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1 SEPTEMBER 1999 3043F E L D S T E I N

q 1999 American Meteorological Society

The Atmospheric Dynamics of Intraseasonal Length-of-Day Fluctuations during theAustral Winter

STEVEN B. FELDSTEIN

Earth System Science Center, The Pennsylvania State University, University Park, Pennsylvania

(Manuscript received 24 April 1998, in final form 29 October 1998)

ABSTRACT

The atmospheric dynamical processes associated with intraseasonal length-of-day (LOD) variability duringthe austral winter are examined with National Centers for Environmental Prediction–National Center for At-mospheric Research reanalysis and outgoing longwave radiation (OLR) data. The method adopted is to regressthe relevant fields against the LOD tendency. All quantities in this study are bandpassed through a 30–70-dayfilter.

The findings from an analysis of the OLR and 200-mb eddy streamfunction fields are consistent with the ideathat large intraseasonal LOD fluctuations coincide with an active Madden–Julian oscillation (MJO). Furtheranalysis suggests that the eddy response to the MJO heating drives both an anomalous meridional circulationthat excites the anomalous global friction torque, and an eddy field that has the appropriate location relative tothe topography for generating the anomalous global mountain torque. These results were obtained by calculatingregressions of the anomalous eddy angular momentum flux convergence, mass streamfunction, surface stress,and surface pressure fields, and each term in the lowest sigma level relative angular momentum budget.

The anomalous global friction and mountain torques are found to be of similar magnitude, with the formerleading the latter by eight days. The largest contribution toward the anomalous global friction (mountain) torquecomes from Australia and the surrounding ocean (the Andes).

1. Introduction

Intraseasonal length-of-day (LOD) and atmosphericangular momentum (AAM) fluctuations have been asubject of increasing interest during the past 15 years.Interest in this subject has in large part been motivatedby the highly accurate space-based geodetic measure-ments of the LOD and the increasingly accurate globalatmospheric observations (Rosen 1993). Both sets ofmeasurements revealed large contemporaneous corre-lations between globally integrated AAM (GAAM) andLOD on timescales less than 10 yr (e.g., Hide et al.1980; Langley et al. 1981; Rosen and Salstein 1983;Hide and Dickey 1991). Such behavior, together withthe observed amplitude of the LOD and GAAM chang-es, indicates that the exchange of angular momentumbetween the atmosphere and solid earth does not involvesignificant changes in the oceanic angular momentum.Furthermore, many studies have found statistically sig-nificant intraseasonal fluctuations in both LOD andGAAM with a period of approximately 50 days (e.g.,Langley et al. 1981; Rosen and Salstein 1983; Lau et

Corresponding author address: Dr. Steven B. Feldstein, Earth Sys-tem Science Center, The Pennsylvania State University, 248 DeikeBuilding, University Park, PA 16802.E-mail: [email protected]

al. 1989; Dickey et al. 1991; Magana 1993), a periodthat overlaps with the tropical Madden–Julian oscilla-tion (MJO; Madden and Julian 1971, 1972). More re-cently, several studies have verified that the large in-traseasonal LOD and GAAM fluctuations do indeedoverlap with periods of active MJOs (e.g., Weickmannet al. 1992; Magana 1993; Weickmann and Sardesh-mukh 1994; Hendon 1995).

Most of the earliest LOD–AAM studies emphasizedthe spatial and temporal characteristics of the AAM fielditself (e.g., Anderson and Rosen 1983; Rosen and Sal-stein 1983). However, within the past several years, re-searchers have broadened their investigation to includean examination of the quantities that drive the LOD–AAM fluctuations, that is, the friction and mountaintorques, in addition to the atmospheric variables that aresuspected of generating these torques. This approachincludes both observational studies (e.g., Kang and Lau1990; Weickmann et al. 1992; Ponte and Rosen 1993;Weickmann and Sardeshmukh 1994; Hendon 1995;Madden and Speth 1995; Weickmann et al. 1997) andalso those with idealized numerical models (Itoh 1994)and GCMs (Feldstein and Lee 1995). However, most ofthese studies either use data that span the entire year,or restrict examination to the the boreal winter. As aresult, there has been little attention focused on theLOD–AAM fluctuations of the austral winter.

