,--2

-3

, , , , , , , , , \ , , , ,

-'~---"---O---"----~--~O'--"----~-C_~'---' -,

-2

-,

o ,

MO

-, , , /MG

-

-,L----"---L---"----"---~O---"----~-,.~,-----,


Jl with a slope between 1/2 and I (MAEKAWA et al., 1987; FRITTS et al., 1988). Since s = 1 is convenient, expressions with this value as weIl as with a general s will be

given. With (s, t) = (1,3), AMG(Jl) and AMD(Jl) become

and

Jl AMG(Jl) = 6 (1 + Jl)4

4 Jl AMD(Jl) =; I + Jl4'

(9a)

(9b)

These spectra divided by their respective constants are also plotted in Figures la and Ib.

The graphs of A(Jl)/C in Figure la appear to indicate that most of the variance lies at small Jl, which is very misleading. A correct indication can be obtained by plotting JlA(Jl) (which MCCOMAS and MÜLLER (1981) call the energy-content spectrum) versus log Jl, since J A(Jl) dJl = J JlA(Jl) d In Jl = In 10 J JlA(Jl) d log Jl. The graph is area-preserving when JlA(Jl) is plotted on a linear scale versus log Jl since equal areas contain equal energies, but it is usually more convenient to plot log JlA(Jl), as in Figure I b. It is interesting to note than when (s, t) = (I, 3) (indeed, whenever s = t - 2) the energy-content graphs of the modified spectra are symmetrical about log Jl = 0, i.e., Jl- 1 A(Jl-I) = JlA(Jl), so that both the mean and mode lie at Jl = 1.

It is evident from Figure la that the transition from the limiting slope at small Jl to the asymptotic slope at large Jl is more rapid with the Desaubies spectra than with the corresponding Garrett and Munk spectra, so that in Figure Ib the peaks of the Desaubies spectra are sharper. Indeed, in the AMD(Jl) spectrum, 50% of the total energy lies within a factor of 1.55 of the mean.

b. A Saturated Vertical Wavenumber Spectrum \

DEW AN and GOOD (1986) and SMITH et al. (1987) have shown that the principle features of the m spectra at large m probably result from the saturation of gravity wave motions by convective and/or dynamical instabilities. With hydrostatic gravity wave motions, this interpretation leads to a saturated total energy spectrum of the form

p + I N 2

F.,(Jl, w) = 20 m 3 B(w). ( 10)

Figure 1 Spectra vs. normalized vertical wavenumber J.L from Eqs. (6a), (6b), (8a), and (8b) with (s, I) = (1,3).

a) Energy spectra A(J.L); b) energy-content spectra J.LA(J.L).


When observed va lues of p and standard atmosphere values of N (which varies by only a factor of two from the troposphere to the mesopause) are inserted into Eq. (10), the resulting amplitudes are in good agreement with observations, inciuding the weak altitude dependence of the spectra at large m and the recently discovered dependence on N (DEWAN and GOOD, 1986; SMITH et al., 1987; FRITTS et al. , 1988).

The energy density Ein Eq. (4) can be estimated from the requirement that the model spectra must be asymptotic to Eq. (10). Then

= ~ p + I (.!!..-)2 E C 20 m* '

( 11)

with p = 5/3, in the troposphere with N = 2n/600 s, and m* = 2n/A.* '" 2n/2000 m, EMG '" 0.25 and EMD'" 1.2(J/kg), and in the mesosphere with N = 2n/300s and m* '" 2n/20,000 m, EMG ", 100 and EMD'" 470(J/kg). The EMG estimates are an order of magnitude smaller than estimates of E inferred by integration of frequency spectra (BALSLEY and CARTER, 1982; VINCENT, 1984; BALSLEY and GARELLO, 1985). The EMD estimates are also rather smalI, but reasonably satisfactory in view of the uncertainties in the spectral models, in the parameters, particularly m * (see SMITH et al. , 1987), and in the observational estimates. Since the modified Desaubies spectrum appears to agree better with observations in both shape and in the estimate of E, only A MD will be used in further calculations, and the subscript MD will be omitted.

4. Theory of Enhanced Saturation

We present in this section the theory of enhanced saturation due to a spectrum of gravity waves impinging on a rapid increase in stability. To motivate our discussion, we first compare the induced mean flow acceleration with that due to the decrease of atmospheric density with height and that due to a vertical shear in the background wind, assuming saturated wave amplitudes in each case. There is, of course, no induced mean flow acceleration in the absence of wave transience or dissipation (ANDREWS and McINTYRE, 1976; BOYD, 1976). We then compare the change in the vertical wavenumber spectrum of wave energy due to WKB scaling with the change permitted by wave saturation and estimate the resulting rate of energy dissipation and mean flow acceleration.

a. A Comparison of Mean Flow Acceleration Effects for a Monochromatic Wave

Previous theoretical treatments of gravity wave saturation and the resulting mean flow acceleration have addressed only those changes due to variations of wave moment um flux due to decreasing atmospheric density or to a vertical shear of the

Val. 130, 1989 Saturation of the Gravity Wave Spectrum 407

background wind (LINDZEN, 1981; FRITTS, 1984). As no ted earlier, however, there

can also be a significant contribution due to the variation of N with height. The

vertical flux of horizontal momentum for a monochromatic wave with the satura

tion amplitude u' = c - Ü, where c is the horizontal phase velocity and Ü and u' are

the background and perturbation horizontal velocity, is given by (FRITTS and VINCENT, 1987)

(12)

Then the induced mean flow acceleration, including the effects of rotation is

I 0 -ü,= - --;-(Pou'w'L) (13)

Po uZ

= _ ~ ~ (ü _ C)\53j2[ _ 0 In Po _ _ 3üz + 0 In N _ ~ 0 In L J. 2 N oz u - c oz 2 oz

Thus, induced me an flow accelerations can arise, in response to wave saturation, as

a result of the decrease of atmospheric density with height, a vertical shear of the

background wind, or a vertical gradient of the buoyancy frequency. Acce1erations

due to increases in N can, in fact, dominate the contributions from the density and

shear terms where N increases rapidly, such as at the tropopause and at the high-Iatitude summer mesopause. The final term in Eq. (13) is a consequence of

gravity wave structure at low intrinsic frequencies. Since w = k(c - ü), this term is also proportional to uzl(ü - c), but it is sm aller than the previous shear term by (f/w) 2/( 1- (f/w) 2), which is negligibly small except when w ~ f

b. Enhanced Saturation of a Gravity Wave Spectrum

Let us suppose that a spectrum of upward-propagating gravity waves described in the above manner impinges on a region where N changes rapidly with height, from Ni below the region to Nt = RNi above it. Below the region the wavenumber spectrum of total energy is

(14)

The corresponding saturated spectrum is

Fslp;;I) = EiC/m·iPi· (15)

The energy-content spectra of Eqs. (14) and (15) are illustrated in Figure 2 with (s, t) = ( I, 3).

Note that since we are dealing only with the upward-propagating portion of the

total gravity wave spectrum, the energy density Ei is less than the total energy E. On

the average, however, a majority of the energy is propagating upward (VINCENT, 1984; FUKAO et al., 1988), so the correction is less than a factor of two.


o - I -2 log fL

Figure 2 Illustration of the effect on the canonical wave spectrum and the saturated spectrum of a rapid increase of buoyancy frequency from an initial value Ni to a final value NI with R = NI/Ni = 3. The energycontent /lF(/l) of the spectra is plotted. The initial (i), WKB-scaled (w), and final (f) canonical wave spectra are from Eqs. (14), (16), and (18), respectively, with A(/l) = AMD(/l) from Eq. (8b) and with (s , r) = ( I, 3). The initial (si) and final (sf) saturated spectra are from Eqs. (15) and (17), respectively, with I = 3. The hatched area is supersaturated and rapidly dissipated and we ass urne that the stippled

area is also dissipated.

According to Eq. (3), as the spectrum of gravity waves passes through the change in N, the energy per unit mass of each wave in the spectrum changes to Eu = REi • According to Eq. (I), the wavenumber m of each wave also changes by a factor R. In terms of the spectrum, this change is accomplished by changing m' i

to m. u = Rm. i . Then the WKB-scaled spectrum above the region, Fw(llw;R), has the same shape as F,{lli; I), but it is shifted in 11 by a factor Rand its energy is changed by a factor R. The WKB-scaled spectrum is then given by

(16)

This spectrum is illustrated in Figure 2 for R = 3, which is a value that can occur at the tropopause, and at the high-Iatitude summer mesopause. The ratio of the peaks and of the energies is R, and in the range where 11 ~ I, Fw(Il;R)/ F,(11 ; I) = R' = R 3.

The saturated spectrum above the region becomes

(17)

This spectrum is also shown in Figure 2.

It is evident that if R > 1, then Fw(J.1w;R) exceeds F,(J.1i;R) in the hatched region.

Indeed, when J.1w ~ 1 it exceeds F,.(J.1i;R) by a factor R. The wave energy in the hatched region is thus unstable or supersaturated, and the waves will undergo rapid

dissipation until the spectral amplitude is reduced to FiJ.1i;R). Spectra are usually observed to have shapes dose to the canonical shape, with

a rounded peak, so there must be a strong process or processes that tend to round the corner where Fw(J.1w;R) and F,(J.1i;R) cross. Then the energy in the stippled region will also be rapidly dissipated. The resulting final, faired spectrum is

( 18)

The final energy per unit mass Ef and characteristic wavenumber m'f can be determined by noting that where J.1r ~ 1, Fr(J.1r;R) = Fw (J.1w;R) and where J.1f ~ 1, Ff (J.1r;R) = F,(J.1i;R). Then with s > 0 and t > 2

Er = E;R 2 + s - s(t - 2)/(s + I) = EwR -(s + 1)(1 - 2)/(s+ t)

(s, t) = ( 1, 3) (19)

and

m - m R(s+2)/(s+l) - m R-(1-2)/(s+l) ~r - *i - ·w

(s, t) = ( 1, 3) (20)

These relations are obviously the same whether A MG(J.1) or AMD(J.1) is used. If R < 1 or if t < 2, then Fw(J.1w;R) is Iess than F,(J.1i;R) at all J.1, that is, the

WKB-scaled spectrum is subsaturated. Sub saturation is of much Iess interest than supersaturation. First, Iarge, rapid decreases of N do not exist in dimatological mean N profiles, indeed, even transient Iarge decreases appear to be uncommon. Second, the resulting effects are less important, as will be noted below.

5. Effects 01 Enhanced Saturation

In this section we discuss the effects of dissipation of the supersaturated energy, inc1uding estimates of the Ioss of vertical fluxes of wave energy and moment um and the resulting enhancements of energy dissipation per unit mass t; and mean flow acceleration u1•

a. Vertical Energy Flux and Enhanced Energy Dissipation Rate

The vertical flux of gravity wave energy is, from Eq. (7),

E 100 A(J.1) iN SE=PO- dJ.1- dwwLB(w) m* 0 J.1 f

= Po~ sin(~(s + 1)/(s + t)) (00 dJ.1 A(J.1)p -1 1(,!)2-P[I_~ (L)2- PJ. (21) m* sm(ns/(s + t)) Jo J.1 2-p 1 p N


With p = 5/3, f - 1O- 4(rad/s), and (N//) - 200, the Q) integral is -103(rad/s), where terms of the order of {f/N)P - 10-4 have been neglected, and with (s, t) = (1,3) the J.l integral J.l- 1 = J2.

The fraction of the energy ftux that is supersaturated and lost in going from below the increase of N to above it is

ASE SE ... - SEf Ew/m·w - Ef/m.f --= SEi SEi Edm.i

= I_R-s(t-2)(S+1)

= 1 - R -1(4 with (s, t) = (1,3) (22)

where Eqs. (19) and (20) have been used. The variation of N in the Q) integral has been ignored, recognizing that above the increase in N intrinsic wave frequencies must remain ~ Ni in the absence of wind shear. ASE/SEi is plotted in Figure 3. The climatological mean value of R at the tropopause is 2, leading to a fractional loss of 16%. An estimate of Rat the high-Iatitude summer mesopause can be derived from the temperature profiles measured by THEON et al. (1967) at Pt. Barrow, Alaska. The mean of these profiles is shown in Figure 4, adapted from BALSLEY et al.

R

Figure 3 The fractionalloss of the vertical f1ux of wave energy flSE/SE; from Eq. (22b), the fractionalloss of the vertical f1ux of horizontal wave momentu~SM/SM; from Eq. (29b), the coefficient of fle from Eq.

(24b), and the coefficient of flUt from Eq. (3Ib). In a11 cases (s, t) =(1,3).

Vol. 130, 1989 Saturation of the Gravity Wave Spectrum 4II

(1984). This results in a loss of 24%. Thus, the losses due to supersaturation are

quite substantial. As gravity waves dissipate, they generate a variety of other motions, including

seeondary gravity waves, inertial sub range turbulenee, and possibly two-dimensional turbulenee. These eomplex interaetions are poorly understood at present, and

we assume'for simplicity that the result ean be represented as an enhaneement of the

turbulent energy dissipation rate 8. A detailed ea1culation of the A8(z) profile is unwarranted beeause of the approximations and uneertainties in the present model.

But as a erude approximation, let us assume that the dissipated energy is distributed uniformly over a vertieal si ab of thiekness AE = 2n/mD where mE is the mean

wavenumber weighted by SEw(ll) - SE}P), Then

mE =

Ew icxc d A(llw) Ef ioo d A(llf) - Ilw-- m -- Il-- m m·w 0 Ilw m'f 0 Ilf

Ew (00 dllw

A(Il,J _ Ef (00 dJ1:r A(J1:r)

m·w Jo Ilw m'f Jo Ilr

E,.Er I

Ew _ Er 11- 1

m· w m'r m., I_R-(s+l)(t-2)/(s+t)

= -' R -------;----:::,-;:---:--11-1 I - R -s(l - 2)/(s + t)

m., = -' R[ I + R - 1/4] with

J2 (s, t) = ( 1, 3).

The enhaneement in the dissipation rate is

E-= 2~ wb _ R[ I - R - (s + 1)(1 - 2)/(s + 1)]

(s, t) = (1, 3)

(23)

(24)

where wb_ is the w integral in Eq. (21). The eoeffieient R[I-R- 1/2] is plotted in Figure 3. Note that the magnitude of the enhaneement does not depend on m.i.

In the upper troposphere E", 5 to 15 J/kg from BALSLEY and CARTER (1982) and BALSLEY and GARELLO (1985), respeetively, so heneeforth we will use a

nominal value of 10 J/kg. Then with R = 2, A8'" 10- 3 W/kg. This enhaneement is eonsiderably larger than the mean value of 8 near the tropopause, 3 x 10- 4 (TROUT

and PANOFSKY, 1969). (SCHEFFLER and LIU (1985) inferred an energy density of

31 J /kg in the upper troposphere at Arecibo, Puerto Rieo, but their results are based

on only 36 hours of data.) The thiekness )"t: of the enhancement with A' i '" 2 km (see

Seetion 3) is about 0.8 km.


In the high-Iatitude summer mesosphere E - 650 to 1300 J/kg, or nominally 1000 J/kg. Then with R = 3, Ae - 0.2 W/kg, which is considerably larger than the median value of about 10-2 for the latitude range from 500 N to 900 N (HOCKING, 1985). Near the mesopause with AOi = 20 km (see Section 3), AE - 5 km.

The foregoing are overestimates of Ae because of the assumption that all of the energy is propagating upward and the neglect of reflection. For a single wave with vertical wavenumber m, reflection is negligible provided that variations in the environment, and so in the wave parameters, are sm all over a vertical distance I/rn (BROUTMAN, 1982). At the tropopause the climatological mean N increases by - 2 over a vertical distance 2: 1 km, and at the high-Iatitude summer meso pause N increases by - 3 over about 4 km, as shown in Figure 4. These distances are much larger than the corresponding values of I/mE = AE/2n, which are 0.13 and 0.8 km, respectively, so most of the supersaturated part of the spectrum passes through the increase in N without appreciable reflection. It should also be noted that 10 J/kg may be an overestimate of the me an E, since the data used by Balsley and Carter and Balsley and Garello were taken ne ar mountainous terrain at Poker Flat, Alaska.

b. Enhanced Radar Reflectivity and Eddy Diffusion

The enhancement of e causes an enhancement of the radar reflectivity '1. The variation of the radar reflectivity with wavenumber k depends on the ratio k/ko, where ko is the wavenumber of the inner scale of turbulence. When k/ko ~ 1, k lies in the inertial subrange of turbulence, and '1 oce 2/3k+ 1/3 (ÜTTERSTEN, 1969). Then the ratio of the enhanced reflectivity to the mean reflectivity '1 is given by

(25a)

But when k / ko ~ I, k lies in the viscous subrange, and '1 is a strongly decreasing function of k, wh ich can be approximated by k - 5 or by the more accurate expression given by HILL and CLIFFORD (1978). If ko were not a function of e, then the ratio of enhanced reflectivity to the mean would still be given by Eq. (25a). But since kooce 1/4 , the curves must also be shifted, so that with the k- 5 law, '1oce2. Then the enhanced reflectivity is given by

(25b)

With Hili and Clifford's expression, the enhancement is as large or larger, but it increases with increasing k.

In the lower atmosphere Eq. (25a) always obtains for VHF radars (A,/2 - 3 m).

Then just above the tropopause with R = 2 the enhancement is '" 4.1 dB. Enhancements of this magnitude would be only marginally detectable, and, in fact, enhancements that can be attributed to echoes from turbulent irregularities are only sei dom observed. (Enhancements just above the tropopause due to Fresnel reflecti on from stratified irregularities are frequently observed, but they are irrelevant to the present discussion.)

Near the mesopause, }.r/2 for VHF radars can be either larger or sm aller than 10 , so that either Eqs. (25a) or (25b) may obtain. With R = 3, if }.r/2 > 10 the enhancement of ~ is '" 9 dB, and if }.r/2 < 10 the enhancement is '" 26 dB.

Figure 4 shows a profile of signal-to-noise ratio (which is proportional to radar reflectivity) averaged over two summer months at Poker Flat, Alaska, from ECKLUND and BALSLEY (1981), together with the mean profile of N 2 from Pt. Barrow, about 800 km north of Poker Flat. The correspondence between the altitude of the rapid increase of N and the enhancement of ~ is very good. It is also evident from this figure that R = 2.5 or 3, depending upon whether the peak value of N 2 at 87 km is compared with the value at 81 or at 83 km.

The model enhancements of reflectivity can be compared with the observed profile in both magnitude and thickness. The model magnitudes from Eqs. (25a) and (25b) with R = 3 are indicated in Figure 4 by bars along the upper abscissa,

Average S/N ( d B )

0 4 8 12 16 20 24 28 32 100

log (7) 17)0) ( dB)

95

90 E

.>:

85 AE

~

'" Q)

80 :c

75

70 0 2 4 6 8 10

N2 X 104 (rod/s)2

Figure 4 Solid circles and lower scale: A mean profile of N 2 from Point Barrow, Alaska (adapted from BALSLEY el al. (1984)). Open circles and upper scale: A profile of signal-to-noise ratio S/N averaged over two summer months at Poker Flat, Alaska. The bar on the upper abscissa is the range of enhanced radar reflectivity,., estimated from the enhanced saturation model. The bar on the vertical axis labeled AE is the

estimated thickness of the dissipation region.


and the model thickness AE is indicated by a bar on the right-hand ordinate. With R = 3, the model enhancement accounts for a substantial part of the observed enhancement. ECKLUND and BALSLEY also observed that the amplitude of the enhancement was quite variable. In terms of the present model this variability might be due to variations of R or to variations of 10 due to variations of e. It must be noted, however, that 1/ depends not only on e but also on the gradient of the electron density. Indeed, the enhancement observed by U LWICK et al. (1988) was attributed entirely to electron density gradients, since at the time of their experiment the rapid increase in N occurred several kilometers higher than the enhancement. The model thickness AE - 5 km is consistent with the 3 dB thickness of the signal-to-noise profile in Figure 4.

Another indication of the height and intensity of turbulence and of the associated wave effects is the height of the zonal wind maximum and the zonal wind shear above this height. The summer profiles presented by BALSLEY et al. (1983) indicate a mean zonal wind maximum at or just below the mesopause with large shears above. This suggests strong wave dissipation and drag concentrated near the summer mesopause with much weaker wave effects at lower levels and is generally consistent with the inferred effects of enhanced saturation.

c. Vertical Momentum Flux and Enhanced Mean Flow Acceleration

The dissipation of the supersaturated wave field mayaiso result in a divergence of the vertical ftux of horizontal momentum and a resulting acceleration of the mean ftow if the wave field is anisotropie. This development follows that of the vertieal energy ftux and the energy dissipation rate in the previous subsection.

Let us consider, in particular, the ftux of zonal momentum. We assurne, for simplicity, that the eastward and westward propagating wave spectra have the same functional dependence and that fractions (0.5 - a) and (0.5 + a) of the energy are propagating eastward and westward, respectively. The vertical ftux of zonal momenturn is then

(26a)

since w'/u' = k/m = wb ~2/N for each component of the wave spectrum, where u'

and w' are the zonal horizontal and the vertical perturbation velocities, Fuw is their cross spectrum and Fu is the autospectrum of u'. If it is assumed that the u'

component contributes half of the horizontal kinetic energy, then Fu(m, w) =

b+F/c.{m, w)/2, so that

SM = apo 1"" dm IN dwF(m,w)J+(w/N)J~2

= -apo - dm -- dw B(w)<5+w<5 ~2 E 100 A(~) iN N 0 m* 'f

= -apo~.1 '~f(~)2-P[I_ 3p -2 (L)2-P] N 2-p f 2p N

(26b)

with p = 5/3 and the same parameters as in the previous subsection. Again terms of the order of (f/N)P '" 10-4 have been neglected.

The fraction of the momentum ftux that is lost in going from below the increase in N to above it is

ASM SM", - SMf E",/Nf - Ef/Nf

SM; SM; E;/N;

E", N; [ Ef ] I Ef = E; Nf I - E", = - RE;

= I_R-(s+I)(I-2)/(s+I)= I-R- 1/2 with (s, t) = ( I, 3). (27)

This is plotted in Figure 3. The momentum ftux divergence ansmg from wave dissipation results in an

acce1eration ofthe mean ftow. As for the enhanced energy dissipation rate, we assume that the resulting acceleration is distributed uniformly over a slab of thickness AM = 2n/mM, where mM is the me an wavenumber weighted by SMw(~) - SMt<~):

mM = [Ewm.w LW d/1 A(/1)~ - Epz'f r" d~ A(~)~]j[Ew - E~ _ [Ewm·w - Epz • .tl

=~ [Ew - E.tl

sin(n(s + I )/(s + t» [1 - R -(s + 2)(1 - 2)/(.>+ 1)] = m.· R =--------;--:---;-::-:----;;:o:-;;--~

I sin(n(s + 2)/(s + t» [1 _ R -(s+ 1)(1- 2)/(s+l)]

[1 - R -3/4]

= m.;J2R [1 _ R -1/2] with (s, t) = (1, 3).

The enhanced acceleration is

(28)

(29)

with Eqs. (28c), (29b), and (30b). The coefficient R[I - R- 3/4 j is plotted in Figure 3.

In the upper troposphere, Po'" 0.4 kg/m3, E; '" 10 J/kg, N; '" 10-2 radis, and A.; '" 2000 m, and at the tropopause R '" 2. The magnitude of a is uncertain. Recently, however, FRITTS et al. (private communication) inferred a '" 0.1 near the tropopause over a 6-day period in March in Japan. Then SM; '" 0.04 N/m2 or SM;/PO'" 0.1 (m/s)2, AM'" 510 m, and l1ut '" -5.7 X 10- 5 m/s2 = -5.0 (m/s)/day.

The foregoing estimates of SM; and I1U t used a value of E; based on long-term averages at Poker Flat, Alaska. This value is not inconsistent, however, with values of E; from other localities. Therefore, these estimates of flux and mean flow acceleration may hold over much of the earth. When the flux is enhanced by mountain waves (see the summary by PALMER et al. (1986)) or other effects, the acceleration due to supersaturation is similarly enhanced. But high mountains cover only a small fraction ( < 10%) of the surface of the earth and other effects that enhance the momentum flux are similarly localized in time and space. Therefore, the background values of SM; and I1U t estimated above may dominate the global averages.

The estimated me an flow acceleration l1ut is comparable with the acceleration found by NURMI (1983) and PALMER et al. (1986) from momentum budgets. But the acceleration due to supersaturation is concentrated in a rather thin region, of the order of 1/2 km thick, which will have additional dynamical effects.

In the high-latitude summer mesosphere, Po'" 8 X 10- 6 kg/m3, E; '" 1000 J/kg, N; '" 2 X 10- 2 radis, and A.; '" 20 X 103 m, and at the mesopause R '" 3. The value of a in the mesosphere is not known, so we will continue to use a value of 0.1. Then SM; '" -4 X 10- 5 N/m2 or SMdPo'" -5 (m/s)2, AM'" 3.6 km, and l1ut '" -6 x 1O- 4 m/s2 = -50 (m/s)/day.

These estimates of SM; and I1Ut are quite comparable in magnitude with the fluxes and accelerations at Adelaide, Australia, during summer reported by REID and VINCENT (1987). Supersaturation may thus account for much of the measured acceleration near the meso pause during summer. Again, the acceleration is concentrated in a rather thin region, of the order of 3.6 km in the mesosphere. Of course, the present estimates must be reduced by the fraction of gravity wave momentum flux that is downward propagating and by the fraction of the flux that is reflected by the mesopause.

The effects of subsaturation are, of course, quite different. Just above a region where N decreases rapidly the spectrum will be subsaturated. But as the wave field propagates upward, the spectral amplitude will grow as 1I Po until the spectrum again reaches the saturation limit, given by Eq. (10). Where the spectrum is subsaturated, the occurrence of turbulent layers due to the random superposition of gravity waves should be reduced, with corresponding reductions in the background values of G, radar reflectivity 1], and me an flow acceleration. Observation of such a reduction of I] would tend to support the present model.


6. Conclusions

We have presented a theory describing the process and the effects of enhanced saturation of a gravity wave spectrum due to an increase in atmospheric stability. This theory represents a considerable generalization of the ideas advanced by BALSLEY et al. (1983) to account for the seasonal variations of MST radar echoes observed near the high-latitude mesopause. It also has significant implications for the gravity wave spectrum and for large-scale atmospheric motions near the tropopause and mesopause.

The principal effect of an increase in atmospheric stability was found to be an increase of wave energy density at large vertical wavenumbers above the level that can be maintained under the influence of saturation processes. This leads to enhanced dissipation of the wave spectrum over some appropriate height interval and results in increased turbulent energy dissipation and, if the wave spectrum has a net momentum flux, to an enhanced momentum flux divergence. These enhanced contributions to turbulence and wave drag may be comparable to or exceed those expected due to the decrease of density with height or in response to a reduction in the intrinsic phase speed of the wave motion. They may, therefore, need to be included in an appropriate fashion in models of the lower and middle atmosphere in order to correctly anticipate the effects of gravity waves on the large-scale circulation and thermal structure.

The effects of enhanced saturation were found to depend strongly on the change in atmospheric stability, with significant effects occurring for R = Nf/N; ~ 2 - 3. Assuming a dissipation depth equal to the weighted me an vertical wavelength of the dissipated wave energy, observed values of energy density, and no wave reflection due to the increase in N, our theory predicts maximum enhancements of the turbulent energy dissipation rate e of ~ 10- 3 and 0.2 W/kg at the tropopause and the high-latitude summer mesopause, respectively. Obviously, these estimates would be less if the dissipation depth is larger or there is any appreciable wave reflection. Also assuming a wave field anisotropy of 20% (excess of westward over eastward propagating components relative to the total) and other quantities as above, the inferred maximum mean flow accelerations Au, at the tropopause and the high-latitude summer mesopause are -5 and -50 (m/s)/day, respectively. Since these enhancements are comparable with median values of t: and with accelerations required to bring GCM's into accordance with observations, they suggest that enhanced saturation due to increases in atmospheric stability is indeed important. Thus, enhanced saturation appears to be consistent with a number of observed or anticipated gravity wave effects in the lower and middle atmosphere. Clearly, however, additional studies are required to further quantify these effects.

Efforts are being made to test the predictions of the model for enhanced saturation, using data from clear-air Doppler radars. The model prediction that the gravity-wave energy density should have a peak just above any rapid


increase in N can be compared with the variance of the energy calculated from radar time series of velocity as a function of altitude. The model prediction that E

should be enhanced just above an increase in N can be tested by comparison with curves of Doppler spectral width versus altitude, since the spectral width is proportional to E 1/2. This prediction also might be tested by comparison with curves of radar echo strength.

Acknowledgments

We wish to acknowledge helpful discussions with Drs. B. B. Balsley, W. K. Hocking, and T. Tsuda. The first author was supported in part by the Air Force Office of Scientific Research under Agreement Nos. ISSA-86-0050 and ISSA-87-0080. Support for the second author was provided by the SDIOjIST and managed by the Office of Naval Research under contract NOOOI4-86-K-0661.

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Atmos. Sei. 40, 1321-1333.

(Reeeived August 17, 1987, revised/aeeepted February 8, 1988)

PAGEOPH, Vol. 130, Nos. 2(3 (1989) 0033-4553(89(030421-23$1.50 + 0.20(0 © 1989 Birkhäuser Verlag, Basel

The Effect of Horizontal Resolution on Gravity Waves Simulated by the GFDL "SKYHI" General Circulation Model

Y. HAYASHI,I D. G. GOLDER,I J. D. MAHLMAN 1 and S. MIYAHARA2

Abstract-To examine the effects of horizontal resolution on internal gravity waves simulated by the 40-level GFDL "SKYHI" general circulation model, a comparison is made between the 30 and 10

resolution models during late December. The stratospheric and mesospheric zonal flows in the winter and summer extratropical regions of the I ° model are much weaker and more realistic than the corresponding zonal flows of the 30 model. The weaker flows are consistent with the stronger E1iassen-Palm flux divergence (EPFD).

The increase in the magnitude of the EPFD in the winter and summer extratropical mesospheres is due mostly to the increase in the gravity wave vertical momentum flux convergence (VMFC). In the summer extratropical mesosphere, the increase in the resolvable horizontal wavenumbers accounts for most of the increase in the gravity wave VMFC. In the winter extratropical mesosphere, the increase of VMFC associated with large-scale eastward moving components also accounts for part of the increase in the gravity wave VMFC.

The gravity waves in the summer and winter mesosphere of the 1° model are associated with a broader frequency-spectral distribution, resulting in a more sporadic time-distribution of their VMFC. This broadening is due not only to the increase in resolvable horizontal wavenumbers but also occurs in the large-scale components owing to wave-wave interactions. It was found that the phase velocity and frequency of resolvable small-scale gravity waves are severely underestimated by finite difference approximations.

Key words: Gravity waves, SKYHI model, horizontal resolution, space-time spectra, Eliassen-Palm flux.

1. Introduction

One of the major problems in numerical simulations of the middle atmosphere is to correctly incorporate the drag force due to internal gravity waves (see a review by FRITTS, 1984). This drag force is not only necessary for simulating the mean zonal flows but it is also important for simulating planetary scale flows (HOLTON,

1983; SCHOEBERL and STROBEL, 1984; MIY AHA RA, 1985). While the drag forces due to unresolvable small-scale gravity waves must somehow be parameterized in a

I Geophysical Fluid Dynamics Laboratory/NOAA, Princeton University, Princeton, NJ 08542, U.S.A.

2 Department of Physics, Kyushu University, Fukuoka 812, Japan.

422 Y. Hayashi et al. PAGEOPH,

numerical model, resolvable large-scale gravity waves also contribute to the momenturn balance. By analyzing a 40-level, 5° latitude resolution (NI8) GFDL "SKYHI" general circulation model with an annual mean condition, HA Y ASHI et al. (1984) found that the simulated vertical eddy momentum flux in the equatorial stratosphere was not only due to planetary-scale Kelvin waves but also to the resolvable gravity waves. KIDA (1985) demonstrated with a numerical model that the zonal mean wind and temperature in the mesosphere can be better simulated with the drag force due to resolvable gravity waves, which were randomly prescribed at the 15 km level.

MIY AHARA et al. (1986) showed that the vertical convergence of eddy momenturn flux acts to decelerate the mean flow in the extratropical stratosphere and mesosphere of a 40-level, 3 degree latitudinal resolution (N30) GFDL "SKYHI" model. This was due to the fact that the model's gravity waves in the westerlies consisted mainly of westward moving components which carry westward momenturn upward, while those in the easterlies consisted mainly of eastward moving components which carry eastward moment um upward. Vertical propagation of the model's gravity waves was affected not only by the zonal me an wind but also by the local wind field as modified by planetary waves. The drag force due to gravity waves acted to suppress stationary planetary waves in the winter mesosphere. Their preliminary analysis of a November simulation indicated that the gravity wave vertical momentum flux was significantly enhanced by increasing the horizontal resolution from 3° to 1°. However, it was not known at that time whether this increase would lead to a dramatic reduction of the unrealistically strong me an flows in December and January, since the high resolution model was not integrated beyond November.

The present paper is an extension of MIY AHARA et al. (1986) and ex amines the effect of horizontal resolution on simulated gravity waves in late December, with respect to the latitude-height distributions and wavenumber-frequency distributions of their vertical momentum flux. Also, tropical gravity waves are analyzed in more detail.

2. Comparison Between Low and High Resolution Models

a. Model Data

The general circulation models analyzed in the present study are 40-level GFDL "SKYHI" models with horizontal resolutions of N30 (3.0° latitude by 3.6° longitude) and N90 (1.0° latitude by 1.2° longitude). Details of the SKYHI models are described in FELS et al. (1980), LEVY et al. (1982), ANDREWS et al. (1983) and MAHLMAN and UMSCHEID (1984). In order to resolve high frequency gravity waves, space-time spectral analysis (see HA Y ASHI, 1982) was performed using bihourly N30 data and hourly N90 data.

Vol. 130, 1989 Effects of Horizontal Resolution on Gravity Waves 423

b. Mean Zonal Wind and Eliassen-Palm Flux Divergence

Figure 1 shows the latitude-height distributions of the mean zonal wind of the N30 and N90 models averaged over the periods 15 December to 3 January and 20-27 December, respectively. The levels of the models are indicated by the standard height corresponding to the model's pressure. It should be noted that the N90 stratospheric and mesospheric westerlies in the northern (winter) high latitudes are much weaker and are more realistic than the corresponding N30 flows, although the latitudinal maximum occurs nearly 20 degrees to the north of that observed (see GELLER et al., 1983, Fig. 2b). The N90 mesospheric easterly zonal flows in the southern (summer) high latitudes are also weaker and more realistic than the corresponding N30 flows, although the latitudinal maximum occurs nearly 20 degrees to the south of that observed (see BARNETT and CORNEY, 1985, Fig. l.l).

The zonal flow is closely related to the Eliassen-Palm flux divergence (EPFD) which is a measure of wave-mean flow interactions (ANDREWS and McINTYRE, 1976; HA Y ASHI, 1985). Figure 2 shows the 1atitude-height distributions of the E1iassen-Palm flux vector divided by press ure and the EPFD for the N30 and N90 models averaged over the respective samp1ing periods. The EPFD is negative (easterly forcing) in the winter mesosphere, while it it positive (westerly forcing) in the summer hemisphere. It shou1d be noted that the mesospheric EPFD in the winter and summer extratropics has nearly doubled with the increase in resolution. The increased EPFD is consistent with the reduced zonal flows.

c. Vertical Eddy Momentum Flux and its Divergence

The EPFD is the combination of eddy momentum flux convergence and the vertical ?erivative of the eddy meridional heat flux. Gravity waves contribute to the EPFD mainly through their vertical momentum flux, while planetary waves do so mainly through their meridional heat flux. Figure 3 shows the latitude-height distributions of the vertical moment um flux (VMF), consisting of zonal and meridional wavenumbers from 5 through 50 for the N30 model (Figure 3a) and from 5 through 150 for the N90 model (Figure 3b) averaged over the respective sampling periods. The VMF in these wavenumbers ranges is interpreted as being due to internal gravity waves and will be referred to as the "gravity wave VMF", although this interpretation is not very appropriate in the troposphere where this VMF would also be associated with synoptic scale disturbanees. The N90 gravity wave VMF in the stratosphere and mesosphere is significantly larger than the corresponding N30 gravity wave VMF and attains its latitudinal negative maximum to the north (600 N) of the N30 maximum (45°N) in the winter hemisphere. Interestingly, the VMF in the winter and summer mid-Iatitude troposphere of the two models are of opposite sign. However, the models' VMF does not play an important role in the mean momen-

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Figure 4 is the same as Figure 3 except for the vertical momentum flux convergence (VMFC). In the N90 model, the gravity wave VMFC accounts for nearly half of the EPFD in the winter extratropical mesosphere and almost all the EPFD in the summer extratropical mesosphere. The N90 gravity wave VMFC occurring in the winter extratropical mesosphere is nearly 4 times as large as the corresponding N30 gravity wave VMFC. However, this increase is much larger than the increase in the total EPFD. This is due to the fact that the planetary wave EPFD hardly increases in the mesosphere. On the other hand, the N90 gravity wave VMFC, occurring in the summer extratropical mesosphere, is nearly twice as large as the corresponding N30 gravity wave VMFC, being consistent with the increase in the EPFD in the region where planetary waves do not pro pagate from below. The above results are summarized in Table I.

Figure 5 shows the time distribution (20-27 December, 0.10 mb) of the gravity wave VMF, consisting of zonal wavenumber k :2': 5. The VMF is associated with positive values in the summer extratropics, while it is associated with negative values in the winter extratropics. The VMF is larger and more sporadic in the N90 model (solid) than in the N30 model (dashed).

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Figure 6 shows the zonal wavenumber-frequency spectral distributions of the VMF at 0.10 mb for the N30 (Figure 6a) and N90 (Figure 6b) models during the period 20-27 December around 45°S. The inner domain indicates the range of wavenumbers and frequencies resolved with the bihourly sampling of the N30 data. In the summer extratropical mesosphere, the VMF in both models are predominantly associated with eastward moving components due to the effect of the mean easterly flow. The characteristic frequency increases significantly with wavenumber

Table I

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Vol. 130, 1989 Effects of Horizontal Resolution on Gravity Waves

-u'wYP, O.lOmb, k25 10r-~~--~----------------------------,

N90[44.5 - 46.5'5[

o N30[43.5 - 49.5'5) -----------------j

N30[58.5 - 64.5'N)

N90[59.5 - 61.5'N)

-15~ __ _L __ -J ____ ~ __ _L ____ L_ __ ~ __ ~ __ ~

20 21 22 23 24 25 28

DATE (DECEMBER)

Figure 5

429

Time distribution (20-27 December, 0.10 mb) of vertical momentum flux (lO-4 ms -2) divided by pressure (-u'w'/p) consisting of zonal wavenumbers > 5. Dashed line (N30 model, 43.5-49.5 S,

58.5--64.5 N), solid line (N90 model, 44.5-46.5 S, 59.5--61.5 N).

up to wavenumber 25 for the N30 model (Figure 6a) and up to wavenumber 95 for the N90 model (Figure 6b). This model eomparison suggests that the phase veloeity and frequeney of high wavenumber eomponents are distorted by finite differenee approximations as studied by KURIHARA (1965). The N90 model has a broader frequency-speetral distribution than the N30 model, while both models have comparable spectral densities in the period range (eastward moving) of 0.5-1.7 days. The broader frequency-speetral distribution is eonsistent with the more sporadic time-distribution (Figure 5) of the gravity wave VMF.

Figure 7 is the same as Figure 6 exeept that it shows the wavenumber-frequeney speetral distributions of the VMF oeeurring at the latitudes around 60oN. In the N30 model, the VMF speetra are eoneentrated in the westward moving eomponents due to the effeet of the mean westerly flow. In the N90 model, the VMF speetra are eoneentrated in the westward moving eomponents for zonal wavenumbers 1-20, while they deerease their dominant frequeneies as the zonal wavenumber increases. The symmetrie frequeney speetral distribution of small-seale waves is probably due to some nonlinear interaetions between gravity waves and stationary waves. As in the summer hemisphere, the N90 model has a broader frequeney speetral distribution than the N30 model.

In order to examine the effeet of the frequeney broadening on the VMF, Table 2 shows the height distribution (near 45°S, 20-27 Deeember) of the gravity wave

430 Y. Hayashi et al.

COSPECTRA (u',- w')/p, OlOmb

FREQUENCY II/DAYI

I)Orl'~--r-~-r~--r-~-r~--r-__ -r~--T-__ ~'2 1.0 (al Nll. 435-495'S 130

120

110

~ 100 CD

~ 90

~ 80 > "" ~ 70 ...J ... 60 z S 50

'0

30

20

10

1~08~10~1~,-7,13~1~7~22~~~~~~~~~~~~~10~08 PERIOD IDAY)

IWESTWARO MOVING) IEASTWARD MOVING)

FREQUENCV (I/DAV)

150 " 12

1.0 (bl N90. 44.5 -46.5·S 130

120

110

a: 100 ... CD :!' 90 ::> z

80 ... > .. ~ 70

:;i 60 z 0 )0 N

. 0

30

20

10

1 08 10 " 13 10 08

PER IOD IOAY)

(WESTWARD MOVING) (EASTWARD MOVI NG)

Figure 6

PAGEOPH,

Frequency-zonal wavenumber spectral distributions (20-27 December) of the cospectral density (l0 -6 ms - 1d) of the vertical fiux of zonal momentum divided by pressure (-u 'w '/p) at O.lOmb (66.0 km) for the N30 model (a. 43.5-49.5 S) and for the N90 model (b. 44.5-46.5 S). The inner rectangular domain indicates the frequency-zonal wavenumber range resolved with bihourly sampling of

the N30 model. Dark shade > I, light shade < - I.


COSPECTRA ( u~- w') p, o 10mb

fREQU(NCY (I , DAY)

1,5.0 11 11

1A0 (a) NJO. 58.5-645 N 130

110

110

~ 100 al ::E 90 :::> ~ ao > « ~ 70 ~ .. 60 Z 0 so .....

'0

30

10

10

1 Da 10 11 13 17 n 17 13 11 10 oa

PERIOD IDAYI IWESTWARD MOVINGI IEASTWARD MOVING)

FREQUENCY II / DAYI

ISOtll~--:i:~~i--.--i-~---T0 ~--T~~-;'--~"':;"'~~'l 1A0 (b) N90. 595-61S'N 130

110

110

ffi 100 al

~ 90

~ 80 :;c ~ 70 .... « 60 z 2 $0

' 0

30

10

10'~0i'n~1i~b-~~~~~~~~~~O~1+.--:,::j 01 ' 08 10 10 06

PERIOD (DAYI

(WESTWARD MOVINGI (EASTWARO MOVING)

Figure 7 As in Figure 6 except for the latitudes (a. 58.5--{i4SN) and (b. 59.5--{iISN).

431

VMF consisting ofzonal wavenumbers 5- 50 and 5- 150. The N90 VMF (5 ~ k ~ 50) of latitudinally smoothed data is indicated in parentheses. This smoothing has been accomplished by averaging zonal and vertical velocities at three adjacent latitudinal grid points with weights of 0.25-0.5- 0.25. This averaging filters out high meridional wavenumber components of the N90 model which would not be resolved by the N30


Table 2

Height distributions (20--27 December) 01 the vertical momentum jiux -u'w' (10- 5 ms -1 mbs -1) due to westward and eastward moving eddies consisting 01 zonal wavenumbers 5-50 and 5-150. N30 model (43. 5-46. 5 "S), N90 model (44. 5-46. 5 0S). The parenthesized numbers indicate that the zonal and vertical

velocities have been smoothed over 3 latitudinal grid points.

N30 (5 ~ k ~ 50) N90 (5 ~k ~ 50) N90 (5 ~ k ~ 150) Level (km) Westward Eastward Westward Eastward Westward Eastward

76.1 0.00 0.61 -0.02 (-0.02) 0.55 (0.46) -0.01 0.87 70.6 0.01 1.55 -0.01 (-0.01) 1.70 (1.46) 0.02 2.49 66.0 -0.01 1.80 -0.07 (-0.06) 2.10 (1.76) -0.04 3.21 62.0 -0.03 1.81 -0.11 (-0.09) 2.15 (1.77) -0.09 3.50 58.5 -0.05 1.74 -0.20 (-0.16) 2.20 (1.78) -0.19 3.69 52.2 -0.09 1.62 -0.40 (-0.34) 2.25 (1.76) -0.45 3.89

46.6 -0.18 1.49 -0.67 (-0.57) 2.14 (1.62) -0.79 3.85 41.7 -0.31 1.37 -0.71 (-0.60) 1.96 (l.48) -0.89 3.66 37.1 -0.55 1.32 -0.81 (-0.65) 1.95 (1.43) - 1.12 3.82 32.9 -0.74 1.28 -0.87 (-0.67) 1.89 (1.32) - 1.33 3.90

29.0 -1.25 1.33 -0.91 (-0.64) 1.86 (1.25) - 1.57 3.98 25.2 -1.50 1.33 -0.97 (-0.62) 2.01 (1.39) - 1.97 4.22 21.7 -2.23 1.27 -1.27 (-0.74) 1.90 (1.28) - 2.72 4.10 18.3 -2.80 1.85 -2.64 (-1.83) 0.45 (-0.09) -4.54 2.32

15.2 -1.95 4.34 - 5.36 (-4.83) -5.23 (-5.70) -7.78 -4.45 12.2 -6.81 -7.60 7.83 (9.23) 19.72 (19.98) 4.85 19.48 9.4 -43.49 -120.92 42.34 (44.78) 105.65 (105.14) 38.14 105.11 6.8 -65.29 -198.26 20.29 (29.12) 53.03 (62.72) 14.88 46.20 4.5 -44.51 -146.33 7.23 (15.47) -0.01 ( 15.41) 3.59 -14.89 2.5 -26.37 -96.20 6.84 (14.46) -6.91 (13.42) 6.37 -17.36 1.0 -14.36 -53.18 12.93 ( 16.52) 37.22 (48.40) 13.58 42.85

model. A comparison between the N90 VMF with and without the latitudinal smoothing suggests that the increase in the eastward moving 5 s k s 50 components of the N90 VMF is mostly due to the increase in resolvable meridional wavenumbers. This means that the increase in the N90 VMF in the summer mesosphere is mostly due to the increase in resolvable zonal and meridional wavenumbers.