3044 VOLUME 56J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S

Two studies that do examine austral winter intrasea-sonal GAAM fluctuations are Kang and Lau (1990) andWeickmann et al. (1992). They find that the intrasea-sonal GAAM fluctuations are associated with frictiontorques in the central tropical Pacific Ocean. Weickmannet al. (1992) also estimate the globally integrated frictiontorque and find a temporal in-phase relationship withthe GAAM tendency. These results indicate that unlessthe globally integrated mountain torque is in phase withglobally integrated friction torque, the globally inte-grated mountain torque must be relatively small duringlarge austral winter intraseasonal LOD–GAAM fluctu-ations. However, as observed values of the surface stresswere not readily available at the time of these studies,the authors resorted to inferring the surface stress field,and hence the friction torque, from the observed 850-mb wind field. More recently, these estimates of thefriction torque have come into question, as Itoh (1994)presented results showing that the use of the 850-mbwinds for estimating the friction torque leads to a largeoverestimation within the Tropics.

The above studies clearly reveal that many of thebasic features of austral winter intraseasonal LOD–GAAM fluctuations have yet to be documented. Notingthe above problem of estimating the tropical frictiontorque with the 850-mb winds, important issues thatneed to be addressed for the austral winter include 1)the relative role of the friction and mountain torquesand 2) the geographical locations that account for thelargest contribution to these torques. A more interestingchallenge, however, is to explain the underlying atmo-spheric dynamical processes that determine thesetorques. Although more definitive statements on thesedynamical processes require the use of simplified mod-els, much can be learned about these dynamical pro-cesses with an appropriate selection of diagnostic tech-niques applied to observational data. In this study, wefollow the latter approach to address issues such aswhether convectively driven Rossby waves excite thetorques and whether the anomalous friction torque isforced by an eddy-driven meridional circulation. Forthis purpose, the National Centers for EnvironmentalPrediction–National Center for Atmospheric Research(NCEP–NCAR) reanalysis dataset is used. One partic-ular advantage to this dataset is that the daily surfacestress field is provided.

The data and methodology are presented in section2. This is followed in section 3 by a detailed docu-mentation of the friction and mountain torques. Section4 presents the results of a diagnostic analysis of theoutgoing longwave radiation (OLR), eddy streamfunc-tion, mass streamfunction, and surface pressure. Theconclusions are presented in section 5.

2. Data and methodology

Most fields to be presented in this study are derivedfrom daily (0000 UTC) NCEP–NCAR reanalysis data

extending from 1 January 1979 to 31 December 1995.This includes the friction and mountain torques, eddyAAM flux convergence, 200-mb streamfunction, sur-face pressure, and mass streamfunction. Additionalquantities utilized are the LOD timeseries, which waskindly provided by P. Nelson of Atmospheric and En-vironmental Research, Inc.; and OLR, which is pro-duced by the National Oceanic and Atmospheric Ad-ministration. The latter quantity is used as a proxy mea-surement for convection within the Tropics. As statedin the previous section, this investigation of intrasea-sonal LOD–GAAM variability is being applied to theaustral winter, which we define as the months of Maythrough September.

The zonally and vertically integrally absolute an-gular momentum M(u, t) can be defined in sigma co-ordinates as

2p 12a2M(u, t) 5 p (u 1 Va cosu) cos u ds dl, (1)E E sg 0 0

where u and ps denote the zonal wind and surface pres-sure, respectively; s, l, and u the vertical, longitudinal,and latitudinal coordinates; t time; a the earth’s radius;V the earth’s angular velocity; and g the gravitationalacceleration. The corresponding equation for the con-servation of M(u, t) can be written as