Table 3 is the same as Table 2 except for the winter extratropicallatitudes where the VMFs attain their maximum. The N90 VMF, with and without latitudinal smoothing, suggests that the increase in the westward moving 5 s k s 50 components is due mostly to the increase in resolvable meridional wavenumbers. However, the eastward moving 5 s k s 50 components increase substantially even with latitudinal smoothing. This increase accounts for part of the total increase in the gravity wave VMF in the winter extratropical mesosphere.


Table 3

As in Table 2 except Jor latitudes N30 model (43. 5-46. 5W), N90 model (59.5-61.5W).

N30 (5 s k s 50) N90 (5 sk s 50) N90 (5 sk s 150) Level (km) Westward Eastward Westward Eastward Westward Eastward

76.1 -0.73 -0.05 -0.46 ( -0.31) -0.09 ( -0.05) -0.64 -0.21 70.6 -1.54 -0.08 -1.29 ( -0.80) -0.49 ( -0.27) -1.88 -1.19 66.0 -1.87 -0.10 -2.60 ( -1.66) -1.11 ( -0.65) -3.74 -2.62 62.0 -2.19 -0.12 -3.61 ( -2.29) -1.59 ( -0.90) -5.19 -3.76 58.5 -2.42 -0.12 -4.30 (-2.70) -1.94 ( -1.04) -6.26 -4.63 52.2 -2.66 -0.07 -5.01 ( -3.04) -2.39 ( -1.19) -7.61 -5.71

46.6 -2.89 0.01 -5.39 ( -3.21) -2.67 ( -1.30) -8.50 -6.35 41.7 -2.98 0.14 -5.73 ( - 3.46) -3.02 ( -1.46) -9.25 -7.03 37.1 -3.28 0.24 -5.96 ( -3.59) -3.32 ( -1.66) -9.73 -7.70 32.9 -3.67 0.46 -6.32 ( - 3.84) -3.89 (-2.13) -10.22 -8.66

29.0 -3.89 0.66 -6.87 ( -4.07) -4.37 ( -2.55) -10.89 -9.46 25.2 -4.50 0.87 -7.39 ( -4.44) -4.71 ( -3.02) -11.64 -9.78 21.7 -5.57 1.14 -7.78 ( -4.31) -4.94 ( -3.20) -12.26 -10.05 18.3 -6.52 1.46 -9.51 ( -4.95) -5.88 ( -3.61) -14.54 -11.16

15.2 -6.85 2.88 - I 1.02 ( - 5.35) -6.99 ( -3.62) -16.42 -12.56 12.2 -5.16 6.43 -9.38 ( -3.29) -4.19 (0.14) -15.19 -10.18 9.4 - 13.06 -12.53 -7.55 ( -0.19) -17.45 ( -9.82) -16.35 -26.54 6.8 -45.00 -96.06 - 56.32 (- 31.44) - I 19.61 ( -93.94) -72.80 -136.79 4.5 - 53.42 - 121.17 -84.37 (-57.61) -186.07 (-143.83) -96.99 -201.47 2.5 -43.28 -100.38 -90.23 (-61.26) -193.72 (-148.91) -98.05 -199.59 1.0 -24.68 -36.32 -50.37 (-31.01) -109.35 (-77.12) -53.38 -99.05

To examine the effect of horizontal resolution on frequency broadening, Figure 8 shows the frequency-height distributions (around 45°S, 20-27 December) of the N30 and N90 VMF (divided by press ure) consisting of zonal wavenumbers 5-50. The N90 data have been smoothed over three latitudinal grid points. At all the levels, the N90 VMF spectra are associated with a broader frequency distribution. The N30 and N90 VMF spectra are biased toward eastward moving components in the mesosphere and stratosphere. In the troposphere, both N90 and N30 VMF spectra are dominated by eastward moving low frequency (period > 1 day) components which are probably associated with extratropical cyclones. These components reverse their sign as the horizontal resolution is increased from N30 to N90. This result indicates that the increase in resolution affects wave components which are resolved by the N30 model.

Figure 9 is the same as Figure 8 except for the winter extratropics around 60oN. The N30 VMF spectra in the mesosphere and stratosphere are concentrated in the westward moving components, whereas the N90 VMF spectra are somewhat biased toward westward moving components. As in the summer extratropics, both

434

• i Q t

y. Hayashi et al. PAGEOPH,

COSPECTRA (11;- Wl ) Ip. 5$k $50. 20-27 DECEMBER

01 N30 435 - 49.55 (bi N90. 44.S 46.5 °5

fREOUENCy " daYI fREQuENCY 11 da."

•• 0 • .1 3 •• 2 •• 1.2 76.1

70-"

66.0

67.0

SI.S

~"

'.ob .1.1

37,1

31.' 2'.0

15.1

71.1

18.3 105.2

11.'2

'.' M ... 2.S 10 0.167 0.71 0.28 0..7 0.83

wESTWAIO MOVINCI

o 1.1 '2." 3.6 4.8 6.0

70-"

~2.2

".7

37.1

37.'

19.0

7~.?

71.7

15.)

1~.2

17.7

'.' •• e •• S

2. ' 1.1 0 1.1 2.. 3.6 •. e 6.0

~~~~~~~~~~~~~~~~ 0.13 0 .• 7 0.71 0.21 0.1.7 0.167 0.71 0.21 0 ... 2 0.13 0.83 0.'7 0.78 0.21 0.167

PUIOO dGyl

EASTWAao MOVINGI IWESfWARD MOVING'

Figure 8 Frequency-height distributions (20-27 December) of the cospectral density (10 - 6 ms - 2 d& of the vertical flux of momentum consisting of zonal wavenumber 5- 50 and divided by press ure ( - u'w ' !p) for the N30 model (a. 43.5-49.5 S) and for the N90 model (b. 44.5-46SS). The zonal and vertical velocities of the N90 model have been smoothed over 3 adjacent latitudinal grid points. Dark shade > I, light

shade < -I .

the N30 and N90 VMF spectra in the troposphere are domina ted by eastward moving low frequency (period > I day) components which are probably associated with extratropical cyclones.

e. Tropical Gravity Waves

Figure 10 is the same as Figure 6 except that it shows the zonal wavenumber-frequency distributions of VMF spectra at equatorial latitudes. These spectra are associated with eastward and westward moving components of comparable magnitude but opposite signs. The N90 VMF has a broader frequency spectral distribution than the N30 VMF.

Table 4 shows the height distributions of the N30 VMF consisting of zonal wavenumbers I-50 and 1- 2, while Table 5 shows that of the N90 VMF consisting ofzonal wavenumbers I- ISO and 1- 2. These VMFs are further partitioned into those due to transient eddies, westward and eastward moving eddies. The transient VMF is the sum of westward and eastward moving VMF. It should be noted that the

! i 8 %

COSPECTRA (u'- w')/P. 5~ k$50. 20 -27 DECEMBER

(al N30. 58.5- 64.5 N [bi N90. 59.5 - 01.5 N

.. 0 0.8 3 •• 16.1

70"

•• ° .2.0

".5

52.2

0."

,, '.1

37.'

31.9

29.0

15.2

21.7

'8.3 '5.1 11.7 9.0 .. ' ' .5 2.5 , 0

0.'.7 0." 0.18

F!llEQuENCy tl d",1 flfOUENCY 11 doy

1 ..

0 .. ,

'.2

0.83

o 1.1 1." J,6 • . 8 0,0 6.0 4.8 3.6 1," I. :l 0 1,1 1," 3.6 4.8 6.0 76.' r-~-r-r-r"T-T~""'~?Z>'::::l<~

70 .•

./1,0

.2.0

~.5

51.1

0',7

37.'

32.9

'9.0

'~.1

11.7

'8.3 ' ~.1 12.2

9.' 6.8 0.5 l . ~ ,.Ol-T-.--T""'T-.-,.......,..-Ti' ..... ~""""c.,......,-r-"T"""T--.-f

0.83 0.'" 0.28 0.21 0.167 0,16" 0.11 0.1JJ 0 '" 0.83 0.83 0." 0.28 0.11 0.'.7

'€AIOO Idorl PERloe Idar l

I WEsrWAITO MOVINGI

Figure 9 As in Figure 8 except for the latitudes (a. 58.5.-64SN) and (b. 59.5-61 SN).

435

wavenumber 1-2 components of both the N30 and N90 models account for only a small portion of the VMF consisting of all the resolvable wavenumbers. This implies that the gravity wave VMF in the equatorial stratosphere accounts for most of the VMF in both the models, while the stratospheric and mesospheric Kelvin waves of wavenumbers 1-2 and periods of3-7 days playa minor role in the momentum balance in a model with seasonal variations. In contrast, HA Y ASHI el al. (1984) found that Kelvin waves and gravity waves play comparable roles in the NI8 annual mean condition SKYHI model in which westward and eastward moving gravity wave VMFs almost cancel each other. The present result is consistent with the recent analysis of the N30 model by HAMILTON and MAHLMAN (1988) who found that the high wavenumber transient components play a dominant role in the momentum balance of the simulated semi-annual oscillation in its westerly phase. In the mesosphere, the N90 transient VFM, consisting ofwavenumbers I-ISO (Table 5), is smaller than the N30 transient VMF consisting of zonal wavenumbers I-50 (Table 4). The decrease in the transient VFM with the increase in horizontal resolution results from the fact that the increase in the westward moving component with negative VMF is larger than the increase in the eastward moving component with positive VMF. The difference in these increases is probably related to the change in the zonal flow.

436 Y. Hayashi et al.

COSPECTRA (u~- w,) P. o 10mb

FREQUENCY (I / DAYI

1S0r"~--T-~-r~--T-~-T~--T-~-T--~T-~~" "0 (a) N30. 4 5'N-4 5'S

'30

'20

110

5 100 al

~ 90

~ 80 > ~ 70

<i! 60 z 2 50

'0

30

20

'0

'~08~'O--,L'~'3~'~7-722~~~~~~~722~~I7~'~3~1I-7'O~08

PERIOD IOAYI

IWESTWARD MOVINGI lEASTWARD MDVINGI

f REQUENCY 11 / DAY)

'50r"~--r-~-r~--r-~-r~--r-~-r6 ____ ~~-;" "0 (b) N90. 2.5 N-2.5'S

'30

'20

110

~ .00 al

~ 90

~ 80

~ 70 -' ... 60 z 2 :sO

'0

30

20

'0 -

'~08~'O--'~'~'3--1~7-722~3~l26~7~'~7~'~7~6~7~3hl~22~~I7~I~3~1I~10~08 PER IOD (DAY)

j'NESTWARD MDVINGI IEASTWARD MOVINGI

Figure 10

PAGEOPH,

Frequency-zonal wavenumber distributions (20-27 December) of the cospectral density (10 - 6 ms - I day) of the vertical ftux of zonal moment um divided by pressure ( -u'w' jp) at 0.10 mb (66.0 km) for the N30 model (a. 4SN-4SS) and for the N90 model (b. 2SN- 2SS). The inner rectangular domain indicates the frequency-wavenumber range which can be resolved with a bihourly sampling of the N30 data. Dark

shade > I, light shade < - I.

Table 4

Height distributions (N30 model, 4.5W-4.5°S, 20--27 December) 0/ the vertical eddy momentum flux - u'w' (/0- 5 ms -I mbs -I) due to transient (deviation /rom 8-day mean) eddies, west ward and eastward

moving eddies consisting 0/ zonal wavenumber 1-50 (le/t) and 1-2 (right).

Wavenumbers 1-50 Wavenumbers 1-2 Level (km) Transient Westward Eastward Transient Westward Eastward

76.1 0.06 -0.13 0.20 0.004 -0.001 0.005 70.6 0.23 -0.38 0.61 0.011 -0.004 0.015 66.0 0.49 -0.60 1.09 0.018 -0.009 0.027 62.0 0.85 -0.80 1.65 -0.003 -0.031 0.028 58.5 1.32 -0.93 2.25 0.022 -0.026 0.048 52.2 2.40 -1.13 3.53 0.055 -0.023 0.079

46.6 3.05 -1.47 4.52 0.02 -0.05 0.07 41.7 2.95 -2.16 5.11 -0.13 -0.16 0.03 37.1 3.09 -3.44 6.54 0.11 -0.01 0.13 32.9 3.57 -4.99 8.56 0.06 -0.05 0.11

29.0 5.58 -6.42 12.00 0.27 -0.04 0.31 25.2 9.65 -7.03 16.69 0.24 -0.02 0.26 21.7 12.01 -7.73 19.79 0.24 -0.01 0.25 18.3 12.72 -10.98 23.70 0.21 -0.05 0.26

15.2 15.92 -26.81 42.74 0.83 -0.19 1.02 12.2 2.66 -42.75 45.41 -4.09 -4.08 -0.00 9.4 -25.61 -28.72 3.11 -10.22 -5.61 -4.60 6.8 -30.98 37.50 -68.49 -9.72 -3.95 -5.77 4.5 -1.35 78.09 -79.45 0.38 0.93 -0.55 2.5 24.50 70.04 -45.59 0.86 0.44 0.42 1.0 26.30 33.29 -6.99 4.93 2.69 2.24

Table 6 shows the height distribution (around the equator, 20-27 December) of the VMF consisting of zonal wavenumbers 5-50 and 5-150. The N90 VMF (5 < k < 50) of latitudinally smoothed da ta is indicated in parentheses. This table suggests that the increase of the VMF in the stratosphere and mesosphere is mostly due to the increase in resolvable zonal and meridional wavenumbers.

In the troposphere and stratosphere, the power spectra for zonal wavenumbers 5-50 and 5-150 of the zonal and meridional velocities are reduced (not shown), whereas the power spectra of the vertical velocity are increased. In the extratropics, zonal, meridional and vertical velocities of gravity waves are increased (not shown). This result implies that the cancellation between the zonal and meridional convergen ce is significantly less in the N90 tropics. The increase in vertical velocity also implies that the convective activity is increased in the tropics. It is difficult to explain why the kinetic energy of gravity waves in the tropics is reduced in the N90 model, although ~is reduction is consistent with the decrease (not shown) of temperature variance (T'2) and energy conversion (T'W').


Table 5

Height distributions (N90 model, 2. 5W-2. 50S, 20-27 December) of the vertical eddy momentum flux - u'w' (10- 5 ms- I mbs- I ) due to transient (deviation from 8-day mean) eddies, westward and eastward

moving eddies consisting of zonal wavenumbers 1-150 (left) and 1-2 (right).

Wavenumbers 1-150 Wavenumbers 1-2 Level (km) Transient Westward Eastward Transient Westward Eastward

76.1 -0.02 -0.31 0.29 0.004 0.000 0.004 70.6 -0.04 -1.00 0.96 0.003 -0.004 0.008 66.0 -0.02 -1.69 1.68 0.003 - 0.010 0.012 62.0 0.08 -2.28 2.36 0.006 -0.011 0.017 58.5 0.29 -2.78 3.07 0.019 -0.007 0.025 52.2 1.52 - 3.46 4.98 0.043 -0.002 0.045

46.6 3.90 -3.89 7.79 0.018 -0.017 0.035 41.7 4.76 -4.70 9.46 -0.023 -0.043 0.020 37.1 4.71 -6.58 11.29 0.032 -0.011 0.043 32.9 2.00 - 1l.58 13.59 0.030 -0.033 0.063

29.0 -2.15 -17.61 15.46 0.06 -0.04 0.11 25.2 -2.42 - 20.42 18.00 -0.03 -0.11 0.09 21.7 1.43 -19.91 21.34 0.17 0.04 0.12 18.3 1.39 - 24.05 25.43 - 0.17 -0.19 0.02

15.2 8.73 -42.27 51.00 0.72 0.32 0.40 12.2 12.18 - 54.72 66.90 4.27 2.19 2.08 9.4 -0.59 - 32.43 31.84 4.16 2.40 1.76 6.8 -2.76 36.51 - 39.27 7.75 4.88 2.87 4.5 - 10.78 77.26 - 88.03 -1.14 0.36 -1.50 2.5 22.76 76.11 - 53.36 - 5.85 -3.54 -2.31 1.0 65.03 73.34 -8.31 -3.04 - 1.58 -1.46

To examine the effect of horizontal resolution on the frequency-spectral distribution, Figure 11 shows the frequency-height distributions (around the equator, 20--27 December) of the N30 and N90 VMF (divided by pressure) consisting of zonal wavenumbers 5-50. The N90 data have been smoothed over three latitudinal grid points to eliminate small-scale meridional components which are not resolved by the N30 model. The N90 VMF in the stratosphere and mesosphere has a broader frequency spectral distribution than the N30 VMF. The eastward and westward moving components of the VMF reverse their sign with height around the 300 mb level. This reversal implies that wave activity propagates upward and downward from an energy source in the upper troposphere, since the energy ftux and momentum ftux of gravity waves are opposite. The energy source of tropical gravity waves is probably the latent heat release by cumulus convection.

Figure 12 is the same as Figure 11 except for the power spectra of the zonal component. In the equatorial troposphere of both models, these power spectra have a red noise distribution and there is no frequency spectral peak corresponding to the


Table 6

Height distributions (20-27 December) 0/ the uertical momentum fiux -u'w'(1O-5 ms -I mbs -I) due to westward and eastward mouing eddies consisting 0/ zonal wauenumbers 5-50 and 5-/50. N30 model (4.5W-4.5W), N90 model (2.5W-2.5°S). The parenthesized numbers indicate that the zonal and uertical

uelocities haue been smoothed ouer 3 latitude grid points.

N30 (5 ,,; k ,,; 50) N90 (5 ,,; k ,,; 50) N90 (5,,;k,,; 150) Level (km) Westward Eastward Westward Eastward Westward Eastward

76.1 -.13 .17 -0.19 ( -0.16) 0.19 (0.16) -0.31 0.28 70.6 -.38 .54 -0.59 ( -0.49) 0.61 (0.49) -0.98 0.93 66.0 -.59 .96 -0.98 ( -0.79) 1.03 (0.84) -1.66 1.63 62.0 -.76 1.45 -1.32 ( -1.06) 1.44 (1.14) -2.23 2.31 58.5 -.90 1.97 -1.58 ( -1.28) 1.85 ( 1.48) -2.27 3.01 52.2 -1.10 3.05 -1.97 ( -1.52) 2.98 (2.37) -3.42 4.86

46.6 -1.40 3.94 -2.22 ( -1.71) 4.62 (3.65) -3.83 7.66 41.7 -1.94 4.54 -2.70 ( -2.08) 5.39 ( 4.27) -4.55 9.36 37.1 -3.35 5.85 -3.94 ( -2.93) 6.29 ( 4.17) -6.46 11.18 32.9 -4.87 7.63 -6.49 (-4.79) 7.48 ( 5.62) -11.45 13.36

29.0 -6.35 10.66 -9.17 ( -6.58) 8.43 (6.78) -17.37 15.15 25.2 -7.04 14.96 -10.27 (-7.16) 10.02 (7.22) -20.11 17.67 21.7 -7.69 18.13 -10.23 ( -7.05) 11.55 (7.94) -19.85 20.97 18.3 -10.71 22.13 -11.92 ( -7.71) 13.25 (9.26) -23.57 25.16

15.2 -25.47 39.51 -21.37 (-12.60) 27.75 ( 16.07) -42.01 50.59 12.2 -39.33 37.51 - 32.45 (- 18.28) 41.31 (17.63) -57.49 63.38 9.4 -28.17 - 3.10 -18.94 ( -6.01) 27.30 ( 11.62) -34.86 30.40 6.8 35.73 -68.33 15.02 (15.45) -15.53 ( -0.99) 27.36 -44.76 4.5 74.44 -77.48 27.76 (16.54) -32.12 (-16.13) 74.28 -87.52 2.5 65.64 -45.66 26.82 (22.60) -22.69 ( -8.28) 77.13 -53.03 1.0 28.98 -9.68 30.13 (21. 98) -2.80 (0.34) 71.19 -8.68

spectral peak occurring in the VMF. However, the low frequency components do not penetrate the stratosphere and mesosphere. The power spectra of vertical velocity (not illustrated) are associated with a similar spectral distribution.

3. Summary and Remarks

Comparing internal gravity waves appearing in la te December in the N30 and N90 models with horizontal resolutions of approximately 3° and 1°, respectively, the following conclusions have been obtained.

1) The N90 stratospheric and mesospheric zonal flows in the winter and summer extratropical regions are much weaker and more realistic than the corresponding N30 flows. The weaker flows are consistent with the Eliassen-Palm flux divergence (EPFD) which has increased by a factor of 2 with increased resolution.

COSPECTRA (11.- w')/P. 5$: k ~ SO. 20-27 DECEMBER

lai 30. 4.5 - 4.5'S Ibl N90. 2.5 N 2.5 S fll:fQUE .... Cy (I day' fuQuENCY 1' ! dCl)"1

0.0 ~.8 1.6 7," 1.2 0 1.2 2.4 3.6 4.tl 6,0 6.0 4.8 3.6 1," 1,1 0 1.1 2." 3.6 ".8 6.0 7 •• 1 7 •• 1 "H'-r'-t--""~""h'nrl1IrtT--r""""'''''''''''''''r'-'rl

70 ..

6b.0

.'.0 58.5

51.1

.... 37.1

70 ..

••• 0

.'.0 58.1

$1.7

' • .6

37.1

lM JU

7 •. 0 79.0

15.1 15.1

11.7 21.7

18.l 18.3

15.1 '5.1 ''1.1 11.2 ~ ~ U U U u 1.5 7.' 1.01-,~~,..,..-,-"':::;;'''''~=;::~~~-.-.,....f 1.0'l--,~-,-,..,..-,-.40-.-L..,--.-,....,..-.-r--r-.--,--I' 0.161 0.11 0.28 0.'" 0 .83 0.83 0."1 0.28 0.21 0167 0.167 0.21 0.2.0 0,'" 0.83 0.83 0. 0lil 7 0.28 0.21 0.\67

PUIOO IdD:r! PU 100 Ido)'1

WUTw"'RD MOVINC IE .... SIWAIitO ",OVINGI IWESTW .... RD MQVINC

Figure 11 Frequency-height distributions (20--27 December) of the cospectral density (10- 6 ms- 1 d<1i'L of the vertical flux ofmomentum consisting ofzonal wavenumbers 5-50 and divided by pressure (-u'w'lp) for N30 model (a. 4SN-4SS) and for the N90 model (b. 2SN-2SS). The zonal and vertical velocities of the N90 model have been smoothed over 3 adjacent latitudinal grid points. Dark shade > I, light

shade < - I.

2) The increase of EPFD in the summer and winter extratropical mesosphere is mostly due to the increase in gravity wave vertical momentum flux convergence (VMFC), while that in the winter extratropical stratosphere is due to the increase of the planetary wave EPFD.

3) The N90 gravity wave VMFC, occurring in the summer extratropical mesosphere, is nearly twice as large as the N30 gravity wave VMFC and accounts for most of the N90 EPFD, while that occurring in the winter extratropical mesosphere is nearly 4 times as large as the N30 gravity wave VMFC and accounts for nearly half of the N90 EPFD.

4) The increase of resolvable horizontal wavenumbers in the N90 model accounts for most of the increase of the gravity wave VMFC in the summer extratropical mesosphere. In the winter extratropics, the increase in large-scale eastward moving components also accounts for part of the increase in the gravity wave VMFC.

i " .. x

POWER SPECTRA (t1), 5S; k:S:50, 20-27 OfCEMBER

(al N30, 4.5 N- 4.5 S [bi N90. 2.5 N- 2.5"S FRfOUfNCY 11/ dllJYI FftEQuEN(r ,I da,1

6.0 "'.8 3.6 2.. I.' 0 1.2 2.. 3.6 .,8 6.0 6.0 •. a 3,0 ,.... 1.2 0 1.1 2... 3.6 ".S 6.0 76.1 76.1 t77...., ........... ~::::-i,......., ............. ~-+-,......".-t 70.1>

66.0

67.0

58.5

<1.7

37.1

37.9

79.0

75.2

11.7

18.3 15.7 11.2 9.< 6.8 <.5 1.5 1.0..,....,~~.....,,~;»+'-r"'~4...!.;...!44-.,-,.~-rl 0.167 0.11 0.1a 0.<1 0.83 0.83 0.0lil1 O.2S 0.1' 0,167

I 'WESTWARO ... OVINGI 11: A S TW ARO MOV tNGt

70.6

66.0

67.0

58.5

52.1

<6.0

"1.1

37.1

31.9

19.0

Figure 12

0.83 0."" o.?i 0.21 0.101

PEIl 100 (dogrl

' WESr'WAftO MOV 0

As in Figure 11 except for power spectral density (10- 2 m2 S-2 day) of zonal velocity (zonal wavenumbers 5-50). Dark shade >200.

5) The N90 gravity waves are associated with a broader frequency-spectral distribution, resulting in a more sporadic time distribution of their vertical momenturn fiux (VMF). The broader distribution is not only due to the increase of resolvable horizontal wavenumbers but also occurs through nonlinear interactions in the horizontal scales which can be resolved by the N30 model.

6) The westward phase velocities of N90 and N30 gravity waves occurring in the winter extratropical regions are slower than their eastward phase velocities in the summer extratropical region. The phase velocity and frequency of resolvable smallscale gravity waves are severely underestimated by finite difference approximations.

7) The gravity wave vertical momentum flux in the tropical stratosphere accounts for most of the VMF in both the N90 and N30 models, implying that the fast Kelvin waves consisting of wavenumbers 1-2 playa minor role in the momentum balance.

8) The N90 gravity wave VMF in the tropical stratosphere and mesosphere is mostly positive and smaller than the N30 gravity wave VMF. The smaller VMF results from the fact that the increase in the westward moving component with negative VMF is larger than the increase in the eastward moving component with positive VMF.


9) The kinetic energy of N90 gravity waves In the tropical troposphere and stratosphere is sm aller than that of N30 gravity waves, while vertical velocity of N90 gravity waves is increased. The kinetic energy of gravity waves in the tropical troposphere has a red noise frequency-spectral distribution. However, low frequency components do not penetrate to the stratosphere.

The present results indicate that the N90 model is associated with broader frequency spectral distributions than the N30 model. This broadening is not only due to the increase of resolvable meridional wavenumbers but is also due to wave-wave interactions. It is likely that this distribution will become much broader if the horizontal resolution is further increased. This tendency is consistent with observations (FRITTS and VINCENT, 1987) that over 70% of the mesospheric vertical momentum flux is due to gravity waves with periods of less than one hour. In spite of the difference in their frequency spectral distributions, both the observed and simulated mesospheric vertical momentum flux u'w' is of the same order of magnitude (I m2 S-2). The vertical scale of the N30 and N90 gravity waves, as estimated from time-height sections (not illustrated), ranges between 20--50 km, being in agreement with the observed value (10--30 km) in the mesosphere (e.g., SMITH et al., 1987). However, the present models do not have sufficient vertical resolution to resolve an adequately short vertical scale (I km) gravity wave as observed in the stratosphere and troposphere (e.g., SMITH et al., 1987). The increase of N90 large-scale gravity waves in the winter extratropical mesosphere is, to some extent, due to wave-wave interactions. The decrease of the kinetic energy of N90 gravity waves in the tropics is somewhat puzzling and remains to be explained.

Acknowledgments

The authors are grateful to Drs. H. Kida and K. Hamilton and two anonymous reviewers for their valuable comments.

REFERENCES

ANDREWS, D. G., and M. E. McINTRYE (1976), Planetary waves in horizontal and vertical shear: The generalized Eliassen-Palm relation and the mean zonal acceleration, J. Atmos. Sei. 33, 2031-2048.

ANDREWS, D. G., J. D. MAHLMAN, and R. W. SINCLAIR (1983), Eliassen-Palm diagnostics 01 wave-mean flow interaction in the GFDL "SKYHI" general circulation model, J. Atmos. Sei. 40, 2768-2784.

BARNETT, J. J., and M. CORNEY (1985), Middle atmosphere relerence model derivedlrom satel/ite data, Handbook for MAP, 16,47-85,318 pp. (Availab1e from SCOSTEP Seeretariat, University ofIllinois, Urbana, Illinois 61801.)

FELS, S. B., 1. D. MAHLMAN, M. D. SCHWARZKOPF, and R. W. SINCLAIR (1980), Stratospheric sensitivity to perturbations in ozone and carbon dioxide: Radiation and dynamical response, 1. Atmos. Sei. 37, 2265-2297.

FRITTs, D. C. (1984), Gravity wave saturation in the middle atmosphere: A review 01 theory and observations, Rev. Geophys. Space Phys. 22, 275-308.

Vol. 130, 1989 Effeets of Horizontal Resolution on Gravity Waves 443

FRITTS, D. c., and R. A. VINCENT (1987), Mesospheric momentum flux studies at Adelaide, Australia: Observations and gravity wave-tidal interaction model, J. Atmos. Sei. 44, 605--619.

GELLER, M. A., M. F. Wu, and M. E. GELMAN (1983), Troposphere-stratosphere (sur[ace-55 km) monthfy winter general circulation statistics[or the Northern Hemisphere-[our year averages, J. Atmos. Sei. 40, 1344-1352.

HAMILTON, K., and J. D. MAHLMAN (1988), General circulation model simulation o[ the seminannual oscillation o[ the tropical middle atmosphere, J. Atmos. Sei. 45, 3212-3235.

HAYASHI, Y. (1982), Space-time spectral analysis and its applications to atmospheric waves, J. Meteor. Soe. Japan 60, 156-171.

HAY ASHI, Y. (1985), Theoretical interpretations o[ the Eliassen-Palm diagnostics o[ wave-mean flow interaction. Part I: Effects o[ the lower boundary, Part ll: Eifects o[ mean dampling, J. Meteor. Soe. Japan, 63,497-512, 513-521.

HAYASHI, Y., D. G. GOLDER, and J. D. MAHLMAN (1984), Stratospheric and mesospheric Kelvin waves simulated by the GFDL "SKYH[" general circulation model, J. Atmos. Sei. 41, 1971-1984.

HOLTON, J. R. (1983), The influence or gravity wave breaking on the general circulation o[ the middle atmosphere, J. Atmos. Sei. 40, 2497-2507.

KIDA, H. (1985), A numerical experiment on the general circulation o[ the middle atmosphere with a three-dimensional model explicitly representing gravity waves and their breaking, Pure Appl. Geophys. 122, 731- 746.

KURIHARA, Y. (1965), On the use o[ implicit and iterative methods [or the time integration o[ the wave equation, Mon. Wea. Rev. 93, 33-46.

LEVY, H., 11, J. D. MAHLMAN, and W. J. MOXIM (1982), Tropospheric NzO variabi/ity, J. Geophys. Res. 87, 3061-3080.

MAHLMAN, J. D., and L. J. UMSCHEID, Dynamics o[ the midd/e atmosphere: Successes and problems o[ the GFDL "SKYH/" general circulation model, in Dynamics o[ the Middle Atmosphere (J. R. Holton and T. Matsuno, eds.) (Terra Seientific 1984) pp. 501-525.

MIY AHARA, S. (1985), Suppression o[ stationary planetary waves by internal gravity waves in the mesosphere, J. Atmos. Sei. 42, 100-107.

MIYAHARA, S., Y. HAYASHI, and J. D. MAHLMAN (1986), Interactions between gravity waves and planetary scale flow simulated by the GFDL "SKYH[" general circulation model, J. Atmos. Sei. 43, 1844-1861.

SCHOEBERL, M. R., and D. F. STROBEL, Nonzonal gravity wave breaking in the winter mesosphere, in Dynamics or the Middle Atmosphere (1. R. Holton and T. Matsuno, eds.) (Terra Seientifie 1984) pp. 45-64.

SMITH, S. A., D. C. FRITTS, and T. E. VANZANDT (1987), Evidence [or a saturated spectrum o[ atmospheric gravity waves, J. Atmos. Sei. 44, 1404-1410.

(Received September 2, 1987, revised/aeeepted Mareh 31, 1988)


Laboratory Observations of Gravity Wave Critical-Layer Flows

DONALD P. DELISI l and TIMOTHY J. DUNKERTON l

Abstract-A new laboratory facility for studying gravity wave critical-Iayer interactions is described, and the results from one experiment are presented. In the experiment, a forced, monochromatic gravity wave is allowed to propagate into a stratified shear flow containing a critical level for the gravity wave. The early evolution of the flow is characterized by turbulent wavebreaking and mean flow modifications which are in qualitative agreement with previous numerical simulations. The late-time critical layer flow is characterized by internal mixing regions which are phase-Iocked to the incoming gravity wave.

Key words: Gravity wave, critical layer, stratified shear flow interactions.

J. Introduction

Atmospheric gravity waves exist over a broad range of frequencies and wavelengths. These waves have two features which make them important for the earth's general circulation: their ability to transport momentum vertically and their potential to generate turbulence and, thereby, produce mixing. A shear flow can have significant effects on gravity wave propagation. As a wave approach es its critical level (where the phase speed of the wave equals the mean flow speed; BOOKER and BRETHERTON, 1967), the wave's vertical propagation is severely modified, wave energy is transferred to the mean flow, and turbulence can be genera ted by unstable breakdown.

Most of OUf present understanding of these gravity wave critical-level interactions comes from theoretical and numerical research (e.g., BRETHERTON, 1966; BENNEY and BERGERON, 1969; MASLOWE, 1973, 1977; GRIMSHAW, 1975; FRITTS, 1978,1979, 1982; BROWN and STEWARTSON, 1980; DUNKERTON, 1980, 1981, 1982;

LINDZEN, 1981; DUNKERTON and FRITTS, 1984; and many others-for recent reviews, see FRITTS, 1984 and MASLOWE, 1986). Observationalists have attempted to isolate and study these interactions (MERRILL and GRANT, 1979) as weil as equatorial wave, mean-flow interactions (WALLACE and KOUSKY, 1968). However,

I Northwest Research Associates. Inc., P.O. Box 3027. Bellevue. W A 98009. U.S.A.

446 D. P. De\isi and T. J. Dunkerton PAGEOPH,

it has been difficult to locate criticallevels accurately and to observe the interactions quantitatively. Similar difficulties have occurred in the ocean.

Because of our inability to study these interactions in the atmosphere, it is useful to observe them under controlled laboratory conditions. Five previous experimental studies of gravity wave-critical level interactions have been reported. The earliest three studies (BRETHERTON et al., 1967; THORPE, 1973; Koop, 1981) were qualitative in nature and were somewhat cursory in that they were reported either in an appendix to a main paper or as part of a much larger investigation. In a more extensive, but still qualitative, study, THORPE (1981) performed a flow visualization study of these interactions. In the most recent study, Koop and MCGEE (1986) followed up on Koop's earlier work (1981) and compared their flow visualization and probe measurements to results from a numerical model.

As pioneering as these earlier studies are, they are by no me ans complete. This is due to the difficulty in establishing a controlled stratified shear flow in the laboratory and propagating known internal waves into that flow. Thus, nearly all of the previous results are qualitative in nature, with few quantitative measurements. Previous studies have also been limited in the evolution times which could be investigated. These temporal constraints are the result of the experimental facilities used to study the flows. The tilting tanks used by BRETHERTON et al. (1967) and THORPE (1973, 1981) have a limited running time be fore surges from the end walls destroy the flow. Similarly, the temporal evolution in the recirculating tank used by Koop (1981) and Koop and MCGEE (1986) is limited by the physical dimensions of the test section and the dimensions and towing speeds of the internal wave sources. A second limitation on long-term evolution in their facility is the nonsteadiness of their velocity and density profile over time scales of approximately ten minutes (Koop, 1981, figures 4 and 6). This nonsteadiness is due to the small but noticeable effect of mixing caused by the pump which is generating their shear flow.

Here, we describe a new laboratory facility for studying gravity wave criticallevel interactions, and we present results from one experiment. The facility is a modification of that developed by PLUMB and McEw AN (1978) who forced a standing internal gravity wave in a cylindrical annulus of stratified salt water and genera ted an analogue of the equatorial stratospheric quasi-biennial oscillation. In this study, we force propagating internal gravity waves into a stratified salt water flow with shear and observe the resulting interactions. Our ultimate goal is to obtain quantitative measurements of both the early evolution and the long-time evolution of critical layer interactions under a variety of experimental conditions.

2. The Experimental Facility

The experiment was performed in an annular tank having an outei diameter of 1.8 m, an inner diameter of 1.2 m, and a depth of 40 cm (Figure 1.) The sides of the tank are made of clear acrylic to allow us to observe the flow inside the tank.

Vol. 130, 1989 Gravity Wave Critical-Layer Interactions

1---- 1.8 m ----I

TOP VIEW

-.\ 40cm --...L

~ Tank --- Side Wall

1 11 ~--- Rubber Sheet

Sheets Piston -L "AcrYliC

Stepper Belt _ - Motor

SIDE VIEW Figure I

The experimental facility. The side view shows one of 32 piston assemblies.

447

The bottom of the tank is comprised of an 0.6 cm thick rubber sheet overlaying thirty-two 1.0 cm thick acrylic sheets of equal size and shape. Each acrylic sheet covers nearly the full width of the annulus and touches adjacent sheets on two sides, forming a continuous ring around the bottom of the tank. The common boundary of each pair of acrylic sheets rests on top of a vertical piston. These pistons are each driven by a stepper motor which is under computer contro!. In an experiment, the computer instructs the pistons to drive the bottom floor of the tank up and down, generating a wave of prescribed amplitude and phase speed which progresses around the tank. The acrylic sheets provide structural rigidity between pistons, and the rubber sheet acts both as a water seal at the bottom of the tank and as a stretching membrane between the acrylic sheets and the sides of the tank.

The wave tank is filled using two 300-liter storage tanks. The filling method is similar to that of FORTUIN (1960), DELISI and ORLANSKI (1975), and others, and yields density profiles which are nearly linear. In our experiment, we use four linear density regions in the density profile (the dashed line in Figure 2 shows the measured density profile be fore the lid is started; in Figure 2 and following figures, the height above the bottom floor is normalized by the total water depth, Zmax = 38.7 cm). The top region is 10 cm thick, with a Brunt-Väisälä frequency, N = 1.63 sec~ \ defined by

N = [_~ op]1/2 P oz

where g is the acceleration due to gravity, p is density, p is average density, and z is the vertical coordinate. Below the top region are two layers each 5 cm thick where N = 1.50 and 1.25 sec ~ I, respectively. In the lower half of the tank, N = 0.83 sec ~ I.

448

>< IV E

N ...... N

D. P. Delisi and T. J. Dunkerton

t.o,-------------------------------~

0.8

0.6

0.4

0.2

, , ,

, ,

, ,

, , , , , ,

o.o+-.-.-.-.-.-.-.--,.-.--.-.-.-.-.~

1.00 1.02 t .04 t .06 t .08

Figure 2

PAGEOPH,

Measured density profiles. The dashed li ne was obtained before the lid was started; the solid li ne was taken at the end of the experiment. Z is the height above the bottom floof. Zmax is the total water depth

of 38.7 cm.

We use several layers of constant density-gradient fluid because of the way we generate the shear flow and the internal waves. The shear flow is genera ted by rotating a lid on the water surface. The lid consists of an annular acrylic channel which floats on the water and nearly covers the water surface. The channel is driven by a large O-ring which runs in a groove on the outer wall of the channel and passes over four pulleys. The lid is rota ted by a variable-speed motor which is connected to one of the pulleys. The lid is self-centering, adjustable in speed, and generates a solid-body velocity profile in the fluid.

Our rotating lid is a modification of a method used previously by KATO and PHILLIPS (1969), SCRANTON and LINDBERG (1983), DEARDORFF and YOON

(1984), and others to study the downward propagation of a mixed region in a density-stratified flow. In their studies, the lid consisted of a screen which was driven from the center of the tank with a rotating shaft and radial arms. They found that the depth of the mixed layer depended on the stratification of the layer into which the mixed region was growing. In order to minimize the depth of the mixed

Vol. 130, 1989 Gravity Wave Critical-Layer Interactions 449

layer in our experiments, we plaeed a high-N region at the top of the tank next to the rotating lid.

To perform an experiment, we first fill the tank with a stratified salt solution. The lid is then started and brought up to a preseleeted speed, and the flow is allowed to reaeh a near-steady state. After the flow is established, the bottom floor of the tank is moved to genera te internal gravity waves. Wave energy propagates vertieally into the tank, and, if the phase speed of the waves is below the maximum eurrent speed, the wave eneounters a eritieal level. In this study, only monoehromatie waves are generated. Onee the floor is started, waves are genera ted eontinuously throughout the experiment.

The dissipation seale height, d, is given by

kc4 d;:;;;

vN3

where k is zonal wavenumber, C = c - U, cis the phase speed of the foreed wave at the bottom floor, U is the mean flow speed, and v is kinematie viseosity (PLUMB

and McEwAN, 1978). The larger the dissipation seale height, the more wave energy that reaehes a given vertieal level above the tank floor. To maximize this wave energy and to minimize wave dissipation, we want d to be as large as possible. Thus, for a given zonal wavenumber and phase speed, we want N to be as low as possible in the bottom of the tank. (A lower eonstraint on N is that we have enough signal in the seeond derivative of density to visualize the flow using a shadowgraph.) For this reason, we have a lower value of N at the bottom of the tank than at the top of the tank (Figure 2). The two middle layers of eonstant N fluid aet as smooth transitions between the top and bottom layers. The variations in N do not eause any notieeable wave refleetions during an experiment.

Neutrally buoyant partieles are added to the storage tanks before the filling proeess is started. Onee in the tank, these particles are illuminated from the top using a 1000-watt theatrieal spotlight. A 2.5-em wide slit at the top of the viewing seetion allows just the particles in a given eonstant-radius plane to be illuminated. In this study, the illuminated plane is loeated 20 em from the inner wall of the tank (5 em from the eenterline towards the outer wall of the tank). A 35-mm eamera is used to obtain streaks of the moving particles. To obtain particle streaks, the film is exposed for either 1 or 4 seeonds. The streaks in the resuiting photographie prints are digitized and eorreeted for parallax to yield instantaneous veloeity profiles.

A shadowgraph is also used to visualize the flow field. A video eamera and a 35-mm eamera are used to reeord the flow field as visualized by the shadowgraph.

3. Results and Discussion

The veloeity profile after the me an flow is established but before the bottom floor is started is shown in Figure 3. Results from two streak photographs are shown in

450 D. P. Delisi and T. J. Dunkerton PAGEOPH,

this figure; the circ1es are from a 4-seeond exposure photograph, and the squares are from a l-seeond exposure photograph. The 4-seeond photograph enables us to measure the slower moving particles with better aeeuraey than is possible using l-seeond exposure photographs. As is evident from the figure, the 4-seeond and l-seeond data are eonsistent in the range where they overlap.

The solid line in Figure 3 is a subjeetive fit through the data. The mixed layer is in the high-N region at the top of the tank; the veloeities in this region are nearly eonstant. Below the mixed layer is a near-exponential profile in the horizontal speed (dashed line in Figure 3).

At a time t = 0, the bottom floor is started. The wave parameters used are the following: wavenumber = 2, amplitude = 4.0 em (peak-to-peak), and phase speed = 4.5 ern/sec. (Due to bottom boundary layer effeets, the effeetive amplitude transmitted to the fluid is approximately half the imposed amplitude.) From Figure 3, a phase speed of 4.5 ern/sec plaees the eritieal level at Z /Zmax = 0.69.

)(

IU

E N ...... N

1 O~------------------------------,

EI

0 . 8

0 . 6

0 . -4

0 . 2

O . O~~'-rT,-ro'-rT'-~~OT~~~~~ -2 o 2 6 8 10

U (cm/s)

Figure 3 The velocity profile at the start of the experiment. Circles (squares) are from a 4-second (l-second)

ex pos ure photograph. The solid li ne (dashed line) is a subjective fit (exponential fit) to the data.

Vol. 130, 1989 Gravity Wave Critica1-Layer Interactions 451

During the first two wave cycles, the shadowgraph shows no evidence of wavebreaking. Wh at is observed, however, is a dark band, tilted from the horizontal, which is located below the critical level, and progresses down towards the bottom of the tank as the wave propagates.

During the third wave cycle, and for all wave cycles thereafter, overturning and turbulence are observed on the shadowgraph below the critical level. A schematic drawing of the early wavebreaking is shown in Figure 4. This figure shows the tank at one instant of time, as if the annulus was cut radially and spread out horizontally. The height of the bottom floor represents the forced wave which is propagating from left to right. The critical level is shown as the dashed horizontal line. Regions of wavebreaking are shown as the regions of rolling motions which are inclined from the lower left to the upper right. All observed regions of wavebreaking occur below the critical level. The dotted rectangular box represents the approximate horizontal and vertical extent of the region illuminated by the shadowgraph. Because each forced wave has a horizontal ex te nt of half the circumference of the tank (wavenumber two), only a small portion of the wave can be visualized at any one time.

Photographs of this early wavebreaking, as visualized by the shadowgraph, are shown in Figure 5. Five examples are shown in this figure to give the reader a feeling for the kind of breaking which is observed. Initially, the observed wavebreaking occurs from just below the critical level to just below the mid-depth of the tank. In subsequent wave cycles, the breaking occurs lower in the tank, as the mean flow is modified (see below). From the videos, this early wavebreaking consists of aseries of rolling motions, alternately increasing then dying out. The rolling appears quasi-two-dimensional initially, but rapidly becomes turbulent and threedimensional. The scales of the rolling motions increase as the breaking progresses further from the critical level, the horizontal and vertical scales being 6-10 cm and 2-3 cm, respectively, near the criticallevel, and 8-12 cm and 3-5 cm just below the mid-depth of the tank.

r-------. : : : : :- ...:-

Figure 4

Critical layer

Bottom floor

Schematic drawing of early wavebreaking. Arrows indicate the direction of the rolling motions.


a

b

c

d

e

Figure 5 Five shadowgraph images of early wavebreaking. The bottom floor is started at 0:00. The times of the photographs are (a) 2:22, (b) 3:11, (c) 3:54, (d) 4:07, and (e) 6:55. The area shown is approximately 36 cm wide by 12 cm high. The right-hand scale is 2.5 cm between tic marks. The arrow on each scale denotes the depth of Z / Zmax = 0.41. The photographs an ta;'en at different phases of the forced wave. The stippled region in each photograph covers the reflec!Juu of the shadowgraph light source from the

side walls of the tank.


Figure 6 shows a streak photograph taken during the fifth wave cycle. The streaks are mostly horizontal, the partieles progressing from left to right in the photograph. lust above the dock, however, the partide streaks are no longer horizontal, and rolling motions are observed. Comparisons were made between this streak photograph, a shadowgraph photograph, and the video pictures, all of which were taken at a similar phase in the bottom wave cyde. The comparisons of vertical depth and horizontal scales confirm that the rolling motions observed in Figure 6 correspond to the rolling motions and turbulence observed in the shadowgraph, similar to the photographs shown in Figure 5.

The comparisons betweeen Figure 6 and the corresponding shadowgraph videos and photographs are confirrnation that the breaking observed in the shadowgraph occurs near the center of the tank and is not a wall effect. Thus, the rolling motions and resulting turbulence are a result of the internal wave critical-level interaction and are not simply an artifact of the experimental facility.

Figure 6 One-second exposure streak photograph showing rolling motions at a depth just above the dock. The

background grid is lO-cm square.


The form of the observed, early wavebreaking is still of some conjecture. In an earlier internal wave critical-level study by THORPE (1981), gravitational overturning was also observed, but the form of the breakdown is not discussed. In the gravity wave critical-level experiment by Koop and MCGEE (1986), where wavebreaking was also observed, the overturning is described as the result of convective instability. In our experiments, however, the overturning is aseries of rolling motions, distinctly reminiscent of Kelvin-Helmholtz ins tabili ti es and similar to the observations of Kelvin-HeImholtz billows reported on by THORPE (1968, 1971, 1973), DELISI and CORCOS (1973), and others. From the instantaneous velocity profiles obtained from streak photographs, we have determined that the wavebreaking coincides with the region of maximum vertical shear. This observation supports the hypothesis that early wavebreaking is the result of Kelvin-Helmholtz and not convective instability. In situ measurements are currently being planned which we hope will shed additional light on the form of the observed wavebreaking.

Around t ~ 6-15 min, the flow gradually progresses from the gravity wave critical-Iayer structure described above to a flow characterized by one or more internal mixing regions. These regions are characterized by lens-shaped masses of fluid propagating around the tank with the bottom wave. The mixing regions have an abrupt front and consistently exhibit overturning on the bottom edge and sometimes on the upper edge. Usually, turbulence appears to exist throughout the entire mass of fluid.

Between t ~ 15-65 min, the mixing regions are mostly distinct from the earlier criticallevel breaking and are not necessarily locked in phase with the forced wave. Around t = 65 min, the flow has evolved into a single mixing region which is located just below mid-depth in the tank. Often, a second, weaker mixing region. is also observed above the dominant one. It may be that this weaker region is always present but is hard to discern on the shadowgraph. The mixing regions are phase-locked to the trough of the forced wave. The bottom mixing region appears to coincide with a jet in the velocity profile and to ride on a sharp density striation.

mixing ~ ,e9;005 .... ;::;:>

Figure 7

_ Critical layer

Bottom floor

Schematic drawing of the la te-time mixing regions. Arrows indicate the direction of (he rolling motions.


This flow is shown schematically in Figure 7. This flow continues with little change to the end of the experiment, at t = 125 min.

Streak photographs have been analyzed to yield information on the instantaneous and mean velocity profiles. An example is shown in Figure 8. Here, circles indicate the measured speed of particles as a function of height above the bottom floor . The solid line is a subjective fit through the data points and represents the instantaneous velocity profile. The dashed line is the mean velocity profile at the start of the experiment (Figure 3). Note in Figure 8 that the vertical wavelength decreases as the critical level is approached (cf, mean flow in Figure 9), consistent with numerical gravity wave critical-level studies (e.g., DUNKERTON and FRITTS, 1984).

To obtain the mean velocity profile during the run, we analyze four streak photographs taken every quarter of a wave period during one wave cycle. The

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Figure 8 Instantaneous velocity profile from a streak photograph around t = 5:00. The solid li ne is a subjective

fit through the data; the dashed line is the initial profile from Figure 3.

average of these four instantaneous velocity profiles is the mean profile. An example is given in Figure 9. Here we show the data from the four streak photographs taken around t = 5 minutes (approximately the fifth wave cycle). The heavy solid line is the average of the four instantaneous profiles, while, again, the dashed line is the mean velocity taken at the start of the experiment (Figure 3). This figure shows that the mean velocity at t = 5 min differs from the initial profile mostly in the range 0.35 < Z/Zmax < 0.7. This mean flow modification is similar to that predicted by numerical codes (FRITTS, 1982; DUNKERTON and FRITTS, 1984; FRITTS and DUNKERTON, 1984).

The evolution of the mean flow with time is shown in Figure 10. Here we see that the mean flow ledge observed in Figure 9 at t = 5 min progresses downwards at t = 10 and 20 min. The mean flow at t = 75 min is similar to the mean flow at t = 20 min except near the bottom floor, where the mean flow has decelerated.

>< IQ

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Figure 9

6 8 10

Four instantaneous velocity profiles taken every quarter of a wave period during one wave cyc1e around t = 5:00 (thin solid lines). The heavy dark line is the mean velocity profile. The dashed line is the initial

profile from Figure 3.

Vol. 130, 1989

>< ca E

N "N

Gravity Wave Critical-Layer Interactions 457

1.0,---------------------------------,

0.8

0.6

0.4

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O.O~~""-..-ro",,-..-,,.-.. _r .. ,,'

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Figure 10 Evolution of the mean velocity profile with time. Times are in minutes after starting the bottom floor.

Figure 11 shows instantaneous particle veloeities from four wave eycles at times of 5, 10, 20, and 75 min. The dashed li ne in eaeh figure indieates the phase speed of the foreed wave (4.5 ern/sec). Whenever u' > c - 0, the wave is eonveetively unstable aeeording to ORLANSKI and BRYAN (1969). In Figure 11, this oeeurs whenever an instantaneous particle velocity exeeeds the wave phase speed of 4.5 ern/sec. The arrows in Figure 11 indieate the depths over whieh wavebreaking is observed to oeeur from the video and photographs of the shadowgraph. In all eases, the observed wavebreaking is seen to extend below the region where the OrlanskiBryan eriterion is satisfied (cf, DUNKERTON and FRITTS, 1984). In our experiment, onee initiated, wavebreaking ean oeeur over a depth reaehing one-half the vertieal wavelength. Thus, in Figure 11, wavebreaking ean oeeur up to one-half a vertical wavelength below that predieted by Orlanski and Bryan. In all eases in Figure 11, the observed wavebreaking is less than one-half a vertieal wavelength below that where 0 + u' = c.

Reeent experimental runs (not shown) indieate that satisfaetion of the OrlanskiBryan eriterion is not neeessary to produee wavebreaking. In those runs, 0 + u'

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D. P. Delisi and T. J. Dunkerton PAGEOPH,

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Figure 11 Instantaneous particle velocities at times of (a) 5, (b) 10, (c) 20, and (d) 75 minutes after starting the bottom floor. The dashed line indicates the phase speed of the forced wave. Arrows indicate the depths

over which wavebreaking was observed from the shadowgraph.


was always less than c, yet wavebreaking occurred which was qualitatively similar to that observed here.

Finally, a density profile was made after the experiment was concluded and the fluid had come to rest. This profile is shown as the solid li ne in Figure 2. Two mixed layers are shown in this profile. The first layer is at the top of the tank and is due to turbulence genera ted by the rotating lid. The second layer is centered at 2 12maz ,...., 0.43 and is the result of fluid mixed by wavebreaking. The dominant mixing region observed in the last half of the experiment was centered at 2/2maz ,...., 0.43, but it is not known at this time whether the mixed layer at that depth is the result of the mixing region or whether the layer existed before the appearance of the mixing region.

4. Summary and Conclusions

In Section 3, we have shown laboratory results of a turbulent gravity wave critical-Iayer experiment. We have shown the early evolution of the critical layer interaction, wh ich results in wavebreaking qualitatively similar to that predicted by numerical studies, as weil as the long-time evolution of the critical layer, which results, at least in our experiments, in steady-state mixing regions.

The early evolution includes turbulent wavebreaking which is reminiscent of Kelvin-Helmholtz billows. Although no quantitative comparisons have been performed yet with numerical predictions, the experimental results agree qualitatively with numerical simulations in the location of the wavebreaking and in the evolution of the mean flow.

Our observations of the long-time evolution of the gravity wave critical-layer interaction were unexpected and are not weil understood. The appearance of steady-state mixing regions is not unique to the experiment presented here and has been observed in several other of our laboratory critical-layer experiments. The evolution of this phenomenon clearly warrants additional investigation.

The results of this study have pointed out several areas that des erve further investigation. First, additional sensors must be utilized to obtain quantitative measurements to examine such questions as the form of the initial wavebreaking, self-acceleration of the incoming wave, reflection from the critical layer, transmission through the critical layer, and the long-time evolution of the critical layer. Second, additional experiments must be performed to examine other parameter ranges. For example, both laminar and turbulent criticallayers need to be investigated. Finally, numerical predictions must be performed which simulate the laboratory environment, and quantitative comparisons must be made between the numerical simulations and the laboratory measurements. Additional experiments are currently in progress, and the results of those investigations will be presented at a later date.


Acknowledgements

The authors would like to thank David C. Fritts for many stimulating discussions during this study. We also thank J. Francis Smith, Robert B. Fraser, and Lee E. Piper for their support in designing and building the facility and assistance in performing the experiments. This study was supported by the Air Force Office of Scientific Research under contract F49620-86-C0015.

REFERENCES

BENNEY, D. J., and R. F. BERGERON (1969), A New Class of Nonlinear Waves in Parallel Flows, Stud. Appl. Math. 48, 181-204.

BOOKER, J. R., and F. P. BRETHERTON (1967), The Critical Layer for Internal Gravity Waves in a Shear Flow, J. Fluid Mech. 27, 513-539.

BRETHERTON, F. P. (1966), The Propagation of Internal Gravity Waves in a Shear Flow, Quart. J. Roy. Meteor. Soe. 92, 446-480.

BRETHERTON, F. P., P. HAZEL, S. A. THORPE, and I. R. WOOD (1967), Appendix to the paper by P. HAZEL, The Effect of Viscosity and Heat Conduction on Internal Gravity Waves at a Critical Level, J. Fluid Mech. 30, 775-383, (Appendix on pp. 781-783.)

BROWN, S. N., and K. STEWARTSON (1980), On the Nonlinear Reflexion of a Gravity Wave at a Critical Level. Part 1, J. Fluid Mech. lOO, 577-595.

DEARDORFF, J. W., and S.-C. YOON (1984), On the Use of an Annulus to Study Mixed-Layer Entrainment, J. Fluid Mech. 142,97-120.

DELISI, D. P., and G. CORCOS (1973), A Study of Internal Waves in a Wind Tunnel, Boundary-Layer Meteorol. 5, 121-137.

DELISI, D. P., and I. ORLANSKI (1975), On the Role of Density Jumps in the Reflexion and Breaking of Internal Gravity Waves, J. Fluid Mech. 69, 445-464.

DUNKERTON, T. J. (1980), A Lagrangian Mean Theory of Wave, Mean-flow Interaction with Applications to Nonacceleration and its Breakdown, Rev. Geophys. Space Phys. 18, 387-400.

DUNKERTON, T. J. (1981), Wave Transience in a Compressible Atmosphere, Part 1: Transient Internal Wave, Mean-Flow Interaction, J. Atmos. Sei. 38, 281-297.

DUNKERTON, T. J. (1982), Wave Transience in a Compressible Atmosphere, Part 3: The Saturation of Internal Gravity Waves in the Mesosphere, J. Atmos. Sei. 39, \042-\051.

DUNKERTON, T. J., and D. C. FRITTS (1984), Transient Gravity Wave-Critical Layer Interaction. Part 1: Convective Adjustment and the Mean Zonal Acceleration, J. Atmos. Sei. 41, 992-1007.

FORTUIN, J. M. H. (1960), Theory and Application of Two Supplementary Methods of Constructing Density Gradient Columns, J. Polymer Sei. 44, 505-515.

FRITTS, D. C. (1978), The Non/inear Gravity Wave-Critical LevelInteraction, J. Atmos. Sei. 35, 397-413. FRITTS, D. C. (1979), The Excitation of Radiating Waves and Kelvin-Helmholtz Instabilities by the

Gravity Wave-Critical Layer Interaction, J. Atmos. Sei. 36, 12-23. FRITTS, D. C. (1982), The Transient Critical-Levellnteraction in a Boussinesq Fluid, J. Geophys. Res. 87,

7997-8016. FRITTS, D. C. (1984), Gravity Wave Saturation in the Middle Atmosphere: A Review of Theory and

Observations, Rev. Geophys. and Space Phys. 22, 275-308. FRITTS, D. c., and T. J. DUNKERTON (1984), A Quasi-Linear Study ofGravity-Wave Saturation and

Self-Acceleration, J. Atmos. Sei. 41. 3272-3289. GRIMSHAW, R. (1975), Nonlinear Internal Gravity Waves and Their Interaction with the Mean Wind, J.

Atmos. Sei. 32, 1779-1793. KATO, H., and O. M. PHILLIPS (1969), On the Penetration of a Turbulent Layer Into Stratijied Fluid, J.

Fluid Mech. 37, 643-655.

Vol. 130, 1989 Gravity Wave Critiea1-Layer Interaetions 461

Koop, C. G. (1981), A Preliminary Investigation of the Interaction of Internal Gravity Waves with a Steady Shearing Motion, J. Fluid Meeh. 113, 347-386.

Koop, C. G., and B. MCGEE (1986), Measurements of Internal Gravity Waves in a Continuously Stratijied Shear F/ow, J. Fluid Meeh. 172,453-480.

LINDZEN, R. S. (1981), Turbulence and Stress Due to Gravity Wave and Tidal Breakdown, J. Geophys. Res. 86C, 9707 -9714.

MASLOWE, S. A. (1973), Finite-Amplitude Kelvin-Helmholtz Bil/ows, Boundary-Layer Meteorol. 5, 43-52.

MASLOWE, S. A. (1977), Weakly Nonlinear Stability Theory of Stratijied Shear Flows, Quart. J. Roy. Meteor. Soe. 103, 769-783.

MASLOWE, S. A. (1986), Critical Layers in Shear Flows, Ann. Rev. Fluid Meeh. 18, 405-432. MERRILL, J. T., and J. R. GRANT (1979), A Gravity Wave-Critical Level Encounter Observed in the

Atmosphere, J. Geophys Res. 84, 6315-6320. ÜRLANSKI, 1., and K. BR YAN (1969), Formation of the Thermoc/ine Step Structure by Large-Amplitude

Internal Gravity Waves, J. Geophys. Res. 74, 6975--6983. PLUMB, R. A., and A. D. McEwAN (1978), The Instability of a Forced Standing Wave in a Viscous

Stratijied Fluid: A Laboratory Analogue of the Quasi-Biennial Oscil/ation, J. Atmos. Sei. 35, 1827-1839. SCRANTON, D. R., and W. R. LINDBERG (1983), An Experimental Study of Entraining, Stress-Driven,

Stratijied Flow in an Annulus, Phys. Fluids 26, 1198-1205. THORPE, S. A. (1968), A Method o{ Producing a Shear Flow in a Stratijied Fluid, J. Fluid Meeh. 32,

693-704. THORPE, S. A. (1971), Experiments on the Instability of Stratijied Shear Flows: Miscible Fluids, J. Fluid

Meeh. 46, 299-319. THORPE, S. A. (1973), Turbulence in Stably Stratijied Fluids: A Review of Laboratory Experiments,

Boundary-Layer Meteorol. 5, 95-119. THORPE, S. A. (1981), An Experimental Study of Critical Layers, J. Fluid Meeh. 103, 321-344. WALLACE, J. M., and V. E. KOUSKY (1968), Observational Evidence of Kelvin Waves in the Tropical

Stratosphere, J. Atmos. Sei. 25, 900-907.

(Reeeived September 28, 1987, revised May 15, 1988, aeeepted May 18, 1988)


Wind Fluctuations near a Cold Vortex-Tropopause Funnel System Observed by the MU Radar

SHOICHIRO FUKAO,' MANABU D. YAMANAKA,2 HIROMASA MATSUMOTO,3 TORU SATO,' TOSHITAKA TSUDA' and SUSUMU KATO'

Abslracl-Vertical and temporal variations of three-dimensional wind velocity associated with an upper-tropospheric cold vortex-tropopause funnel system were observed by an MST radar in Japan (the MU radar). Marked changes of vertical velocity and horizontal wind direction were found between the inside and outside of the cold vortex. The vertical velocity activity outside the vortex was asymmetrie; it was most active in a sector before the vortex. Unsaturated internal gravity waves in their generation stage contribute predominantly to the vertical velocity activity, suggesting that tropospheric occluded cyclones may be a possible source of middle-atmospheric gravity waves through the geostrophic adjustment process.

Key words: MST radar observation, cold vortex, tropopause funnel, internal gravity waves.

I. lntroduction

Synoptic structures of the polar front and the tropopause jet stream were weil analyzed, mainly based on l2-hourly rawinsonde observations before the 1970's (see, e.g., PALMEN and NEWTON, 1969), whieh were followed by sub-synoptie-scale studies using aircraft observations (e.g., SHAPIRO, 1974). It is noted among them that the oeclusion of an extratropical cyclone in the lower troposphere is attended by a eold vortex (or cut-off cyclone) in the upper troposphere and also by a tropopause funnel (see Chapter 10 of PALMEN and NEWTON). This is one of the typical structures found in the final stage of a baroclinic disturbanee development. However, even now, weather prediction in this stage is very diffieult, partly beeause we do not have sufficient information on the contribution of sub-synoptic scale phenomena, which should be based on continuous high-resolution observations.