2p 1]M 1 ] p my cosus5 2 a cosu ds dlE E 1 2]t a cosu ]u g0 0

1 T 1 T 1 T ,F M G (2)

where m 5 (u 1 Va cosu)a cosu, y is the meridionalwind, TF the friction torque, TM the mountain torque,and TG the gravity wave drag torque, which is includedin (2) for completeness. (Note, however, that TG asso-ciated with the intraseasonal LOD–GAAM fluctuationsis found to be substantially smaller than the othertorques, so we will not consider it further in this study.)This equation relates the absolute angular momentumtendency to the absolute angular momentum flux con-vergence and the sum of the three torques. The frictionand mountain torques can be expressed as

2p ]h2 2T 5 2a cos u p dl;M E s ]x0

2p

2 2T 5 a cos u (t ) dl, (3)F E l s51

0

where h is the topographic height, x is the zonal lengthcoordinate, and the sign of the surface stress (t l)s51 isdefined to be positive when there is a transfer of angularmomentum from the solid earth to the atmosphere. Thecalculations of these torques are straightforward, as theps, h, and (t l)s51 fields are included within the NCEP–NCAR reanalysis dataset. A straightforward latitudinalintegration of (2) yields


FIG. 1. The anomalous global friction torque (long dashed line),anomalous global mountain torque (short dashed line), and the anom-alous LOD (solid line) regressed against the LOD tendency. Thetorques (LOD) are divided (multiplied) by 1.0 3 1018 kg m2 s22 (50ms).

p /2](GAAM)5 (T 1 T ) du. (4)E F M]t

2p /2

The relationship between the LOD tendency and thetorques can then be easily determined with the followingrelationship: d(LOD) 5 1.68 3 10229 d(GAAM) (Rosenand Salstein 1983). The units for GAAM are kg m2 s21

and for LOD, s.As discussed above, we will also analyze the eddy

AAM flux convergence and the mass streamfunction. Theeddy AAM flux is defined as [u*(psy)*], where the squarebrackets denote a zonal mean, and the asterisk a deviationfrom the zonal mean. The mass streamfunction is ob-tained from the zonally averaged y by vertically inte-grating the zonally averaged continuity equation down-ward from the reanalysis model’s top sigma level [thistechnique is described in Peixoto and Oort (1992)].

With the exception of the mountain torque and OLR,all other quantities are generated from data at rhom-boidal-30 horizontal resolution. As the mountain torqueis found to exhibit some sensitivity to the horizontalresolution, we have retained the reanalysis model’s orig-inal triangular-62 horizontal resolution for both the sur-face pressure and the topographic height fields. The re-duction in resolution from triangular 62 to rhomboidal30 for the other quantities was done to save computerstorage. For the zonal mean quantities examined in thisstudy, such resolution changes are expected to be in-consequential. Various tests with limited amounts ofdata verify this to be the case. The OLR has a resolutionof 2.58 longitude by 2.58 latitude. With regard to thevertical resolution, all 28 of the reanalysis model’s sig-ma levels are used for calculating M(u, t) and the ab-solute angular momentum flux convergence. These lev-els range from s 5 0.995 to s 5 0.0027.

All quantities to be presented in this study are gen-erated by first applying a 30–70-day bandpass Fourierfilter followed by a linear regression against the 30–70-day bandpass LOD tendency. A 30–70-day filter is se-lected in order to encompass the periods associated withthe MJO. [Not surprisingly, given the large correlationbetween the LOD and GAAM time series, essentiallyidentical results to those presented in this study are ob-tained if the regression is performed against the 30–70-day bandpass GAAM tendency. For this set of calcu-lations, the AAM was determined following the pro-cedure in Feldstein (1998).] In the regression equation,the amplitude of the LOD tendency anomaly is alwaysspecified as one standard deviation.

Statistical significance is determined from the cross-correlation fields, with the number of degrees of free-dom (NDOF) being estimated with the procedure ofDavis (1976), that is,

NDOF 5 Ndt/t, (5)

t 5 C (kdt)C (kdt)dt, (6)O x yk

where N is the number of days in the time series; dt is

the time interval between adjacent values, that is, oneday; and Cx and Cy are the autocorrelations of the LODtendency and the regressed field, respectively. For mostfields and at most latitudes, it is found that NDOF iswell in excess of 200.