On the other hand, the most controversial problem of middle-atmospheric

gravity waves is related to the wave sources. Orographie stationary waves must

I Radio Atmospheric Science Center, Kyoto University, Uji, Kyoto 611, Japan. " Faculty of Education, Yamaguchi University, Yamaguchi-shi, Yamaguchi 753, Japan. 3 Department of Electrical Engineering, Kyoto University, Yoshida, Kyoto 606, Japan.

464 S. Fukao et al. PAGEOPH,

break alm ost entirely below middle stratospheric altitudes (MATSUNO, 1982; TANAKA and YAMANAKA, 1985; ZHU and HOLTON, 1987); nevertheless, both theory and observation of the mesosphere require waves coming from some nonstationary source at the lower altitudes (see FRITTS, 1984, for a review). Since a tropospheric cyclone occlusion radiates momentum and energy through the geostrophic adjustment processes, this may be one of the major sources of middleatmospheric internal gravity waves. In order to verify this, continuous high-resolution observations of three-dimensional wind variations associated with the frontal jet stream are necessary. In particular, the vertical velocity is more important than the horizontal velocity for gravity waves in their generation stage and/or near the wave source, wh ich is the opposite case as for inertio-gravity waves near their critical levels [see (A9) in Appendix].

The MV radar (a VHF-band MST radar at Shigaraki, Japan; 34.85°N, 136.100 E) has recently started frontal phenomenon observations (W AKASUGI et al., 1985; FUKAO et al., 1988). This technique provides three-dimensional wind data from the middle troposphere through the lower stratosphere with far higher resolution in both time ('" 1 min) and altitude ('" 150 m) than was previously possible by conventional meteorological instruments. Both meridional-vertical circulation near the frontal surface and individual cloud convection can be observed by this powerful technique. The previous observations by the MV radar were made over a typical "axi-symmetric" front (symmetric with respect to the earth's rotation axis) in the Baiu season (FUKAO et al., 1988).

In this paper we show results of a typical cold vortex-tropopause funnel system observed on 3-7 June, 1985. Details of the radar system and observational technique can be found in FUKAO et al. (1985a,b) and SATO et al. (1985). The full capabilities of the MV radar have been employed since November 1984, and the reliability and continuity of data shown in this paper are much improved from the previous observations.

2. Synoptic-scale Situations

In this section we show the synoptic-scale features during the period of the MV radar observation, based on the 6-hourly observations of wind, temperature, press ure, geopotential height and humidity by the Japan Meteorological Agency (JMA, 1986) and the 12-hourly objective analyses of JMA (1983, 1985a,b).

Figures la--(; show the frontal contours, tropopause height contours and the isotherms at the 250 hPa level (10-11 km), respectively, at 0900 LST (0000 VT) 6 lune, 1985. Clearly we find typical structures of the cold vortex and tropopause funnel. The locations of the lowest tropopause height (center of the funnel) and the lowest temperature are not the same; the latter is also shifted from the center of vortex motion at the same level (not shown). The streamlines (geopotential height

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contours) are, in general, not parallel with the isotherms, and the temperature over the tropopause funnel center is not a minimum but is highest at stratospheric altitudes, which will be confirmed later.

In Figure 2 the geopotential height contours and isotherms are plotted in time-latitude cross-sections at 400, 200, and 100 hPa (7, 12 and 16 km). The lowest temperature appears to the north of the MV radar at 200 hPa, which is consistent with the 250 hPa chart of Figure lc. However, in the 400 hPa chart of Figure 2, the lowest temperature appears to the south of the radar. Thus, the lowest temperature shifts southwards with decreasing altitude. The geopotential height contours in Figure 2 show that the center of the vortex motion also shifts southwards as the altitude decreases. Based· on these features, we conclude tentatively that the

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center of the cold vortex (lower than the 10 km altitude) passed south of the radar on 5-6 June.

Figure 3 shows the pseudo-adiabats in a time-altitude cross-section over Shionomisaki (33.45°N, 135.77°E; about 150 km south ofthe MU radar). There are two tropopauses throughout the observational period; the higher one 10cated at 16-17 km altitude is continued equatorward whereas the lower one at 10--14 km extends poleward. We can reconfirm in this figure that the temperature at a specific altitude is lowest in the tropospheric cold vortex while it is highest in the tropopause funnel, and that the system passed by the radar on 5--6 June.

Figure 4 shows models of the tropospheric wind variations expected to be observed by the MU radar, following the synoptic studies on a cold vortex as summarized in PALMEN and NEWTON (1969). We consider here two alternative cases: the vortex center passes either north or south of the MU radar. Particularly note that the observed zonal wind direction inside the cold vortex is reversed between the two cases (see the two panels at the bottom of Figure 4). Namely, in the case that the cold vortex passes south of the radar, as tentatively concluded above, we would expect to observe easterlies inside the vortex region.

These synoptic studies on the atmospheric motions, in general, enable us to observe and predict the horizontal wind variations only. However, by using the MU radar, we can also observe the vertical velocity field which, as mentioned before, cannot be disregarded, and is possibly more important than the horizontal wind variation in discussing the generation stage of internal gravity waves. This is an important result of the present paper.

;tm-~ -------- ;t~f----~----------------------. x - -x

y -

~ -5-':;-;Z--~-----~ - - -- ;t-~~-'<------ . t

Figure 4 Model of a cold vortex (top; the vortex center is indicated by a cross) and corresponding wind distributions at the MV radar latitude (middle and bottom). The left and right columns are the cases where the cold vortex center passes north and south of the MV radar, respectively. Arrows indicate zonal-meridional winds expected by the model. Symbols x, y, z and t denote eastward, northward and

upward directions and time, respectively.

Vol. 130, 1989 Cold Vortex Observed by MV Radar 469

3. MV Radar Observations

Figure 5 shows the variations of three-dimensional wind velocity observed by the MV radar on 3-7 lune, 1985. The horizontal wind changes its direction in the vicinity of the frontal surface shown in Figure 3. In particular, we find a c1ear revers al of the horizontal wind direction between the outside and inside of the cold vortex (below the lower tropopause). Comparing Figure 5a with Figure 4, this fact is quite consistent with the case that the vortex center passes south of the radar. The wind variation inside the cold vortex is relatively weak, which suggests a rather stable stratification. Although there is a change of horizontal wind direction between the outside and inside of the tropopause funnel, this change is not so strong as to reverse the zonal component completely. These features are weil confimed by vertical shears of the horizontal wind shown in Figure 6.

We notice in Figure 5 that the three-dimensional wind in the sec tor before the passage of the cold vortex (3-5 lune) is quite different from that in the sector after the passage of the cold vortex (6--7 1 une). First of all, the vertical velocity field is more active before the cold vortex and calmer after it. If the sector before the cold vortex has a character like a warm front in the lower-tropospheric levels, this sector may be less stable because of the warmer-air advection from the south of the vortex. The variations of vertical velocity in the preceding sector take wavy or cell-like structures on a time scale of several hours.

Strong downdrafts (maximum speed -0.5 m/s) were observed at altitudes lower than 16 km on the afternoon of 4 lune, but their concrete interpretation has not yet been given. In the previous observation over the Baiu front, FUKAO et al. (1988) suggested the existence of updraft events of 22-hour intervals. We find a similar feature also in the present observation; updrafts of -0.2 mls appeared at altitudes below 10 km at -18 LST 5 lune, 15 LST 6 lune and -12 LST 7 lune. Although this feature is much more disturbed than in the previous observation by the vertical velocity activity asymmetrie to the cold vortex, the coincidence of the updraft intervals in the two observations should be noted.

Furthermore, we can find a strong northerly at upper-tropospheric altitudes in the sector after the cold vortex. This may be caused by a tropopause jet stream curving around the cold vortex. This is, in general, consistent with the results of the aforementioned synoptic studies (see PALMEN and NEWTON, 1969).

In the above we have considered phenomena with time scales larger than several hours, since Figure 5 shows velocity vectors averaged over - 1 hour. The wind velocity activity in the period after the cold vortex seems calmer in Figure 5, but it involves some phenomena with smaller time scales. So we replot the wind velocity variations during this period in the similar cross-sections with a higher time resolution (-15 min) (see Figure 7). An interesting feature of weak upand down-drafts with cell-Iike patterns is found inside the cold vortex below the frontal surface bordering the sector behind the vortex (see also Figure 7). The amplitudes of these vertical motions are not strong (-0.2 m/s), but their

470

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Figure 7 Time-altitude cross-sections of (a) zonal-vertical and (b) meridional-vertical winds in the sector after the

passage of the cold vortex-tropopause funnel system. Winds are averaged over - 15 min.

temporal behaviors are highly systematic. The time scale of this cell-like structure is

'" I hour. Figure 8 shows the distributions of echo power and echo power ratio. Strong

echoes are distributed surrounding the cold vortex. They correspond weil with the strong stratifications and shears (Figures 3 and 6) as demonstrated in detail by

TSUDA et al. (1988). Thus severe turbulence may be induced by shear instabilities

(e .g., Kelvin-Helmholtz billows) rather than convective ones. Comparing Figures 8a and b, we suppose that the turbulence in the troposphere is principally on the curved plane surrounding the cold vortex, and that the turbulence in the stratosphere IS

embedded in thin horizontal layers induced by inertio-gravity wavefronts.

Vol. 130, 1989 Cold Vortex Observed by MU Radar 473

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contours are drawn at 8 dB intervals. In the latter, the contours are drawn at 3 dB intervals.

4. Discussion 0/ the Vertical Velocity Field

In order to discuss the mesoscale atmospheric motions more quantitatively, we analyze the vertical-wavenumber (m) spectra F,.,.(m) ofthe vertical velocity (w) for an altitude range of 6-20 km. The observed horizontal velocity (u) is highly modulated by synoptic-scale structures of the cold vortex-tropopause funnel system, and so we do not show horizontal velocity spectra Fu(m). As mentioned in Section I and also described in (A9) of the Appendix, F,.,.(m) becomes more important than Fu(m) in discussing the generation stage of internal gravity waves.

9

6

3

0

Figure 9 gives some "area-preserving" spectra m· F.,(m) wh ich are useful for evaluation of the relative contributions of each wavenumber component to the


variance or mean-square f1uctuation of a physical quantity (cf, BRETHERTON et al., 1969). m·Fw(m) monotonically increases as m approaches the minimum in the observed range. This indicates that the components with vertical wavelengths longer than several kilometers (m ;5 10-3 m -I) contribute predominantly to the vertical ve!ocity f1uctations. In an average, m ·Fjm) has an approximated slope of m - I, hence F.,.(m) is elose to a - 2 power !aw for m. These features of Fw(m) differ from the so-ca lied "universal" features of Fu(m) in a similar range of m (e.g., SMITH et al., 1987).

In the quasi-monochromatic theory described in the Appendix, the m -2 law of Fw(m) corresponds to unsaturated interna! gravity waves [see (A4)]. Such unsatura ted waves may coexist with saturated waves wh ich have a similar value of m and different values of frequency and/or horizontal wavenumber. The former dominates the latter in the w field whereas the latter becomes predominant over the former in the u field, because lul/lwl becomes larger and smaller for saturated and unsaturated

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spectral curve.

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476 S. Fukao et af. PAGEOPH,

waves, respectively. Therefore, the feature of Fw(m) presented here is not inconsistent with the predominance of saturated waves universally found in FJm). For the same reason, unsaturated gravity waves hardly appear in the hodograph analyses used in the accompanying paper (Y AMANAKA et al., this issue).

Figure 10 shows the temporal variation of m ·F,vCm). It is observed that the spectral density increases on 4-5 lune, that is, just before the cold vortex-tropopause funnel system passed by. Therefore, we can consider that the activity of internal gravity waves in the unsaturated stage is also asymmetrie between the regions before and after the system; it is stronger before the system. Detailed considerations of the unsaturated wave generation and eoexistenee of the saturated and unsaturated waves (possibly including some interaetions between both types of waves) should be made, but they are beyond the seope of the present paper.

5. Conclusion

Figure ll shows a tentative model of the eold vortex-tropopause fun ne I system observed here. The most interesting feature is that the tropospherie vertieal motions indueed by unsaturated gravity waves are more aetive in the region be fore the passage of the system whereas they are less aetive after the passage of the system. This seems very important for diseussing the mesoseale motions organized in synoptic-seale baroclinie disturbanees. In the middle and lower troposphere, eonsiderable energy may be supplied into the synoptie-scale system, possibly through cloud eonveetion. On the other hand, at the top of the troposphere, both momenturn and energy may be emitted by gravity waves through the geostrophie adjustment proeesses. Stratospherie inertio-gravity waves might be mueh amplified by this mechanism (cf, Y AMANAKA et al., this issue).

Sueh an asymmetrie strueture should be studied in the future in relation to the non linear stage of tropospherie baroclinie disturbanees, and also to the nonorographie souree of middle-atmospherie gravity waves. The present paper has shown one vivid example to prove the importanee of the MST radar teehnique for these meteorologieal studies.

z ""-15km

-IOkm

x

Figure 11 A tentative model of the cold vortex-tropopause funnel system. See text for details.


Acknowledgements

The Numerical Prediction Division of the Japan Meteorological Agency kindly permitted us to use their charts and technical reports of routine objective analyses for Figures land 2. Special thanks are given to P. T. May, W. L. Oliver, Jr., and J. P. McClure for their careful reading of the manuscript, and to the anonymous reviewers whose comments improved the paper. The MU radar belongs to and is opera ted by the Radio Atmospheric Science Center of Kyoto University.

Appendix ABrief Description of Quasi-monochromatic Gravity Wave Spectra

Monochromatic waves are derived as solutions of a homogeneous perturbation equation for steady, uniform waveguides. Although the actual atmosphere is unsteady and nonuniform, the solutions are quasi-monochromatic when the temporal and spatial variations are sufficiently slow so that the WKB approximation is valid. Such a situation for the wave fieJd has been considered by YAMANAKA (1985) and SMITH el al. (1987).

At first, we consider a simple unsaturated noninertial gravity wave, of which the vertical velocity perturbation w is derived under the WKB approximation as

(Al)

with the dispersion relation

(A2)

where W, k and mare the intrinsic frequency, horizontal and vertical wavenumbers, respectively. N is the Väisälä-Brunt frequency. From the Boussinesq' continuity equation (density conservation) we can write the horizontal velocity perturbation u

as

Iml lul = TkT ·Iwl· (A3)

We symbolize a functional form of the power spectral density as F",(v), where t/J is a physical quantity and v is one of the wave parameters W, k and m. In general, we can write F",(v) ocDIt/J12/Dlvl, where 1t/J12 corresponds to the variance or mean-square of t/J in an adequate bandwidth of v. Then the power spectral density for vertical veJocity, as a function of the vertical wavenumber, F .... (m) , is derived from (Al)

(A4)


Similarly, using (AI)--{A3), we have

alul2 0 Fu(m) oc alml oc Iml = const. (A5)

Next we consider a saturated (or breaking) wave. (A2) and (A3) still hold but the wave amplitude is damped from (A I). In the case of local convective (or nonlinear) saturation, the wave amplitude is given by the saturation condition

Ikl'I~1 = Iml·I'1 = 1 (A6)

where ~ = ft u dt and ~ = ft w dt are the horizontal and vertical displacements, respectively (Y AMANAKA and T ANAKA, 1984). Considering that lu I = Iw I . I~ land Iwl = Iwl'I~I, (A6) can be rewritten as

Ikl'lul = Iml'lw! = Iwl, (A6)'

which is the same form as that derived originally by ORLANSKI and BRYAN (1969) for an external gravity wave on ocean surface.

Using (A6)', we have

(A7)

(A8)

for saturated quasi-monochromatic waves. YAMANAKA (1985) and SMITH et al. (1987) have derived (A8).

From (A2) and (A3), we have

lul-+O and Iwl-+ 00 for

lul-+oo and Iwl-+O for

Iwl-+ 00,

Iwl-+O. (A9)

Hence, Iwl of a quasi-monochromatic wave in the saturation stage (small Iwl) is vanishingly small, and lu I in the generation stage (large Iw I) is also small. When a saturated quasi-monochromatic wave coexists with an unsaturated wave, Fu(m) approaches the saturated spectrum (A8) whereas Fw(m) becomes the unsaturated one (A4).

REFERENCES

BRETHERTON, F. P., BULL, G., LINDZEN, R. S., PAO, Y.-H., REITER, E. R., and WILHELMSSON, H. (1969), The Specral Gap, Radio Sei. 4, 1361~1363.

FRITTS, D. C. (1984), Gravity Wave Saturation in the Middle Atmosphere: A Review 0/ Theory and Observations, Rev. Geophys. Spaee Phys. 22, 275~308.

FUKAO, S., SATO, T., TSUDA, T., KATO, S., WAKASUGI, K., and MAKIHIRA, T. (1 985a), The MV Radar with an Active Phased Array System, 1. Antenna and Power Amplijiers, Radio Sei. 20, 1155-1168.


FUKAO, S., TSUDA, T., SATO, T., KATO, S., WAKASUGI, K., and MAKIHIRA, T. (l985b), The MV Radar with an Active Phased Array System, 2. In-House Equipment, Radio Sei. 20, 1169-1176.

FUKAO, S., YAMANAKA, M. D., SATO, T., TSUDA, T., and KATO, S. (1988), Three-Dimensional Air Motions over the Baiu Front Observed by a VHF-Band Doppler Radar: A Case Study, Mon. Wea. Rev. 116, 281-292.

JAPAN METEOROLOGICAL AGENCY (JMA) (1983), The Northern-Hemisphere and Fine-Mesh Numerical Prediction Models (8L NHM and IOL FLM) and Analysis System, JMA-Numerical Computation Center Tech. Rep., No. 29, 75 pp.

JAPAN METEOROLOGICAL AGENCY (JMA) (l985a), JMA-Numerical Prediction Division 250-, 200- and loo-mb Objective Analyses, 3-8 June, 1985.

JAPAN METEOROLOGICAL AGENCY (JMA) (l985b), Daily Weather Maps, June 1985, 242 pp. JAPAN METEOROLOGICAL AGENCY (JMA) (1986), Aerological Data of Japan, June 1985, 247 pp. MATSUNO, T. (1982), A Quasi-One-Dimensional Model ofthe Middle Atmosphere Circulation Interacting

with Internal Gravity Waves, J. Meteor. Soc. Japan 60, 215-226. ORLANSKI, 1., and BRYAN, K. (1969), Formation ofthe Thermocline Step Structure by Large-Amplitude

Internal Gravity Waves, J. Geophys. Res. 74, 6975-6983. PALMEN, E., and NEWTON, C. W. (1969), Atmospheric Circulation Systems: Their Structureand Physical

Interpretation (Acadernie Press) 603 pp. SATO, T., TSUDA, T., KATO, S., MORIMOTO, S., FUKAO, S., and KIMURA, I. (1985), High-Resolution

MST Observations of Turbulence by Vsing the MV Radar, Radio Sei. 20, 1452-1460. SHAPIRO, M. A. (1974), A Multiple-Structured Frontal Zone Jet Stream System as Revealed by

Meteorological/y Instrumented Aircraft, Mon. Wea. Rev. 102, 244-253. SMITH, S. A., FRITTS, D. c., and V ANZANDT, T. E. (1987), Evidence for a Saturated Spectrum of

Atmospheric Gravity Waves, J. Atmos. Sei. 44, 1404-1410. T ANAKA, H., and Y AMANAKA, M. D. (1985), Atmospheric Circulation in the Lower Stratosphere Induced

by the Mesoscale Mountain Wave Breakdown, J. Meteor. Soc. Japan 63, 1047-1054. TSUDA, T., MAY, P. T. SATO, T., KATO, S., and FUKAO, S. (1988), Simultaneous Observations of

Refiection Echoes and Refractive Index Gradient in the Troposphere and Lower Stratosphere, Radio Sei. 23, 655-665.

WAKASUGI, K., FUKAO, S., KATO, S., MIZUTANI, A., and MATSUO, M., (1985), Air and Precipitation Particle Motions within a Cold Front Measured by the MV VHF Radar, Radio Sei., 20, 1233-1240.

YAMANAKA, M. D. (1985), The Power Spectrum of Internal Gravity Waves: Stratospheric Bal/oon Observations and Interpretations, WRI-MAP Research Note-6, Water Research Institute, Nagoya University, 13 pp.

YAMANAKA, M. D., FUKAO, S., MATSUMOTO, H., SATO, T., TSUDA, T., and KATO, S. (1988), Internal Gravity Wave Selection in the Vpper Troposphere and Lower Stratosphere Observed by the MV Radar, Pure Appl. Geophys., /30 (2/3), 481-495.

YAMANAKA, M. D., and TANAKA, H. (1984), Multiple "Gust Layers" Observed in the Middle Stratosphere, in Dynamics of the Middle Atmosphere (eds. J. R. Holton and T. Matsuno) (TERRAPUB/D. Reidel) pp. 117-140.

ZHU, X., and HOLToN, J. R. (1987), Mean Fields Induced by Local Gravity-Wave Forcing in the Middle Atmosphere, J. Atmos. Sei. 44, 620-630.

(Reeeived August 31, 1987, revised/accepted February I, 1988)


Internal Gravity Wave Selection in the Vpper Troposphere and Lower Stratosphere Observed by the MV Radar:

Preliminary Results

MANABV D. YAMANAKA, I SHOICHIRO FVKAO,2 HIROMASA MATSVMOTO,3

TORV SATO,2 TOSHITAKA TSVDA,2 and SVSVMV KAT02

Abstract-Marked wavelike variations of the lower stratospheric wind observed on 7-10 May, 1985 by an MST radar in Japan (by the MV radar) are analyzed assuming that they are induced by monochromatic internal inertio-gravity waves. These variations are mainly composed of two modes (periods: 22 and 24 hours), both of which have zonal phase velocities (C x) slower than the mean westerly wind (u). A statistical analysis of the zonal phase velocity shows that C x :'f u above and C x - u below the tropopause jet stream, which is considered to be a vivid proof of wave selection due to the tropospheric mean flow and upward wave emission from the tropopause jet. A comparison between the MV radar results and routine meteorological observations leads to the conclusion that the marked waves appear when the jet stream takes a maximum wind speed.

Key words: MST radar observation, internal gravity waves, monochromatic analysis, wave-mean flow interaction.

1. Introduction

Observational studies of stratospheric (inertio-) gravity waves can be classified

into two categories. One is the computation of a continuous spectrum from the

observational data; some universal shapes of spectral functions have been found

and fitted to models based either on two-dimensional turbulence theory (e.g., GAGE

and NASTROM, 1985) or else on the superposition of gravity waves (e.g., VAN

ZANDT, 1985). Such studies have become possible after the recent progress of the

MST radar technique which has provided us continuous high-resolution wind data

in time and altitude.

The other category is the analysis of monochromatic wave parameters from a

selected or filtered portion of observational data. This category was originated by

I Faculty of Education, Yamaguchi Vniversity, Yamaguchi-shi, Yamaguchi 753, Japan. 2 Radio Atmospheric Science Center, Kyoto Vniversity, Uji, Kyoto 611, Japan. 3 Department of Electrical Engineering, Kyoto University Y oshida, Kyoto 606, Japan.

482 M. D. Yamanaka et al. PAGEOPH,

the pioneering study of SA WYER (1961) using several rawinsondes, and followed by many studies in the last decade using rawinsondes (THOMPSON, 1978; CADET and TEITELBAUM, 1979), instrumented large balloons (SIDI and BARAT, 1986), rocketsondes (HIROTA and NIKI, 1985) and MST radars (MAEKAWA et al., 1984; HIROTA and NIKI, 1986). It is more straightforward to compare the observations and theories in the second rather than the first category, because most of the theories of the middle-atmospheric gravity waves assume slowly-varying quasi-monochromatic waves (see, e.g., FRITTS, 1984).

In the present paper we show some examples of the second category, using an MST radar called the MV radar which is located at Shigaraki, Japan (34.86°N, 136.100 E; cf, FUKAO et al., 1985a,b, 1988, 1989). In Section 2 we report two marked wavelike structures observed by the MV radar on 7-10 May, 1985, and analyze them by assuming a theoretical structure for monochromatic gravity waves. In Section 3 we perform a statistical analysis on the gravity-wave phase velocities for the same observational data. Section 4 discusses the results, including comparison with the routine meteorological observations.

2. Monochromatic Analysis

Figure 1 shows the temporal-vertical distributions of zonal and meridional wind perturbations from the average profiles during the observational period. We find a predominance of the following two wave modes in the lower stratosphere (14-24 km): one has aperiod (t) of about 22 hours and a' vertical wavelength (A,z) of 2-3 km, and the other is t - 44 hours and A,z - 1 km. Hereafter these two predominant modes are called the 22- and 44-hour modes. It should be noted that the amplitudes of these modes are not constant throughout the observational period and altitude range; they are particularly strong during 8-9 May at altitudes higher than the tropopause jet stream (-12 km). Also note that the inertial period t i

( = 2n //; / is the Coriolis parameter or inertial frequency) is about 21 hours at the latitude of the MV radar (34.85°N).

In order to examine the structures of the 22- and 44-hour modes we made 30-min averages in time and then filtered out 1.5--4.5 and 0.6-1.6 km bands in vertical wavelength as shown in Figures 2a and b, respectively. It can be clearly confirmed in this filtered data that the marked wave modes are particularly strong during 8-9 May at altitudes higher than the tropopause jet stream. We can also find that the phases propagate downward whereas the strong amplitudes proceed upward, which suggests an upward energy radiation in a shape of wavepacket as described in many foregoing studies (e.g., CADET and TEITELBAUM, 1979; MAEKAWA et al., 1984; HIROTA and NIKI, 1985, 1986).

For each filtered da ta set we analyzed hodographs (cf, HIROTA and NIKI, 1985, 1986) and determined the wave parameters such as U~ (amplitude of horizontal

Vol. 130, 1989 Gravity Wave Se1ection Observed by MV Radar 483

wind variation), i (intrinsic period), AH (horizontal wavelength), Cl( (direction of horizontal wavenumber vector), C x (zonal phase velocity) and E (kinetic energy density) assuming a monochromatic inertio-gravity wave. The results for the 22-and 44-hour modes shown in Figures 2a and bare plotted in Figures 3a and b, respectively. It should be noted that the parameters shown here are averaged in time throughout the observational period and smoothed in the vertical by an approximately 2 km running mean. First of all, the energy densities of both modes are concentrated in a layer between 10--17 km altitude. In this layer, variations of i, AH, Cl( and C x are small enough to use the assumption of a monochromatic wave for these analyses.

Both waves have almost southward wavenumber vectors in the whole altitude range observed. The wavefronts are aligned almost zonally and so the zonal phase velocities are significantly larger than the meridional phase velocities. However, the horizontal wavelengths are different ('" 200 and '" 50 km, respectively). For the 22-hour mode in the 10--17 km layer, we find from Figure 3 that Cx ",7m/s and that the zonal wavelength (Ax ) is ",600 km. For the 44-hour mode in the 10-17 km layer, we have C x'" 3 m/s and Ax '" 500 km. Parameters U~, i, AH , C x and E of the 44-hour mode are sm aller than those of the 22-hour mode.

The intrinsic periods of the 22 and 44 hour modes are estimated as 7 and 5 hours, respectively, so that we have i /r I = 0.33 and 0.24 for the respective periods. These values of i /r I are dose to the most predominant ones (0.3--0.4) in the middleand upper-stratospheric rocket sonde data (HIROTA and NIKI, 1985), and are out of the inertio-gravity wave critical layer (i/r / ;;:: 1/J2) predicted by YAMANAKA (1985). The modulation of such apredominant mode by the earth's rotation (or the inertial effect due to the Coriolis force) is considerable for the wave polarization (hence the hodograph becomes an ellipse), but it is not so effective for the wave dispersion (hence the ellipse is much elongated in the wavenumber vector direction). Therefore, we can describe the vertical propagation of the marked wave modes using the simple noninertial wave theory in a valid approximation.

In the simple theory, the criticallevel is defined by an altitude at which ü = C x,

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Vol. 130, 1989 Gravity Wave Seiection Observed by MV Radar 489

result ofwavebreaking (cf YAMANAKA, 1985; ZHV and HOLTON, 1987). It should be noted that C x < ü is satisfied for both modes within the 1 (}-17 km layer.

The echo power distribution (not shown) suggests a turbulence layer structure approximately along wavefronts of the 22- and 44-hour modes. These resemble turbulence layers observed by many MST radar observations (e.g., SATO and WOODMAN, 1982; WOODMAN and RASTOGI, 1984; SATO et al., 1985). Theoretical studies predict that the turbulence layers made by breaking internal gravity waves might be very thin and require a higher vertical resolution for their detection (TANAKA, 1983; Y AMANAKA and TANAKA, 1984a,b). Such a thin structure has been found in some in situ observations (e.g., BARAT, 1982, 1983; Y AMANAKA and

T ANAKA, 1984a,c, 1985; Y AMANAKA et al., 1985; SIDr and BARAT, 1986). In order to decide whether the turbulence found by the echo power data is genera ted direct1y by the predominant wave modes seen in the Doppler-frequency data, we are going to analyze both types of da ta in detail in a subsequent paper.

3. Statistical Analysis 01 Waue Phase Velocities

In the preceding section we have studied monochromatic wave parameters averaged throughout the observational period. However, as noted in Figures 1 and 2, two predominant modes are amplified in particular during 8-9 May. We consider that activities and wave parameters of the predominant modes might vary with time, and that some other modes might be activated. Among the various kinds of wave parameters, the zonal phase velocity C x is the most important quantity to compare the observation al evidence with the wave-mean flow interaction theory (cf, FRITTS, 1984). In this section we perform a statistical study on the variability of Cx

during the observational period in each altitude. We take the 1.5-4.5 km band data set of which the meridional component wind

has been shown in Figure 1 a. Figure 4 shows the histograms of C x and analyzed from this data set for each altitude. The mean value of C x at each altitude has been plotted in a panel of Figure 3a, that is, C x of the 22-hour mode discussed in Section 2. The thick curve in Figure 4 is the mean zonal wind ü transcribed from the right-hand side panel of Figure la.

We find c1early from Figure 4 that C x ~ ü throughout the observational altitude range and period. This feature is consistent with the wave selection mechanism by the mean flow as predicted theoretically by MA TSUNO (1982). This mechanism is essentially explained by the fact that the upward propagating waves should be trapped under their criticallevels. Since the wave breaks near the criticallevels, each wave becomes predominant at an altitude where C x = Ü + a and a is a nonzero unknown parameter. This implies that f[ = Axl(Cx - ü)] is almost constant, if a and Ax are alm ost constant. Therefore, f/! becomes almost constant for a latitude (see the preceding section and also HIROTA and NIKI, 1985), when a and Ax are almost constant.


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mean zonal flow profile.

However, we notice in Figure 4 that the values of Cx are concentrated near ü at altitudes lower than the peak of the tropopause jet stream (the tropospheric side), and that it is spread in a broad range less than ü above the jet peak (the stratospheric side). The feature of the tropospheric side can be easily understood by the selection mechanism of the predominant mode at each altitude, but the feature of the stratospheric side cannot be explained by assuming that all the waves are

Vol. 130, 1989 Gravity Wave Selection Observed by MU Radar

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491

genera ted near the ground. Although topographie stationary waves are not deteeted by single-station observations, most ofthem are eonsidered to be trapped in the lower troposphere unless C x varies greatly during the propagation (cf, TANAKA, 1986). Therefore, most of stratospheric gravity waves appear to be genera ted at altitudes higher than the jet stream peak.

Figure 5 shows a tentative model based on the present observations: "A" denotes the stratospheric waves genera ted mainly at the tropopause jet stream, and "B" indicates the tropospheric waves which have eonsiderable amplitudes only near their critieallevels. The upward wave emission from the jet stream has been described by several authors (e.g., CADET and TEITELBAUM, 1979; HIROTA and NIKI, 1986), but at least in the present observations downward wave emission from the jet as described by Hirota and Niki is not clearly seen. Mechanisms of the two wave-generation sources will be left as an important problem for future study (cf, FUKAO et al., 1989).

4. Further Discussions and Conclusions

In Seetion 3, we have obtained a model to explain why the two modes deseribed in Seetion 2 ean be predominant at the observed altitude range. However, we have

not explained why such marked waves appeared so strongly on 8-9 May. Although the wave generation mechanism is a problem of future studies, here we point out an interesting feature related possibly to the wave generation, based on routine meteorological observations. Figure 6 shows that a wind-speed maximum passed over the MV radar on 8-9 May. If the tropopause jet stream can generate the marked waves by some instability or adjustment mechanism, such wave generation most probably appears near the maximum-speed portion of the jet stream (cf, MASTRANTONIO et al., 1976; CADET and TEITELBAUM, 1979).

Furthermore, Figure 6 shows some wavy patterns at the particular times when the marked waves were observed by the MV radar. Pressure-surface analyses, on

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Vol. 130, 1989 Gravity Wave Se1eetion Observed by MV Radar 493

which Figure 6 is based, are objective using an optimum interpolation method (JMA, 1983). Thus we consider that detection of long-wavelength stratospheric gravity waves by the routine observations and analyses is not impossible, although the time resolution is 12 hours. Such a study is very important not only for estimation of horizontal wavelengths and horizontal dimensions of wavepackets, which cannot be directiy measured by the single-stationed radar observations, but also to illustrate the utility of the MST radar da ta to assimilate and initialize numerical weather predictions.

In summary, the observed internal gravity waves seem to be selected essentially by the mechanism of MA TSUNO (1982). They are predominant above the peak altitude of the tropopause jet stream. They may break and decelerate the me an flow in the lower stratosphere as considered by T ANAKA and Y AMANAKA (1985), but we cannot find any evidence that they are generated directiy by the surface orography. In the present observation most of the tropospheric waves have phase velocities around the me an flow. If both stationary and travelling waves are generated near the ground by some mechanisms, most of them would be trapped in the tropospheric altitudes and could not arrive in the tropopause altitude.

A cknowledgments

Staff members of the Numerical Prediction Division, Japan Meteorological Agency kindly permitted us to use their charts of routine objective analyses and their technical reports for our analysis of Figure 6. Special thanks are also due to P. T. May and W. L. Oliver, Jr. for their careful reading of the manuscript. The MU radar belongs to and is opera ted by the Radio Atmospheric Science Center, Kyoto University.

REFERENCES

BARAT, J. (1982), Some Characteristic 0/ Clear-Air Turbulence in the Middle Stratosphere, J. Atmos. Sei. 39, 2553-2564.

BARAT, J. (1983), The Fine Structure 0/ the Stratospheric Flow Revealed by Differential Sounding, J. Geophys. Res. 88, 5219-5228.

CADET, D., and TEITELBAUM, H. (1979), Observational Evidence o/Internal Inertia-Gravity Waves in the Tropical Stratosphere, J. Atmos. Sei. 36, 892-907.

FRlTTS, D. C. (1984), Gravity Wave Saturation in the Middle Atmosphere: A Review 0/ Theory and Observations, Rev. Geophys. Spaee Phys. 22, 275-308.

FUKAO. S., SATO, T., TSUDA, T., KATO, S., WAKASUGI, K., and MAKIHIRA, T. (1985a), The MV Radar with an Active Phased Array System, 1. Antenna and Power Amplijiers, Radio Sei. 20, 1155-1168.

FUKAO, S., TSUDA, T., SATO, T., KATO, S., WAKASUGI, K., and MAKIHIRA, T. (I 985b), The MV Radar with an Active Phased Array System, 2. In-House Equipment, Radio Sei. 20, 1169-1176.

FUKAO, S., YAMANAKA, M. D., SATO, T., TSUDA, T., and KATO, S. (1988), Three-Dimensional Air Motions over the Baiu Front Observed by a VHF-Band Doppler Radar: A Case Study, Mon. Wea. Rev. 116, 281-292.


FUKAO, S., YAMANAKA, M. D., MATSUMOTO, H., SATO, T., TSUDA, T., and KATO, S. (1989), Wind Fluctuations near a Cold Vortex-Tropopause Funnel System Observed by the MV Radar, Pure Appl. Geophys. 130 (2j3), 463-479.

GAGE, K. S., and NASTROM, G. D. (1985), On the Spectrum 0/ Atmospherie Veloeity Fluetuations Seen by MSTjST Radar and Their Interpretation, Radio Sci. 20, 1339-1347.

HIROTA, 1., and NIKI, T. (1985), A Statistieal Study o/Inertia-Gravity Waves in the Middle Atmosphere, J. Meteor. Soc. Japan. 63, 1055-1066.

HIROTA, 1., and NIKI, T. (1986), Inertia-Gravity Waves in the Troposphere and Stratosphere Observed by the MV Radar, J. Meteor. Soc. Japan 64, 995-999.

JAPAN METEOROLOGICAL AGENCY (JMA) (1983), The Northern Hemisphere and Fine-Mesh Numerical Prediction Models (8L NHM and lOL FLM) and Analysis System, JMA-Numerical Computation Center Teeh. Rep., Special Issue No. 29, 75 pp. (in Japanese).

JAPAN METEOROLOGICAL AGENCY (JMA) (1985a), JMA-Numerical Prediction Division 250-, 200- and 100-mb Objective Analyses, lrll May, 1985. (unpublished)

JAPAN METEOROLOGICAL AGENCY (JMA) (1985b), Daily Weather Maps, May 1985, 242 pp. JAPAN METEOROLOGICAL AGENCY (JMA) (1985c), Aero1ogical Data of Japan, May 1985, 247 pp. MAEKAWA, Y., FUKAO, S., SATO, T., KATO, S., and WOODMAN, R. F. (1984), Internal Inertia-Gravity

Waves in Ihe Tropical Lower Stratosphere Observed by the Arecibo Radar, J. Atmos. Sci. 41, 2359-2367.

MASTRANTONIO, G., EINAUDI, F., FUA, D., and LA LAS, D. P. (1976), Generation o/Grauity Waves by Jet Streams in the Atmosphere, J. Atmos. Sei. 33, 1730--1738.

MATSUNO, T. (1982), A Quasi-One-Dimensional Model 0/ the Middle Atmosphere Cireulation Interaeting with Internal Grauity Waves, J. Meteor. Soc. Japan 60, 215-226.

SATO, T., TSUDA, T., KATO, S., MORIMOTO, S., FUKAO, S., and KIMURA, I. (1985), High-Resolution MST Observations 0/ Turbulence by Vsing the MV Radar, Radio Sci. 20, 1452-1460.

SATO, T., and WOODMAN, R. F. (1982), Fine Altitude Resolution Observations 0/ Stratospherie Turbulent Layers by the Arecibo 430 MHz Radar, J. Atmos. Sci. 39, 254lr2552.

SAWYER, J. S. (1961), Quasi-Periodie Wind Variations with Height in the Lower Stratosphere, Quart. J. Roy Meteor. Soc. 87, 24-33.

SIDI, S., and BARAT, J. (1986), Observational Evidence 0/ an Inertial Wind Structure in the Stratosphere, J. Geophys. Res. 91, 1209-1218.

T ANAKA, H. (1983), Turbulence Layer Thickness in the Stratosphere under the Presence 0/ Viseosity and Newtonian Cooling, J. Meteor. Soe. Japan 61, 805-811.

TANAKA, H. (1986), A Slowly-Varying Model o/the Lower Stratospheric Zonal Wind Minimum Indueed by the Mesoscale Mountain Wave Breakdown, J. Atmos. Sci. 43, 1881-1892.

T ANAKA, H., and Y AMANAKA, M. D. (1985), Atmospherie Circulation in the Lower Stratosphere Indueed by the Mesoscale Mountain Wave Breakdown, J. Meteor. Soc. Japan 63, 1047-1054.

THOMPSON, R. O. R. Y. (1978), Observation o/Inertial Waues in the Stratosphere, Quart. J. Roy. Meteor. Soe. 104, 691-698.

VANZANDT, T. E. (1985), A Modelfor Gravity Wave Speetra Observed by Doppler So unding Systems, Radio Sei. 20, 1323-1330.

WOODMAN, R. F., and RASTOGI, P. K. (1984), Evaluation 0/ Effeetive Eddy Diffusive Coefficients Vsing Radar Observations of Turbulence in the Stratosphere, Geophys. Res. Lett. I I, 243-246.

YAMANAKA, M. D. (1985), Inerlial Oscillation and Symmetrie Motion Induced in an Inertio-Grauity Waz'e Critical Layer, J. Meteor Soe. Japan 63, 715-737.

Y AMANAKA, M. D., and TANAKA, H. (1984a), Multiple "gust layers" observed in the middle stratosphere, in Dynamics of the Middle Atmosphere (eds. J. R. Holton and T. Matsuno) (TERRAPUBjD. Reidel) pp. 117-140.

YAMANAKA, M. D., and TANAKA, H. (1984b), Propagation and Breakdown o/Internal Inertio-Gravity Waves near Critical Leueis in the Middle Atmosphere, J. Meteor. Soe. Japan 62, 1-17.

YAMANAKA, M. D., and TANAKA, H. (1984c), Meso- and Miero-Scale Struetures 0/ Stratospherie Winds: A Quick Look of Balloon Observation, 1. Meteor. Soc. Japan 62, 177-182.

Y AMANAKA, M. D., and TANAKA, H. (1985), Hierarchical Strueture 0/ Stratospheric Wind Fluetuations, MAP Handbook 18, 232-236.

Vol. 130, 1989 Gravity Wave Seleetion Observed by MU Radar 495

YAMANAKA, M. D., TANAKA, H., HIRosAwA, H., MATSUZAKA, Y., YAMAGAMI, T., and NISHIMURA, J. (1985), Measurement of Stratospheric Turbulence by Bal/oon-Borne "Glow-Discharge" Anemometer, J. Meteor. Soe. Japan 63, 483-489.

ZHU, X., and HOLToN, 1. R. (1987), Mean Fields Induced by Local Gravity-Wave Forcing in the Middle Atmosphere, J. Atmos. Sei. 44, 620-630.

(Reeeived August 31, 1987, revised/aeeepted February I, 1988)


High Time Resolution Monitoring of Tropospheric Temperature with a Radio Acoustic Sounding System (RASS)

T. TSUDA,1 Y. MASUDA,2 H. INUKI,2 K. TAKAHASHI,2 T. TAKAMI,1 T. SATO,1

S. FUKAO,1 and S. KAT0 1

Abstract-We have observed the time-height vanatIon of the temperature field in the upper troposphere using a Radio Acoustic Sounding System (RASS) which consists of the MV radar and a high-power acoustic transmitter. The fast beam steerability of the MV radar has made it possible to measure temperature profiles in a fairly wide height range in the upper troposphere (5-11 km), even under intense wind conditions. Observations were continued for about 32 hr on 24-26 December, 1986 with a time-height resolution of 30 min and 150 m. During the observation period, the tropospheric jet was so intense that the acoustic wavefronts were severely distorted. Using wind velocity profiles observed by the MU radar we have numerically estimated the propagation of acoustic wavefronts, and further determined favorable pointing directions for the MV radar to receive significant backscattering from refractive index fluctuations produced by the acoustic waves. Conventional radiosonde so undings were carried out every 6 hr, which showed a temperature decrease of 4 K/day in the upper troposphere during the observation period. Temperature profiles taken by RASS agree weil with the radiosonde results.

Key words: RASS, troposphere, temperature profile, MV radar, acoustic transmitter, radiosonde, remote sensing.

1. Introduction

The Radio Acoustic So unding System (RASS) is a ground-based remote sensing technique of atmospheric temperature in the troposphere and lower stratosphere (e.g., MARSHALL et al., 1972). The RASS utilizes the physical principle that radar echoes are scattered from periodic fluctuations in refractive index due to the density fluctuations produced by acoustic waves.

There are two fundamental conditions to receive significant RASS echoes by using a monostatic radar. First, the radar be am must be pointed in a direction such that the beam is normal to the acoustic wavefronts so that the reflections are back to the radar antenna. MASUDA (1988) extensively studied modification of acoustic

1 Radio Atmospheric Science Center, Kyoto University, Vji, Kyoto 611, Japan. 2 Communications Research Laboratory, Ministry of Posts and Telecommunications, Koganei,

Tokyo 184, Japan.

498 T. Tsuda et al. PAGEOPH,

wavefronts attributed to me an vertical gradients of both temperature and wind fields, and proved the importance of this condition by investigating a two-dimensional numerical model and RASS observations with the MV radar.

Second, the refractive index fluctuation should have a scale equal to half of the radar wavelength to satisfy the Bragg condition. So that, frequencies of the transmitted acoustic waves must be appropriately tuned according to mean temperature and wind profiles.

Because intensity of the RASS echoes becomes the largest when the Bragg condition is completely satisfied, it is often assumed, for intense RASS echoes, that the Doppler frequency corresponding to the propagation speed of acoustic pulses is the same as the transmitted acoustic frequency. However, MATUURA et al. (1986) pointed out that the Doppler shift of RASS echoes is not necessarily equal to the transmitted acoustic frequency. In other words, the intense RASS echoes could be received even when the Bragg condition is not strict1y satisfied, which seems to be attributed to a delicate balance between the first and second conditions (MATUURA et al., 1986). Therefore, it is important to determine the apparent sound speed from actual measurements of Doppler shift of the RASS echoes by the radar. The apparent sound speed thus obtained as a function of height is further converted to the temperature profile after compensating the Doppler shift effect due to the radial wind velocity.

By combining the MV radar (KATO et al., 1984; FUKAO et al., 1985a,b) with a high-power acoustic transmitter, MATUURA et al. (1986) have observed the temperature profile at the altitude range of 6-22 km in August 1985. In summer, the tropospheric jet becomes relatively weak, therefore, acoustic waves stay over the MV radar even in the 10wer stratosphere. On the other hand, in winter the maximum speed of the jet sometimes exceeds 100 mjs, thus, it becomes difficult to measure the temperature profile above the tropopause. In this paper, we report continuous monitoring of the tropospheric temperature profile using the RASS with the MV radar on 24-26 December, 1986. During the observation period the jet was fairly intense, so that the height range was limited to the 5-11 km altitude range.

2. Experimental Setup and Data Analysis

The RASS used in this paper consists of a high-power acoustic transmitter (MATuuRA et al., 1986) and the MV radar with a radio wavelength of 6.45 m wh ich is described in detail elsewhere (KATO et al., 1984; FUKAO et al., 1985a,b). Figure 1 shows a block diagram of the acoustic transmitter. High pressure air flow with around 7 atm of pressure is ga ted by an electromagnetic valve. Sinusoidal acoustic waves are produced by modulating the pulsed air flow by a pneumatic transducer, and further transmitted upward from a hyperbolic horn with a diameter of 72 cm wh ich is efficient in a frequency band of 77-110 Hz. The double side beam

Vol. 130, 1989 Monitoring of Tropospheric Temperature with RASS

HYPERBOLIC HORN

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Figure I A block diagram of the acoustic transmitter.

499

width of the horn is approximately 100°. The sound pressure level of the acoustic wave I m above the horn is 500 W/m2 • The pulse repetition frequency and duration of the acoustic pulse, as weIl as the acoustic frequency, are controlled by a system-installed small computer.

MASUDA (1988) found that the height range of the RASS measurement is mainly determined by vertical gradients of background temperature and mean winds, and is also a strong function of distance between sound and radar antennas. We have regularly observed vertical, northward and eastward components of wind velocity by the MV radar, and temperature profiles using conventional radiosondes be fore and during the RASS observations.

A two-dimensional ray tracing of the acoustic waves, which is described by MASUDA (1988) in detail, is applied to estimate the shape of the wavefronts and the effective reflection region of the RASS echoes. Figure 2 shows typical profiles of temperature and eastward radial winds measured by a radiosonde and the MV radar. The radial wind velocity shown in Figure 2 was sampled at a zenith angle of 10°, therefore, the corresponding maximum horizontal wind velocity at around ll km altitude was as large as 90 m/s. This wind profile is approximated by linear sections in several altitude regions for the numerical computations of the acoustic ray-tracing (MASUDA, 1988). Two reflection regions appear in the windward and leeward directions at zenith angles of around 30 and 50°, respectively, as shown in Figure 2. The former direction is preferable for the MV radar observations. The initial numerical ray-tracing of acoustic waves was done in advance of the continuous RASS observation. By taking the results into account, the acoustic transmitter

500

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HORIZONTAL DISTANCE (km)

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10

(m/sl

PAGEOPH,

Temperature (top left) and eastward radial wind velocity (top right) profiles measured by a radiosonde and the MV radar, respectively, at around 11:30 on Dec. 25, and a two-dimensional numerical model of the effective reflection region of RASS echoes (bottom). The distance between the sound and radar

antennas is assumed to be 120 m.

was located 120 m west of the center of the MV radar antenna, because the me an winds were nearly in the eastward direction. The ray-tracing was continued during the observations in order to determine suitable beam directions on a real-time basis. In general, time variation of the gradient and direction of mean winds is larger than that of the temperature gradient, therefore, the mean wind structure should be more frequently monitored than the temperature profile.

In the actual observations, several beam directions are necessary to cover the large height range, and follow small-scale excursions of the reflection regions from the directions which were deduced from the numerical model. Since the MV radar can change the azimuth and zenith angles of the antenna beam every 5° and 1-2°,

Vol. 130, 1989 Monitoring of Tropospheric Temperature with RASS 501

respectively, we have steered the radar beam in four directions as listed in Table L Because the meridional component of the me an wind varied slightly with time, we have steered the antenna beam towards the north or south from the westward direction. We did not move the acoustic transmitter throughout the RASS observations. However, it might become necessary to relocate the acoustic transmitter such that it is placed in the windward direction from the center of the radar antenna, when the meridional wind varies largely from the initial condition.

As shown in Figure 3, we have transmitted two sets of eight successive acoustic pulses with a pulse width of approximately 0.5 sec and an interval of 2 sec. Each pulse contained 50 cycles of acoustic waves. Because of the mean temperature decrease in the troposphere, the acoustic frequency suitable for the Bragg condition decreases with height. Therefore, the frequency was changed from 88 to 95 Hz and from 81-88 Hz for temperature soundings in the lower and upper height ranges, respectively, as shown in Figure 3.

The transmitted radar pulse was phase-modulated by a 16-bit complementary code with a subpulse width of 1 J.1sec. The RASS echoes were sampled with a range resolution of 150 m, and transferred into Doppler spectra using a 1024-point FFT. The number of coherent integration is limited to two in each antenna direction, giving an effective sampling rate of 3.2 msec in order to cover a wide Doppler velocity range corresponding to the sound speed of around 300 m/s. The total height range was separated into two regions consisting of 32 altitude points, because of restrietions of the memory area for Doppler spectra in the MO radar.

Although the RASS observations can be finished in a few min as recognized from Figure 3, they are repeated every 30 min, with the repetition frequency mainly limited by the refilling time of the high-pressure tanks by the air compressor. The three components of the wind field are observed by the MO radar using anormal MST radar technique during the observation gaps of two successive RASS measurements.

An apparent sound speed is determined at each range gate by applying a least-square fitting of a Gaussian to the Doppler spectra of the RASS echoes. By

Table 1

Antenna beam direClions 0/ the MV radar during the RASS observations.

Observation Period

16:00 Dec. 24 - 8:30 Dec. 25

8:30 Dec. 25 - 13:00 Dec. 25

13:00 Dec 25. ·17:30 Dec. 25

17:30 Dec. 25 - 00:00 Dec. 26

[Azimuth angle, Zenith angle (0)]

[270, 30], [275,28], [275,30], [275,32] [260,30], [265,28], [265, 30], [265, 32] [260,30], [260,32], [260,34], [265,32] [260, 32], [265, 32], [265, 34], [270, 32]

502

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TIME (sec)

Figure 3

PAGEOPH,

--- r t"....,. r ...--.--.-..-r-150

A timing chart of the acoustic pulses and the MV radar observations. Eight successive pulses with width and repetition period of 0.5 and 2 sec, respectively, are transmitted twice for the RASS observations of lower (5-9 km) and upper (8- 12 km) altitudes. The RASS echoes are sampled by the MV radar 29 and

42 sec after the transmission of acoustic pulses.

linearly interpolating the wind fie\ds detected before and after the RASS observations, we can recompose the radial wind velocity in the antenna beam direction for the RASS measurements. A true sound speed, C (ms - ') is determined after compensating this radial wind velocity from the apparent sound speed, and furt her transferred into the atmospheric temperature T (OK) by utilizing a relation of C = 20.067To 5• Temperature profiles independently determined in four beam directions are projected onto a single altitude axis with a step of 100 m after interpolation. These temperature profiles are further smoothed by applying a moving average of five adjacent altitude points with a triangular weighting. A representative value of the atmospheric temperature is determined, when the discrepancy among the four different determinations is small. Thus, temperature profiles with a time resolution of 30 min are found from the RASS observations. We have further averaged over three profiles, again using a tri angular weighting when these are compared with the radiosonde measurements.

3. Results and Discussions

Figure 4 shows the eastward and northward components of the mean wind velocity observed by the MV radar in aperiod from 16:00, Dec. 24 to 00:00 Dec.

26, 1986, and atmospheric temperature profiles averaged over five radiosonde

Vol. 130, 1989

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Monitoring of Tropospheric Temperature with RASS 503

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Figure 4 Eastward (solid line) and northward components (broken line) of the mean horizontal winds observed by the MV radar in aperiod from 16:00, Dec. 24 to 00:00 Dec. 26, 1986 (Ieft panel), and atmospheric temperature profiles (solid line) averaged over five radiosonde measurements which were made every 6 hr starting from 23:00, Dec. 24 at the MV radar site (right panel). The latter is compared with a mean temperature profile averaged over 24 hr of RASS observations (circle) made on 24--26 December, 1986. Error bar corresponds to standard deviation of temperature fluctuations during the observation period.