3. Documentation of the torques

We first examine the temporal evolution of the anom-alous global friction and mountain torques and theanomalous LOD, by regressing these quantities againstthe LOD tendency (Fig. 1). The key features seen arethat the maximum values of the two torques are aboutequal and that the anomalous friction torque leads theanomalous mountain torque by approximately eightdays. A similar phase lag is found in most studies ofintraseasonal LOD–GAAM variability, both when datafrom the entire year are used (Hendon 1995) and whenthe data are limited to the boreal winter (Weickmannand Sardeshmukh 1994; Madden and Speth 1995;Weickmann et al. 1997).

Before examining the temporal and spatial propertiesof the anomalous global friction and mountain torques,we examine the extent to which the angular momentumbudget is balanced at each latitude. Figure 2a showsboth the observed AAM tendency (contours) and thepredicted AAM tendency (shading) as determined fromthe sum of each of the terms on the right-hand side (rhs)of (2). The difference between these two quantities isindicated in Fig. 2b. As can be seen, the budget is rea-sonably well balanced at most latitudes, particularly inthe Southern Hemisphere where the torques are largest


FIG. 2. (a) The observed anomalous AAM tendency (contours) and the predicted anomalous AAM tendency(shading) and (b) the difference between the observed and predicted AAM tendencies. The contour intervalis 1.0 3 1017 kg m2 s22. Shaded values exceed a magnitude of 1.0 3 1017 kg m2 s22, with dark (light) shadingdenoting positive (negative) values.

(Fig. 3). Interestingly, the balance is weakest near theequator and in the Northern Hemisphere Tropics, therange of latitudes where the OLR anomalies is greatest(Fig. 6). A similar relationship between the latitude ofthe maximum OLR anomalies and the degree of angularmomentum balance can also be seen in the boreal winterLOD–GAAM study of Weickmann et al. (1997, cf. theirFig. 9).

A decomposition of the two torques into functions oflag and latitude is shown in Fig. 3. Contours illustratethe value of the torque and stippling denotes values thatexceed the 95% confidence level. It can be seen that thelargest anomalous friction and mountain torques bothoccur within the subtropics and midlatitudes of theSouthern Hemisphere. However, fairly substantialanomalous friction and mountain torques do extend intohigh latitudes. The most striking of these high-latitude

anomalous torques is the large mountain torque thatreaches Antarctica at 808S.

We next examine the particular geographical locationsthat are the dominant contributors toward the anomaloustorques. This is performed for the friction torque byillustrating the anomalous (t l)s51 cos2u as a functionof longitude and latitude at lag 26 (when the anomalousglobal friction torque is largest) and lag 12 days (seeFig. 4). As can be seen, the main contribution to theanomalous global friction torque comes from southeastAsia and Australia, and from the subtropical Indian andwest Pacific Oceans.

We next address the question of whether it is the landor ocean contribution that dominates the anomalousglobal friction torque. The motivation for this question,as discussed in the introduction, arises from the obser-vation of the large contemporaneous correlation be-


FIG. 3. (a) The anomalous zonal mean friction torque and (b) the anomalous zonal mean mountain torqueregressed against the LOD tendency. The contour interval is 3.0 3 1017 kg m2 s22. Solid contours are positive,dashed contours negative, and the zero contour is omitted. Shaded values exceed the 95% confidence level,with dark (light) shading denoting positive (negative) t values.

tween the LOD and GAAM time series. This impliesthat if the oceanic friction torque is large, then most ofthe angular momentum exchanged between the atmo-sphere and ocean must be rapidly transfered to the solidearth [using a barotropic ocean model, Ponte (1990)proposes that this rapid angular momentum transfer canbe accomplished by barotropic Kelvin waves]. A cal-culation of the separate land and ocean contributions tothe anomalous global friction torque does indeed verifythat the ocean torque dominates at most lags. For ex-ample, at lag 26 days, the ratio of the ocean to landfriction torque is found to be 3.1, and at lag 12 daysthis ratio equals 1.5.