measurements made every 6 hr starting from 23:00, Dec. 24 at the MU radar site. The latter is compared with a me an temperature profile from the RASS measurements averaged over 24 hr corresponding to the entire observation period of radiosonde soundings. The tropospheric wind is nearly eastward in the whole height range, and its maximum exceeds 60 ms - I at around 11 km. The meridional wind becomes slightly northward above 5 km. Agreement of the temperature profiles is excellent, although the standard deviation around the mean value becomes large at around 6 km altitude, which may be attributed to a rapid change in the temperature fields as described later.

Figure 5 shows relatively large fluctuations in the temperature profiles in the troposphere from radiosonde observations made every 6 hr from 23:00 Dec. 24 to 23:00 Dec. 25, 1986. The temperature beJow 10 km altitude decreases by 5- 10 K in 24 hr, which is most clearly seen at around 5 km altitude, while it generally increases in the altitude region above 10 km.

Invividual temperature profiles taken by the radiosondes plotted in Figure 5, are reproduced in Figure 6 with successive soundings shifted by 72 K, and are

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Figure 5 Temperature profiles observed by five radiosondes.

PAGEOPH,

compared with RASS observations. AIthough there exists a general temperature decrease in the observed height range as shown in Figure 5, temperature profiles from RASS measurements agree fairly weIl with the conventional radiosonde resuIts. Furthermore, the phase progression of wave-like structure can be recognized from RASS observations at 5-7 km in the first third of the observation period.

Figure 7 shows contour plots of the tropospheric temperature from radiosonde and RASS observations. Because there are only five profiles from radiosonde measurements, the time variation in the upper panel looks fairly smooth. Isotherms in the 7-9.5 km altitudes generally stay at the same height until 12:00 Dec. 25, then linearly decrease at an approximate rate of 60 m/hr. The aItitude of the - 15°e isotherm drastically falls during the first four hr. The 200 e isotherm starting at an altitude of 6.2 km at 23:00 on Dec. 24 also descends by about I km during the first ten hr, and then does not vary largely in the middle of the observation

\

-80 -40 <0 60 t10 1&0 200 280 J'O TE"'PERATURE (OC)

Figure 6 Temperature profiles taken every 30 min by RASS (dots) and radiosondes (solid lines), Horizontal axis is shifted by 6 and 72 K for every temperature profile determined by RASS and radiosonde measure

ments, respectiveJy,

12 ')

11

10

--------------------===== ---------~

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Figure 7 Contour plots of the tropospheric temperature by radiosondes (top) and RASS (bottom).

506 T. Tsuda et al. PAGEOPH,

period. This isotherm then falls linearly during the latter part of the observation period.

The RASS observations show overall agreement with the radiosonde results and furthermore, they exhibit fine structure of temperature fluctuations in addition to the general trends. For an example, we can recognize a core of local high temperature centered at 5.5 km altitude and 01 :00 on Dec. 25. In general, RASS is a powerful tool to investigate meso-scale fluctuations in temperature fields with relatively good time and height resolution.

4. Conc/uding Remarks

In this paper, we have presented RASS measurements of atmospheric temperature in the upper troposphere (5-11 km) made every 30 min for 32 hr on 24-26 Dec., 1986. The mean temperature profiles, averaged over 24 hr of RASS measurements, agree very weIl with the conventional radiosonde observations. Individual temperature profiles taken by the radiosonde are fairly weil reproduced by the RASS measurements, even though there was a large decrease of background temperature during the observation period.

The sampling interval of temperature profiles is mainly determined by the recovery time of the air pressure in the tank and therefore by the refilling capacity of the compressing system. The time resolution can be fairly easily improved up to several minutes by improving the air compressor installed on the acoustic transmitter. When the me an wind is relatively weak, acoustic wavefronts are not severely modified, and the effective reflection regions of RASS echoes do not move windward, but stay near the acoustic transmitter even at an altitude of 25 km (MATUURA et al., 1985; MASUDA, 1988). In such a condition, we would be able to continuously monitor variation of lower stratospheric temperature with a timeheight resolution of several min and a few hundred m. If the fine structure of temperature fields are observed by using the RASS technique in addition to precise measurements of wind velocities by the MST radars, we will acquire a new perspective on meso- and micro-scale fluctuations in the troposphere and lower stratosphere.

Acknowledgements

Helpful suggestions by Drs. T. E. VanZandt, P. T. May and R. J. Doviak are warmly acknowledged. Data used in thid paper were obtained by using a pneumatic transducer borrowed from Ship Research Institute, Japanese Ministry of Transport. The MV radar is operated by the Radio Atmospheric Science Center, Kyoto Vniversity.

Vol. \30, 1989 Monitoring of Tropospherie Temperature with RASS 507

REFERENCES

FUKAO, S., T. SATO, T. TSUDA, S. KATO, K. WAKASUGI, and T. MAKIHIRA (l985a), The MV radar with an active phased array system: 1. Antenna and power amplifiers, Radio Sei. 20, 1155--1168.

FUKAO, S., T. TSUDA, T. SATO, S. KATO, K. WAKASUGI, and T. MAKIHIRA (l985b), The MV radar with an active phased array system: 2. ln-house equipment, Radio Sei. 20, 1169-1176.

KATO, S., T. OGAWA, T. TSUDA, T. SATO, I. KIMURA, and S. FUKAO (1984), The middle and upper atmosphere radar: First resu/ts using a partial system, Radio Sei. 19, 1475-1484.

MARSHALL, J. M., A. M. PETERSON, and A. A. BARNES, Jr. (1972), Combined Radar-Acoustic Sounding System, Appl. Opties 11, 108112.

MASUDA, Y. (1988), The dependence 0/ altitude limit 0/ Radio Acoustic So unding System (RASS) upon wind and temperature gradients, Radio Sei. 23, 647--{j54.

MATUURA, N., Y. MASUDA, H. INUKI, S. KATO, S. FUKAO, T. SATO, and T. TSUDA (1986), Radio acoustic measurement 0/ temperature profile in the troposphere and stratosphere, Nature 323, 426-428.



Falling Sphere Observations of Anisotropie Gravity Wave Motions in the Upper Stratosphere over Australia

STEPHEN D. ECKERMANN 1 and ROBERT A. VINCENT 1

Abslracl~A study of inertial seale gravity wave motions in the region of the atmosphere between 30 and 60 km has been undertaken, using wind and temperature data derived from rocket-borne falling sphere density experiments performed over Woomera, Australia between 1962 and 1976. The gross features of the wave field eompare favorably with those found in similar northern hemispherie studies. Wave propagation is found to be both vertically and horizontally anisotropie. A rotary speetral analysis indieates predominately upgoing wave energy, suggesting that the majority of sources of these waves lie below 30 km. A detailed statistical investigation of the waves, made using the Stokes parameters technique, reveals that phase progression is also highly direetional in the horizontal, with a signifieant zonal component in summer, but with a strong meridional component in winter. Propagation towards the southeast is inferred in summer, with the waves possibly emanating from tropospherie sources in equatorial regions to the north of Australia. The technique also shows that, on average, the waves appear to have mean ellipse eccentrieities ( =f/w) around 0.4-{).45. Indirect estimates of a number of important wave parameters are made. In particular, u'w' and v'w' flux estimates are made over several height intervals. The vertical gradient of density weighted flux implies wave-induced mean flow aceelerations of the order O. I I ms-'day-'. This suggests that dissipating gravity waves are a significant source of the moment um residuals that are eneountered in studies of satellite data from this region.

Key words: Middle atmosphere, inertial seale gravity wave, Stokes parameters, momentum fluxes.

I. Introduction

It has long been known that vertically propagating internal gravity waves can

efficiently transfer energy and momentum between different regions of the atmos

phere. The theoretical study of LINDZEN (1981) was amongst the first serious

attempts to quantify these effects into a simple, workable mathematical framework.

It was demonstrated that such waves can grow in amplitude to become convectively

unstable at some altitude, and break. This results in an acceleration or deceleration

of the mean zonal wind and an enhanced production of turbulence at this breaking

level. Recent suggestions that the gravity wave field may be limited in amplitude, or

I The University 01' Adelaide, Department of Physics and Mathematieal Physies, G.P.O. Box 498, Adelaide, South Australia, 5001.

5\0 S. D. Eckermann and R. A. Vincent PAGEOPH,

saturated, at many heights in the atmosphere (e.g., FRITTS 1984; VINCENT, 1984; HIROTA and NIKI, 1985; SHIBATA et al., 1986) indicates that gravity waves may well influence the state of the entire atmosphere. A proliferation of research into both linear and nonlinear saturation mechanisms for internal gravity waves has resulted (FRITTS, 1984; MÜLLER et al., 1986).

UHF, VHF and HF backscatter radars have become the principal sources of information on both the spatial and temporal scales of atmospheric gravity waves. However, such radars provide information from the troposphere, lower stratosphere, and mesosphere only. Consequently, a large portion of the atmosphere between 30 and 60 km remains difficult to probe experimentally, although the advent of lidar technology may redress the problem. This field, however, is still in its infancy. Nevertheless, the vital role that gravity waves might play in driving the stratospheric circulation (e.g., PLUMB et al., 1986) necessitates their investigation by whatever means are available.

To this end, rocket-borne observations still provide one of the main ways to investigate gravity wave activity in this "gap" region. HIROTA (1984) provided an initial study in this regard, utilizing data from twelve rocket stations, ranging in latitude from 77°N to 80 S, to establish a climatology of the basic gravity wave parameters in this height region. This work was further extended by HIROTA and NIKI (1985) to include a statistical study of the amplitude growth and intrinsic frequency of these wave motions.

The current study uses data from one mid-latitude southern hemispheric rocket station (Woomera, 31 oS, 136°E). In contrast to the gross climatological emphasis of previous investigations, a detailed statistical examination is provided of the gravity wave characteristics at this site.

2. Data Reduction

The data used hereafter are derived from 102 "Falling Sphere" experiments performed approximately monthly between 1962 and 1976. Densities are calculated by an application of the drag equation, temperatures are derived hydrostatically

from the density determinations, and wind velocities are measured by radar tracking of the sphere (PEARSON, 1966; JONES and PETERSON, 1968). The vertical resolution of the data is 1 km. Some dropsonde measurements (VINCENT et al., 1977) were also available, but the two data sets were not combined due to observed systematic differences in the temperature (QUIROZ and GELMAN, 1976); the zonal wind velo city data deduced by each method also differed somewhat (Figure 1). The sm all mass and symmetry of the falling sphere suggest it should give the more reliable wind velocity determination of small-scale motions by radar tracking.

Following the approach ofHIROTA (1984), a high pass vertical spatial filter was applied to each profile using a Fast Fourier Transform. Vertical scales greater than

Vol. 130, 1989 Anisotropie Gravity Wave Motions over Australia

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Seatter plots of monthly averaged temperature and zonal wind derived from falling sphere and dropsonde measurements. The data eodes indieate the altitude range of the measurement; "3" =

30-40 km, "4" = 40-50 km, "5" = 50-60 km, "6" = 60-70 km.

512 S. D. Eckermann and R. A. Vincent PAGEOPH,

10 km, wh ich have tidal and planetary wave contamination, are removed in this process. Prior to application of the filter, the monthly mean winds and temperatures at each level were subtracted from the individual profiles, which were then linearly detrended and "windowed" in order to minimize data distortion upon transformation. Windowing involved tapering of the end points of each profile with a squared eosine envelope, in order to reduce edge effects.

3. Results

3.1 Can the Sphere Track Gravity Waves?

As a sphere falls through the atmosphere, it is also moved horizontally by the wind. Using Newton's Laws to determine the momentum transfer rate between the atmosphere and the sphere, one finds that the horizontal acceleration aH exerted upon a sphere of radius r, mass M and horizontal velocity Vs by an atmosphere of density p and wind speed Va, is given approximately by the following formula.

pnr 2(va - VS )2

aH = M (1)

Consider a "worst case" of tracking a gravity wave of 10 ms -I amplitude and 2 km vertical wavelength at a height of 60 km, where the sphere falls at a speed of about Mach 0.5 (150 ms - I) and the atmospheric density is around 3 x 10-4 kg.m - 3. Since the sphere has a mass of 0.61 kg, a radius of 1 m, and the velocity difference during descent due to the wave was about 10 ms -I, the resulting acceleration was about 0.2 ms - 2. As the fall velocity of the sphere was about 150 ms - I, it would have descended 1 km in about 7 seconds, increasing the horizontal velocity of the sphere only 1-2 ms-I. At an altitude of 30 km, however, the density is ~2 x 10- 2 kg.m- 3,

giving a sphere acceleration of 10 ms- 2, and so the gravity wave is tracked more faithfully.

From this idealized calculation, where accelerations due to background wind changes have been neglected, we conclude that all gravity waves are well tracked by the sphere at lower altitudes, but that, at the highest altitudes, wave amplitudes may be underestimated, and longer vertical wavelength waves may be tracked better than sm aller ones. The much greater mass of a dropsonde payload will result in even smaller accelerations again, and explains the systematic bias in the zonal wind scatter plot (Figure 1).

3.2 Correlation between the Zonal and Meridional Wind Oscillations

For the case of a quasi-inertio-gravity wave of intrinsic frequency w, propagating in an atmosphere with Coriolis parameter f, the meridional (v') and zonal (u')

Vol. 130, 1989 Anisotropie Gravity Wave Motions over Austra1ia 513

wind oscillations differ in amplitude and phase, and are related through the following expression (GOSSARD and HOOKE, 1975),

(2)

where k and I are the zonal and meridional components of the horizontal wavenumber, respectively. This formula implies elliptical wave polarization, with a frequency dependent ellipse eccentricity of (f/w). The phase motion of such an inertio-gravity wave will have a horizontal component, lying along the major axis of this motion ell!pse, which is better defined as w increases from! Consequently, for an ensemble of gravity wave motions where the orientation of the major axes has no preferred direction in the horizontal, the spatial correlation PUl> between u' and v' over several wavelengths should be zero, assuming individual wave events do not dominate the wave field. Figure 2a shows the distribution of Pu,' using all the available profiles. It tends to be centered about zero, as HIROTA (1984) also found. If, however, the horizontal velocity motions have some preferred direction of oscillation, then the me an phase relation of (2) will be biased somewhat, and PUL' will have a nonzero mean value (VINCENT and STUBBS, 1977). On separating the correlation data into summer and winter distributions, a small nonzero offset, which is negative in summer and positive in winter, emerges (Figure 2b).

Using Fisher's z-distribution (SNEDECOR and COCHRAN, 1980), a PUl' calculation from a single 26 point profile has a 95% confidence interval of about ± 0.4, if the determined value is near zero. The histograms of Figure 2b group together such PUl' calculations from 42 summer and 60 winter profiles, and their mean value' has a standard error at the 95% significance level of around ±0.03. On this basis, the skewed nature of the histograms in Figure 2b, though slight, seems to be statistically significant.

Care must be exercised when using this correlation to investigate horizontal localization of waves. For example, if wave motions are essentially aligned along either the EW or NS axes, the correlation will still be smalI. Rather, one should successively rotate the axes and recalculate Pu,. each time. An isotropic wave field will produce a uniformly zero correlation after each rotation, whereas, for an anisotropically orientated wave field, Pu,' will maximize at some angle, then tend to zero and reach its most negative value after further 45° and 90° rotations respectively. The angle where Pu,. tends to zero helps define the mean direction of oscillation and the angular width of the maximum gives an indication of the directionality. On rotating the axes in 10° steps from east towards north, it was found that Pu" was zero after a 70° rotation in both seasons. A 30° rotation resulted in Pu,. becoming distinctly negative in summer and positive in winter (Figure 2c). This suggests that the wave motions were aligned along an axis at 70°/250°

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Figure 2 Histograms ofcorrelation between u' and v' for all data, (a) for summer (dashed) and winter (solid) data (b), and for summer and winter data after rotation of the axes through 30° from east through north (c).

Winter is taken as the six months from March to August inclusive.

(antielockwise from east) in winter, while the summer motions were more nearly aligned at 160°/340°. Figure 7 may help in visualizing these correlation changes on rotation.

3.3 Vertical Wavenumber Spectrum

Each wind profile may be regarded as a nearly instantaneous snapshot of the wind motions in the vertical. In general, the wave motions will be elliptically polarized (see formula (2», with the sense of rotation depending on whether the wave energy is up- or downgoing; in the Southern Hemisphere (/ < 0) waves propagating energy upwards will have motions which rotate antielockwise with increasing height. A convenient way to characterize the sense of rotation of the wave motions is to calculate the rotary spectrum (e.g., VINCENT, 1984), which decomposes the wave motions into circular antielockwise and elockwise rotating components as a function of vertical wavenumber. This spectrum, averaged over all 102 profiles for vertical wavelengths between 2 and 10 km, is shown in Figure 3. The antielockwise and elockwise spectra are also plotted, and their sum gives the total power spectrum. It can be seen that this latter spectrum has apower law form E(m) oc m -I, where the spectral index t ~ 1.25. The suppression of small wavelength motions at greater altitudes may mean that this spectrum is even flatter. Spectra for the 30-45 km and 45-60 km height ranges (Figure 4) reveal smaller peak spectral densities and smaIIer spectral indices in the lower height regime.

Integration under these curves gives the spectral energy density. We find for the 2-10 km band that 65% of the gravity wave energy is of antielockwise rotating form, which indicates an upgoing wave energy flux. This value is almost certainly a lower limit, since the greater the eccentricity of the wave motion ellipse, the more incomplete is the partitioning of elockwise and antielockwise rotating circular wave motions in the wavenumber spectrum, to a point where linearly polarized wave motions give equal antielockwise and elockwise spectral amplitudes, regardless of the vertical sense of the wave phase propagation. This result is very similar to the mesospheric results of VINCENT (1984) and the lower stratospheric baIIoon results of THOMPSON (1978), both of wh ich used data from sites very elose to Woomera. These resuIts show that most inertial scale gravity waves in the atmosphere above southern Australia originate from heights below 10-15 km. On separating this spectrum into summer and winter spectra, we find about 70% of the energy is upgoing in summer, and about 60% in winter. The absolute energy densities and spcctral indices are also slightly larger in summer.

3.4 Grm'ity Wave Activity

A plot of the mean square gravity wave wind speed with height is shown in Figure 5. A wave growth with increasing aItitude less than Po 1/2 is evident,

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data. The anticlockwise (large dash) and clockwise (small dash) spectra are also shown.

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-1.2 < slope < -1.0

' ... - - - -*- - - - *-. ...•...............•. ..... ....

.•......... -2' 9 -2' 8 -2' 7 -2' 6 -2' 5

loglO of wave number (rn-I)

wavelength 4

(km) 3

TaTAL ROTARY WIND SPECTRUM FROM 45-60

large dash : anticlockwise componen small dash : clockwise corrponen

-2.0 < slope < -1.8

.....

' ...

..... .... *-.

" . .................. " " " " .... '."""-'.:{:"

...:. <.

-2'9 -2' 8 -2' 7 -2' 6 -2' 5

loglO of wave number (rn-I)

Figure 4

517

Rotary spectra ofhorizontal gravity wave velocity ftuctuations from (a) 30 to 45 km and (b) 45 to 60 km, averaged over aIl data. The antic10ckwise (large dash) and c10ckwise (small dash) spectra are also shown.


)1(

GRAVI1Y WAVE ACfIVI1Y * 56 *

)(

54 *

* 52 *

)I(

50 )(

* 48 *

* 46 *

~ 44 )K

)(

42 *

40 /' )( ..-..-..-..-..-

..-38 ..-

36

~ /

34

I I I I I o 20 40 60 80 100

Figure 5 Mean square horizontal gravity wave velocity fluctuations and standard errors, averaged over all data, from 33 to 58 km. The dotted curve shows the theoretical growth in amplitude of a linear, conservative

wave in a nonmotile, isothermal, inviscid atmosphere of scale height 7 km.

Vol. 130, 1989 Anisotropie Gravity Wave Motions over Australia 519

although it must be remembered that the sphere may underestimate the amplitude of the wind oscillations at the uppermost heights. These results are similar to those of HIROTA and NIKI (1985), who found only slow growth with height of wave amplitudes in the stratosphere from rocket studies, as also did SHIBATA et al.

(1986), who used Lidar Rayleigh backscatter observations. This result is superfi

cially suggestive of wave dissipation. However, a background wind shear can

conservatively reduce wave growth with height, particularly if the intrinsic phase

speed of the wave is small (LINDZEN, 1985).

A study of the seasonal variations in wave activity was complicated by the

relatively small number of soundings made in a given month. The wave motions tended to show a weak annual variation at the lower levels, with a minimum in

activity in summer, but at upper levels near 50 km a clear seasonal variation in - -

(U'2 + U'2) was less evident. The seasonal variation in (T'/To) showed a more semi-annual character, with maxima occurring at the equinoxes. The r.m.s. wind amplitude varies between 6 and 8 ms - I, while the fractional temperature perturba

tion T'/To lies between 0.01 and 0.02. These findings are in general accord with

those of HIROTA (1984), who found an annual cycle at polar latitudes, grading to

a semi-annual cycle at tropical latitudes. At latitudes near 30oN, HIROTA (1984)

found !ittle seasonal variation in the wind motions, but a semi-annual variation in

temperature with equinoctial maxima.

3.5 Waue Characteristics

To date, a standard method of analysis of low frequency gravity wave properties has been by inspection of wind hodographs, making use of formula (2) and its

prediction ofa wave ellipse eccentricity of(f/w) (KUNDU, 1976; HIROTA and NIKI, 1985; COT and BARAT, 1986). This method, however, assumes a monochromatic wave, whereas a number of superimposed waves are probably present. Many studies

using this technique have concentrated on individual large amplitude quasi-inertial gravity wave events that dominate the wind oscillations. Such occurrences, however, are not common (FRITTS et al., 1984).

In order to provide a more statistical description of the wave field, we use the technique introduced by VINCENT and FRITTS (1987) of determining the so-called

Stokes parameters of the gravity wave field. This method makes the analogy

between partially polarized gravity waves and partially polarized electromagnetic waves (KRAUS, 1966). In this study, so as to decompose the generally polychro

matic wave field, the Stokes parameters are calculated in the Fourier domain. If one

uses the Fourier Cross-Correlation Theorem (BRACEWELL, 1978) for real spatial

data, and assumes u'(z) and v'(z) have peak amplitudes u~ and v~ and transform as

UR(m) + iUlm) and VR(m) + iVlm) respectively, the following expressions are

easily derived.

520 S. D. Eckermann and R. A. Vincent

1= u'Ö + v'Ö = A[U~(m) + Ui(m) + V~(m) + Vi(m)]

D = u'5 - V'5 = A[U~(m) + Ui(m) - V~(m) - V;(m)]

PAGEOPH,

(3)

( 4)

(5)

( 6)

Overbars denote time averages and A is a constant. In optical terms, I is the throughput parameter, D is the throughput anisotropy parameter, P is the linear polarization parameter, and Q is the circular polarization parameter (positive is anticlockwise, negative is clockwise). The phase difference b, major axis orientation r, and ellipse axial ratio AR are given by (KRAus, 1966)

b = arctan( ~)

2r = arctan( ~)

AR = cot ~ where 2~ = arcsin(g). d.I

(7)

(8)

(9)

The variable d = (D 2 + p 2 + Q2) 1/2/1 is a measure of the ratio of the polarized to irregular motions and is usually termed the degree oi polarization if the Stokes parameters of a given wave motion are averaged in time. It is easy to show, however, that d = I at a given wavenumber for a single falling sphere wind profile (similar to the coherence variable, to which d is related, in conventional cross-spectral analysis).

To achieve statistical reliability, the quantities I, D, P and Q are averaged at a given wavenumber, m, from the spectra computed for all profiles in a given season. The average values are plotted in Figure 6, with their associated standard errors. This was achieved for the angular variables by circular statistical techniques (MARDIA, 1972). The dav values were evaluated by using mean values of I, D, P and Q and the (i/ru) ratios were found using

i/ru = AR - I = tan ~aL"

It must be stressed that a Stokes parameter determined at a given wavenumber has little significance. This may be seen by considering the dispersion relation for quasi-inertio-gravity waves (GOSSARD and HOOKE, 1975)

Nkh

m(z) = (ru2 _ .f) 1/2' (10)

Here kh is the horizontal wavenumber, where k~ = (k 2 + 12). From the equation it is apparent that the vertical wavenumber, m, will vary as a function of height in an

Vol. 130, 1989

6000

~ 4000 ... '" NE

:::::: 2000

Anisotropie Gravity Wave Motions over Australia

---. ~

~ 50 a. "o ci> ~ -0

O~---r--------r---~ o J

E 1000 --:

N

v. Ng

0 Cl

- 1000

500 E "'" '" 0 ~i

"- 500

1000

3000

E .;;<

;: 2000

E 0 1000

o

2

~,

~ - '" ~

1 I I

2

2

2 wavcnumber (km-I)

2

bO ou ~ 100 !3 ~ "0 50

0 2

0·4

~ .., t:.ll 0)

g 0·2 <:::-

0·0 2

150 $ , '

~ 100 \ ; ~

50 $ o '----y---

wavenumber (km-I)

Figure 6

521

Stokes parameters of horizontal gravity wave veloeity fluctuations and standard errors, averaged over aB data. The solid line is winter data (W) and the dashed li ne is summer da ta (S).


atmosphere where the background wind, which affects the intrinsic frequency w, and temperature, wh ich affects the Brunt-Väisälä frequency N, both vary with altitude. Therefore, particularly in June and December when there are strong eastward and westward zonal wind jets respectively, a single vertically propagating wave event will be smeared throughout wavenumber space.

Several features are immediately apparent on inspection of Figure 6. The Q parameters in each season are uniformly positive, with Qsummer> Qwinter' This indicates once again that anticlockwise rotating waves are more prevalent than clockwise rotating waves, as the rotary spectrum revealed. A clear seasonal trend in the throughput anisotropy (D) and linear polarization (P) parameters also arises. At large vertical wavelengths a winter meridional anisotropy and a summer zonal anisotropy in throughput are observed. The P parameters are positive in winter and negative in summer, except at smaller )'z where Psummer> O.

The orientation direction r shows strong meridional alignment in winter, and zonal alignment in summer. To investigate these trends in more detail, a broadband r determination was obtained for each profile by averaging the P and D parameters over the 3-10 km band. The values obtained from all 102 profiles are plotted in Figure 7. The mean orientations of 83° ± 6° in winter and 1580 ± 9° in summer are also shown. These plots can readily be reconciled with the correlation coefficients in Figures 2b and 2c. The observed summer zonal anisotropy may be slightly enhanced by the sphere, since waves propagating in the same direction as the mean zonal wind diminish in vertical wavelength with height, and may not be tracked reliably at greater heights. Similarly a meridional anisotropy may be overestimated, since the sm all mean meridional winds cause little vertical wavelength change, and so there is much less chance of the wave motion being shifted out of our 2-10 km observation al window. Yet the fact that one orientation scheme does not dominate in all seasons suggests that neither biasing effect dominates the observations. There is considerable agreement amongst these results, using upper stratospheric rocket wavenumber data taken between 1962 and 1976, and the recent observations from a nearby location (Buckland Park, 35°S, 138°E), using mesospheric HF radar frequency data taken between 1983 and 1984 (VINCENT and FRITTS, 1987). Earlier studies of data from the latter site also provided preliminary suggestions of preferred horizontal motion directions in winter (VINCENT and STUBBS, 1977), with meridional alignment seemingly preferred (HOCKING, 1983). On plotting the orientations in conventional seasonal groupings, the winter meridional and summer zonal alignment trends become even more distinct, whereas the spring and autumn plots have features characteristic of both the summer and winter plots, suggesting that these are transition periods in gravity wave orientation. This is consistent with the idea of criticallevel filtering, since spring and autumn are the periods of revers al in direction of the mean zonal wind.

To investigate critical level filtering further, orientations evaluated at three height intervals in both summer and winter are shown in Figure 8. From 33-40 km,

Vol. 130, 1989 Anisotropie Gravity Wave Motions over Australia

Summer .4 Y

Winter N

s

!l_ 11 ~

11 T ' 9 I

I s

Figure 7

523

Polar histograms of broadband orientation direetions for gravity waves in winter and summer, using all data. The broken line indieates the mean orientation direetion.

524 s. D. Eckermann and R. A. Vincent PAGEOPH,

winter Summer

-..:,.

• ......... ~ E

.. ~

s

Figure 8 Polar histograms of wave orientation directions at three separate height intervals. Both winter and

summer orientations are displayed.


the plots in both seasons look remarkably similar, with a preferred NE-SW bias, However, in the NW-SE quadrant, a preferred winter meridional and summer zonal alignment is evident. On progressing to the upper height regimes, these winter meridional and summer zonal trends intensify, as the mean zonal winds increase in magnitude, consistent with critical level filtering taking place,

The flw sampie averages are around 0,35, and a drop in value with decreasing wavenumber is observed, However, these values have necessarily neglected the d

dependence in formula (9), since d = I for a single profile at a given wavenumber, and so can only be considered as lower bounds on this ratio. A broadband determination, where d is calculated for one profile over the 3-10 km range, gives flw as 0.41 ± .03 in winter and 0.47 ± .04 in summer. These results agree well with HIROTA and NIKI (1985), who found (flw)RMs ~ 0.4 by hodographic methods. HIROTA and NIKI (1985) also found at White Sands (32°N, 106°W) that the ratio is larger in summer than in winter, as found here. However, a study still currently proceeding in our group has recently shown that the form of the flw distributions of HIROTA and NIKI (1985) depends only on the degree of horizontal anisotropy in wave propagation directions. Consequently, these and other "flw" values must be treated with some caution (ECKERMANN and HOCKING, 1989).

The degree of polarization dU!, is around 35%--40% in winter, but, due to larger Q values, it is nearer 50% in summer. The phase difference, c5, is strongly biased towards 90° in both seasons, with broadband sam pie averages of 85° ± 5° in winter, and 100° ± 5° in summer. This bias is a result of the preferred axial alignment of wave oscillations, which produces small P values. FinaIly, a curious minimum in the Q and d parameters can be seen around A= ~ 3.5 km (m ~ 1.6 - 1.8 km-I) in both seasons. Its manifestation is evident in the anticlockwise and c10ckwise rotary spectra in Figure 3. Interpretation of this feature is difficult due to the nonconstant nature of m with height.

4. Discussion

This study of gravity wave motions in the vertical wavelength region between 2 and 10 km in the middle and upper stratosphere shows that most of the waves are propagating energy upwards, and that the total energy spectral density follows a power law of the form E(m) rx m -125, where m is the vertical wavenumber (Figure 3). Recent theories concerning a model universal gravity wave spectrum (GARRETT and MUNK, 1975; VANZANDT, 1984; SMITH el af., 1987) have assumed power law spectra which best fit experimentally determined spectra (e.g., VINCENT, 1984; DEWAN el af., 1984). The most recent theoretical wavenumber spectrum for the atmosphere proposed by SMITH el af. (1987) predicts a saturated spectral density E(m) rx m -3, which turns over to a uniformly flat spectrum at some cutoff wavelength A ~. In the stratosphere a cutoff wavelength of 5 km is predicted, rising to a


20 km cutoff in the mesosphere. This indicates that, if the model holds, the wavenumber spectrum of Figure 3 should lie in the transitional turnover region. Our observation of a spectral index between 1.2 and 1.3 provides weight for this assertion. The absolute values of spectral density, aIthough larger, are also of the same order of magnitude as the values predicted in the model. However, none of the convex curvature present in the turnover of the model spectrum is evident in Figure 3. This could be due to the small vertical wavenumber band covered, aliasing near the Nyquist vertical wavelength of 2 km, and inefficient wave tracking by the sphere.

On splitting the spectra into height regions (Figure 4), one finds a smaller peak spectral density and a sm aller spectral index in the region between 30 and 45 km than between 45 and 60 km. This is also consistent with the model of SMITH et al. (1987), which predicts that the turnover wavelength increases with altitude, so that the turnover should be more complete in the lower atmosphere for spectral observations in the same vertical wavenumber range. However, poor tracking of small wavelength gravity waves between 45 and 60 km also contributes to this increased spectral index.

Gravity wave oscillations are essentially transverse, with the horizontal component of wave motion aligned along the direction of horizontal propagation. The results shown in Figure 7 suggest that the waves pro pagate horizontally within a relatively sm all range of azimuths (i.e., they have narrow angular spectra). However, it is not possible to determine from the alignment of the horizontal perturbations alone, in which direction the waves are travelling. For example, in summer the waves could be travelling predominately either eastward or westward. Noting that in summer the strong westward (easterly) prevailing winds would be expected to remove preferentially those waves travelling to the west through critical layer interactions, we suggest that the angular spectrum is directed to 22° south of east. In winter the prevailing eastward winds are expected to remove eastward pro pagating waves, leaving an excess of westward propagating waves in the middle atmosphere. This suggests that the preferred direction of propagation in winter is towards 263 0 anticlockwise from east (i.e., just west of south).

These inferred directions of propagation, arrowed in Figure 7, should be compared with those reported by VINCENT and FRITTS (1987) for mesospheric gravity waves observed by radar techniques at Buckland Park. For waves in the 1-8 and 8-24 hour period bands, they found south-eastward propagation in summer and to just west of south (1-8 hour band) and north-westward (8-24 hour band) propagation in winter. The great similarity in the orientation of the wave motions and the inferred directions of travel of the waves observed here in the stratosphere by rocket techniques, and in the mesosphere by radar, strongly suggests that they are common features of quasi-inertio-gravity waves in the middle atmosphere over Australia. Perhaps the most interesting property of both sets of observations is the relatively narrow range of azimuths within which these waves seem to preferentially


propagate in a given season. This property eannot be due to eritieal layer filtering alone but must be souree related. This high direetionality has many implieations. One is that it implies a wave drag in the mesosphere that is more direetional than previously thought. Another is that it will aid in the modelling of Doppler shifting effeets on gravity wave frequeney speetra (FRITTS and VANZANDT, 1987).

These observations have enabled a number of important properties of inertiogravity waves in the stratosphere to be measured, some of whieh are summarized in Table I as a funetion of season. Other quantities ean be derived from the gravity wave polarization relations (GOSSARD and HOOKE, 1975), and some of the more important of these are shown in Table 2. The aspeet ratio Ah/Az (see Table 2) of about 130: I also gives approximately the ratio of the horizontal to vertieal group veloeities, so that in propagating upwards from some hypothetieal souree region at say 15 km altitude to heights near 45 km, the gravity waves would travel about 4000 km horizontally. This is only a erude estimate, sinee the mean winds and temperatures in the middle atmosphere eontinually alter the group veloeity ratio of wave paekets as they propagate away from souree regions, but it does suggest sources well to the north of Australia. VINCENT and FRITTS (1987) noted similarities between their observations of south-eastward propagating waves in the summer mesosphere and the results of MIY AHARA et al. (1986) from a high resolution general eirculation model, whieh showed waves propagating away from conveetive

Table I

Measured Parameters o/Inertio-Gravity Waves

RMS Velocity Amplitude RMS Relative Temperature Perturbation

pm

SUMMER

WINTER

SUMMER

WINTER

SUMMER

WINTER

Mean Intrinsic Period SUMMER

WINTER

33-40 km 41-49 km 50-58 km

33-40 km 41-49 km 5058 km

33-40 km 41-49 km 5058 km

33-40 km 41-49 km 50-58 km

6-8 ms- I

0.01-D.02

l.l m2s- 2

~O.I m2s- 2

~4.2 m2s- 2

~O.I m2s- 2

2.5 m2s- 2

2.0 m2s- 2

44 ±8 271 ±9' 348' ± 10'

247 ±8 253 ±6' 263 ±6

0.47

0.41

11.0 ho urs

9.5 hours


Table 2

lIiferred Properlies o/Inerlio-GraviIY Waves

Aspect Ratio (m/kh = Ah/Az) 120-140 Mean Horizontal Wavelength 480-570 km Vertical Phase Speed (Az = 4 km) 0.1 ms- 1

Intrinsic Phase Speed I3-14ms- 1

33-40 km 1.410-4 Nm- 2

SUMMER 41-49 km 3.1 10-6 Nm- 2

50-58 km I.3 10-4 Nm- 2

Pou'w' 33-40 km -6.9 10-6 Nm- 2

WINTER 41-49 km -4.810- 5 Nm- 2

50-58 km -1.010- 5 Nm- 2

33-40 km I.3 10-4 Nm- 2

SUMMER 41-49 km -1.710- 4 Nm- 2

50-58 km -2.710- 5 Nm- 2

Pov'w' 33-40 km -1.6 10- 5 Nm- 2

WINTER 41-49 km -1.510- 4 Nm- 2

50-58 km -8.610- 5 Nm- 2

SUMMER 41-58 km 0.8 ms-1day-l -I/Pod/dz(pou'w')

WINTER 41-58 km -0.3 ms-1day-l

SUMMER 41-58 km -1.2 ms-1day-l -I/Pod/dz(pov'w')

-0.4ms- 1day-l WINTER 41-58 km

sources in the equatorial troposphere to the north of Australia. Much has still to be learned about gravity wave sourees. With the more detailed information about middle atmospheric gravity waves which this and other studies provide, it should be possible to better locate sources by tracing the waves back through the atmosphere.

If we assume the orientations derived above, then a number of other quantities, such as u'w' and v'w', the vertical fluxes of horizontal and meridional momentum respectively, can be inferred. Using formula (2), the dispersion relation (10), and the following polarization relation relating the zonal component of the perturbation velocity, u', to the vertical component, w' (GOSSARD and HOOKE, 1975)

, -k [ 1 + GY ] , w =-;; I+i(f)(f) u

( 11)

it can be shown that vertical fluxes of zonal and meridional momentum can be related to u'v' by the following transformations.


, , khu'v' uw =------

m sin ,( 1- a) ( 12)

, , khu'v' V W = ----"-------

m cos ,(I - a) (13)

where a = (f/w) 2 and , is the azimuth angle (anticlockwise from east) towards which the waves are travelling such that k = kh COS , and 1= kh sin ,. On inserting into the above relations appropriate values for I/w, kh/m (inferred from formula (10)), atmospheric density Po (BARNETT and CORNEY, 1985) and u'v' and , values from various height regimes (see Table I), we can estimate mean Pou'w' and Pov'w'. These values are shown in Table 2.

Information about the u'w' and v'w' fluxes is important because of the role that the vertical convergence of the density weighted gravity wave flux plays in determining the large-scale circulation and thermal structure of the middle atmosphere (LINDZEN, 1981). Such effects are known to be important in the Southern Hemisphere mesosphere, with gravity wave induced mean flow accelerations of the order 10-100 ms-1day-1 (VINCENT and REID, 1983; REID and VINCENT, 1987; FRITTS and VINCENT, 1987). However, it has yet to be ascertained wh at role gravity waves play in the stratosphere. Studies of northern hemispheric satellite data have shown that breaking planetary waves produce significant wave induced accelerations of ",5-lOms- 1day-1 in this region in winter (e.g., GELLER et al., 1983). However, even allowing for planetary wave effects, SMITH and LYJAK (1985) find monthly mean moment um residuals that produce me an flow accelerations in the range - 5 to 5 ms -Iday-I at 30 0 N at heights near 50 km, which they suggest may be caused by dissipating gravity waves. However, these values may be overestimated, particularly near the poles, by using the quasi-geostrophic approximation to evaluate the Eliassen-Palm flux (ROBINSON, 1986). Nevertheless, SCHOEBERL (1985) has shown that a superposition of orographically produced gravity waves can give rise to instability and a resulting deposition of momentum in the stratosphere.

Mean gravity wave-induced accelerations for the height range 41-58 km have been estimated from the rocket data and are shown in Table 2. The values are dependent on the inferred aspect ratios, and the me an orientation directions that are used in formulae (12) and (13). Oue to the number of assumptions made, the values can only be considered order of magnitude estimates. Nevertheless, the values for this one location seem to be of the order of the moment um residuals evaluated from satellite data, suggesting that a small but significant me an gravity wave drag indeed exists in both the summer and winter stratosphere. The gravity wave drag is especially important in summer when planetary waves are excluded from the stratosphere. Some ca re must be used in assessing the height variations of the wave fluxes that we find he re because of the possibility that they may be artifacts of the data processing techniques used, and, in particular, to the filtering applied to exclude waves with scales greater than '" 10 km. To check this possibility the


calculations were redone to include all vertical scales less than ~ 16 km. While the use of larger scales may allow for some tidal contamination, our results and conclusions are essentially unchanged.

Clearly our investigations of horizontal orientation, critical level filtering, and momentum flux in particular, have been restricted by the resolution and paucity of the da ta available to uso It is to be hoped that similar analysis techniques are in the future applied to the more extensive stratospheric data sets from some northern hemispheric rocket stations and the new lidar instruments, so that our knowledge of the morphology and climatology of the stratospheric gravity wave field becomes more detailed.

5. Conclusions

Sm all-sc ale wind and temperature oscillations observed in atmospheric rocket data from Woomera, Australia, have been identified as being chiefly due to low frequency internal atmospheric gravity waves with horizontal r.m.s. velocity perturbations of around 7 ms -I, though this may be underestimated.

The gross climatological characteristics of the waves at this location agree with the more geographically extensive studies of similar motions in the Northern Hemisphere. These include only weak seasonal cycles in gravity wave activity, a mostly upward flux of gravity wave energy, and an apparent mean ellipse eccentricity (=f/w) of about 0.4.

More detailed investigation of the wave field, however, revealed that the waves had a preferred direction of horizontal phase propagation, which was meridional during winter and zonal in summer. Inferred absolute directional senses were consistent with an earlier study (VINCENT and FRITTS, 1987). The zonal anisotropy was consistent with critical level filtering by the mean zonal wind in the stratosphere, whereas the observed meridional anisotropy is suggested to be source related. Observations of increasing directionality in orientation with altitude provided corroborating evidence of wave filtering.

Indirect estimates of the mean vertical fluxes of both the zonal and meridional momenta were made. A decrease in flux with height was found. The calculated wave-induced mean flow accelerations, though smalI, seem to be important for the momentum closure of the stratosphere.

A cknowledgemen ts

The data used in this study were kindly supplied by the Weapons Research Establishment, Salisbury, South Australia. The many helpful suggestions and preliminary readings of Dr. W. K. Hocking are gratefully acknowledged, as are


discussions with Dr. B. H. Briggs, Mr. A. Phillips and Dr. M. Yamamoto. We also thank Mr. L. Campbell for supplying his plotting programmes. The comments of a reviewer were encouraging and extremely helpful. This work was conducted while one of us (S.D.E.) was in receipt of a Commonwealth Postgraduate Scholarship.

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532 S. D. Eckermann and R. A. Vineent PAGEOPH,

MIYAHARA, S., HAYASHI, Y., and MAHLMAN, J. D. (1986), Interactions Between Gravity Waves and Planetary Scale Flow Simulated by the GFDL "SKYHJ" General Circulation Model, J. Atmos. Sei. 43, 1844-1861.

MÜLLER, P., HOLLOWAY, G., HENYEY, F., and POMPHREY, N. (1986), Nonlinear Interactions Among Internal Gravity Waves, Rev. Geophys. Spaee Phys. 24, 493-536.

PEARSON, P. H. O. (1966), Seasonal Variations 0/ Density, Temperature and Pressure between 40 and 90 km, Woomera, South Australia, March 1964-March 1965, J. Atmos. Terr. Phys. 28, 1057-1064.

PLUMB, R. A., ANDREWS, D. G., GELLER, M. A., GROSE, W. L., O'NEILL, A., SALBY, M., and VINCENT, R. A. (1986), Dynamical Processes, Atmospheric Ozone 1985, Assessment of our Understanding of the Processes Controlling its Present Distribution and Change, WMO Global Ozone Research and Monitoring Projeet, Report No. 16, I, 241-347.

QUIROZ, R. S., and GELMAN, M. E. (1976), An Evaluation 0/ Temperature Profiles From Falling Sphere Soundings, J. Geophys. Res. 81, 406-412.

REID, I. M., and VINCENT, R. A. (1987), Measurements 0/ Mesospheric Gravity Wave Momentum Fluxes and Mean Flow Accelerations at Adelaide, Australia, J. Atmos. Terr. Phys. 49, 443-460.

ROBINSON, W. A. (1986), The Application 0/ the Quasi-Geostrophic Eliassen-Palm Flux to the Analysis 0/ Stratospheric Data, J. Atmos. Sei. 43, 1017-1023.

SCHOEBERL, M. R. (1985), The Penetration 0/ Mountain Waves into the Middle Atmosphere, J. Atmos. Sei. 42, 2856--2864.

SHIBATA, T., FUKUDA, T., and MAEDA, M. (1986), Density Fluctuations in the Middle Atmosphere over Fukuoka Observed by an XeF Lidar, Geophys, Res. Lett. 13, 1121-1124.

SMITH, A. K., and LYJAK, L. V. (1985), An Observational Estimate 0/ Gravity Wave Drag /rom the Momentum Balance in the Middle Atmosphere, J. Geophys. Res. 90, 2233-2241.

SMITH, S. A., FRITTS, D. c., and VANZANDT, T. E. (1987), Evidence 0/ a Saturated Spectrum 0/ Atmospheric Gravity Waves, J. Atmos. Sei. 44, 1404-1410.

SNEDECOR, G. W., and COCHRAN, W. G., Statistical Methods (lowa State University Press, Iowa, 7th edition 1980).

THOMPSON, R. O. R. Y. (1978), Observation o/Inertial Waves in the Stratosphere, Quart. J. R. Met. Soe. 104, 691-698.

VANZANDT, T. E. (1984), Spectral Description 0/ Mesoscale Fluctuations, Handbook for MAP-16., SCOSTEP Secreteriat, Dep. Elec. Computer Eng. Univ. IL, Urbana-Champaign, 149-156.

VINCENT, R. A. (1984), Gravity-Wave Motions in the Mesosphere, J. Atmos. Terr. Phys. 46, 119-128. VINCENT, R. A., and FRITTS, D. C. (1987), A Climatology o/Gravity Wave Motions in the Mesosphere

at Adelaide, Australia, J. Atmos. Sei. 44, 748-760. VINCENT, R. A., and REID, I. M. (1983), HF Doppler Measurements 0/ Mesospheric Gravity Wave

Momentum Fluxes, J. Atmos. Sei. 40, 1321-1333. VINCENT, R. A., and STUBBS, T. J. (1977), A Study 0/ Motions in the Winter Mesosphere Using the

Partial Refiection Drift Technique, Planet. Spaee Sei. 25, 441-455. VINCENT, R. A., STUBBS, T. J., PEARSON, P. H. 0., LLOYD, K. H., and Low, C. H. (1977), A

Comparison 0/ Partial Refiection Drifts with Winds Determined by Rocket Techniques-l, J. Atmos. Terr. Phys. 39, 813-821.

(Reeeived Oetober 16, 1987, revised/aeeepted April 21, 1988)

PAGEOPH, Vol. 130, Nos. 2/3 (\989) 0033-4553/89/030533-14$1.50 + 0.20/0 © 1989 Birkhäuser Verlag, Basel

Constraints on Gravity Wave Induced Diffusion m the Middle Atmosphere

DARRELL F. STROBEL]

Abstract~A review of the important constraints on gravity wave induced diffusion of chemical tracers, heat, and momentum is given. Ground-based microwave spectroscopy measurements of H20 and co and rocket-based mass spectrometer measurements of Ar constrain the eddy diffusion coefficient for constituent transport (K=z) to be (I - 3) X 105 cm2s -I in the upper mesosphere. Atomic oxygen data also limits Kzz to a comparable value at the mesopause. From the energy balance of the upper mesosphere the eddy diffusion coefficient for heat transport (DH ) is, at most 6 x 105 cm2s- 1 at the mesopause and decreasing substantially with decreasing altitude. The available evidence for mean wind deceleration and the corresponding eddy diffusion coefficient for moment um stresses (DM) suggests that it is at least 1 x 10" cm 2s I, in the upper mesosphere. Consequently the eddy Prandtl number for macroscopic scale lengths is > 3.

Key words: Gravity waves, turbulence, heat transport, tracer transport, eddy diffusion, mesosphere.

J. Introduction

The importance of gravity waves in the mesosphere and lower thermosphere has been known for more than twenty-five years. The seminal paper by HINES (1960) opened up an area of research which unfortunately took over twenty years to realize the full significance of gravity waves in this region of the atmosphere. Research efforts by PITTEWAY and HINES (1963), LINDZEN (1967, 1968), and HODGES

(1969) provided the needed foundation for present-day research on gravity wave induced diffusion, but did not then yield a parameterization of the gravity wave stresses on the mean circulation and structure of the middle atmosphere. It was not until 1981 when LINDZEN ( 1981) published his perceptive recipe for parameterizing

the gravity wave moment um stresses on the mean zonal flow that the full impact of

gravity waves on the middle atmosphere was comprehended. An unfortunate result

of this important paper was the almost sole emphasis on the moment um balance of

the middle atmosphere.

1 Department of Earth and Planetary Sciences, Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, MD 21204, U.S.A.

534 Darrell F. Strobel PAGEOPH,

Dynamical models were constructed which examined in great detail the deceleration effects of gravity waves on the zonal flow but omitted any thermodynamic effects on the global mean temperature structure (e.g., HOLTON, 1983; GARCIA and SOLOMON, 1985). However in the GARCIA and SOLOMON (1985) study diffusive effects on temperature departures from the global mean temperature were included. The consensus of these studies was that the eddy diffusion coefficient for momentum stresses (DM) is '" 106 cm2s- 1 (LINDZEN, 1981; HOLTON, 1982, 1983; GARCIA and SOLOMON, 1985). It should be noted that this quantity is proportional to (ü - C)4, where ü is the mean zonal wind and c is the phase speed of the gravity wave. This extreme sensitivity of DM to (ü - c) makes an accurate calculation of its value very difficult from observed values of ü and c. Because the mean circulation and associated transport of constituents and heat are also directly dependent on DM/(ü - c), theoretical prediction of their strengths is also subject to the uncertain magnitude of (ü - C)3 through the uncertainties associated with the computed radiative drive and the input gravity wave spectrum of phase speeds.

JOHNSON and WILKINS (1965) noted that the observed lower thermospheric temperature gradient was inconsistent with molecular conduction of heat alone and concluded that eddy transport of potential temperature was required. In a more quantitative study JOHNSON and GOTTLIEB (1970) inferred from the globally averaged heat balance that the eddy diffusion coefficient for heat transport (DH ) was I x 105 cm2s - I at 60 km and increased to 1 x 107 cm2s - I at 120 km. Of more

importance to us are the values in the 75-85 km region which they deduced to be (4-7) x 105 cm2s- l • HUNTEN (1974) argued that these analyses ignored an essential aspect of the physics, namely that dissipation of mechanical energy to genera te turbulence might yield net heating rather than net cooling of the mesospause region. His inference of net heating depended crucially on the assumption that turbulence persists only if the Richardson number of the flow (Ri) remains at its critical, onset value, generally ~ 0.2. JOHNSON (1975) noted that turbulence can persist in a flow with Ri as large as land thus argued that steady-state turbulence would maintain the very stable lower thermosphere near Ri '" 1, which implies net cooling by the action of turbulence on the mean circulation.

In a similar vein, chemical tracers bear signatures of transport effects and

COLEGROVE et al. (1965, 1966) used the 0/02 density ratio to infer the vertical eddy diffusion coefficient for tracer transport (KzJ. Their average value in the 80--120 km region was in the range of (0.8-8) x 106 cm2s - I, with a preferred value of 4 x 106 cm2s - I. It is standard practice in 10 photochemical models with eddy and molecular diffusive transport to empirically deduce the eddy diffusion coefficient profile with a minor constituent whose density profile is extremely sensitive to the adopted values. In the one extreme, HUNTEN and STROBEL (1974) used argon measurements by VON ZAHN (1970) to deduce a homopause value of K== '" 3 x 105 cm2s - I. In the other extreme KENESHEA and ZIMMERMAN (1970)

argued for highly structured profiles of Kzz with peak values in excess of

Vol. 130, 1989 Constraints on Gravity Wave Induced Diffusion 535