The boreal winter LOD–GAAM study of Weickmannet al. (1997) also finds that the dominant anomaloussurface stresses occur over water. However, comparedwith the present study, there are important differences

in the regions that are the primary contributors to theanomalous global friction torque. Although the tropicalPacific Ocean is important during both seasons, duringthe austral winter, the subtropical Indian Ocean alsoplays an important role, and during the boreal winter,it is the north Atlantic Ocean that also has a large anom-alous friction torque. As there must be a rapid exchangeof angular momentum between the ocean and solid earthduring both seasons, these seasonal differences in thegeographical locations of the ocean friction torque implythat there must be corresponding seasonal differencesin the oceanic dynamical processes that account for thisangular momentum exchange.

A similar analysis is performed for the anomalousmountain torque, shown as ps(]h/]x) cos2u (Fig. 5). Wefirst examine this quantity at lag 14 days, the time ofthe maximum anomalous global mountain torque (see


FIG. 4. The regression of the anomalous surface stress (t l)s51 cos2u as a function of longitudeand latitude at (a) lag 26 days and (b) lag 12 days. The contour interval is 0.003 N m22,and shaded values exceed a magnitude 0.006 N m22, with dark (light) stippling denotingpositive (negative) values. Solid contours are positive, dashed contours negative, and the zerocontour is omitted.

Fig. 5a). At this lag, it is obvious that the largest con-tribution to the anomalous global mountain torquecomes from the Andes. The fractional contribution byparticular mountain ranges toward the anomalous globalmountain torque can be quantified by calculating themountain torque due to particular regions. This calcu-lation reveals that at lag 14 days, the fractional con-tribution by the Andes is 0.74, and that from the Him-alaya and Rockies is 0.25 and 0.01, respectively. Wealso illustrate the anomalous ps(]h/]x) cos2u at lag 118days (Fig. 5b). At this lag, the anomalous Antarcticmountain torque reaches its largest value. Although theAntarctic mountain torque does not dominate the anom-alous global mountain torque, it is nevertheless inter-esting that a torque of relatively large magnitude canexist so close to the earth’s axis of rotation. As can beseen, the primary contribution from Antarctica is as-sociated with Victoria Land, where there are high, steepmountains on the western boundary of the Ross Sea.

4. Dynamical processes associated with the torques

In this section, we first examine the OLR and eddystreamfunction fields, as anomalies of these quantitiesare closely linked to the generation of both friction andmountain torques. Next, we investigate the character-istics of the anomalous meridional circulation, in orderto examine whether the anomalous friction torque isdriven by fluctuations in the meridional circulation. Thisis followed by a calculation of the anomalous surfacepressure field, in order to better understand the prop-erties of the anomalous mountain torque.

a. Outgoing longwave radiation

Many studies have presented results that relate theanomalous friction and mountain torques associatedwith intraseasonal LOD–GAAM fluctuations to tropicalconvection. It has been suggested that the tropical con-vection can excite poleward-propagating Rossby waves


FIG. 5. The regression of the anomalous mountain torques, expressed as ps(]h/]x) cos2u,as a function of longitude and latitude at (a) lag 14 days and (b) lag 118 days. The contourinterval is 0.02 N m22, and shaded values exceed a magnitude 0.02 N m22, with dark (light)stippling denoting positive (negative) values. Solid contours are positive, dashed contoursnegative, and the zero contour is omitted.

whose surface eddy wind and pressure field can generateanomalous friction and mountain torques, respectively(Feldstein and Lee 1995). This process must involve theeddy, that is, deviation from zonal mean, component ofthe tropical convection. It has also been proposed thatfluctuations in the zonal mean tropical convection cangenerate anomalous friction torques via fluctuations inthe Coriolis torque acting on the low-level branch ofthe anomalous Hadley cell (Hendon 1995). For thesereasons, in this section, we examine the detailed evo-lution of the OLR field, including its zonal mean.