1 X 107 cm2s ~ I. In the 10wer thermosphere the uncertainty in the heating and cooling rates at that time could not exclude such large values of the eddy diffusion. In a turbulent atmosphere, tracer and potential temperature transport by eddies should be described by the same coefficient, i.e., DH = Kw in the limit of a chemically inert species and adiabatic motion. For chemically active species one must include chemical acceleration of vertical transport which arises physically because the mixing ratio perturbation for chemical species with finite chemicalloss undergoes a phase shift relative to the wave velocity fields such that the eddy fluxes are nonzero rather than in quadrature, as in the limit of no chemicalloss (STROBEL, 1981). STROBEL et al. (1987) in a study of mesospheric chemistry found this term to be potentially important for only odd oxygen and then in a subtle way.

The focus on this paper is on gravity wave induced diffusion over macroscopic vertical length scales on the order of the atmospheric scale height, H. There is a significant body of literature on measurements and interpretation of smaller scale diffusion observed by rocket experiments and radars and reviewed in depth by HOCKING (1985). Turbulent layers observed by these techniques tend to be "sub-macroscopic". There is the difficult question on how to relate diffusion on these smaller scales to the larger scales of interest here. The reader should keep in mind that additional constraints may be supplied by this broad data base, although the extrapolation to larger scales is not obvious and straightforward.

2. Constraints on Kzz

The momentum stresses of saturated gravity waves are largest in the upper mesosphere and it is there that independent constraints on gravity wave diffusion are most important. Investigations by ALLEN et al. (1981) and STROBEL et al. (1987) identified H20, CO, 03' and ° as the chemical species most diagnostic of tracer transport in the upper mesosphere. Of these species STROBEL et al. (1987) argued that the vertical H 20 profile was best suited to infer the correct magnitude of vertical mixing in the mesosphere.

In their study they derived an approximate expression for the vertical eddy diffusion coefficient, in terms of the eddy diffusion coefficient for heat transport and chemical acceleration of vertical transport

(1)

with the numerical value in cgs units, A is a measure of gravity wave amplitude and equal to 1 at the saturation limit, and Li is the chemical loss rate of specie i. According to recent measurements by VINCENT and FRITTS (1987), gravity wave amplitudes vary throughout the year in the range of A = 0.6-2. With the exception of odd oxygen, all other species which undergo significant transport in the mesosphere have LiA ~ 5 X 1O~9 D H and thus Kzz(i) = D H •


In Figure theoretical H2ü mixing ratio profiles from an ID eddy diffusion, photochemical model (ALLEN et al., 1981 with updates discussed in STROBEL et al., 1987) are compared with observed values. The corresponding vertical eddy diffusion coefficient (DH ) profiles are illustrated in Figure 2. The mesospheric water vapor measurements were obtained by ground-based microwave spectroscopy from the let Propulsion Laboratory in Pasadena, California during the time period April to lune 1984 (BEVILACQUA et al., 1983). At this time vertical motions associated with the me an meridional circulation would be expected to be upward (GARCIA and SOLOMON, 1985) and the inferred values of DH ( = Kzz) from the observed H2ü mixing ratio profiles should be upper limits. The water vapor is most sensitive to transport in the 70-80 km region and there the observations clearly constrain D H to a range of (1-2) x 105 cm2s -I as Models B, C, and D show in comparison to Model A. Model A was preferred by ALLEN et al. (1981, 1984) in order to satisfy the water vapor measurement by H. Trinks (private communication, 1979) at 90 km. Groundbased microwave spectroscopy measurements imply that the H2ü mixing ratio at 80 km is comparable to the Trinks' value at 90 km. The rapid dissociative loss of H 2ü in the 80-90 km region requires a basic incompatibility between these

90

85

80

75

:[ -8 70

3 :;:l :cl 65

60

55

\~ \\

\ " ,"-" " "" "' ... '-

Model D

,

(1984 data and :m.odels)

"

Mixing ratio (ppznv)

Figure 1

6 7 8

Comparison of ground-based, observed H20 mixing ratios with 1 (J error bars (BEVILACQUA el al., 1985) and model results for the D H profiles given in Figure 2 and with chemical acceleration for 0 and 03.

After STROBEL et al. (1987). Copyright by the American Geophysical Union.

Vol. 130, 1989

130 _

120 ~

110 f-

:[ 100 f

~ 90 I

.a :;j :ii! 80 r-

70 I-

80 r-

50 f-

Constraints on Gravity Wave Induced Diffusion

Model A

Model B

Model C

Model D

I i

1

I / i

i i

l i ! 1- ___ !

! : , 'I ~'--------:. / ,,~,? ,I i , ., '---

, f , ,. I i 1

I i. ,,/ i 1

/ !. / ! 1

/' I I ..

/ i _-( /' / , .... I

-

-

-

-

-

--

40~~~~~~~/~~~~~~>_-__ L-I~~~L-~~~~~

537

1000 10000 1E+5 1E+6 1E+7

Eddy diffusion eoeffieient (eIn-see-1 )

Figure 2 Vertical eddy diffusion coefficient (DH ) profiles for indicated models in Figure I. After STROBEL et af.

(1987). Copyright by the American Geophysical Union.

measurements. If one examines the microwave signature of H 20, the signal to noise increases with increasing altitude with the highest quality data in the 7(}-'80 km region (BEVILACQUA et al., 1987a). The associated error bars clearly exclude the observation of a water vapor profile even remotely close in mixing ratio to Model A in Figure 1.

Ground-based microwave spectroscopy measurements of CO (BEVILACQUA et al., 1985) confirm the deduction of slow vertical mixing in the mesosphere (STROBEL et al., 1987). But it must be kept in mi nd that the large vertical scale height of the CO density profile makes it somewhat insensitive to diffusive transport and hence more susceptible to advective transport. This follows from a comparison of

the respective time constants (H2/Kzz) and (H/w), where w is the zonally averaged vertical wind. In addition, the Solar Mesosphere Explorer (SME) near-infrared spectrometer measurements of absolute 0 3 concentrations are best understood with slow vertical mixing wh ich yields low H 20 mixing ratios and odd hydrogen densities. This produces reduced catalytic destruction of 0 3 by odd hydrogen and hence high ozone mixing ratios in better agreement with SME measurements. BRASSEUR and OFFERMANN (1986) analyzed ° concentration measurements and concluded that the vertical eddy diffusion coefficient is about 105 cm2s ~ I at the

538 DarreIl F. Strobel PAGEOPH,

mesopause, also consistent with the above results. Note that ° unlike CO has a very small-scale height at and below the meso pause which renders it extremely sensitive to diffusive transport. It is interesting to note that the argon measurements that guided HUNTEN and STROBEL (1974) to adopt low vertical mixing in the mesopause

region are in excellent agreement with inferences from other species. Evidence from absolute concentrations of chemical tracers of mesospheric transport thus suggest that K zz( = D H, for all tracers but ° and 03) is '" ( 1-3) X 105 cm2s -1 in the upper mesosphere.

3. Constraints on D H

As alluded to in the Introduction it is more difficult to obtain powerful constraints on the eddy diffusion coefficient for heat transport because it involves extracting a small residual from large terms in approximate balance in the thermodynamic heat equation. The importance of diffusive transport of potential temperature by breaking gravity waves was demonstrated by SCHOEBERL et al. (1983) in a numerical study of gravity wave breaking and stress in the mesosphere. CHAO and SCHOEBERL (1984) emphasized that it is the turbulence created by the breaking gravity wave that transports potential temperature rather than coherent, w'T' heat transport by the gravity wave. APRUZESE et al. (1984) in a study of the globally

averaged temperature of the mesosphere and lower thermosphere concluded that D H must be less than 106 cm2s -1. STROBEL et al. (1985) reiterated the arguments of

APRUZESE et al. (1984) and argued that the eddy Prandtl number (Pr = DM/DH )

over macroscopic scale lengths must be large if DM exceeds 106 cm2s - 1, because D H S; 6 X 105 cm2s - 1.

To quantify this discussion, let us examine the thermodynamic heat equation for the globally averaged temperature field, <1"), with <> denoting global average and overbar zonal average

--=-<QUV-QIR)+-- 2- -- - <pwT)+<H -C) 0< 1") 1 1 0 \ 01") 1 (0) __ ot pCp pCp oz oz pCp oz g g

(2)

where Quv is the solar heating rate due to O2 and 0 3 absorption, QIR is infrared cooling rate, p is the mass density of the atmosphere, )0 is the molecular heat

conductivity, cp is the specific heat at constant pressure, W is the zonally averaged

vertical velocity,

(3)

is the conversion rate of wave energy to heat with efficiency e, and

C = -- - pc DM - +-1 0 ( (01" g)) g PCpPr OZ p OZ Cp

( 4)

is the cooling rate due to the divergence of the downward turbulent or eddy heat f1ux. Here

N2=~(Ot +.f) T oz cp

( 5)

is the buoyancy frequency. Note that when DM10DM/oz is less than H- 1 the heat f1ux is divergent and there is cooling, whereas if it is greater than H- 1 the heat f1ux is convergent and heating occurs. The expressions for Hg and Cg were derived by SCHOEBERL et al. (1983) under the assumption of LINDZEN (1981) that when gravity waves break or saturate their amplitudes remain constant with altitude.

Equation (2) has been solved for the globally averaged, steady-state temperature without the term <plVT) which represents the convergence of the downward heat f1ux associated with the anticorrelation of the zonal mean vertical velocity (a result of gravity wave breaking) and the zonally averaged temperature. For a Prandtl number of I, Figure 3 shows illustrative globally coefficient profiles in Figure 4. These results lead APRUZESE et al. (1984) and STROBEL et al. (1985) to deduce an upper limit on DH of 6 x 105 cm2s 1 from thermodynamic considerations only. Model A in Figure 4 is the appropriate height dependent upper limit on D H' A comparison of these results with the earlier work of JOHNSON and GOTTLlEB

110

E 90 .:.:. N

70

100

TEMPERATURE

200 300

(K)

Figure 3

400 500 600

Calculated globally averaged temperature profiles for the DJI profiles given in Figure 4, with P, = I, and compared with the CIRA 1972 temperature profile. After STROBEL el al. (1985). Copyright by the

American Geophysical Union.

540

110

~ 90 N

70

...........

Darrell F. Strobel

DIFFUSION COEFFICIENT

MODElA~ l I :-- MODEL

MODEL D! : C MODEL I I

I

./

I : I I

I : I I 1 1 I

\ /

/

PAGEOPH,

// 50L-~~~~~~--~~~~~--~~~~~L-~~~~~

1~ 1~ 1~ 107

Figure 4 Vertical eddy diffusion coefficient (D II ) profiles for indicated models in Figure 3. After STROBEL et al.

(1985). Copyright by the American Geophysical Union.

(1970), based on the KUHN and LONDON (1969) IR cooling rates, indicates agreement in the critical mesopause region to within 50%, the Johnson and GoWieb D H values being larger. It should be noted that they did not include gravity wave heating in their calculation and other input guantities such as solar flux, IR cooling rates, 0 recombination heating rates, eIe., were different from values used by APRUZESE el al. (1984) and STROBEL el al. (1985). But the JOHNSON and GOTTLIEB (1970) resuIts are still an accurate representation of heat balance constraints on

gravity wave induced diffusion. The gravity wave heating term (Hg, Eg. (2» is at

most 25% of the total solar UV and 0 recombination heating rate in the

calculations of APRUZESE cl al. (1984) and STROBEL el al. (1985). To further illustrate aspects of the above discussion, the analytic expressions üf

STROBEL el al. (1985) are adüpted für the gravity wave terms in Eg. (2) with c = 1

, (7 H 6) 6 2-1 I H~ - Cg = 1.5 -- + I -- DM(lO cm s ) units(Kd-) P, H D P,

( 6)

where


When Pr = I and DM is constant, then Hg - Cg = -7.5 and -22 Kd- I for DM = 106 and 3 X 106 cm2s -I, respectively. These values should be compared to the total, globally averaged, solar heating rate including 0 recombination of APRUZESE et al. (1984),

z(km) = 65 Quy(Kd- l ) = 3.2

70 75 1.6 1. 7

80 5.0

85 9.2

90 8.9

95 13

100 18.

The upper mesosphere (70-80 km) is thus seen to be a critical region where the solar heating rate is low. With constant DM ( = DH ) a value as small as 2 x lOS cm2s- 1 is sufficient to balance solar heating at 75 km. In competition with solar heating is CO2 infrared cooling primarily in the 15J.t bands. The most accurate caIculations of this cooling are by DICKINSON (1984) who included as accurately as possible non-LTE effects. His globally averaged cooling rates are

~km)=65 m 75 80 85 90 95 100 QIR(Kd- l ) = 3.0 1.0 0.5 l.l 3.0 4.4 7.4 11.5.

A comparison of Quv and QIR below the meso pause suggests that gravity waves are not driving the globally averaged structure of the mesosphere far from radiative equilibrium. If one deduces values of DM from a balance of QUY - QIR with Hg - Cg given by Eq. (6) one would infer mesospheric values similar to Model A in Figure 4. These values up to 80 km would be consistent with the constraints on K zz( = D H )

derived from ground-based microwave spectroscopic data discussed above. One possibility for strong gravity activity in the mesosphere without substantial

effects on the transport of constituents and heat is for the induced diffusion over macroscopic scale lengths to have a large effective Prandtl number, a point advocated by STROBEL et al. (1985, 1987) with strong theoretical support from FRITTS and DUNKERTON (1985). FRITTS and DUNKERTON (1985) examined constituent and heat fluxes driven by localized gravity wave, breaking where the breaking zones are small in vertical extent in comparison to the vertical wavelength. In their analysis localization of turbulence yields an eddy Prandtl number greater than 2 between saturation (A = 1 for saturation amplitude) and modest supersaturation (A '" 1.3). Only for large supersaturation (A '" 2) does Pr approach 1.

For constant DM in Eq. (6), Pr = 6 yields Hg - Cg = 0, i.e., no net heating or cooling from gravity waves. High effective eddy Prandtl number turbulence would allow significant deceleration of the mean zonal winds without a substantial diffusive signature in the thermal structure. The physical reason for this result is that the conversion of the gravity wave's kinetic energy still produces significant heating of the atmosphere although conversion of internal energy is reduced. High Prandtl number turbulence leads to sluggish eddy transport of heat and Iarge reductions in the associated divergence of the eddy heat flux. As a consequence the conversion of gravity wave energy into heat can approximately balance the divergence of the eddy heat flux.


It is also worthy to note that JUSTUS (1967) determined Pr to be '" 3 from photographic tracking of rocket released chemical clouds and analysis of turbulent wind data in the 90-110 km region. There was considerable scatter in his data points but according to his error bars Pr was at least 2.2.

Net gravity wave heating occurs also when DM increases sufficiently rapidly with height (small H D ); but at some altitude it must level off with a consequent large divergence in the eddy heat f1ux. The model results of APRUZESE et al. (1984) and STROBEL et al. (1985) yield gravity wave heating by this circumstance of, at most, 0.4 Kd -I and Iimited to below 80 km.

In Eq. (2) the term involving the divergence of (pwT) has been omitted in the above quantitative discussions. The only model results available to consistently ascertain its importance are from GARCIA and SOLOMON (1985). For solstitial conditions at the mesopause with a mean circulation driven by gravity wave breaking, their globallyaveraged va lues are DM = D H = 1.5 x 106 cm2s -I, and (~t/f) = 16 K cms -I. The wand T fields have an approximate height dependence of I/JP. The convergence of this heat f1ux is spread over at least 2-3 scales heights and has a magnitude of '" 1 Kd - I, substantially less than the value of Hg - Cg '" 11 Kd -I for this high diffusivity, Pr = 1 model of the middle atmosphere. If the convergence of the (pwT) f1ux were this large for values of DH ", 105 cm2s- l , then this downward heat f1ux would have to be evaluated more carefully in globally averaged heat budgets. The fact that this heat f1ux is not large is not surprising as wand T have large amplitudes only at polar latitudes.

4. Constraints on DM

Of all the eddy diffusion coefficients discussed so far this is the most difficult to evaluate. The fundamental effect is the deceleration of the mean zonal and meridional winds. Theoretical models of the mean circulation of the middle atmosphere are sensitive to a number of input parameters. The radiative drive depends on the net imbalance of Quv and QIR' Whereas the former can be reasonably accurately calculated in a large dynamical model, the latter cannot be computed at the level of detail and accuracy of DICKINSON'S (1984) non-L TE model with present-day computer resources. The infrared cooling acts also to damp temperature perturbations associated with the mean circulation, and accurate simulation of the temperature and wind fields depends critically on the radiative damping.

The deceleration of the mean zonal wind by gravity wave stresses is written as

au 1 a ~,-, N 2 D M - + ... = - - - (pu w ) ;:::; - -_-. at p az u - c (7)

Thus an approximately accurate value of DM can only be inferred from the


deceleration if independent knowledge of the phase speeds of the gravity waves is available. Furthermore the right-hand side of expression (7) holds only if a saturated gravity wave maintains constant amplitude with height, as LINDZEN (1981) originally hypothesized. Recently this hypo thesis has been questioned; SCHOEBERL (1988) argues that the amplitude of a saturated gravity wave can still grow with height. Only when the convection zone is comparable in vertical extent to the vertical wavelength will wave growth be significantly attenuated.

On the basis of available estimates for DM from LINDZEN (1981), HOLTON (1982, 1983), and GARCIA and SOLOMON (1985), it would appear that deceleration of the mesospheric zonal winds requires that DM exceed 106 cm2s - 1 on a globally averaged basis in the upper mesosphere, a value definitely in excess of K zz and D H .

For example, a typical deceleration rate of 100 ms --Id -I (HOLTON, 1983), would for (ü - c) = 40 ms- I yield DM'" 1.3 X 106 cm2s- l •

5. Concluding Remarks

The most stringent constraint on gravity wave induced diffusion is obtained from ground-based microwave spectroscopy measurements of H20 with support from microwave measurements of CO and rocket-based mass spectrometer measurements of Ar (VON ZAHN, 1970). These data constrain K zz( = D H ) to be (1-3) x 105 cm2s- 1 in the upper mesosphere. Atomic oxygen data also limit K zz to '" 105 cm2s - 1 at the meso pause, but indicate an drder of magnitude increase in Kzz in the first 10 km of the lower thermosphere (BRASSEUR and OFFERMANN, 1986).

The evidence cited above, wh ich leads to the conclusion that K zz is low in· the mesosphere, is based on the absolute concentrations of the selected chemical tracers. An alternate point of view can be advanced, based on the seasonal variations of ° and 03' The green line radiated by ° shows a semiannual variation wh ich GARCIA and SOLOMON (1985) argued can only be explained by a semiannual variation in the gravity wave induced diffusive transport. The equinoctal periods are characterized by weak zonal winds and hence, by the LINDZEN (1981) parameterization in their model, weak gravity wave induced diffusion. Solstitial periods have characteristicallY strong zonal winds and are accompanied by strong diffusion, thus creating the semiannual variation in diffusive transport. This variation in diffusive transport should also produce a semiannual component in the seasonal variation of the mesospheric H20 mixing ratio profile. But BEVILACQUA et al. (l987b) found from ground-based microwave measurements of water vapor no obvious semiannual component, only a pronounced annual component. Ozone mixing ratios inferred from SME data exhibit a pronounced semiannual variation, particularly in the spring of the first two years of data acquisition (1982-1983) at 80 km. Data from later years do not contain such a distinctive component. The existence of this semiannual component may depend to so me degree on vertical displacements of the

ozone profile as it contains a minimum value in mixing ratio at '" 80 km, which if displaced by a few kilometers could create the appearance of a time varying component at a fixed height with the periodicity of the vertical displacement.

Consideration of the energy balance of the upper mesosphere indicates weak departures from radiative equilibrium, consistent with D H < 6 X 105 cm2s -I at the mesopause and decreasing substantially with decreasing altitude. The uncertainty attached to the independent calculations of solar UV heating and atmospheric IR cooling cannot exclude the possibility of the upper mesosphere being in radiative equilibrium and the inferred values of D H being upper limits. Similarly the uncertainty cannot exclude a value of D H as large as 105 cm2s -I.

The available calculations to date suggest that DM is at least 106 cm2s -I. The consequences of an order of magnitude smaller momentum diffusion coefficient due to more modest reductions in zonal wind deceleration and in (ii - c) have not been adequately explored, although we note that SCHOEBERL (1988) advocates reduced wave stress on the mean flow in the mesosphere. It is worth citing the lidar studies of the nightime Na layer over Urbana, IL by GARDNER and VOELZ (1986). They found average values for mean flow deceleration of - 27.2 ms -- 1 d - 1 and a corresponding eddy diffusion coefficient, presumably DM, of 1.8 x 105 cm2s- I. Individual measurements yielded deceleration rates up to - 200 ms - Id -I, but the long term averages were an order of magnitude less. But REID and VINCENT (1987) found the mean zonal flow deceleration to be typically between - 50 and - 80 ms - I, with occasional values as large as - 190 ms - I. Also they measured comparable mean meridional deceleration rates. Likewise MEEK et al. (1985) obtained comparable deceleration rates. Clearly aglobai climatology mean wind deceleration needs to be constructed from the available, but sparse data base and more precise altitude information is needed to determine where the deceleration actually occurs. For the present we are in somewhat of a dilemma; depending on what evidence is adopted, a case can be made for the Prandtl number (DM / D H) applicable to turbulent mixing over macroscopic scale lengths to be anywhere between land 10, although model values of DM clearly suggest a large Prandtl number. In this author's judgment the available evidence suggests that the Prandtl number is > 3.

Most of the inferences of eddy diffusion coefficients for constituent and heat transport were accomplished with I D models. The exclusion of me an circulation transport of constituents and heat may ren der the inferred values of gravity wave induced diffusion, in many instances, to be only upper limits. The low values deduced for Kzz and D H, in fact, suggest that the mesosphere is advectively controlled rather than diffusively controlled.

Acknowledgments

This work was supported by NASA Grants NAGW-826 and NAG5-796 at The lohns Hopkins University.


REFERENCES

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PAGEOPH, Vol. 130, Nos. 2(3 (1989) 0033--4553(89(030547-23$1.50 + 0.20(0 © 1989 Birkhäuser Verlag, Basel

Temperature and Heat Flux Spectra in the Turbulent Buoyancy Sub range

C. SmI! and F. DALAUDIER!

Abstract-The physical nature of motions with scales intermediate between approximately isotropic turbulence and quasi-linear internal gravity waves is not understood at the present time. Such motions play an important role in the energetics of small scales processes, both in the ocean and in the atmosphere, and in vertical transport of heat and constituents. This scale range is currently interpreted either as a saturated gravity waves field or as a buoyancy range of turbulence.

We first discuss some distinctive predictions of the cIassical (Lumley, Phillips) buoyancy range theory, recently improved (Weinstock, Dalaudier and Sidi) to describe potential energy associated with temperature fluctuations. This theory predicts the existence of a spectral gap in the temperature spectra and of an upward mass flux (downward buoyancy and heat fluxes), strongly increasing towards large scales. These predictions are contrasted with an alternate theory, assuming "energetically insignificant" buoyancy flux, proposed by Holloway.

Then we present experimental evidences of such characteristic features obtained in the lower stratosphere with an instrurnented balloon. Spectra of temperature, vertical velocity, and cospectra of both, obtained in homogeneous, weakly turbulent regions, are compared with theoretical predictions. These results are strongly consistent with the improved cIassical buoyancy range theory and support the existence of a significant downward heat flux in the buoyancy range.

The theoretical implications of the understanding of this scale range are discussed. Many experimental evidences consistently show the need for an anisotropic theory of the buoyancy range of turbulence.

Key words: Turbulence, atmospheric turbulence, cIear air turbulence, middle atmosphere, heat flux.

I. Introduction

The energetics of turbulence in stratified fluids must take into account the work done by buoyancy forces during the vertical motions of fluid particles. The spectral scale range where buoyancy forces dominate the inertia forces is usually referred to as "buoyancy subrange" (B.S.R.). A few theories predict possible B.S.R. kinetic energy spectra in the equilibrium range (at scales much sm aller than those of the energy containing eddies, i.e., the scale of the turbulent kinetic energy sourees), the most known being those proposed by BOLGIANO (1959) and LUMLEY (1964). The underlying physical hypotheses are delineated at their best in a penetrative paper by

I Service d'Aeronomie du CNRS, B.P. 3, 91371 Verrieres le Buisson CEDEX, France.

548 C. Sidi and F. Dalaudier PAGEOPH,

PHILLIPS (1965). They both admit the physieal idea that the energy eonversion rates, from a kinetie to a potential form, may be important in a stably stratified medium.

While notieing, on experimental (see SHUR, 1962) and theoretieal grounds, that Lumley's theory seemed to be the most eonvenient, PhiIIips derived a eorresponding theoretieal temperature speetrum under the assumption of negligible energy sources in the seale range eonsidered. LUMLEY (1965), relaxing somehow this last assumption, derived also a temperature speetrum in the B.S.R. Both theoretieal speetra should vary like k -I, k being wave veetor modulus. The lack of any experimental support to this predietion may explain, at least partly, why the whole theory has been somehow overlooked for years, However, WEINSTOCK (l985a), following earefully PhiIIips derivation, showed that this speetrum should, in fact, vary like k -3 within most of the B.S.R. Though using quite different hypotheses, HOLLOWAY (1986) obtained kinetie energy and potential energy speetra showing the same funetional form as Lumley's kinetie energy speetrum, with a radieally distinet physieal interpretation. The physieal idea is, here, that the energy eonversion rates are negligible. Reeently, we emphasized (DALA UDIER and SmI, 1987) that a distinetive signature of the physieal hypotheses involved in Lumley-Phillips-Weinstoek's theory should be a speetral gap separating, in the temperature (or potential energy) speetra, a buoyaney dominated range from a "passive range" where the speetra tend to reduee to the well-known Obhukov-Corrsin k - 5/3 speetrum. Furthermore, we showed some experimental evidenee of this gap in stratospherie temperature data.

This renewal of interest in B.S.R. theories is linked with the inereasing number of observations showing energy speetra versus vertieal wavenumbers with speetral slopes close to - 3 at seales somehow larger than the turbulent isotropie inertial ones, in the atmosphere (DEWAN et al., 1984) and in the oeean as weil (GREGG, 1977; GARGETT et al., 1981). In the atmosphere, this speetral range has been reeently interpreted as a saturated random gravity waves field speetrum (DEWAN and GOOD, 1986; SMITH et al., 1987) while WEINSTOCK (1985b) suggested that it eould be interpreted as an anisotropie Lumley's speetrum. In any ease, a sudden transition between a linear or weakly non linear random internal wave speetral domain, showing a fully preseribed anisotropy for eaeh field variable, and a strongly nonlinear isotropie inertial turbulent one, eannot be expeeted. B.S.R. theories, whieh only rely upon classical fluid meehanies statistieal equations, may provide the eonvenient physieal understanding of these transition scales, depending on the adequaey of the simplifieations used and of the physieal hypotheses retained by one or the other theory.

In the next seetion, we will review the reeent developments of the classical B.S.R. theory initiated by Lumley and reeall the main differenees with Holloway's view (Seetion 11). Then we will present new experimental data, obtained by a balloonborne instrumentation in the upper troposphere and lower stratosphere. Data

Vol. 130, 1989 Temperature and Heat F1ux Spectra 549

acquisition and processing leading to estimates of vertical velocity (W) and temperature (T) spectra and cospectra will be discussed in Section 111, while the results will be presented in Section IV. The cospectrum of Wand T (the real part of their cross-spectrum) is a key quantity for the B.S.R. theories as it represents, within a constant factor, the spectrum of the rate (per unit mass and unit time) at which the kinetic energy of the fluid particles is extracted, as a result of their work against buoyancy forces, and converted into potential energy (see Section 11). The predicted magnitude of these spectra is the central debate between the Lumley's and Holloway's theories. As a whole, our results point toward the adequacy of the physical basis underlying classical views while showing strong evidences of the B.S.R. anisotropy. This analysis is, may be, limited to weakly turbulent layers, as analysed in this paper.

In Section V, some implications of the "success" of the classical theory will be discussed in a more speculative way.

II. The Classical B.S.R. Theory

a) Lumley's Spectrum

B.S.R. theories rely upon a pair of spectral equations expressing the conservation of kinetic and available potential energies spectral densities in the approximately steady-state equilibrium range, far from both the sources and the dissipative scales (PHILLlPS, 1965). Though most authors consider density or temperature fluctuations spectra, we believe that the theory is markedly clearer by considering directly the available potential energy, as HOLLOW A Y (1986) does. In the stable atmosphere, PHILLIPS (1965) pointed out that temperature fluctuations are, indeed, available potential energy and the spectral functions of both (energy densities or energy spectral fluxes, for instance) are related by one and the same proportionality constant that will be introduced below. These two equations, in that spectral range, are reduced to

deK _ (= 0 dk

(I)

Here e~k) is the kinetic energy spectral flux, i.e., the net kinetic energy transfer rate (per unit mass and unit time) from wavenumbers sm aller than k to wavenumbers higher than k. In the inertial subrange, e~k) reduces to eKo, the well-known kinetic energy dissipation rate. ep(k) is the corresponding spectral flux of available potential energy. (k), which is often termed "buoyancy flux spectrum", is the net rate (per unit mass, unit time and unit wavenumber) at which the work of the


buoyancy forces increases the kinetic energy of turbulent eddies at wavenumber k. In the ca se of stable stratification (k) is negative and equations (I) express both the kinetic energy spectral density loss and the potential energy spectral density gain resulting from the turbulent motions. In the physical space, such an energy conversion corresponds to a positive vertical mass flux and, in the atmosphere, we have:

100 W'p' W'T' (k)dk = -g-=g--

o Po To

where the overbar means ensemble average

g = acceleration of gravity W' = fluctuation of vertical velocity p', T = fluctuations of density and temperature with mean values Po and To.

(2)

A vailable potential energy and temperature variance are related by the proportionality constant al ready mentioned:

joo E dk =~ T2 Jo P 2TÖN2

where N = Brunt-Väisälä frequency. Equations (I) are strictly equivalent to equations (2.7) and (2.8) of PHILLIPS

(1965) (and equations (I) and (5) of HOLLOWA Y (1986», but for a sign change presumably due to the downward orientation of the z axis, following oceanographers practice). Phillips noticed that they imply the constancy of the total energy spectral flux (cp(k) + c~k» all along the buoyancy inertia range as by simply adding

them:

(3)

Lumley suggested that Kolmogorov's hypo thesis of locality, wh ich states that the statistical properties of the turbulence at wavenumber k in the inertial subrange are fully determined by the spectral kinetic energy flux at that wavenumber, could be extended to the buoyancy subrange. He suggested further that the spectrum of the buoyancy flux should be proportional to the potential temperature gradient d8/dz, or, equivalently, to the squared Brunt-Väisälä frequency, g8 -I d8/dz. Using these physical hypotheses, it is a matter of simple algebra to get the following expressions for the buoyancy flux spectrum, (k), the kinetic energy spectral flux, c~k), and the kinetic energy scalar spectrum, E~k):

(k) = -2N2[C~k)ll/3k-7/3

c~k) = cKO[ 1 + (k /kB ) -4/3P/2

Ek(k) = cxK[c~kW/3k -5/3

( 4)

(5)

( 6)

Vol. 130, 1989

where

Temperature and Heat Flux Spectra

IY. K = Kolmogorov constant '" 1.5

(N 3)1/2

k B = buoyancy wavenumber = -eKO

551

A characteristic feature of Lumley's spectrum (6) is its sharp increase towards small wavenumbers, approaching a universal (i.e., only dependent on the characteristics of the medium and not on eKO) limit, EK "'IY.KN 2k- 3 • This increase results, in the framework of the "extended" Kolmogorov locality hypothesis, from the dramatic increase (like k -2) of the kinetic energy spectral flux. Such high fluxes at any kare necessary in order to feed the important kinetic energy leakage occurring at higher wavenumbers and converted into potential energy.

By contrast, HOLLoWA Y (1986), rejecting Lumley's hypotheses, used a more elaborated relationship between EX<k) and eX<k) involving a scale dependent "decorrelation time" related to both N and the characteristic eddy time Te ~ e -1/3

k -2/3. The form of this relation results from theoretical considerations on wave interactions developed elsewhere (HOLLOWAY, 1983, 1979). As a result, he obtained a kinetic energy spectrum close to Lumley's but having a quite different significance: now, eX<k) may only be weakly different from eKO and the sharp increase of EX<k) towards small k is related to the weaker efficiency of the nonlinear energy transfers (shorter decorrelation times) assumed at these scales.

b) The Potential Energy Spectrum

Straightforward integration of (3) leads to

(7)

The physical significance on the integration constants is clear: eKO' as mentioned above is the kinetic energy dissipation rate and ePO' the spectral flux of potential energy at large k, is a potential energy dissipation rate. This dissipation is directly connected to the dissipation by molecular conduction of the temperature fluctuations, that occur at sm aller scales.

Relation (7) is equivalent to relations (4.1) of Phillips and (8) of WEINSTOCK (l985a). Weinstock pointed out that it implies -ep(k) ~ ePO' as ex<k) ~ eKO' He interpreted this negativity as areverse cascading potential energy spectral flux (from large to small wavenumbers). As a matter of fact, inspection of (7) reveals that this assertion is true if ePO is not much larger than eKO' Conversely, Philips k- I

prediction results from the implicit opposite assumption ePO ~ eKO which is hidden behind his explicit assumption ep(k) ~ O(ePO)' Available atmospheric data (this paper and also GOSSARD and FRISCH, 1987) as weH as oceanic data (see, for instance, GARGETT 1985, table 1, column r) suggest that ePO ~ O(eKO) or even lower


so that areverse cascade of potential energy is likely to occur in a stably stratified medium, if Lumley's hypotheses are true.

Using some simplifying assumptions, Weinstock predicted the temperature spectrum limit in the buoyancy subrange, scaling like k- 3 , while, relaxing these unnecessary assumptions, we derived the exact potential energy spectrum corresponding to Lumley's hypotheses (DALAUDIER and SIDl, 1987), valid in the whole buoyancy-inertia ranges. The potential energy spectral flux may be deduced from (7) and (5):

(9)

where d = ratio of potential over kinetic energies dissipation rates. 8P(k) reverses at wavenumber k G given by

( 10)

Following Phillips arguments for the temperature spectrum, we obtain the potential energy scalar spectrum:

( 11)

where IY. p = Batchelor constant ~ I. To account for negative spectral fluxes, we use the absolute value of 8p since, as

pointed out by Weinstock, Phillips original derivation depends on the magnitude of the flux and not on its direction. Relation (11) shows that E P(k) presents a gap at k G, the wavenumber at which 8p vanishes and reverses. From a physical point of view, this gap results from the "extended" Kolmogorov hypothesis and from the inability of the molecular processes to dissipate at a sufficient rate all the increased density (temperature) fluctuations created by the turbulent vertical motions in the stably stratified medium. Figure 1 from DALAUDIER and SmI (1987), shows in a nondimensionalized form the associated spectra E p and EK for two values of the parameter d, the spectral fluxes and the kinetic energy spectral density loss being qualitatively represented by black and white arrows.

The potential energy spectrum (11) is strictiy equivalent to Lumley's temperature spectrum (LUMLEY, 1965, eq. (14» but for the absolute value of 8 p • Thus, it inc\udes, as a special case, the k -1 domain which appears when d ~ I.

HOLLOWA Y (1986) predicted a potential energy spectrum having the same functional form as Lumley's kinetic energy spectrum, thus showing no gap. The corresponding (direct cascading) potential energy spectral flux increases only slightly from the buoyancy to the inertial subrange, as a result of the weak buoyancy flux spectrum. Here again, the essentially similar spectra predicted by both theories (from a -3 spectral slope to a -5(3 one) correspond to radically different physical interpretations. The sharp increase of potential energy spectral densities towards small k corresponds either to the increase of the reverse cascading flux or, to the weaker efficiency of the nonlinear (potential) energy transfers.

Vol. 130, 1989 Temperature and Heat Flux Spectra 553

EK =~(1+X-413) x- S13 (*10)

E = I d+ 1- (1 +X- 413) 3/2 (1 +X- 4/3) -1/2 X- S13 W//////////h. P

2

1

o

-1

-2

-3

-2 -1 o 1 log (x) 2

Figure I Theoretical representation of scalar spectra of kinetic energy (solid line, multiplied by 10) and potential energy (hatched lines) for two values of parameter d (5 and .2). The spectra are plotted in nondimensional log-log coordinates (Iog[kjkBl-log[Ej(N2jk1)]). Solid arrows represent the direction and strength ofthe spectral flux while open arrows indicate the leakage of the kinetic energy flux towards potential form.

It is worth nohcmg that both theories predict the same (k) '" k -7/3 in the inertial subrange. In the buoyancy range, the classical theory predicts (k) '" k- 3

while Holloway's allows a range ofpossibilities spanning from k- 7 /3 to k lf3 • This is why experimental vertical heat flux spectra, as weIl as potential energy spectral gaps observations are important clues in this debate.

c) Scalar Spectra and Experimental Spectra

In the next seetions, we will compare these theoretical results with experimental spectral estimates of vertical velocity temperature and heat fluxes. Some difficulties

arise from the faet that theories deal with sealar speetra (the 3-D speetra integrated . upon spherieal shells with radii k) while experimental data allow estimation of one-dimensional speetra (the 3-D speetra integrated upon plane surfaees perpendieular to the direetion of measurements). Conversion formulae from the one to the other are well-known in the ease of isotropie sealar and veetor fields but the very existenee of a stratifieation and assoeiated fluxes (in physical spaee), implies that the turbulent field may only be approximately isotropie in the inertial subrange and is clearly anisotropie in the buoyaney subrange. Convenient eonversions from sealar to one-dimensional speetra require a precise knowledge of the 3-D speetra anisotropy, which is not given by available theories or observations.

In order to eompare theory and observations, we will use nevertheless, the isotropie eonversion formulae (MONIN and YAGLOM, 1975, ehapter 6, seetion 12)

k 3 d [1 dSwJ EK ="2 dk k dk

g2 dST

Ep = - 2T~N2k dk

,= -!Ik dSWT T dk

(12)

where Sw, ST, SWT are respeetively the one-dimensional speetra of vertical velocity, temperature and the eospeetrum of both.

Notiee that we use the longitudinal eonversion formulae for Sw, as the measurements are mainly along the vertical direetion. Notiee also that we eonsider the eospeetrum SWT as the speetrum of a sealar field and that the speetral gap in Ep(k) should appear as a flat seetion around kG in Sr<kz ). Theoretieal Sw, ST and SWT will be eomputed numerieally, using (12), (6), (11), (4) and the experimental values of BKO and d determined in the inertial subranges. Diserepaneies between theoretieal isotropie eurves and experimental ones will be interpreted, partly, as a consequenee of the fields anisotropy.

IIl. Data Analysis

The data diseussed below have been obtained using a balloon-borne instrumentation and a teehnique described by BARAT (1983). The balloon flight occurred on May, 24, 1984, starting from the CNES launehing site at Aire sur l'Adour (43°42'N, 0° 15'W). Measurements were made, during the balloon aseent to its ceiling (~18 km), from an instrumented gondola hung ~ 142 m below the balloon. This distanee and the balloon ascent velocities (~5 ms - I in the troposphere and ~ 3 ms - I in the stratosphere) ensure that the instruments are rarely influeneed by the wake of the balloon (BARAT et al., 1984). Furthermore, within the three


particular layers discussed below (Section IV), the estimated dissipation rates are much weaker than those reported by these authors in the wake, thus allowing exclusion of any contamination.

The instrumentation included high resolution ionic anemometers (BARAT,

1982), pressure sensor and temperature sensors (coarse and fine microbead thermistors), the sampling frequency being 64 Hz. Owing to the rapid ascent velocities, the horizontal component of the wind velocity (relative to the sensor) could not be measured unambiguously and we will only refer to the anemometric data along the vertical measurement axis, Wa • Using hydrostatic approximation, an altitude time series may be computed from the pressure and temperature data. Time derivation of this series gives the vertical velocity of the balloon-gondola system with respect to the ground, Wp • Inflight calibration of the (density-dependent) anemometric signal is achieved by assuming that the mean values, over the whole balloon ascent, of - Wa and Wp are equal. This procedure may influence the ultra low frequencies in the anemometric data but not the higher frequencies discussed here. The r.m.s. noise of the digitized Wa series was estimated to be '" 1.10 - 2 ms -I.

The air vertical velocity (relative to the ground), W, can be computed by

(13)

However, owing to the derivation process, experimental Wp includes a noise contamination growing roughly like.f (fbeing the frequency). Once converted into space scales and taking into account the press ure sensor noise level, it appears that W series may not be analyzed at scales shorter than '" 200 m. Thus, the results discussed hereafter, have been obtained mostly by using Wa instead of W. The spectral significance of such an exchange is discussed in the Appendix. We show that towards the shortest scales, Wa and W may be exchanged. At scales larger 'than the balloon dimension ( '" 15-20 m), the Wa spectrum, S Wa' gently oscillates around (2. x Sw) and the cospectrum, SWaT> oscillates around SWT, with a somehow more important relative amplitude.

The fine temperature sensor was designed to operate under stratospheric conditions so that data are available only above '" 8 km altitude, with a r.m.s. random noise level of 5.10- 3 K. Its time transfer function was approximated by that of a (density-dependent) time constant r '" .3 s at the ground level up to r '" .5 s at the ceiling. Consequently, the raw temperature spectral estimates will be corrected by a multiplicating factor (I + (2n/r)2) and the cross-spectra estimates by (1 + 2in/r) as an approximate correction.

Within the frozen field approximation, time spectra are transformed into space spectra using the mean Wa during the data section considered. Some error results from the neglect of the horizontal relative velocity. Assuming that the balloon is a perfect wind sensor, the me an squared horizontal relative velocity is the vertical structure function of horizontal velocity at the balloon-gondola distance. A vailable measurements (BARAT and BERTIN, 1984) suggest a r.m.s. horizontal relative


veloeity of the order of 2 ms - I. The negleet of this horizontal eomponent leads to a slight overestimation of the speetral densities, in the ease of an isotropie field ( ~ 30%, at most) and has an even more negligible influenee in the ease of an anisotropie field along the vertieal, as may be expeeted at seales larger than Lumley-Shur seale, LB = 2.n/kB• More worrying are the non turbulent Wo variations that may occur during a da ta seetion as a result of sudden aeeelerations of the balloon during its ascent. However, as the seleeted results shown below eorrespond to seetions without any strong variations of Wa, we eonsider that, in sueh eases, Wo variations result in some inereased smoothing of the speetral estimates, only.

The speetral estimates eorresponding to any da ta seetion are eomputed by Fourier transform of windowed auto- or eross-eovarianee funetion. The data

Wavelength (m)

1000 100 10 1 0.1 2 i I ~~ r- ,----,

LA \!/vl i' . ~( z=O.1 ... 1.9 km 1 ' VI,

...,... 0 -:1' !Q. 'CG ..Q

- 1 ~

2 t"roreUcal Sw

-2

-3 -

-4 ~

-5

10 2 10 1 10 Wavenumber (cyc1es/m)

Figure 2 Vertical velocity spectral versus vertical wavenumber in the lowest part of the atmosphere. The spectrum of anemometric velocity SWa is used to deduce the theoretical spectrum Sw (smooth solid line). As shown in the Appendix, SWa oscillates around 2 x theoretical Sw (dashed line) for scales larger than the balloon dimension (::dO m here). The spurious spike around 5-10 m comes from gondola oscillations. The experimental Sw spectrum, computed with pressure and anemometric data, is consistent with theoretical S W towards largest scales. The "error bars" corresponds to 90% statistical confidence level.

section is prewhitened by first differencing, divided in segments corresponding to the required spectral resolution, the residual mean value is withdrawn on each segment be fore computing the covariance functions. Windowing is made using a Kaiser-Bessel window (HARRIS, 1978). Notice that for cross-spectral estimates, we reduce further the window width at the expense of spectral resolution in order to achieve sufficient statistical significance of the results.

Figures 2 and 3 illustrate the validity of the different approximations used during these spectral estimations. They show respectively the experimental and theoretical vertical velocity and heat flux spectra obtained in the lowest '" 2000 m data section. This section, which corresponds roughly to the boundary layer, has been chosen because the turbulence appears there sufficiently strong and

Wavelength (m)

1000 100 10 1 0.1 2 ,.----r-."..~~--,r' nl i'-' rr, I Ir---'--'-'I ,..,., ....... ,. ---r- rr, r-o I

,.

0

~ -1 ~ Cf)

, "'<fi.

'CL

-2 f \ '1.'?--t-.2 '«

"'" V

-3

-4

::r I I

10 3 10 2 10 I 1 10 Wavenumber (cyc1es/m)

Figure 3 Vertical velocity-temperature cospectrum ("hcat flux") in the same region as Figure 2. Owing to the use of coarse temperature sensor, the small scales range is not significant (hatched region). For larger scales, the cospectrum is negative and very dose to its theoretical value (smooth line with - 7/3 slope) deducted from S w in Figure 2 (the agreement is obtained without any adjustment). The level of the statistical noise

for cospectrum estimates is also shown (solid broken line).

homogeneous. The Lumley-Shur scale, L B, is here '" 300 m so that the comparison with isotropie predictions is presumably valid on an extended scale range.

The spike which appears in Figure 2 (and on many other W spectra), in the vicinity of '" 5 m vertical wavelength, is spurious and corresponds to a parasitic oscillation of the gondola. The kinetic energy dissipation rate is estimated from the sm aB scales range ( < 10 m) showing clearly a - 5/3 spectral slope. The corresponding theoretical Sw is plotted (smooth curve). It may be seen that, in the 20 m-200 m scale range, S Wa gently oscillates in the vicinity of two tim es S w, as predicted in the Appendix. Towards larger scales, the agreement of S Wa and experimental S W (the V shaped speetrum at the upper left) appears satisfaetory.

In Figure 3, the "heat flux" speetrum is computed using the eoarse temperature sensor with a '" 5 stirne constant. The aeeessible seale range is therefore reduced. However, it appears clearly that the isotropie theoretieal predietion in the inertial subrange and the measurements agree fairly weB.

IV. Experimental Results

The data set described above is unique and has been submitted to extensive speetral analyses eorresponding to different spectral ranges, from the turbulent inertial seales up to the mesoseale. Here, we are more specially interested in the seale range extending up to a few times the Lumley-Shur seale L B , minimally. L B is about 10 m in the stratosphere (see below). Consequently, the required speetral resolution of the estimates must be of the order of '" 1.10 - 2 cycle rn-I. Taking into account the band widening associated with windowing, the data segments length must be at least '" 250 m and in order to achieve sufficient statistieal confidence, a data section submitted to speetral analysis must eorrespond to a height interval '" 1 km.

Such an interval is much wider than the width of turbulent layers usually observed in the stratosphere, ranging from a few tens to a few hundred meters. Therefore, it appears diffieult to delimit atmospherie layers that are statistically homogeneous and wide enough so that unambiguous eomparisons between experiment and theory ean be made.

This diffieulty is illustrated in Figure 4 whieh shows the vertical profiles of temperature and vertieal veloeity varianees, filtered within narrow spectral bands in the high wavenumbers range. These profiles have been obtained by integrating eaeh Fourier transforms of 10 seconds length data seetions, within the frequency bands eorresponding to the wavelengths bands (2.5--4 m) for T and (0.2-1 m) for W. These profiles are thus illustrative of the small scale turbulent layers, as they appear on temperature and vertical ve\ocity data. The general features of similar profiles ha ve been discussed elsewhere (DALA UDIER et al., 1985), the most striking being that there is no obvious eorrespondence between the temperature and velocity varianees. When eonsidering only the veloeity varianee profile, where turbulent

Vol. 130, 1989

18

17

16

15

14

13

12

11

10

9

E ~ v '0 ;l ..... -'

"<

Temperature and Heat Flux Spectra

Temperature variance

VerUcal Velocity variancc

8L-__ ~ __ ~ __ ~ __ ~~ __ L-__ ~ __ ~ __ ~ __ ~ __ ~

25 20 15 10 5 1 2 3 4 5 Variancc T [2.5 - 4 ml 10 1 K2 Variance W [0.2 - 1 m[ 10:1 m2 2

Figure 4

559

Vertical profiles of temperature and vertical velocity smaIJ-scale variance. Spectral bands used are shown in the figure. Each variance estimate is based on 10 s data seetion. The difference between troposphere and stratosphere appears cJearly, both on temperature and velocity fluctuations : the increased stability in the stratosphere, simultaneously reduce Wand increase T amplitudes. Wand T fluctuations do not appear always simultaneously. The 3 selected regions where i) the velocity variance is approximately homogeneous, ii) the temperature gradient is roughly constant and iii) the length of the homogeneous

layer is ::::; 1 km are shaded and identified in thc figure.

layers appear more distinctly, wide enough homogeneous data sections can only be defined in weakly turbulent regions.

The number of eonvenient data seetions is further redueed by eonsidering the mean temperature profile: the temperature gradient must be roughly eonstant within eaeh data seetion so that a mean N ean be unambiguously defined. As a result, we have seleeted three atmospherie layers eorresponding to these various eriteria: those labelled (1) to (3) in Figure 4.

Vertieal veloeity and temperature speetra relative to these layers appear in Figures 5a, b, e. (Figure 5a is identieal to Figure 3 in DALAUDIER and Sml, 1987). The smooth eurves superimposed on the experimental ones are the theoretical isotropie speetra eomputed as explained in seetion He). The only adjustments to the data are as folIows: First N and Ta are determined from the best straight li ne fit to the temperature profile. Then SKO and d are determined by fitting to the experimental speetra theoretieal ones in the inertial domain, taking into aeeount the time eonstant eorreetion effeet on the temperature observed white noise level (whieh produees the +2 slope towards the high wavenumbers limit). These parameters along with other relevant information, are listed in Table I.

560

2

:; 1 rJl • 8 -~ 0

.... o

-2

-3

-4 10.3

C. Sidi and F. Dalaudier

Layer CD

;

kc

10 1 10 Wavenumber (cycles/m)

Figure 5a

PAGEOPH,

The main observations relative to these figures are qualitatively the same as those already published. The temperature experimental speetra show the signature

of possible gaps in the vieinity of the predieted wavenumbers k G : their loeal slope tends there towards zero or even beeomes positive (layers (1) and (3)) suggesting anisotropy of the temperature fluetuating field at k G . Anisotropy of the veloeity field is also evideneed by the W speetra that beeome weaker than the isotropie predietion at k ~ k B , inasmueh as these experimental speetra are about twiee the atmospherie W speetra (see seetion III).

Figure 6 shows the eorresponding experimental "heat flux" speetra. These estimates are really significant in the se ale range extending from - 50 m (limitation by the speetral resolution) down to '" 5 m (limitation by the parasitic oseillation, c\early visible on the W speetra). In this limited spectral domain the spectral estimates are roughly one order of magnitude larger than the statistical noise.

Vol. 130, 1989 Ternperature and Heat Flux Spectra 561

Layer (2) 2

I

J • 0 0

~ 0

.... 0

~ -1

~

-2

J 10-1 10

Wavenumbcr (cycle Im)

Figure 5b

Table I

Same characlerislics a( Ihe Ihree layers shall'n on Figure 4. Assacialed lemperature and verlical velacily .I'peclra are sholl'n on Figures 5a, h, c and ('ospeclra on Figure 6.

To N f. KO kB kG

Layer (K) (rad s- I) (rn2 s-') (rad rn-I) d (rad rn , l)

(I) 218.7 2.27 10 - 2 1.6 10 5 .81 2.1 .74 (2) 218.1 1.7810- 2 2.4 10- 5 .49 1.2 .65 (3) 213.6 2.5610- 2 4.310- 5 .63 .95 .97

562

..,.. rh b 0

E' .... 0

~ "C{;

.2

2

0

- 1

-2

-3

C. Sidi and F. Dalaudier

Laycr @

10 1 10

W,\\'cnumbcr (cyclcs/mJ

Figure 5c

Figure 5a, b, e

PAGEOPH,