The temporal evolution of the anomalous OLR fieldat specific lags is illustrated in Fig. 6 (note that a neg-ative OLR anomaly implies enhanced convection). Inorder to emphasize its planetary-scale features, the OLRfield is truncated to wavenumber three in the zonal di-rection. Calculations at less severe truncations, such asat zonal wavenumber six, yield essentially the samelarge-scale spatial patterns. As can be seen, at lag 28

days (Fig. 6a), which is two days before the anomalousglobal friction torque maximum, there is a large negativeOLR anomaly confined primarily to the tropical IndianOcean. Also, there are weak positive OLR anomaliesover southeast Asia and the far northeastern tropicalPacific. At lag 23 days (Fig. 6b), the negative OLRanomaly in the Indian Ocean has further strengthened,expanded poleward in both hemispheres, and expandedeastward to cover the the tropical northwestern Pacific.The positive OLR anomaly in the far northeastern trop-ical Pacific has also strengthened. At lag 12 days (Fig.6c), which is two days prior to the anomalous globalmountain torque maximum, the negative OLR anomalyin the Indian Ocean has slightly weakened and hasmoved farther northward into the Asian continent. Atthe same lag, the negative OLR anomaly in the westand central tropical Pacific has strengthened. At lag 17days (Fig. 6d), the negative OLR anomaly over southernAsia has weakened, and a positive OLR anomaly has


FIG

.6.

The

anom

alou

sO

LR

regr

esse

dag

ains

tth

eL

OD

tend

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at(a

)la

g2

8da

ys,

(b)

lag

23

days

,(c

)la

g1

2da

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and

(d)

lag

17

days

.T

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0.6

Wm

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Sol

idco

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epo

siti

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dash

edco

ntou

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ve,

and

the

zero

cont

our

isom

itte

d.


FIG. 7. The anomalous zonal mean OLR regressed against the LOD tendency. The contour interval is 0.15W m22. Solid contours are positive, dashed contours negative, and the zero contour is omitted. Shaded valuesexceed the 95% confidence level, with dark (light) shading denoting positive (negative) t values.

formed over much of the equatorial Indian Ocean. Thispattern for the OLR field is very similar to that at lag213 days (not shown), but of opposite sign.

Two notable features in the above description of theOLR temporal evolution are also found in studies thatexamine the seasonal variation of the MJO. These arethe northward propagation of an OLR anomaly from theequatorial Indian Ocean into the Asian continent duringthe austral winter, and the eastward OLR anomaly prop-agation from the Indian to the west Pacific Ocean thattakes place throughout the year (e.g., Madden 1986;Knutson and Weickmann 1987; Wang and Rui 1990).Such northward OLR anomaly propagation has beenassociated with the active and break periods of the Asiansummer monsoon (e.g., Yasunari 1980; Sikka and Gadg-il 1980; Murakami 1984).

We next examine the anomalous zonal mean OLR asa function of lag and latitude (see Fig. 7). The moststriking feature of the anomalous zonal mean OLR isits northward propagation. For example, proceedingfrom lag 210 days to lag 110 days, the extremes ofthe negative zonal mean OLR anomaly has shifted fromabout 108S to 158N. An examination of Fig. 6 revealsthat much of this northward movement can be attributedto the northward movement of the negative OLR anom-aly from the Indian Ocean into southeast Asia. Also,

Fig. 7 indicates that the convection is not simply astrengthening and weakening of a single sign anomaly,but at most stages during the LOD evolution, the anom-alous zonal mean OLR takes on a dipole structure inthe latitudinal direction.

b. Eddy streamfunction

In this section, we examine the anomalous 200-mbeddy streamfunction field and its relationship to theOLR field. In later sections, we will investigate the re-lationship between the anomalous 200-mb eddy stream-function field and the anomalous friction and mountaintorques. To the extent that there is a consistent rela-tionship between the eddy streamfunction field and eachof these quantities, we can hypothesize that the anom-alous eddy streamfunction field provides the connectionbetween the anomalous tropical convection and theanomalous friction and mountain torques.

One prominent feature in the temporal evolution ofthe eddy streamfunction field (see Fig. 8) is an eastward-propagating zonal wavenumber-one disturbance in theTropics. In general, this disturbance consists of one pairof anticyclonic anomalies and another pair of cyclonicanomalies, both pairs straddling either side of the equa-tor, with the anticyclonic (cyclonic) anomalies being


FIG

.8.

The

anom

alou

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0-m

bed

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func

tion

regr

esse

dag

ains

tth

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OD

tend

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at(a

)la

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6da

ys,

(b)

lag

21

days

,(c

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4da

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and

(d)

lag

19

days

.T

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Sol

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the

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FIG. 9. The anomalous eddy AAM flux convergence regressed against the LOD tendency. The contourinterval is 1.5 3 1017 kg m2 s22. Solid contours are positive, dashed contours negative, and the zero contouris omitted. Shaded values exceed the 95% confidence level, with dark (light) shading denoting positive(negative) t values.

positioned west (east) of the maximum negative OLRanomaly. Furthermore, the location of these anomaliesdoes bear some resemblance to what is found in steady-state primitive equation models that are forced by trop-ical diabatic heating anomalies (e.g., Ting and Sardesh-mukh 1993). This same spatial relationship between therelative location of OLR, anticyclonic, and cyclonicanomalies is found for the MJO (e.g., Knutson andWeickmann 1987), providing further support for a closelink between the MJO and intraseasonal LOD variabilityduring the austral winter.

The anomalous eddy streamfunction field can also berelated to the anomalous eddy AAM flux convergence(see Fig. 9). This relationship is important for betterunderstanding the LOD fluctuations, since, as we willsee in the next section, the amplitude and structure ofthe anomalous friction torque is closely linked to thatof the anomalous eddy AAM flux convergence, via themeridional circulation. Before examining these rela-tionships, it is helpful to first break up the anomalouseddy AAM flux into several contributing terms and writeit as the vertical integral of the sum of linear, [u*(psy)9*]1 [u9*(psy )*], and nonlinear, [u9*(psy)9*], terms (seeWeickmann et al. 1997), where an overbar (prime) de-notes a time mean (deviation from the time mean). The

linear terms arise from the interaction between the tran-sient eddy field, such as that displayed in Fig. 8, andthe climatological eddy field, and the nonlinear termsresult from the interactions among transient eddies. Acalculation of the vertical integral of the meridional con-vergence of these terms finds that the linear terms con-tribute approximately 50% equatorward of 308 latitudein both hemispheres. Thus, if we were to assume thatthe anomalous wind field is primarily rotational, at thetime of the largest anomalous linear eddy AAM fluxconvergence, the anomalous eddy streamfunction fieldshould be near quadrature with the climatological eddystreamfunction field, as this longitudinal phase relation-ship maximizes the anomalous linear eddy AAM flux.A comparison of the location of the eddy streamfunctionfield in Fig. 8 with the upper-tropospheric climatologicaleddy streamfunction field (cf. James 1994, p. 167) doesindeed reveal this relationship (not shown). Thus, thelocation of the anomalous eddy streamfunction fielddoes contribute in an important manner to the strengthof the anomalous eddy AAM flux, and hence, as wewill see, to that of the anomalous friction torque.

Using scaling arguments, it is straightforward to showthat the meridional convergence of the linear eddy AAMflux terms is proportional to k(l2 1 2lL 1 L2), where


k(l) is the zonal (meridional) wavenumber of the dis-turbance, and L the dominant meridional wavenumberof the austral winter climatological mean flow. Sincezonal wavenumber one dominates the climatological up-per-tropospheric eddy streamfunction within the Tropicsduring the austral winter (cf. James 1994, p. 167), dis-turbances with zonal wavenumber one and a large me-ridional wavenumber, such as the eddies shown in Fig.8, have the preferred spatial structure for generating alarge linear eddy AAM flux convergence.

c. Meridional circulations

In this section, we examine the role of anomalousmeridional circulations in generating anomalous frictiontorques. In addition to the mechanism involving zonalmean tropical convection (Hendon 1995), as discussedat the beginning of section 4a, it has also been suggestedthat eddy-driven anomalous meridional circulations canalter the friction torque via the Coriolis torque actingon the anomalous low-level mean meridional winds(Weickmann and Sardeshmukh 1994; Weickmann et al.1997). This process is simply an adjustment of the cir-culation toward thermal wind balance by the anomalousmean meridional circulation in response to the anom-alous eddy momentum and heat fluxes. [For a reviewof the equations for the response of the meridional cir-culation to mechanical and thermal forcing, and drivingby the eddy momentum and heat fluxes, see chapter 3of Andrews et al. (1987).]