Temperature (bottom) and vertical veloeity (muItiplied by 100) speetra for the 3 selected regions shown on Figure 4. Theoretical speetra (smooth eurves) are fitted to experimental ones in the inertial domain and then, extended in the B.S.R. using isotropie formulas. Spurious spikes on W speetra are explained in Figure 2 eaption. The increase of temperature speetra for the smallest seal es eorresponds to the noise level after time-eonstant eorreetion. Temperature speetra show evidenee for a gap in the vieinity of kc (indieated at the bottom). In the B.S.R. temperature speetra agree quite weil with theory while W speetra (a faetor 2 below Wa speetra) are systematieally lower than (but approximately parallel to) the isotropie

predietion.

We may notice first that most of these estimates are negative as they should be. The few positive estimates (see layer (2) or (3» may result from contamination by randomly high values of the quadrature speetrum as explained in the Appendix. They mayaiso correspond to areal variability of heat flux with scale.

As a whole, these heat flux spectra appear somewhat weaker than predicted by the (isotropie) theory, though their magnitude increases towards large scales, weil

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inside the B.S.R. This weaker level appears consistent with the weaker Sw observed at k < kB• The available scale range does not allow discrimination between possible slopes ( - 3 or - 7/3), but in any case, these spectra do not suggest a decrease towards larger scales. Thus, in the sc ale range considered here, they are clearly inconsistent with HOLLOWAY'S (1986) lower bound, SWT '" k lf3 •

Obviously, these results are limited to the weak turbulent layers analysed and may not be representative of more general conditions. In that respect, an interesting result appears when considering the temperature spectra, irrespective of the turbulent conditions encountered. The whole temperature data set has been divided in eight

Wavelength (m)

100 10 1 0.1

l ·ranj(C N R3 \1.6 l.uut;-u:.l 9.7 11.2 1.35E-02

11.3 12.3 2.74E-02 4 12.3 13.4 2.43E-02

13.4 14.6 1.92E·02 14.6 15.8 1781:":-02 15.8 16.8 2.37E·02 16.8 17.6 2.17E-02

2

o

10 1 10 Wavenumber (cycl s(m)

Figure 7 Collapse of normalised temperature spectra obtained in 8 seetions between 8 and 18 km with rough1y constant temperature gradient in each. This col\apse indicates that the prediction of a universal level = (2/3) (N 4 T 2Ig 2k.1) is weB verified by experimental data, even in inhomogeneous regions. The shaded region indicates the range for the theoretical normalised spectrum for various values of the anisotropy.


sections, each showing a nearly constant temperature gradient. The corresponding N varies from 1 to 2.7 10- 2 rad s - I. The eight temperature spectra, multiplied by the local scaling factor g2/(T2 N 4) appear in Figure 7. In the low wavenumber range, they conveniently coincide with the (isotropie!) B.S.R. normalised spectrum: 2/3 k -3. This result does not discriminate between elassical B.S.R. theory and Holloway's postulate: it shows that basic hypotheses of B.S.R. theories, namely that energy sources are negligible, are probably true.

It neither constitutes an indication of the isotropy of the 3D temperature spectra. Indeed if the 3D spectrum is assumed to be highly anisotropie and vertically axisymmetric, one should expect ST = ET instead of the isotropie relation ST = ET /3 in the ca se of a - 3 slope. This identity between seal ar and 10 spectra results from the negligible contribution of 3D spectrum to both integrals in regions where the spherical shell significantly differs from its tangent planes, compared to that from directions elose to the vertical. Thus, the expected range for the theoretical 10 spectra is only a factor 3 wide and is indicated as a shadowed region on Figure 7. Experimental spectra are consistent with any value of the anisotropy.

V. Discussion

The experimental results discussed above appear basically consistent with the predictions of the elassical B.S.R. theory initiated by Lumley-Shur. They show, however, that the isotropy assumption at scales larger than L B is certainly not valid: an anisotropie B.S.R. theory is crucially needed. They do not necessarily rule out other B.S.R. theories as they are limited to weak turbulent conditions and to seal es shorter than ~ 5 to 10 L B • Furthermore, they have been obtained during a single balloon flight, and a elimatology of such observations is still to be done. It is clear that the upward mass flux cannot occur simultaneously everywhere in the atmosphere.

LUMLEY (1965) discussed the very existence of scale range influenced by buoyancy and not by feeding. He considered the two basic types of feeding, shear and flux divergence (the transport in physical space of turbulent kinetic energy by the turbulence itself). Flux divergence is likely to be unimportant within the three layers discussed here: assuming that the vertical velocity variance (Figure 4) and the turbulent kinetic energy behave similarly, their vertical gradients are weak and, thus, the flux divergence is probably weak. LUMLEY (1965) argued that if the shear source is important at some scale, it should be important at every scale and preelude the occurrence of a true B.S.R. He coneluded that, in the absence of flux divergence, a true B.S.R. could only occur within old decaying turbulence. This may be the ca se within our three layers which show very weak dissipation rates,


though the available data do not allow direct confirmation of the weakness of the shear sources.

LUMLEY (1964, 1965) also pointed out that the use of the locality hypothesis is subject to the condition (h -1 df,/dk) ~ 1. The theoretical spectra lead to a somehow higher value ( = 2.) in the B.S.R. It may be noticed that the experimental results do fulfill Lumley's condition as the heat flux spectra (Figure 6) are clearly weaker than predicted. Here again, isotropy appears to be the most doubtful shortcoming of the present theory while its physical hypo thesis seems to describe nature conveniently, at least in some circumstances.

The success of the B.S.R. theory raises numerous questions relative to the transition between waves and small-scale turbulence. It is widely believed that most of turbulence generation in the stable atmosphere occurs through the process of wave breaking or wave saturation that generates instabilities in the flow (FRITTS, 1984; FRITTS and RASTOGI, 1985). In the framework of B.S.R. theory, such energy input would increase df,K/dk (make it less negative) and thus reduce the slope of E~k), as can be seen by differentiating (6). The observation of a -3 slope implies that these instabilities occur at scales larger than ~ 10 L B • Consequently, sm aller scales may not be relevant to the "saturated gravity wave spectrum" theory. An indirect proof is given by the experimental W-spectra which are much more energetic than predicted by linear gravity wave theory (the velocity field is much less anisotropic than that of the gravity waves field).

Another related question concerns the rate of nonlinear transfer of kinetic energy: in the B.S.R., this rate increases dramatically towards large scales while, in the nonsaturated gravity wave domain, it is believed to be negligible. Some transition must occur in the intermediate saturated domain with an increasing transfer towards sm aller scales, thus acting as the energy source for the turbulent kinetic energy cascade. This region of maximum energy transfer is reminiscent of the Holloway's conjecture but should take pi ace at scales larger than a few L B •

A major question raised by HOLLoWA Y (1986) as an objection to classical B.S.R. theory is "what becomes of the reverse cascading potential energy flux?" The present results, if limited to old decaying turbulence, suggest that the reverse cascade may play some role in maintaining the long-lived sawtoothed temperature profiles associated with former strongly turbulent layers. The contribution of a reverse cascade to the very formation of these potential energy reservoirs, as suggested in DALAUDIER and SmI (1987), is actually unclear. Further theoretical efforts are required in order to understand how this potential energy is converted back into a kinetic one.

Finally, we emphasize the importance of gathering spectral information for varous oblique directions, in order to describe conveniently the anisotropy of the fluctuating fields in the B.S.R. As explained in Section IV, spectra versus vertical wavenumbers discussed here, only give information about the scalar spectra, in a strongly anisotropic turbulence.

Vol. 130, 1989 Temperature and Heat Flux Spectra 567

Appendix

Let us discuss now the significance of using Wa instead of W in the spectral estimates. Following (13) we have

(Al)

Wp being the vertical velocity of the balloon relative to the ground. Two limiting situations must then be distinguished depending on both the turbulent vertical velocity vertical scales, L, and the balloon dimension D.

Fluctuations with L ~ D do not influence W p while those with L ~ D do. Consequently, the shorter wavelengths in the Wa(z) signal only come from the atmospheric signal W(z) while the situation is somehow more elaborated for wavelengths roughly larger than D. Then, Wp may be expanded as

Wp(z) = W(z + h) + WB(z + h) (A2)

where

h = balloon gondola distance WB = balloon vertical velocity relative to the ambient air.

(A2) simply states that the balloon follows the atmospheric vertical velocity fluctuations when its ascent velocity reduces to zero. Introducing (A2) in (Al) and expanding the auto-covariance function of Wa shows immediately that

Rwa(r) ::::: 2Rw(r) + RWB(r) - Rw(r + h) - Rw(r - h) (A3)

where R = auto-covariance function of the variables Wa , WB or W. In (A3), we assurne that Wand WB are negligibly cross-correlated. Furthermore,

we implicitly admit that balloon and gondola lie within the same, statistically homogeneous, atmospheric layer. Fourier transform of (A3) gives

(A4)

where S = power spectra. Assuming that the spectrum of WB has negligible energy in the turbulent scales

range, (A4) shows that the spectrum of Wa oscillates, with a periodicity (2n/h) around two times the W spectrum. However, the apparent amplitude of this oscillation on the spectral estimates depends on their spectral resolution. Owing to the da ta segment lengths and to the window smoothing effects, the spectral resolution of our estimates will be typically of the other 3/h rad m -I. Thus the

parasitic spectral oscillation will partly be smoothed out. A similar analysis may be made as regards the cross-spectrum of temperature

and anemometric velocity. We obtain

eTWa = eTw( 1- e -ikh)

where eTW = cross-spectrum of Wand T.

(A5)

(A5) is valid at scales L > D, assuming that the temperature at z and the balloon ascent velocity WB at (z + h) are negligibly cross-correlated while at scales L < D we have eTWa = e TW' (A5) shows again that the cross-spectrum eTWa differs from e TW

by a (col1'~lex) oscillating function, the amplitude of which being more or less smoothed out by the spectral estimation process. The relative amplitude of the residual oscillation on the cospectrum STW is, however, more worrying than in the case of the Sw computations. Before smoothing, the amplitude of the oscillation is the cross-spectrum modulus, as shown by (A5) and sometimes may be much more important than the cospectrum itself, depending on the local amplitude of the quadrature spectrum. This may explain the occurrence of some structures like arches (and sign changes) in the cospectra estimates discussed in the text.

Acknowledgements

Many thanks to G. Holloway for friendly discussions and to an anonymous reviewer who pointed out the importance of LUMLEY'S (1965) paper.

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WEINSTOCK, J. (l985a), On the theory 0/ temperature spectra in a stably stratijied jluid, J. Physieal. Oeeanog. 15, 475-477.

WEINSTOCK, J. (1985b), Theoretical gravity wave spectrum: Strong and weak wave interactions, Radio Seienee 20, 1295-1300.

(Reeeived August 17, 1987, revised/aeeepted Deeember 15, 1987)


Interpretation, Reliability and Accuracies of Parameters Deduced by the Spaced Antenna Method in Middle Atmosphere Applications

W. K. HOCKING,' P. MAy2 and J. RÖTTGER3

Abstract-The spaced antenna method has proved to be an important and relatively inexpensive radar technique for making measurements of atmospheric wind velocities and other parameters. This discussion examines the reliability and accuracies of various parameters which can be measured with the technique.

After abrief introduction, aseries of comparisons of winds measured by the spaced anten na method and simultaneously by other techniques are presented. It is concluded that when using weak partial reflections in the height range 0-100 km, the spaced antenna technique provides reliable estimates of the neutral air motion. Following this the assumptions made in applying the method are considered in more detail. The possibility of systematic errors and the likelihood of erroneous measurements are examined, and the accuracy of any particular measurement of wind speed is discussed. Previous objections to the technique are discussed, and in general shown to be invalid.

Other parameters apart from wind speeds can be measured with the spaced antenna technique, such as pattern scale, the rate of natural fading, and angles of arrival. The meanings of these parameters are discussed in terms of physical quantities such as turbulent energy dissipation rates, small-scale gravity wave velocity fluctuations, and aspect sensitivities of scatterers, and it is indicated when and how these derived parameters can be applied to deduce meaningful physical quantities. The need for great caution in making these interpretations is discussed; for example it is not always possible to use the rate of natural fading to estimate the intensity of turbulence, although in some cases this is possible. Finally, interferometric applications of spaced antenna systems are discussed.

Key words: Winds, spaced antennas, correlation analysis, scatterers, interferometry.

J. Introduction

Originally developed in the 1950's, the spaced antenna method for measuring wind velocities in the atmosphere has become a commonly used radar technique. It was originally used for total reflection experiments, subsequently modified for D region work using partial reflections (FRASER and KOCHANSKI, 1970; BRIGGS,

I Department of Physics and Mathematical Physics, University of Adelaide, Adelaide, 5001 Australia.

2 Radio Atmospheric Science Center, Kyoto University, U1I KYOTO 611, Japan. 3 Permanent Affiliation, Max Planck Institut für Aeronomie, Kaltenburg-Lindau, Federal Republic

of Gcrmany.

572 W. K. Hocking et al. PAGEOPH,

1977), and later still used for tropospheric and stratospheric wind measurements with VHF radars (e.g., RÖTTGER and VINCENT, 1978; RÖTTGER, 198Ia). A variety of parameters can be deduced with the technique, in addition to the horizontal wind speed, but the interpretation of some of these parameters is still in doubt. Furthermore, it has only recently become possible to calculate error estimates. The main purposes of this paper are to discuss the reliability of wind measurements, the interpretation of the additional parameters, and to consider the errors associated with both the wind speed estimates and the associated parameters. New applications of spaced antenna systems, including interferometric applications, are also considered.

2. The Technique in Brief

The principle of the spaced antenna (SA) method is quite simple and is illustrated in Figure I. A radio transmitter sends pulses of radio waves vertically upwards into the atmosphere, and these are backscattered to form a moving and changing diffraction pattern on the ground. The magnitude (and possibly phase) of this pattern is sampled with antennas at three or more spaced points, and these time-varying signals are cross-correlated in order to find the time shifts between each pair of antennas which are required to make the signals most similar. From these time shifts, estimates of the velocity of drift of the diffraction pattern can be made. It can be shown that this velocity is twice the horizontal velocity of the scatterers in the radar volume (FELGATE, 1970; BRIGGS, 1980). An estimate of the vertical velocity can also be made from the complex autocorre1ation function for any one of the antennas by measuring the me an Doppler shift. This estimate can be improved upon by using the three antennas as an interferometer to deduce angles of arrival (as discussed later).

Figure I is based on an experiment conducted at Townsville in Australia to study the ionospheric D region. The experiment was designed and opera ted by the Department of Physics, University of Adelaide, Australia (VINCENT and BALL, 1981). It represents perhaps the most compact and simplest form of the SA experiment. The radio waves (1.94 MHz) were transmitted from the square antenna array in the center of Figure I. The sm all black rectangle inside this square represents the transmitter and receiver building, and the four lines leading from it represent transmission lines to four half-wave dipoles, wh ich form the outer square. Three simple crossed dipoles (A, Band C), arranged for circular polarization, were used for reception. The contours in the diagram represent part of the diffraction pattern amplitude. In the general case this is complex, (magnitude and phase) and the large arrow "2 W" represents the diffraction pattern's velocity. As it moves, the diffraction pattern will cause temporal variations at the aerials A, Band C, and these temporal variations will be similar, but will be displaced in time (see the

Vol. 130, 1989 Spaced Antenna Method in Middle Atmosphere Applications 573

N Seole 1: 2.000

Reeeiving

~ 10m

1 • 1.000

Figure 1 The principle of the spaced antenna method.

illustrative amplitude variations as a function of time in the bottom left-hand corner of Figure I). In the simplest case, where the diffraction pattern is assumed to be statistically isotropie, and to move without changing, the time displacements of the signals A, Band C can readily be used to determine the velocity 2 W. Determination of the "wind velocity" under these assumptions leads to a quantity known as the "apparent velocity" .

An alternative way of viewing the temporal fading is as folIows: As the radio wave scatterers in the atmosphere move across the radar beam, scatterers at different zenith angles cause a range of Doppler-shifted frequencies to arrive back at the antennas. The addition of these various frequency components causes the fading. The spectrum of the returned signal has a finite width; this is called "beam broadening", and arises simply because of the finite beam-width together with the horizontal motion (HOCKING, 1983a).

In addition to this, there may be other sources of fading, which cause the spectrum to be further broadened. These include any fluctuating random motions of the scatterers, and possible growth and decay of the scatterers. The fading arising


from such contributions will be called "natural fading"; it is the fading which would still occur even if there were no wind.

If there is no "natural fading", then the diffraction pattern drifts with unchanging form and it is a simple matter to calculate its velocity across the ground, by simply using the time lags between pairs of antennas and the separation of the antennas, as discussed above. However if there is natural fading, the pattern changes as it moves and the calculation of this so-called "apparent velocity" produces an estimate of the drift velocity which is gene rally greater than the true velocity. A more sophisticated analysis, called "full correlation analysis" (FCA) (BRIGGS et al., 1950; PHILLIPS and SPENCER, 1955; BRIGGS, 1984) is required to extract the "true velocity".

This analysis technique also permits the diffraction pattern to be elongated (nonisotropic) with mean orientation which is at an arbitrary angle with respect to the wind direction. With this method, it is not only possible to determine the real velocity more accurately, but it is also possible to calculate the scale of the diffraction pattern, the degree of elongation, the orientation, and to find the degree of natural fading.

3. Experimental Tests of the SA Method

Before beginning to discuss the methods and associated errors in detail, it is worthwhile to first ex amine the accuracy of the method from an experimental viewpoint. Having established the broad validity of the technique for the measuring winds, the following sections will consider the assumptions made in utilizing the method, the associated errors, so me of the subtleties of the technique and the interpretation of the parameters other than winds.

The best way to test the SA method is, of course, by comparison with other methods. Extensive tests of the method have been carried out. They suggest that the SA method is a reliable means of estimation of wind velocity in the mesosphere (at MF and HF) and in the troposphere and stratosphere (at VHF), when using weak partial reflections. In the mesosphere, the reflections are from weakly ionized irregularities, and in the troposphere and stratosphere are from irregularities in the neutral air.

FRASER and KOCHANSKI (1970) and GREGORY and REES (1971) initially showed that SA measurements at MF and HF in the D region produced reliable winds. STUBBS and VINCENT (1973) and STUBBS (1973) then showed that the SA winds agreed weil with meteor measurements of winds at 80-100 km altitude. Further comparisons with meteor measurements by WRIGHT et al. (1976) also showed good agreement. VINCENT et al. (1977) compared the SA method with measurements of D-region winds made by rocket techniques, and again good agreement was obtained. BRIGGS (1977) presented further comparisons with meteor

Vol. 130, 1989 Spaced Antenna Method in Midd1e Atmosphere App1ications

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Comparison of winds in the mesosphere measured by spaced antenna and Doppler techniques.

measurements. Measurements of daily mean winds at Adelaide, Australia (e.g ., VINCENT and BALL, 1981) and Saskatoon, Canada (e.g., MANSON et al., 1981,

1985) show that these means are consistent with accepted models of mesospheric circulation (e.g. , BARNETT and CORNEY, 1985; KOSHELKOV, 1985; MANSON et al.,

1985). VINCENT et al. (this issue) presents some comparisons of SA and satellite geostrophic daily mean winds, with good agreement.

In the troposphere and stratosphere, several sets of SA measurements have been compared with wind measurements made by more conventional meteorological means. The first such report was by RÖTTGER and VINCENT (1978). Good agreement was found between balloon measurements and VHF SA wind measurements. Likewise, results presented by VINCENT and RÖTTGER (1980) showed good agreement. Subsequent comparisons by RÖTTGER (I98Ia,b) and RÖTTGER and CZECHOWSKY (1980), have also given no cause to doubt the SA method. VINCENT et al. (1987) have presented a comparison of SA wind measurements with over 80 rawinsonde profiles wh ich show RMS differences of the order of 4-5 ms - I in wind speed in the troposphere. This is of the same order as the estimated error, inc\uding measurement errors and the effect of the spatial separation of the balloon and the radar; the latter contributes the largest term. (However, a systematic

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PAGEOPH,

Comparison of wind speed and direction (scatter plot) measured with the spaced antenna set·up of the SOUSY-VHF·Radar. The circJes in (a) indicate simultaneous aircraft wind measurements above the radar, and in (b) radiosonde winds at a distance of 100 km. The scatterer plot of the SA data is from single one-minute sampIes collected over 27 min intervals. The scatterer is mostly due to meteorological

wind f1uctuations (from RÖTIGER and CZECHOWSKY, 1980).

difference of around 1- 2 ms - I was also seen in this study, which should be noted but is not a major cause for concern; it will be discussed later.) This level of agreement is comparable to or better than that obtained using radar measurements using the Doppler technique, where there were similar distances between the radar and balloon launch sites.

Figures 2-6 show some examples of the types of comparisons discussed above. Figures 2a and 2b show comparisons of radiosonde measurements of horizontal winds with measurements made with a VHF radar using the SA technique, (VINCENT et al., 1987). Figure 3 shows comparisons of tropospheric horizontal winds deduced by the SA technique and Doppler methods, and Figure 4 shows a similar comparison using an HF radar to measure mesospheric winds. Figure 5 shows comparisons of VHF SA height profiles of winds with aircraft wind measurements and radiosondes, and Figure 6 shows comparisons of a time series of


10

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Figure 6 Meridional wind speed measured every 6 hours with the SOUSY VHF radar by the SA method at the lower stratospheric altitude of 12 km, and compared to radiosonde measurements made at the stations of Essen and Berlin. Essen is west and Berlin is east of the SOUSY-VHF-Radar. The oscillating wind pattern is due to a synoptic-scale wave moving from west to east over the radar. The cross-correlation is similar between radar-radiosonde and radiosonde-radiosonde data, if one considers the time delay

due to the eastward propagating synoptic scale wave (from RÖTTGER, 1983).

SA winds at 12 km altitude with radiosonde measurements. Agreement is excellent. Note that there is a slight height difference in the two profiles measured in Figure 4, but since the measurements were separated by about an hour, this is probably real. In fact the measurements suggest that the winds were due to a gravity wave propagating with upward vertical phase velocity.

4. Approximations in Full Correlation Analysis

Having seen that the method does work, at least to reasonable accuracy, 1t IS

now necessary to subject the method to c10ser scrutiny. Both the accuracies of the method, and some of the additional parameters which can be deduced, will be discussed. We shall begin by looking at some of the assumptions made in applying the method.

In order to apply the "full correlation analysis" method, certain assumptions must be made. Although these appear to be quite reasonable, it is important to state them, since this paper attempts to examine errors in the method, and so we must consider the effects of any approximations made. A fundamental function necessary

for the application of FCA is the temporal and spatial correlation function, defined by

(" r) = <f*(x, y, t) . fex + (, y + 1/, t + r) > p, .,,1/, <V(x, y, tW> (1)

where x and y are orthogonal coordinates on the ground (East and North), ~ the displacement in the x direction, 1/ the displacement in the y direction, t is the time, r is time lag, fex, y, t) is the (possibly complex) amplitude of the diffraction pattern (after removal of the mean) and <> denotes an average over (in principle) all x, all y, and all t; f* is the complex conjugate of f

The first approximation makes use of a so-called "ergodicity theorem". In practice it is unrealistic to determine p(~, 1/, r), exactly, since this would require measurements of fex, y, t) at all points (x, y) on the ground. Nevertheless if it can be assumed that taking time averages for fixed values of ~ and 1/ is the same as taking ensemble averages over all points (the ergodicity theorem), then the required values of p(~, 1/, r) can be estimated from determinations of the temporal autocorrelations and cross-correlation of the signals at three or more antennas.

Another important assumption used in full correlation analysis is that the three-dimensional correlation function p described by (I) has surfaces of constant p which have the form of similar concentric ellipsoids centered on the origin. This necessarily implies that the temporal auto-correlation function due to the natural fading has the same functional form as the spatial auto-correlation function of the ground pattern. These latter assumptions have not been extensively tested, but at least some experimental confirmation of their validity exists. In particular, GOLLEY and ROSSITER (1970) have examined the validity of the last assumption, and found it to be true for the data wh ich they recorded.

If the last assumption is true, then it implies that the temporal cross-correlation function between two antennas has the same functional form (apart from time-displacement and scaling) as the temporal auto-correlation function for a single antenna, and indeed in FCA this is assumed in order to extract the true velocity. It is not actually necessary to know what this functional form iso However, in some versions of "full correlation analysis", it was assumed that the temporal auto-correlation function had a particular shape, often Gaussian. There also exists a more complicated version of the analysis which relaxes the assumption of the similarity of the correlation functions (BRIGGS and MAUOE, 1978).

The details of the FCA technique have been described by BRIGGS (1984), but it is useful to summarize the procedure briefly. Essentially, certain key time lags must be calculated from the auto- and cross-correlation functions between individual antennas. If aerials are located at (0,0), (x, 0) and (0, y), to take the simplest case, then the key time lags are (a) ro.s, the time for the auto-correlation function to fall to 0.5,


(b) (r~, r~), the r values at which the cross-correlation functions in the x and y directions maximize,

and (c) T." T.v' rxY' the r values at which the auto-correlation function falls to a value

equal to the value of the cross-correlation function at r = 0, for the pairs of aerials {(O,O), (x,O)}, {(O, 0), (O,y)} and {(x,O), (O,y)}.

These six parameters are then used to determine the correlation function (I), which with the assumption of ellipsoidal surfaces of constant p, must be of the form

(2)

The details of this procedure can be found in BRIGGS (1984). Variants on the procedure described by BRIGGS (1984) also exist, such as that proposed by MEEK

(1980), but the underlying principles remain the same. It is not possible to say much more about the likely effects of these assumptions,

but at least the reader will now be familiar with their existence. However, the need for such assumptions requires that ca re is taken in using the technique, and leads to the need for certain criteria to be satisfied by the data when using the technique. Discussion of these criteria is the topic for the next section.

5. Acceptance Criteria

Because the SA method requires estimation of the function p(~, 1/, r) (equation (I» from a few simple auto- and cross-correlation functions, it is important to ensure that the fitting is reasonable. Therefore proper application of the FCA method requires that certain acceptance criteria are satisfied. These acceptance criteria (also called rejection criteria) are quite stringent, and must always be applied. Failure to apply these criteria may allow erroneous wind speed estimates to be accepted, and this can bias the results and perhaps even give the appearance that the SA method is unreliable. The rejection criteria which are used for da ta obtained at the Buckland Park Research Station of the University of Adelaide, are listed below (e.g., BALL, 1981). A data sam pIe is rejected if: ( 1) The receiver was saturated for a significant time during the data interval; (2) The digitized signal levels are only of the order of a few digital units (weak

signal); (3) The mean auto-correlation function has not fallen below 0.5 after about 20

times the sampling interval (slow fading); (4) Any cross-correlation maxima are less than 0.2; (5) Any cross- or auto-correlation functions are oscillatory in nature over the first

20 time lags;


(6) Polynomial fits to the cross-correlation functions break down, preventing determination of the crucial time lags;

(7) The sum of the three time displacements of the peaks of the cross-correlations between aerial pairs, AB, BC and CA, divided by the sum of the moduli of these time displacements (MEEK et al., 1979) (the so-called normalized time discrepancy, or NTD), is greater than 0.4;

(8) The "true" and "apparent" velocities are very different; (9) The quantity "V;''' estimated in FCA, which relates to the level of natural

fading, is significantIy less than O. (In the ca se that Vz is only slightly less than zero, the apparent velo city can be used in place of the true velocity, since this probably indicates very little natural fading);

( 10) The signal-to-noise ratio is small; ( 11) The numerical values of certain constants indicate that the spatial correlation

function cannot be represented by elliptical contours (formally they indicate hyperbolic contours, which is physically unreasonable).

Despite the apparent complexity of these tests, they are not difficult to apply with a digital computer, and they do not normally result in excessive rejection rates. The most important of these are (3), (7) and (10).

A potential problem with adopting such criteria is that "unacceptable" data might tend to be associated with particular geophysical events, so that these events may tend to be excIuded in any caIculations of me an parameters. If, for example, situations with low wind speeds resulted in data which frequentIy did not satisfy these criteria, then the mean winds might be biased towards larger values. At present this does not see m to be true, but the possibility of such systematic biases must be considered and these rejection criteria must be continually re-examined. Indeed recently MA Y (1987) showed that the previous maximum allowed normalized time delay (criterion (7)), wh ich was 0.2, should be relaxed to 0.4.

One possibility which could produce systematic bias concerns criterion (9). Oue to statistical ftuctuations, it is probable even in the ca se of no natural fading, that the observed fading time will be different from that expected due to beambroadening of the spectrum alone. If the experimental auto-correlation width is decreased by such a statistical ftuctuation, a positive "V~" parameter will result, and the program will proceed as usual. However, if the auto-correlation width is too wide, a negative "V~" results, and the data will be rejected. HOCKING (1986) has shown, using spectral widths, that this statistical variation can be substantial, even when there are no significant ftuctuating velocities of the scatterers, and that the experimental widths can be either greater or less than those due to purely to beam-broadening. By rejecting half of these cases (when the auto-correlation width is too wide), and not the other half, it is possible that systematic biases could be built into the results. The effect would be to produce "true" velocities which were systematically smaller than the real winds. Such systematic errors must

Vol. 130, 1989 Spaced Antenna Method in Midd1e Atmosphere Applications 583

of course be considered, and this will be done in due course. However, before doing this the statistical or random errors which result from the method will be examined.

6. Random Statistical Errors

Although the SA technique has been used for many years, there have been few attempts to estimate the random errors associated with it. The two main approaches have been a "least squares" approach, where the errors are estimated from errors in fitting the observed correlation functions to some idealized function such as a Gaussian (e.g., FEDOR, 1967), and numerical simulations (e.g., AWE, 1964a,b). A difficulty arises in the first method because the errors in adjacent points on the correlation functions are themselves highly correlated (AWE, I 964a), wh ich may cause significant biases in the error estimates. Also, these studies did not give analytic expressions for the errors in the parameters obtained from the correlation functions, and such expressions are essential for error estimation for routine analysis. The correlation of the errors makes a rigorous approach difficult, but MA Y (1988) showed that analytical estimates can be obtained using straightforward arguments when a Gaussian functional form is assumed to describe the shape of the correlation functions. May's analysis actually only applied to a one-dimensional mode, but it is not unreasonable to ass urne that similar results would apply in two dimensions.

Expressions for the errors in determination of the positions of the maxima of the three cross-correlation functions (r'<, r", and r',y) can be obtained assuming that the errors in a single correlation coefficient are given by (AWE, 1964a)

(3)

where T is the record length. The time variation of the errors has a time scale of the order of rO.5 and a functional form for the error in the determination of the positions of the maxima is given by

( 4)

where the numerical constant of 0.5 was found from the numerical simulations (M A Y, 1987). There is also a difficulty in the estimation of the error (Jx in the T." in that the errors in the auto-correlation function and cross-correlation are themselves correlated. rf it is assumed that this reduces the errors by a numerical factor then an cquation 01' the form:

(5)

can be derived, wherc again the numerical factor was found from simulations. The random errors obtained using simulated da ta showed very good agreement with


these expressions over a wide range of parameters. These expressions may be applied to data with significant noise by using the values of correlation before any noise correction is carried out.

These error estimates may be applied to the SA analysis to give estimates of the uncertainty in wind estimates if the expressions for the wind components are written explicitly in terms of the values of ,~, ,~, "9" T" and 'y- MA Y (1988) presented results of an experiment where two simultaneous independent SA experiments were opera ted using the large 2 MHz array at Buckland Park. This experiment enabled comparison of the theoretical errors and observed differences in the wind estimates. It was found that the theoretical expressions were of the correct form, but that the errors were overestimated by a factor of 1.5. This was attributed to the effect of the rejection criteria, as was mentioned in Seetion 4, but a further complication is that in the real experiments the values of, for example, 'x and ,~ mayaiso be correlated. The measured differences had modes at around 10% of the magnitude of the wind, which was around 90--100 ms - I during the observations. Nevertheless, it appears that satisfactory estimates of the random statistical errors in wind measurements may be made using the above theory.

Perhaps a more serious problem is the possible existence of systematic errors. This will now be discussed.

7. Sources of Systematic Error

As mentioned earlier, rejecting cases with negative" VZ" values represents one possible source of systematic error, although to date it does not appear that this is a major problem. There are, however, two other effects which can introduce errors into the FCA. The first of these is the so-called "triangle size effect", and the second effect arises when vertical velocities are considered.

The so-called "triangle size effect" has been reported by several authors, and one of the most careful studies of this effect is that due to GOLLEY and ROSSITER (1970). When the FCA is applied to data recorded on three antennas, it is found that the "true velocity" deduced is a function of the antenna spacing, and an optimum spacing must be chosen before applying the method. Generally the "true velocity" gets larger with increasing antenna spacing, and tends to the real velocity at the larger spacings. This effect has been mostly studied with E-region total reflections, and it is not certain that it occurs for D-region and lower atmospheric studies. Various causes of the effect have been suggested, such as antenna coupling (FEDOR and PL YW ASKI, 1972), and even errors in the assumptions involved with FCA, but no cause has yet been isolated. Aerial coupling does not seem to be the problem. One possibility which may need to be considered is that it is related to the rejection of negative "V~" values discussed earlier~it is possible that the likelihood of negative "V~" values arising due to statistical reasons is less if the aerials are

Vol. 130, 1989 Spaced Antenna Method in Midd1e Atmosphere App1ications 585

more widely spaced, since the peaks in the cross-correlation functions occur at larger lags and so have less relative error.

Another source of systematic error relates to vertical velocities. The signal received on any antenna is the sum of scatterer from a variety of off-vertical angles, each returned with a different Doppler shift. A positive Doppler shift arises from directions looking into the wind, zero from overhead, and a negative shift from directions along the wind. A uniform vertical wind has no effect on the measurement of horizontal velocity, but if there is also a vertical velocity which has a systematic variation across the beam, from positive on one side to negative on the other, say, then this will simulate an apparent horizontal wind. Thus vertical winds which vary across the beam may make a spurious contribution to the "horizontal winds" deduced from the SA method. This possibility was first suggested by ROYRVIK (1982), and preliminary numerical simulations performed by us have indicated that it can indeed occur. Nevertheless, rather special conditions are necessary; for example a gravity wave of an appropriate horizontal scale of 10-20 km wavelength or less must exist over the radar, and it must have a fairly high frequency so that the vertical velocities are large enough to be important. Therefore it seems that this effect will be most important if high frequency wind fluctuations are being studied and will not be important when one or even half-hour averages are used. Nevertheless, it is a possibility which must be considered.

The problems discussed so far represent, in general, possible sources of error for the analysis, either systematic or random. In due course, these effects will be quantified. However, more profound objections have been raised-objections which question the very validity of the technique. It is useful to discuss briefly these more profound objections.

8. Philosophical Objections to the SA Met/rod

As has been seen, tests of the spaced antenna technique in the mesosphere (at MF and HF) and in the troposphere and stratosphere (VHF) have shown it to be reliable. Nevertheless, from time to time objections to the method arise, and it is a useful exercise to consider these objections in more detail. It will be argued that while there may be situations wh ich can, in principle, produce erroneous results, they do not occur commonly in the atmosphere. Furthermore, it will be shown that objections can be raised to almost any method of remote wind measurement, and in all such observations a degree of care and selection is necessary.

BRIGGS (1980) has shown that, for the ca se that all scaUerers in the radar volume move with the same horizontal velocity, and have zero vertical velocity, then the SA method must give identical results to the so-called Doppler method of wind measurement, provided that the measurements are made at the same radio frequency and the same radio wave scatterers are involved. If however, there are


also vertical motions, these will affect the Doppler estimates of the horizontal velocity. Nevertheless, if a vertically pointing radar is also used, these vertical velocities can be measured and their effects can be taken into account with the Doppler method, provided the vertical velocities are the same everywhere in the field of view. Difficulties can arise with Doppler methods if the velocities vary horizontally, because the off-vertical beams probe separated regions of the atmosphere.

The main difference between the SA method and the Doppler method lies in the direction of the radar beams. The SA method uses vertically directed beams, whilst the Doppler method uses beams tilted off-vertical to obtain horizontal wind velocity components (plus a vertical beam to obtain vertical winds). Often, also, the SA method uses beams with wide half-widths, whilst Doppler estimates require very narrow beams. (Nevertheless, the SA method can also be applied with narrow beams such as those used in VHF radar systems.)

Most objections to the SA method are based on the assumption that there are two (or even more) types of scatterers in the radar volume, and that these different types of scatterers move at different velocities. The most common assumption is that there are specular scatterers, aligned approximately horizontally, which scatter primarily from the vertical, together with more isotropic scatterers. Specific mechanisms are then invoked to propose that the specular scatterers may move at different velocities to the isotropic scatterers. It is then claimed that, since the SA method is more susceptible to scatter from the vertical, it will measure a drift speed associated with these specular scatterers. It is most common to invoke gravity waves as the cause of these effects but unfortunately, for middle atmosphere applications, it is never stated exact1y how gravity waves cause these specular reflectors. These points will be closely examined in this article.

Perhaps the most comprehensive discussions of the possible effects of gravity waves on the SA method can be found in HINES and RAO (1968); HINES (1972) and HINES (1976), although other authors (e.g., BROWNLIE et al., 1973) have also made contributions. However, it should be rem em bered that those papers primarily applied to measurements of drifts by totally reflected radio waves from the E and F ionospheric regions. In those cases, total specular reflection was the main means of backscatter. Gravity waves curved the electron density isopleths, producing focusing and defocusing and interference effects and therefore fading of the radio signal at the ground. In the D-region and lower atmosphere, it is not nearly so easy to see that this model is relevant. It is necessary to consider carefully how gravity waves can influence only the specular reflectors, and also to consider the scales at which these effects occur. Two models will be considered, which cover the most likely situations which could conceivably result in errors in the SA method.

Model I: To begin with, let us assume that these specular reftectors form independent of the gravity wave, by some unspecified mechanism, and are then influenced by it. Figure 7a illustrates the situation. Specular reftectors are indicated

Vol. 130, 1989 Spaced Antenna Method in Middle Atmosphere Applications

(0)

Tx2

(b)

--I=t1

.... l=t2

'. -

Tx1

Figure 7

587

Two models of reflectors in the atmosphere. Heavy lines and dots represent actual reflectors, and fine lines and dots represent gravity wave isopleths hut without any scatterers present.

at times t = t 1 and t2 . In this case, it is assumed that the specular reflectors (thick lines and dots) are only separated by short distances, and cover most of the sky at the altitude under examination. In the limit, they may form continuous sheets. A gravity wave oscillation is assumed to tilt the reflectors at these two times. An essential feature of this model is that the specular reflectors are also blown by the mean wind, although they are still subject to gravity wave tilting effects. For diagrammatic purposes the mean wind is taken to be zero in Figures 7a,b, but this is not assumed in the model. Radio waves incident from transmitters TXl and TX2 are "focused" and "defocused", respectively. Therefore as the gravity wave moves across the ground, it produces fading at any single site. An SA experiment may then measure the speed of this gravity wave.

Is such an argument valid? This situation may be applicable for reflection from the ionospheric E or F regions at HF, because the isopleths of electron density are continuous, and reflection is total. However, for MF, HF and VHF scatter from the mesosphere, Figure 7a is not applicable. Rather, the specular reflectors which exist there are much more tempo rally and spatially intermittent (e.g., HARPER and WOODMAN, 1977; HOCKING, 1979; JONES, 1982). The same is often true for VHF tropospheric and stratospheric echoes (e.g., RÖTTGER et al., 1979). A situation like Figure 7b is more likely, in which only a small fraction of a gravity-wave cycle contains the reflectors. It is likely in a real situation that the gravity-wave period is

588 W. K. Hocking et af. PAGEOPH,

much longer than the typical data duration (typically 30-120 s) used to perform an SA measurement, and then the tilting of the reflectors may be too slow to have a measurable effect. Rather "roughness" on the reflector (e.g., RÖTIGER 1980, refers to "diffuse reflection") will produce most of the fading, as the reflector moves with the wind, and the SA method will give the true wind velocity. If there is no such 'roughness' then the signal will fade very slowly, and the data will be rejected due to the 'slow fading' criterion.

The point concerning the scale of the gravity waves is also pertinent to Figure 7a. If the scale of the diffraction pattern produced is similar to that of the gravity wave, then the gravity-wave-induced fading will be very slow and faster fading (which the SA method will utilize) will occur due to motions to the more isotropie irregularities, and to roughness on the surfaces of the reflector. Both the scatterers and the reflectors move with the wind, so that the SA method will measure this true wind speed. One of the few catalogued tropospheric cases observed in which such stratification occurs has been presented by GAGE et al. (1981), and the wave had a period of about 18 minutes. It is unlikely that any effects of the phase velocity of the gravity wave would have shown in any SA measurements of the wind in this case; at worst, the SA technique would have rejected the data because of slow fading.

However, it can occur, particularly when many waves are present and the layer of sheets join up to produce a near continuous layer, that the scales of the diffraction pattern produced by gravity wave reflections can be considerably smaller than the gravity-wave scale ("interference fading": e.g., HINES and RAO, 1968; BROWNLIE et al., 1973), so that fast fading may at times be produced by gravity waves. In such cases, the SA method could produce erroneous results. Nevertheless, for VHF, HF and MF partial reflection work, such gravity-wave-perturbed continuous reflectors seem rare and when they do exist, it can also be difficult to obtain horizontal wind speeds by Doppler methods. Indeed, FELGATE and GOLLEY (1971) never found evidence for interference fading for the case of D-region partial reflection, despite the fact that they found many examples with totally reflected radio waves. This is quite consistent with the observation that scatterers and reflecting layers in the middle atmosphere tend to be intermittent in time and space.

As an extra point, if large amplitude gravity waves occur, they may tilt these specular reflectors quite markedly, in which ca se Doppler radars mayaiso observe the specular reflections and therefore measure Doppler shifts related to the wave speed rather than the wind. This point has been emphasized by RÖTTGER (198Ia). The SA method, with its more stringent acceptance criteria, is more likely to reject such cases. HINES (1968) and RÖTTGER (198Ia) have also pointed out that such large amplitude waves are most likelY to occur in the region of critical level interaction, in wh ich ca se the horizontal phase velocity of the wave equals the component of the mean wind in the direction of phase propagation anyway. Furthermore, if more than one wave is present then the pattern formed by a number

of critical waves propagating in different directions moves with the mean wind (HINES, 1968). But to be fair, the above case is probably rare and in most instances of critical level interaction, both the SA and Doppler methods will measure a wind equal to the sum of the mean wind and the wind due to the gravity wave, which is of course the desired value.

Therefore this attempted criticism of the SA method is not, in reality, applicable, except perhaps in rare circumstances. In such circumstances, these erroneous measurements should stand out from the rest of the data, thereby enabling them to be rejected. Such post hoc rejection procedures are quite common, and are not unique to the SA method. For example, LARSEN et al. (1982) using Doppler recorded winds, rejected so-called 'outliners' which were clearly different from the rest of the wind speeds.

Model II: The second way in which we could imagine gravity waves to inftuence the specular reftectors is that the gravity waves actually are the reftectors. For partial reftection, the refractive index gradient is the important quantity, rather than the absolute refractive index. Any change of refractive index must occur within less than about one quarter of the radar wavelength----<:hanges which occur more slowly with increasing height are very inefficient reftectors (e.g., ATLAS, 1964; HOCKING and VINCENT, 1982). Therefore we need only to look at the case where the gravity wave wavelength is of the order of the radar wavelength. The most likely mechanism is that reftection occurs from the compressional wavefronts of the gravity wave. Both HINES ( 1960) and V ANZANDT and VINCENT ( 1983) have proposed such a model; HINES (1960) has proposed that at 6~ 70 km altitude, gravity waves with vertical wavelengths of a hundred metres or so can explain observed HF and MF specular reftection from this height range, whilst V ANZANDT and VINCENT were particularly interested in VHF stratospheric echoes. The gravity wave must have a wavelength perpendicular to its wavefront equal to one-half of the radar wavelength. Such a process, however, would give strongest scatterer from the off-vertical, as will now be seen; indeed HINES (1960) has also made this point.

As an example, consider wavelengths of 3 m at 10 km altitude. Could such waves exist, and produce the observed VHF specular scatterer? HINES (1960, equation (49)), showed that the smallest vertical wavelength which would not be dissipated by viscosity is

Az(min) = 2n N, (6)

where T is the wave period (sec) and 1] is the kinematic viscosity. Above 10 km, 1] ~ 3 x 10 5 m2s I. For aradar wavelength of 6 m, we require Az ~ 3 m, so T", 100 min in order to achieve such a short wavelength. At 18 km, T '" 40 min. Yet, Az/Ax ~ w/N, where w is the wave (angular) frequency and N is the BruntVäisälä frequency, so this means that all such wavefronts must be tilted at angles of ~ 2°_3° from the horizontal at 10 km altitude, (also see HINES, 1960, Figure 9). At 18 km altitude, the tilt must be ~ 6°. At 65 km, 3 m waves cannot exist even if


T = 5 min, and even 75 m waves (capable of Bragg reflection at 150 m radio wavelength) must have tilts of greater than 10°. This effect of preferred scatterer from off-zenith angles has never been observed, yet if it exists it should be quite obvious. Therefore it seems unlikely that the wavefronts of gravity waves cause specular reflections directly. Further, even if equation (6) is in error and gravity waves can cause specular reflections, the waves must be at least of very long period, in order to have near-horizontal wavefronts. As discussed earlier, long period oscillations do not have a substantial effect on the recorded signal when time durations of less than a minute are considered; the specular signal would just produce a constant offset in the received signal. Thus any fading of the signal during each data collection period would be due to other irregularities blown by the wind, and the SA method would still measure the true wind speed. If there were no such irregularities, the data would again be rejected due to slow fading.

It should also be noted that if the situation did occur in which two different types of scatterers moved at different velocities, and the two types of scatterer contributed approximate1y equal power, and both had ve10cities significantly different from zero, then two peaks would occur in the cross-correlation functions. This would also mean that the data sam pIe would be rejected.

It therefore appears that in most cases, gravity wave phase ve10cities are unlikely to bias SA measurements of wind ve1ocities. As an interesting aside it has been seen that the scale plays an important role in determining the applicability of the method. Using data lengths of aminute with points sampled at steps of a fraction of a second, and spatial separations of a few 100's of metres, allows the wind vectors to be determined. Yet if the same method is applied using receiving sites spaced say 10's of kms apart, and the records used are, for example, 30 min time series comprising half-minute means of power, then gravity wave phase ve10cities could indeed be measured. This is not a paradox, but simply a question of scale.

This completes the discussion of measurements of wind speeds with the SA method. It has been seen that the method has good re1iability, although there are some subtleties which still need investigation.

9. Other Parameters

With FCA it is possible to determine not only the wind speed but also other parameters of the correlation ellipse. In the past, however, some of these parameters have been difficult to interpret physically. STUBBS (1977) presented details of the seasonal and diurnal variations of the pattern scale, pattern elongation and orientation, and the so-called "characteristic velocity" Ve , but offered no real interpretation of the physical meaning of these parameters. More recently, some of these parameters have been better interpreted, particularly the "characteristic time"


'c of the signal, and the pattern scale. The "characteristic time" is the fading time wh ich would be measured by an observer moving over the ground with the mean diffraction pattern velocity and is directly related to Vc• As such, it is the fading time of the natural fading, with the spectral beam-broadening effects removed.

9.1 Fading Times

Several interpretations of the characteristic time 'c (or equivalently the characteristic velocity, VJ have appeared in the literature. WRIGHT and PITTEWAY (1978) suggested that if all the natural fading was due to random horizontal motions of the scatterers, then V, equals the horizontal root-mean-square velocity of these fluctuating velocities. On the other hand, several authors have assumed that the "natural fading" was largely due to the vertical components of isotropic turbulent motions, in which ca se the characteristic time of the signal could be used to make an estimate of the energy dissipation rate for the turbulence (e.g., MANSON et al., 1981). It is then possible to estimate the RMS vertical velocity of the scatterers as VRMS =

(A/4n) . ~/'c (assuming that complex data are recorded), and then the turbulent energy dissipation rate can be deduced as E = 0.4 V~MS . N, where N is the Brunt-Väisälä frequency of the atmosphere (WEINSTOCK, 1981).

Recent observations suggest that, if narrow beams are used, and all the scatterer is indeed due to turbulence, and sampling lengths of less than 1-2 minutes are used, then this latter procedure is valid, and in this ca se the natural fading is due to the effects of vertical fluctuating motions (HOCKING, 1983b). The horizontal velocities still vary spatially and in time, but the radial components of these velocities are relatively small. However, this procedure is NOT valid if relatively wide beams are used, since in this ca se variations in the horizontal wind can be substantial, particularly from regions at large zenith angles. Both wind shears and horizontal variations over the beam width contribute to this effect. Estimates of "turbulent energy dissipation rates" made with such wide-beamed radars will most certainly be overestimates. For example, HOCKING (1983a,b) has shown that within a volume of the mesosphere with a depth of about 4 km and a horizontal extent of about 20 km, horizontal fluctuating motions with a value for VRMS of about 20-40 ms -I can occur, so to reduce the RMS radial velocity to less than say 2 ms- I (and to less than the typical vertical RMS velocity) requires half power beam half widths of less than 2°_3°. Thus, although in principle the possibility exists of deducing turbulence intensities from FCA measurements, this should ONL Y be done when be am widths of less than say 2-3 0 are used, and if wider beams are used, extreme caution must be exercised. Furthermore, it must also be ascertained that the scatterer is indeed due to turbulence, and not some other process. For example at VHF, stratospheric echoes are often quasi-specular in nature, and at MF and HF echoes from below ~ 80 km are also often specular. In these cases, it makes no sense to convert RMS velocities to E.

592 W. K. Hocking et af. PAGEOPH,

9.2 Pattern Scale

The spatial correlation function of the diffraction pattern over the ground is the Fourier trans form of the combined polar diagrams of the transmitter array, the receiving array, and the backscatter polar diagram of the scatterers (BRIGGS and VINCENT, 1973; HOCKING, 1987). If the polar diagrams of the transmitter and receiving arrays are known, the pattern scale can be used to estimate the backscatter polar diagram of the scatterers (BRIGGS and VINCENT, 1973). That is, if the effective combined polar diagram of the transmitter, scatterer and receiver is of the form exp( - sin2 e /sin2 ee) then the complex spatial auto-correlation over the ground falls to 0.5 in magnitude at a lag of ~05 ~ 12.0/ee , where ee is in degrees and ~O.5 is in wavelengths. This relation is not exact, but represents a very accurate approximation, as can be seen by comparing it to the more accurate but more complicated function derived by BRIGGS and VINCENT (1973).

It has recently been shown by HOCKING (1987) that such estimates of the backscatter polar diagrams of the scatterers can in turn be used to estimate the mean width-to-depth ratio (L/h, say) of the scatterers. This ratio will be called the aspect ratio. This is to say, if the scatterers have apolar diagram of the form exp( - sin2 e /sin2 eJ, then es can be found from the pattern scale. Then e., is related to the aspect ratio of the scatterers, although this relationship also depends on h. Fortunately the radar is rather selective as to which values of h are important

Figure 8 Aspect ratio of scatterers, L Ih, as a function of 8" for half-depth h = .15,1. (upper curve), .195,1., .25A, and

.32,1., where ,1. is the radar wavelength, and L is a half-measure of the half-width of the scatterers.


in producing backscatter, and only a relatively small range of values of h are important. Figure 8 shows the relation between Os and L/h for several values of h within the range of the most important values of h. The curves are fairly similar, so given any value of Os it is a simple matter to read off a range of values of L/h within which the true value lies. The details of these graphs were derived by HOCKING ( 1987).

Thus the pattern scale is useful in that it gives information about the shape of the scatterers; and of course the orientation and axial ratio give information about the orientation and shape of the scatterers in the horizontal plane.

10. "Interferometer" Applications

Recently it has been possible to record the phase of the radio wave field with radio antennas, such aradar being described as "coherent". Using such measurements it is then possible to turn the antenna arrangement used for FCA to even better use, by using the antennas as "interferometers". Spaced antennas have been used in radio astronomy for many years, and in that context the term "interferometer" usually refers to a pair (or more) of antennas with a spacing of many wavelengths, to form a "fringe pattern" polar diagram. In the following discussions, the three spaced antennas will be considered as an "interferometer", although their spacing is only of the order of a few wavelengths, and so they do not form an interferometer in the strict sense. Nevertheless, the terminology will be maintained, and the following sections will discuss the use of the spaced antenna aerials as a direction finding tool. It should be noted that these later applications are not particularly tied to the preceding discussions about the FCA technique, and can be considered independently.

10.1 Comp/ex Analysis and "Interferometer" Applications

Using a coherent spaced antenna radar and computing the complex correlation functions from the in-phase and quadrature components of the signals has several advantages with respect to the traditional application of spaced antenna systems which uses only the amplitude correlation function. In a coherent radar, phases and amplitudes can be measured, since the receiver is phase-locked to the transmitter, whereas for measuring the amplitude only, the system need not necessarily be phase-locked, and sometimes a square-law detector instead of a quadrature detector is used. Recording the amplitude fading alone is sufficient for the correlation as weIl as the full correlation analysis. However, processing of the complex time series substantially reduces (or, for coherent integration over sufficient points, virtually eliminates) the uncorrelated noise, and so improves the effective signal-to-noise ratio. This consequently improves the reliability of the wind velocity estimates as seen in Figure 9.

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PAGEOPH,

. i

b

i

30

Scatterer plot of wind speed u deduced from a single data set, but using the amplitude, (square root of power) (a), and the complex amplitude (b) correlation analysis. It appears that more data points were selectable in (b) than in (a) after the same selection criteria were applied (from RÖTIGER and

CZECHOWSKY, 1980).

Furthermore, the availability of the phase variation as a function of time allows computation of the radial velocity, and the availability of the phase differences of the signals measured at the three receiving antennas allows determination of the angles of arrival of the signals returned from the scatterers. The combination of both these measurements yields the most correct measurement of the real vertical velocity, as described in the following section. Further advantages of recording phases and amplitudes are the application of post·recording beam steering (phasing of the antenna system through transformation of the digital data records) which can be used to deduce winds from the Doppler spectra, measure gravity wave parameters (RÖITGER and IERKIC, 1985), and deduce the anisotropy of the scatteringj reflecting medium aloft. It is also possible to track turbulence patches moving

Vol. 130. 1989 Spaced Antenna Method in Midd1e Atmosphere App1ications 595

through the radar beam and determine their vertical and horizontal velocities. One can even apply Doppler sorting of individual scatterers, locate their position and track their motion, growth and decay. Of course there are limitations, and the method cannot be applied if for ex am pie scatter is due to a random ensemble of many scatterers, but if there are only a few dominant long-lasting scatterers within the beam then the method is indeed valid. Whether or not this is the case can be determined by examining the individual scatterers for persistence; if the "scatterers" appear to jump randomly in position and radial velocity, then it can be concluded that they are not real, but if the motion of the "scatterer" can be followed then it can be taken to be real. By tracking many of the scatterers it is possible to deduce the three-dimensional average velocity, which should be equal to the mean wind velocity if the turbulent scatterers are "frozen in" the background wind pattern. This technique is known as radar interferometry (RÖTTGER and IERKIC, 1985) or as imaging Doppler interferometry (ADAMS et al., 1985). It thus appears that the spaced antenna arrangement offers the possibility of measuring several interesting parameters rather than measuring just the wind velocity.

10.2 Radar "InterJerometry"

Neither the Doppler nor the spaced antenna drift method separately evaluate the spatial distribution of the phases of the field pattern at the ground. With the spaced antenna arrangement the amplitudes and the phases can be measured. Combining the complex signals from different antennas with appropriate phase shifts will be considered here as the application of the interferometer technique in the widest sense. In the first spaced antenna measurements of the troposphere with VHF radars, RÖTTGER and VINCENT (1978) and VINCENT and RÖTTGER (1980) applied this method to measure the angular spectrum of the radar returns. It can be expected that further valuable additional information about structure shapes and motions as weil as atmospheric waves can be obtained with this technique.

The first essential point wh ich has to be stressed is the improvement of the vertical velocity measurements by using spaced antennas to determine more accurately the location of an individual scatterer. The basic principle of the technique is sketched for a 2 antenna set-up in Figure 10. Let us assume a diffuse reflector (dashed ellipse) wh ich is sufficiently far from the radar antenna and whose effective reflector surface is slightly tilted to the horizontal by an angle 15. This structure moves with a velocity given by the horizontal component u and the vertical component w. Aradar with a vertically pointing beam, but with a beam width larger than 15, measures a radial velocity

v' = W cos 15 - u sin 15.

Thus, even if the horizontal velocity u is known, the real vertical velocity is still unknown, since 15 is unknown (RÖTTGER, 1981).

-"""':;::--1-- U

............ d ................................

...... ...... ...... ...... ...... ......

Figure 10 Schematic of an off-vertically positioned scatterer/reftector, indicated by the dashed ellipse, causing a phase difference of signals received at 2 antennas Aland A 2 • When the scatterer moves horizontally, the phase changes from 4>a to 4>b, where 4>a = 2nda/A.o and 4>b = 2ndb/A.o, and from the rate of phase change the horizontal velocity u can be determined. Measuring simultaneously the radial velocity v yields the real

vertical velocity w when the phase variation crosses zero (from RÖTIGER and IERKIC, 1985).

The reflected signal can also be received at two separate antennas Al and A2 ,

and the complex cross-correlation function then computed. The full corre\ation analysis of signals received at three antennas yields the horizontal velocity u as described in Section 2 of this paper. The phase derivative d<jJ /dt of the phase of the auto-correlation functions near zero temporal lag yields the radial velocity:

where Ao is the radar wavelength.

, Ao d<jJ v =- '-(0)

4n dt


The tiIt angle ()' which is equal to the incidence angle (), is given by the phase of the cross-correlation function in radians at zero temporal lag:

This yields the corrected, i.e., the real vertical velocity

w = (v' + u sin {»/cos ().

For a typical ratio of u/w = 100, and () = 0.6°, the vertical velocity estimate would be incorrect by a factor of 2 (0.5) if this correction were not applied. The angle ()' is also equal to the inclination of the reflecting structures. Its average can give an estimate of the inclination of isentropic surfaces (baroclinicity), which is of interest for meteorologie al applications (GAGE, 1983).

The uncertainty in the measurement of the phase of the cross-correlation function at zero lag, a", (in degrees) can be found using simulated data, formed in a manner similar to that described in MA Y (1988). The resuIts of the simulations for various values of cross-correlation at zero lag, (PxiO», fading times, «0,5), and ratios of the signal power to the noise power, (S/N) are shown in Figure 11. A crude approximation to these curves is given by the purely empirical formula:

a~ ~ fo· [50(1 - p;iO»F + 65N/S

where T is the record length in lags. Note that the only value of T used has been 256 points. Clearly there are significant errors for low values of cross-correlation and poor signal-to-noise ratio, although this is somewhat mitigated by the value of A/2nd12 which is usually quite small for VHF radars.

A pair of spaced antennas can be regarded as a rudimentary phased array. The effective pointing direction can be altered by changing the phases of the signals. For reception, the signals from the antenna modules are added with appropriate phase delays, whilst for transmission the phases of the signals distributed to the modules are given appropriate phase delays. These phase lags can be introduced either instrumentally at the recording stage, or aIternatively (for reception, anyway) during post-recording analysis. An instrumental delay can be created by including analogue delay lines between the antennas and the receivers. In this case (preselected beam direction), the signals from both antennas would be added in an analogue coupler. In the second case (post-selected beam direction), the digital sampies would simply be added as vectors during data processing. This procedure is equivalent to electrically swinging the beam to different angles. When separate transmission and receiving antennas are used, it is possible to utilise both methods. The transmitter anten na beam can be kept fixed and the receiving antenna beam can be swung by post-selecting as long as the tilt angle of the effective receiving beam is less than the beam half-width of the transmitter antenna. The advantage of this latter method is that the post-selection of any angle is possible, whereas the former


PHASE ERRORS FOR VARIOUS CROSS-CORRELATION FUNCTIONS

S/N= 00 p=07 100 80

60

40 • • • p=0.3 ••

20 •• • •••••• S/N=-4dB

• • • • • • p=0.5 •• 0'", • •••••• S/N= 0 dB

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4 • • • •• ·P=0.9

• • 2

1 0 2 4 6 8 10 0 2 4 6 8 10

T o .• (tags) T o .• (Iags)

Figure ll Plots of the standard deviation of the phase of the cross-correlation function at zero lag, as a function of the fading time !O.5' for various values Px/O), and various signal to noise ratios. Note that !O.5 is scaled in units of lags. For the plots with poor signal to noise, the population value of the cross-corre-

lation function at zero lag was 0.7.

method preselects an angle wh ich cannot be changed after the data are taken. Naturally, however, if one swings the receiver beam significantly outside the main transmitter beam a significant reduction in received power results. The range of available effective pointing angles is restricted by the width of the main transmitting beam. Of course, the method can be easily extended from this one-dimensional example to a two-dimensional application, and even to multiple arrays of more than two antenna modules.

This kind of radar interferometer method allows not only measurement of the horizontal wind components by the Doppler method, but also the tilt, the aspect sensitivity and the horizontal phase velocity and wavelength of atmospheric waves. Another potential application of post-selected beam steering is determination of momentum fluxes in the atmosphere. If u' represents the horizontal fluctuating velocity, and w' the vertical fluctuation velocity, then the vertical flux of zonal momentum is given by u'w', and this can be determined either by separately

calculating u' and w' and then finding u'w', or by applying a coplanar dual beam experiment to measure u'w' directly. The former method was applied by RÖTIGER (1980), who calculated u' with the FCA technique, and w' from the phase derivative with respect to time of the recorded signal. The second method was pioneered (at least for upper atmospheric applications) by VINCENT and REID (1983), who used two symmetrical fixed beam directions at zenith ± <5 angles with an HF radar to study mesospheric dynamics. They showed that this generally allows measurement of the cross-correlation or covariance (u'w') of the fluctuations w' and u'.

where V'2(<5) and V'2( -<5) are the mean square velocities measured with the beams pointing at zenith angles +<5 and -<5, respectively.

Originally, VINCENT and REID (1983) used two fixed transmitter/receiver antenna beams. It is also possible to apply the method of post-selecting the effective receiver beam directions, with the limitation that once again the effective receiving beam cannot be steered to angles outside the transmitting beam. This is illustrated by one measured example shown in Figure 12. Here the beam of the spaced receiving antennas of the SOUSY-VHF-Radar was "steered" to ± 1.2° by digitally inserting a phase delay to the recorded data. This allowed observation at two different phase locations of a wave in the stratosphere, which becomes clear due to the phase shift between the two time series of the displayed radial velocity. From these measurements, either by using post- or preselected be am directions, the horizontal wavelength and phase velocity, the momentum flux and the me an horizontal and vertical velocities can be deduced. The full three-dimensional information has to be obtained by post-steering the antenna in two orthogonal vertical planes. The vertical wave-Iength and phase velocity can be found from just one, preferably vertical, beam direction. There are also influences on spectral width and received power due to gravity waves, which were analyzed by GAGE et al. (1981).

Another application, originally used by PFISTER (1971) and BROWNLIE et al. (1973) for studies of E-region total reflections, and later by FARLEY et al. (1981) to study ionospheric plasma turbulence, was recently applied to MST radars by RÖTTGER and IERKIC (1985) to trace discrete structures, such as blobs of turbulence moving through the antenna beam. By making use of a cross-spectrum analysis, the echoes from reflectors/scatterers with different velocities can be distinguished (frequency-selective interferometer). By observing the change of<5 and v' as a function of time, as shown in Figure 10, not only the location of the blobs but also their vertical and horizontal velocities can be measured more accurately. Once again, however, care must be taken to ensure that the blobs are real by ensuring that they persist over a reasonable length of time. The interferometer technique was also recently applied to the MF spaced antenna radar in Saskatoon to follow scatterers passing through the beam, but it was concluded that the traditional

600

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Figure 12

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I 0600 U TC

Radial (vertical) velocity due to gravity waves observed with the digital post-beam steering method (from RÖTTGER and IERKIC, 1985).

spaced-antenna analysis is physically and practically more appropriate for this kind of mesospheric investigation (MEEK and MANSON, 1987).

The measurements of c5 and its temporal variations are very useful to avoid erroneous interpretations of measurements of the radial velo ci ti es, as has already been discussed. If a scatterer exists at a slightly off-vertical angle, and its radial velocity is determined, then any horizontal component of the velocity may make a large contribution to the measured radial velocity. Standard Doppler techniques do not allow for such factors, whereas use of the interferometer methods allows a better measure of the real vertical velocity. All these techniques, which involve evaluating the temporal as well as the spatial variations of amplitude and phase of the field pattern, can be described as "MST radar interferometry". Their applicability to these radars has already been tested, but more refinement is needed to fully exploit this promising technique.

Recently observations with the Chung-Li VHF radar in Taiwan (CHAO et al., 1986) have been performed in the frequency-selective interferometer mode. These preliminary measurements indicate that spectral components with negative frequeneies are generally seen on one side of the zenith, whereas positive frequency

Vol. 130, 1989 Spaced Antenna Method in Midd1e Atmosphere Applieations 601

components occurred on the opposite side of the zenith. This indicates that the spectral width is broadened by horizontal wind components, as was computed in detail by HOCKING (1983a). These interferometer observations will be more extensively described elsewhere.

By measuring the incidence angle as a function of Doppler frequency with this frequency-selective interferometer mode, the horizontal as weil as the vertical wind component can be deduced (e.g., RÖTTGER, 1984; ADAMS et al., 1985). This principle is the same as the Doppler beam swinging technique with off-zenith beams. However, it makes use of the fact that echoes are incident from many off-zenith directions in a vertically pointing, finite width narrow beam, and these can be evaluated with the Doppler sorting interferometry to yield the three-dimensional velocity vector. One interesting potential application of this technique is to test the proposal due to BRIGGS (1980) that the spaced antenna technique and Doppler techniques are in principal the same, provided that the same types of scatterers are involved in each measurement.

11. Conclusions

Experimental tests have shown that the Full Correlation Analysis (FCA) method using spaced receiving antennas produces reliable estimates of horizontal wind speeds in the middle atmosphere and troposphere. The errors in using FCA, (both systematic and random) have been discussed and quantitatively stated where possible. It appears that the error in an individual wind measurement is of the order of 10-15%. The interpretation of other parameters deduced in FCA have been discussed, and it has been shown how these parameters can be used to determine the shape of the radio wave scatterers, including their depth-to-length ratio (e.g. Figure 8). The possibility of using the natural fading time to deduce turbulent energy dissipation rates has been discussed, but it has been concluded that this should only be done with narrow beam radars. Finally, new applications of the spaced antenna arrangement, including direction-finding applications, have been summarized.

Acknowledgements

The helpful comments of Dr. B. H. Briggs are gratefully acknowledged.

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CRAIG, R. L., ROPER, R. G., AVERY, S., BALSLEY, B. B., FRASER, G. J., SMITH, M. J., CLARK, R. R., KATO, S., TSUDA, T. EBEL, A. (1985), Mean winds 0/ the upper middle atmosphere (60--'110 km): A global distribution /rom radar systems (M. F., Meteor, VHF), Handbook for MAP 16, (eds. K. Labitzke, J. J. Barnett and B. Edwards), 239-253 (pub!. by SCOSTEP Seeretariat, Univ. of Illinois, Urbana, I11.).

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MA Y, P. T. (1988), Statistical errors in the determination 0/ wind veloeities by the spaced antenna techniques, J. Atmos. Terr. Phys. 50, 21-32.

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MEEK, C. E., and MANSON, A. H. (1987), Medium /requency interferometry at Saskatoon, Canada, Physica1 Scripta 35, 917-921.

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Full-Correlation Analysis of Turbulent Scattering Layers In the Mesosphere Observed by the MV Radar

MAMORU YAMAMOTO,I TORU SATO,I TOSHITAKA TSUOA,I SHOICHIRO FUKA01

and SUSUMU KAT0 1

Abstract-We have applied a full-correlation analysis technique to the echo power fluctuations observed by the MU radar (35"N, 136"E), and analyzed the horizontal structure of the scattering pattern in the mesosphere as well as their horizontal motions. The ve10city of the scattering pattern did not agree with the background wind velocity, but was associated with the horizontal propagating direction of a saturated inertia gravity wave identified in the wind field. The length of the long axis of the characteristic ellipse of the scattering pattern was approximately 50 km, and the direction was almost perpendicular to the propagating direction of the wave. The correlation time of the scattering pattern was approximately 700 s, wh ich is much longer than the lifetime of the isolated turbulence itself. This implies that the observed scattering pattern is associated with a region where the saturated inertia gravity wave generates turbulence.

Key words: MU radar, mesosphere, turbulence, scattering layer, full-correlation analysis technique, gravity wave, wave breaking.

I. Introduction

Theoretical works have revealed that the gravity wave breaking in the mesosphere produces instabilities, and the me an wind is accelerated by the momentum deposition of the gravity wave (LINOZEN, 1981; HOLTON 1982). The acceleration of the mean wind has been observed using a partial reftection radar by calculating the

convergence of the momentum ftux due to the gravity waves (VINCENT and REIo, 1983; FRITTS and VINCENT, 1987). On the other hand, MST radars detect returns from turbulence which is expected to be genera ted by dissipating gravity waves in the mesosphere. Echo power observed by the MST radars is a good measure of intensity of turbulence, and can be utilized to obtain refractivity turbulence structure constant C;, in the atmosphere (V ANZANOT et al., 1978). Evidence of the relationship between turbulence layers and gravity waves was shown by Y AMAMOTO et al. (1988), where they observed that turbulence scattering layers in the mesosphere appear around the altitudes where gravity waves are most unstable.

I Radio Atmospheric Seien ce Center, Kyoto University, Uji, Kyoto 611, Japan.

606 M. Yamamoto et al. PAGEOPH,

Horizontal motions of echo power bursts in the mesosphere were observed by KLOSTERMEYER and RÜSTER (1984) and RÜSTER and KLOSTERMEYER (1987) by calculating the cross-correlation functions between echo power bursts observed in beams pointing in the different directions, although they did not consider the random changes of the scattering pattern in time. RÜSTER and KLOSTERMEYER (1987) have shown that motions of the echo power bursts agree with the background wind on average. Full-correlation analysis is a technique to observe the structure and motion of horizontal patterns by taking the spatial correlation into account (BRIGGS, 1984). This technique is utilized with both MF partial reflection and VHF radar observations in order to obtain horizontal wind velocities from the fading patterns detected by three spatially separated receivers.

The MV radar (35°N, 136°E), which has been operated since 1983, is a monostatic pulse Doppler radar with a carrier frequency of 46.5 MHz (KATO et al., 1984; FUKAO et al., 1985a,b). The advantage of the MV radar over conventional MST radars is that the MV radar can steer its beam every Inter-Pulse-Period so that it can observe several areas which are spatially separated from each other almost simultaneously. This capability enables us to investigate small-scale structure in the turbulence and wind fields.

A saturated gravity wave has been found by Y AMAMOTO et al. (1987) in the mesosphere by the MV radar observations on February 8, 1985. The gravity wave produced a region with negative Richardson number and with large fluctuations in radial wind velocities, which implied that the wave dissipated its energy through shear or convective instabilities. In this paper, we apply the full-correlation analysis to this saturated gravity wave in order to observe horizontal structures of the scattering layers, and investigate the generation of turbulence by the saturated gravity wave.

2. Full-correlation Analysis

Observations of the mesosphere were carried out on February 8, 1985 using the parameters shown in Table 1. Vsing a least squares fitting method, we determined echo power, radial wind velocity and spectral width from the power spectrum of radar returns. The height and time resolution of the observations were 300 m and two minutes, respectively. As shown in Figure 1, we used four beams, pointing northward, eastward, southward and westward with a zenith angle of 10°. Thus we could observe the echo power at four spatially separated positions.

Figure 1 schematically shows the horizontal pattern of the echo power that moves with velocity V. We assurne that the pattern f(x, y, t) of echo power is a function of position (x, y) and time t, where x and y-axes correspond to the

Vol. 130, 1989 A Full-Correlation Analysis Technique

Table I

Observation parameters 0/ the MV radar.

Observation period

Observation range Number of beams Beam direction (11: Zenith angle)

Range resolution Time resolution Inter pulse period Pulse compression Coherent integration Incoherent integration

February 8, 1985

60-98.1 km 4

Northward (11 = \00) Eastward (11 = \00)

Southward (11 = \00) Westward (11 = \00)

300m 120 s 730 JlS

16 bit complementary 30 times 10 times

607

eastward and northward directions, respectively. The spatial and time scales of the horizontal pattern is described by the three dimensional correlation function

( J' ) _ <f(x, y, ()f(x + ~, y + 1], ( + r) > p ;" 1], r - < {fex, y, t) P> ' (I)

where <> denotes an average, r is the time lag and ~ and 1] are spatiallags along the x and y-axes, respectively. The correlation function can be approximated by a family of concentric ellipsoids with the center at the origin (BRIGGS, 1984). We therefore write

(2)

where A, B, C, F, G and H are constants. Here, we assume that the correlation function is described by an exponential function as follows

p(~, 1], r) = exp{ _(A~2 + B1]2 + Cr 2 + 2F~1] + 2G1]r + 2H~1])}. (3)

Because we observe echo power in the four beams, the cross-correlation functions between echo power observed in different beams can be described by p(~, 1], r); e.g., the cross-correlation function between the echo power observed in the northward beam (0, 1]0) and the eastward beam (~o, 0) corresponds to p(~o, -1]0' r). In order to determine the parameters of Eq. (3), we have utilized a least squares fitting technique to the cross-correlation function between the echo power in the four beams. An example of the cross-correlation functions is shown in Figure 2, which corresponds to the scattering pattern observed in 10-16 LT at 71.4 km. In this figure, we chose three cross-correlation functions of the echo power observed in the beams pointing eastward, southward and westward, although we used the

608 M. Yamamoto er a/. PAGEOPH,

orth

MU RADAR

Figure 1 Beam assignment used in the MV radar observations on February 8, 1985 together with a schematic diagram of the scattering pattern which moves horizontally with velocity V, where x and y-axes

correspond to the eastward and northward directions, respectively.

HEIGHT ; 71.4(km) (CI) (d)

1 Ig 0 ..... -I -20 -10 0 10 20 0 10 20

(b) TIME LAG (min) z 1 0

~ 0 w ... ac er 0 U _I

-20 -10 0 10 20 (c)

1

0 .. -1 -20 -10 0 10 20

TIME lAG (min)

Figure 2 Cross-correlation functions between echo power observed in 10-16 LT at 71.4 km. The panels (a), (b) and (c) correspond to the cross-correlation functions obtained between the southward and eastward, the southward and westward and the westward and eastward beams, respectively. The echo power in the eastward beam lags behind that in the southward beam, the westward behind the southward, and the eastward behind the westward. The panel (d) shows the autocorrelation function averaged over all beams. The solid line in each panel corresponds to p(l;, 1), ,) obtained by using the least squares fitting method.

Vol. 130, 1989 A Full-Correlation Analysis Technique 609

cross-correlation functions with all the combinations of the four beams in the determination of the parameters. The auto-correlation function used is an average of those calculated in the four beams. The solid curves in Figure 2 show the result of the fitting. We cannot apply the fit to the negative correlation coefficients because of Eq. (3), but the fitted curves are close to the observed values for positive correlation coefficients.

When we obtain the parameters, the horizontal velocity of the scattering echo pattern is calculated as a 'tiIt' of one axis of the ellipsoids relative to the ,-axis. The x and y components of V are V< and Vv, respectively, and are given by

AV< + HVv =-F

HV, +BVv =-G ( 4)

(BRIGGS, 1984). The motion of the scattering pattern shown in Figure 2 has been estimated to be V< = 9.6 ms - land Vy = 27.5 ms - I. In order to find a spatial scale for the scattering pattern, the particular ellipse for which p = 0.5 may be defined as the 'characteristic ellipse', which is described by

(5)

where '0.5 is a time lag at wh ich the autocorrelation function is equal to 0.5, i.e., p(O, 0, '05) = 0.5 (BRIGGS, 1984).

3. Results

Figure 3 shows a time-height distribution of the scattering layer observed on February 8, 1985 (after Y AMAMOTO et al., 1987). Within the scattering layers, we find an intense and thick scattering region during 12-16 L T at 69-73 km, which

8-FEB-1985 80~---r----.----.~--~----.----'

65L---~----~--~----~--~--~

S/N (dB)

-J ~ -6 1000 1200 1400 1600

TIME (LT) Figure 3

Time-height sections of the signal-to-noise ratio observed in the southward beam on February 8, 1985 (after Y AMAMOTO et al., 1987).

610 M. Yamamoto el al. PAGEOPH,

consists of many iso la ted patchy structures. We have tried the full-correlation analysis for the data observed during 10-16 L T at 69-73 km, and the fitting was successful at 69.4-71.7 km. Figure 4 shows the motion ofthe scattering pattern. All of the da ta are distributed in the region with positive V. and Vv' and show that the fluctuation patterns in this altitude range move toward the north-northeast. The average of the horizontal velocities, which is shown by an arrow, is V. = 9.5 ms- I

and Vv = 24.2 ms-I.

The characteristic ellipses of the scattering pattern are shown in Figure 5. The size and the direction of these ellipses are similar to each other. The long axes of the ellipses lie in the east-west direction, wh ich is almost perpendicular to V. The length of the long and short axes of the characteristic ellipse, which show the spatial scale of the scattering pattern, are approximately 50 and 20 km, respectively. Because the three-dimensional correlation function for the scattering patterns is obtained, we can calculate the correlation time along the horizontal motion of the pattern. As shown in Figure 6, they are approximate\y 700 s at all altitudes.

As shown by Y AMAMOTO et al. (1987), we could recognize a clear monochromatic wave-like structure in the wind profile. The vertical wavelength was approximately 5.6 km. Figure 7 shows a hodograph of the wind vector in 1230-1330 LT at 68.8-76.5 km (after Y AMAMOTO et al., 1987), which is obtained after subtracting the vertical linear trend of the profile. The tip of the wind vector moves clockwise with increasing height throughout the whole altitude range. The elliptic motion of the wind vector implies that the wave is an inertia gravity wave, and its energy propagates upward. The intrinsic period of the wave is estimated to be 8 hr from the ratio between long and short axes of the elliptic motion in the hodograph. Y AMAMOTO et al. (1987) has inferred that the inertia gravity wave propagates

-+-' c: Q) c: o Cl. 20 E.--.. o~ () 'CI)

-oE o t-----+---~

~'-" 1 -20 t o z -40~~~~~~~

-40 -20 o 20 40 Eastward component

(ms-1)

Figure 4 Horizontal motion of the scattering pattern observed in 1G-16 LT in the altitude region of 69-72 km. A square symbol denotes the tip of the velocity vector obtained by using the full-correlation method at each

altitude. An arrow shows the averaged velocity vector.

Vol. 130, 1989 A Full-Correlation Analysis Technique

"E 0 t----~--t--""""'""~-__f o ~

=2 -20 o z - 40 L-J.----L----L....-L---L-...L--.L...-J

-40 -20 0 20 40 Eastward lag (km)

Figure 5

611

The characteristic ellipse of the scattering pattern observed in 10-16 LT in the altitude region of 69-72 km.

horizontally toward the north along the long axis of the ellipse. The horizontal wavelength of the gravity wave is approximately 600 km, and the horizontal phase velocity of the wave is 20 ms -I toward the north. Also, they have ca1culated the Richardson number modified by the gravity wave, and found that the minimum Richardson number was slightly negative. This means that the gravity wave was saturated and the wave breaking set in.

72 .......... 1"""T"""1,....,11"""T"""1,...."....,,....,

• E71 -

• • • • •

-~ '-/

+-' .c C\

'ij) I 70 I- -

• 69 L..L-~ ..... I .................... '-'

o 500 1000 Correlation time (sec)

Figure 6 The correlation time of the scattering pattern along the horizontal motion observed in 10-16 LT in the

altitude region of 69-72 km.

612

I CIl

E 20 ........ .... c: ~ c: o a.

M. Yamamoto et al.

8-FEB-1985 12:30-13:30

E 0 r------t------1+-++---~ o u 'E o ~

=2 -20 o z

-20 0 20 Eastward Component (ms-1)

Figure 7

PAGEOPH,

A polar plot of the wind velocity averaged over 1230-1330 LT on February 8, 1985. The verticallinear trend of the wind velocity is subtracted. The open and solid triangles indicate the lowest (68.8 km) and highest altitudes (76.5 km), respectively. Circular symbols are plotted at 70, 72, 74 and 76 km (after

Y AMAMOTO et al., 1987).

Figure 8 shows a velocity profile averaged over 10-16 LT. The wind velocities still consist of the gravity wave component. We have calculated the vertical trend of the wind profile, which is more representative of the background wind than the wind profile itself. The zonal component of the vertical trend shows eastward velocity at all height range. The meridional component, on the other hand, changes

80 80

78 78

76 76 "'" E 674 74 ..... .r:

'~72 72 I

70 70

68 68

66 66~~~~~~~

-50 0 50 -50 0 50 Velocity (ms-1) Velocity (ms-1)

Figure 8 The wind profile averaged over 10-16 LT on February 8, 1985. Left and right panels correspond to the northward and eastward components, respectively. Dashed lines show the vertical linear trend of the

wind profile.

Vol. 130, 1989 A Full-Correlation Analysis Technique 613

its sign around 74 km, At the altitude of 70 km, the eastward and northward components of the vertical linear trend are 20 and - 17 ms -1, respectively, which

means the background wind toward the southeast. This direction is not consistent with (V" VJ shown in Figure 4. The horizontal phase velocity of the gravity wave is 20 ms ···1 northward, which is similar to the averaged V,. = 24.2 ms - 1. The

direction of the motion of the scattering pattern is better associated with the horizontal propagation direction of the gravity wave than of the background wind velocity.

4. Discussions

The contribution of the atmospheric turbulence to the spectral width (J measured

by aradar is given by the integration of the three-dimensional kinetic energy spectrum of turbulence from ko to k h where ko is the wavenumber associated with the largest vortex in the turbulence, and k; is the radar Bragg wavenumber, respectively (SATO and WOODMAN, 1982). If k; is within the inertial subrange, it is given by

( 6)

where iJ. is the Kolmogoroff's constant of about 1.6, and G is the energy dissipation rate per unit mass and time. The MV radar observes turbulence with the 3-m scale,

which is slightly less than the minimum scale of turbulence in the inertial subrange (e.g., GAGE and BALSLEY, 1980). In this case, the integral in this equation must be modified to include the viscous dumping of the spectra. However, since k; ~ ko,

this modification does not affect the result of the integration, so that G can be written as

(7)

ko can be approximated as ko = wB/(J, where WB is the Brunt-Väisälä frequency (WEINSTOCK, 1981). Assuming the turbulence energy per unit mass E '" (J2 and WB ~ 2 X 10- 2 s, the lifetime of the dissipating turbulence is estimated as

E 2 " = - ~ - '" 100(s). (8)

G WB

This value is much smaller than the time scale of the scattering pattern shown in

Figure 6. As shown by FRITTS and RASTOGI (1985), the Brunt-Väisälä frequency is

modified by the gravity wave, and WB becomes zero when the wave breaking sets in.

In our analysis, the Richardson number modified by the gravity wave is possibly smaller than the background value at 69-72 km (Y AMAMOTO et al., 1987). The

614 M. Yamamoto el af. PAGEOPH,

li fe time of the dissipating turbulence can also be estimated by the thickness of the scattering layers. From Eq. (8) we can write

(9)

where L o = 2n/ko is the diameter of the largest vortex in the turbulence layer. We assurne (J = 3 m, which is consistent with the spectral width shown by Y AMAMOTO et al. (1987). In order to estimate Lo, we refer to the thickness of the scattering layers. In the time-height distribution of the echo power (Figure 3), thickness of the contour region with the signal-to-noise ratio above 6 dB is typically I km and less than 2 km at 69-73 km. Assuming Lo = I km, we obtain L, = 110 s from Eq. (9). This value is consistent with that estimated by using Eq. (8), and is less than the observed time scale.

RÖTTGER and IERKIC (1985) have observed horizontal trajectories of turbulence blobs in the mesosphere. The motions were detected by using the interferometer technique within 3-4 km of the echoing region of the vertical beam. The blobs showed the horizontal motions in the same direction of the background wind determined by the Doppler shift. It is because the analysis technique is equivalent to the spaced antenna drift and Doppler shift measurements. The interferometer technique traced the motion of the iso la ted region of turbulence itself. In our analysis, on the other hand, the distance between echoing regions of eastward and northward beams was approximately 17 km at the altitude of 70 km. Considering the large correlation time of the scattering pattern, the motion we observed is not the one of isolated turbulence detectable within a transmitting beam, but the motion of the region where turbulence is being genera ted. Another filtering effect may arise because we used the echo power averaged in the echoing region, while RÖTTGER and IERKIC (1985) could detect the micro-structures inside the beam.

KLOSTERMEYER and RÜSTER (1984) have observed the horizontal motion of the echo power bursts by using a simple correlation technique, and mentioned that the motion was identical to the background wind velocity. Because of their actual zenith angle of 6°, the distance between vertical and eastward beams was 8.4 km at the altitude of 80 km. It is not sure if the motion of the isolated turbulence was detectable with the grid of this size. It is possible that the trace velocities represented the same motion as that of our analysis. In our case, however, we observed the inertia gravity wave with the slightly negative Richardson number in the wind field, and the wave strongly produced turbulence through instabilities. Although KLOSTERMEYER and RÜSTER (1984) used the simple correlation technique, the differences in the analysis techniques do not largely affect the observational results since we still have the northward motion of the scattering pattern with the simple correlation technique.

Recently, RÜSTER and KLOSTERMEYER (1987) have statistically shown that the motion of the echo power bursts agrees with the background wind on average. The

Vol. 130, 1989 A Full-Correlation Analysis Teehnique 615

horizontal spacing of the beams was 5 km at the altitude of 70 km, and the simple correlation technique was used. The motion of the echo power bursts distributed widely around the average, and the direction of the motion is sometimes different from that of the background wind by approximately 90°. The results of our analysis may be attributed to one of the extreme cases. We infer that the magnitude of gravity waves in the background wind field could change the situation whether the motion of the scattering pattern is parallel to the background wind or not.

5. Concluding Remarks

In this paper, we have shown a new technique to observe the horizontal motion of the scattering layers by fully utilizing the fast beam steerability of the MU radar. The full-correlation analysis technique has also allowed us to obtain the horizontal scale and the correlation time of the moving scattering pattern. The direction of the horizontal motion did not agree with that of the background wind velocity, but was associated with the horizontal propagation direction of the inertia gravity wave observed in the wind field. Because the gravity wave showed a negative Richardson number, we infer that the motion of the scattering pattern is that of the region where turbulence is locally generated by the saturated gravity wave.

Acknowledgement

The authors thank Drs. W. K. Hocking, J. Röttger and B. H. Briggs for helpful discussions and suggestions. The authors are also grateful to Dr. P. T. May for his careful reading of the manuscript. The MU radar belongs to, and is operated by the Radio Atmospheric Science Center, Kyoto University.

REFERENCES

BRIGGS, B. H. (1984), The analysis or spaced sensor recordv by correlation techniques, Handbook for MAP 13, 166-186.

FRITTS, D. c., and RASTOGI, P. K. (1985), Convective and dynamieal instabilities due to gravity wave motions in the lower and middle atmosphere: Theory and observations, Radio Sei. 20, 1247-1277.

FRITTS, D. c., and VINCENT, R. A. (1987), Mesospherie momentum jiux studies at Adelaide, Australia: Observations and a gravity wave-tidal interaction model, J. Atmos. Sei. 44, 605-619.

FUKAO, S., SATO, T., TSUDA, T., KATO, S., WAKASUGI, K., and MAKIHIRA, T. (1985a), The MV radar with an aetive phased array system, 1. Antenna and power amplijiers, Radio Sei. 20, 1155-1168.

FUKAO, S., TSUDA, T., SATO, T., KATO, S., WAKASUGI, K., and MAKIHIRA, T. (l985b), The MV radar with an active phased array system, 2. ln-house equipment, Radio Sei. 20, 1169-1176.

GAGE, K. S., and BALSLEY, B. B. (1980), On the seattering and rejiection mechanisms eontributing to dear air radar eehoes /rom the troposphere, stratosphere, and mesosphere, Radio Sei. 15, 243-257.

HOL TON, J. R. (1982), The role or grar'ity wave induced drag and diffusion in the momentum budget 0/ the mesosphere, J. Atmos. Sei. 39, 791-799.

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KATO, S., OGAWA, T., TSUDA, T., SATO, T., KIMURA, 1., and FUKAO, S. (1984), The middle and upper atmosphere radar: First results using a partial system, Radio Sei. 19, 1475-1484.

KLOSTERMEYER, J., and RÜSTER, R. (1984), VHF radar observation ofwave instability and turbulence in the mesosphere, Adv. Space. Res. 4, 79-82.

LINDZEN, R. S. (1981), Turbulence and stress owing to gravity wave and tidal breakdown, J. Geophys. Res. 86, 9707-9714.

RÖTTGER, J., and IERKIC, H. M. (1985), Postset beam steering and interferometer applications of VHF radars to study winds, waves, and turbulence in the lower and middle atmosphere, Radio Sei. 20, 1461--1480.

RÜSTER, R., and KLOSTERMEYER, J. (1987), Propagation of turbulenee structures detected by VHF radar, J. Atmos. Terr. Phys. 49, 743-750.

SATO, T., and WOODMAN, R. F. (1982), Fine altitude resolution observations of stratospheric turbulent layers by the Arecibo 430 MHz radar, J. Atmos. Sei. 39,2546-2552.

VANZANDT, T. E., GREEN, J. L., GAGE, K. S., and CLARK, W. L. (1978), Vertieal profiles ofrefractivity turbulence structure constant: Comparison of observations by the Sunset Radar with a new theoretical model, Radio Sei. 13, 819-829.

VINCENT, R. A., and REID, I. M. (1983), HF Doppler measurements of mesospheric gravity wave momentumfiuxes, J. Atmos. Sei. 40, 1321-1333.

WEINSTOCK, J. (1981), Energy dissipation rates of turbulence in the stable free atmosphere, J. Atmos. Sei. 38, 880-883.

YAMAMOTO, M., TSUDA, T., KATO, S., SATO, T., and FUKAO, S. (1987), A saturated inertia gravity wave in the mesosphere observed by the Middle and Upper atmosphere radar, J. Geophys. Res. 92, 11993-11999.

YAMAMOTO, M., TSUDA, T., KATO, S., SATO, T., and FUKAO, S. (1988), Interpretation of the structure of mesospheric turbulence layers in terms of inertia gravity waves, Physiea Seripta 37, 645-650.

(Reeeived September 7, 1987, revisedjaeeepted April 12, 1988)

PAGEOPH Reprints from Pure and Applied Geophysics

New In the series:

Scatterlng and Attenuatlon 01 Selsmlc Waves. Part I. Edited by

Ru-Shan Wu Riehter Seismologieal Laboratory, University of California, Santa Cruz, CA, USA

Keiiti Aki D:partment .of Geological SClences, Unlversity of Southern California, Los Angeles, CA, USA

1988. 454 pages, Paperback ISBN 3-7643-2254-3

During the last decade the interest of geophysieists in seismic wave scattering and attenuation has gr~wn rapidly; the nU':'lber of publicatlons per year has trlpled. Th.is reflects the broad applications and great potential of this field for many geophysical problems, such as the lithospherie and mantle heterogeneities, identification and mon itoring of underground nuclear ex~Iosions, oil and mineral exploration, earthquake prediction and hazard mitigation, etc. The authors feel that a turning point in this field is now approaching, due to the progress in theory and the accumulation of experimental data, espeeially high-frequency, three-component digital data. The aim of Scattering and Attenuation of Seismic Waves is to summarizetoday's stock of research and to point out some new directions and approaches for the future. Part I will be comprised of 22 papers addressing the problems of the influence of scattering and anelastic attenuation on the characteristics of seismic waves, especially with respect to their contribution to the seismic coda.

lonospherlc ModelUng Edited by

lurij N. Korenkov Kaliningrad Observatory of IZMIR AN, Kaliningrad, USSR


This .c~lIection of papers by leading speclahsts from different countries focuses on one of the main tendeneies in the present development of ":Jod ern seience, the general applicatlon. of ":Jat~~matical modeling in solvlng sClentlflc and practical problems of solar-terrestrial environmental physics. Modern achievements and problems of concern to research scientists working in the field of mathematical modelingof near-earth spacearediscussed in detail: atmospheric photochemical processes; ionospherie dyna~ics of neutral and charged constltuents; and the impact of some artificial and natural disturbances on temporal and space behavior of ionospheric parameters. Different local microprocesses and large-scale processes simulated by three-dimensional global models, as weil as the analysis of numerical experiments and program realization. on computers of different generations are also considered.

Prevlously publlshed:

Intermedlate-Term Earthquake Predlctlon Edited by

William D. Stuart U. S. Geological Survey, Pasadena, CA, USA

Keiiti Aki Department of Geologieal Seiences, University of Southern California, Los Angeles, CA, USA

1988.544 pages, Paperback ISBN 3-7643-1978-X

Intermediate-term earthquake prediction, which is the attempt to forecast earthquake parameters a few weeks to a few years in advance has until now received little study: ~any of the papers in this special Issue report new observations of intermediate-term anomalies in hydrologic, geochemical, seismologie, and geodetic data. Other papers analyze mechanical models formulated to explain certain seismologic and geodetic precursors. The papers collectively present a broad and detailed account of the current state of intermediate-term earthquake prediction, and point to the most promising topics for future study.

Please order through your bookseller or Birkhäuser Verlag, P. O. Box133, CH-4010 Basel / Switzerland or, for orders originating from the USA and Canada, through Birkhäuser Boston, Inc., clo Springer-Verlag New York, Inc., 44 Hartz Way, Secaucus, NJ 07096 - 2491/ USA

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. Electrlcal Propertles of the Earth's Mantle Edited by

Wallace H. Campbell United States Department of the Interior Geological Survey, Denver, co, USA


Physlcsof Fracturlng and Selsmlc Energy Release Edited by

Jan Kozak and Ludvik Waniek Geophysicallnstitute, Praha, CSSR

1987. 370 pages, Paperback ISBN 3-7643-1863-S

Advancesln Volcanlc Selsmology Edited by

Emile A. Okal Northwestern University, Evanston, IL, USA


Frlctlon and'Faultlng Edited by

Terry E. Tullis Dept. of Geological Sciences, Brown University, Providence, RI, USA


InternalStructure of Fault Zones Edited by

Chi-yuen Wang University of California, Berkeley, CA, USA


Earthquake Hydrology and Chemlstry Edited by

Chi-Yu Kin2 U.S. GeologicaJ' Survey, Menlo Park, CA, USA

1985.480 pages, Paperback ISBN 3-7643-1743-4

Earthquake Predlctlon Edited by

Kunihiko Shimazaki Earthquake Research Institute, University of Tokyo, Tokyo, japan

William D. Stuart U. S. Geological Survey, Pasadena, CA, USA

1985.240 pages, Paperback ISBN 3-7643-1742-6

Please order through your bookseller or Birkhäuser Verlag, P. O. Box 133, CH-4010 Basel / Switzerland or, for orders originating from the USA and Canada, through Birkhäuser Boston, Inc., c/o Springer-Verlag New York, Inc., 44 Hartz Way, Secaucus, Nj 07096-2491 /USA

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