If anomalous meridional circulations play an impor-tant role during large LOD fluctuations, then the anom-alous Coriolis and friction torques must be of similarmagnitude at the lowest sigma level in the reanalysismodel. We show this by examining the relative angularmomentum equation, which can be written as

][p m ]s r]t

1 ]5 2 ([p m y] cosu) 2 p f [y]a cosus r sa cosu ]u

] ]f2 [p m s] 1 ga cosu[t ] 1 (a cosu) sp ,s r l s[ ]1 2]s ]x

(7)

where t l is the viscous stress, mt 5 ua cosu, f is theCoriolis parameter, and f is the geopotential height. Acalculation of each term in (7) at the reanalysis model’slowest sigma level finds that the zonal mean Coriolistorque [the second term on the rhs of (7)] is typicallyat least one order of magnitude larger than each of theother terms on both sides of (7), except for the frictiontorque term [the friction torque term in (7) is not cal-culated, because the internal viscous stresses are notreadily available in the NCEP–NCAR reanalysis data-set]. This indeed verifies that the primary balance is

between the anomalous Coriolis and friction torques atthe lowest model level. As an additional measure of therelationship between the Coriolis and friction torques,the linear pattern correlation between the lowest-levelanomalous Coriolis torque and the anomalous surfacefriction torque is calculated and then averaged for eachlag between 630 days [note that the surface frictiontorque, expressed in (3), differs from the lowest levelfriction torque in (7), since it does not involve a verticalderivative]. The resulting mean pattern correlation hasa value of 20.91. To some extent, this large correlationis not surprising, because the lowest-level friction torqueis expected to be approximately proportional to the sur-face torque, since the viscous stresses decrease veryrapidly with height.

The above relationship between the anomalous Cor-iolis and friction torques can be seen by examining theanomalous mass streamfunction [note that positive (neg-ative) mass streamfunction contours correspond to aclockwise (counterclockwise) circulation in the merid-ional plane] (see Figs. 3a, 10). Inference of the anom-alous Coriolis torque from the anomalous mass stream-function shows that at each lag these two torques havea very similar spatial structure with opposite sign.

We next use this balance between the anomalous fric-tion and Coriolis torques to address the question whetherthe friction torque is due to eddy surface wind anom-alies, as described at the beginning of section 4a, or isgenerated by the anomalous meridional circulation. Inorder to examine this question, we separate the anom-alous zonal mean surface stress into its zonal mean andeddy contributions. As the NCEP–NCAR reanalysisdata uses a bulk parameterization scheme for the surfacestress, that is, (t l)s51 5 2CDu|V|, where CD is the sur-face drag coefficient, |V| is the magnitude of the surfacewind, and u is the surface zonal wind, one can writethe anomalous zonal mean surface stress as

[(tl)s51]9 5 2[(CD |V |)*(u9)*] 2 [(CD |V |9)*(u )*]

2 [CD |V |][u9] 2 [CD |V |9][u ]. (8)

This representation for the zonal mean surface stressneglects the temporally nonlinear terms, which werefound to be negligible. The first and second terms onthe rhs of (8) can be interpreted as representing theinteraction between the anomalous surface eddy windfield and the climatological surface eddy wind field. Ifthese terms were to dominate, it would imply that theanomalous meridional circulation and the associatedCoriolis torque are primarily driven by the anomalousfriction torque. In this case, the adjustment to thermalwind balance by the anomalous meridional circulationis driven by the change in the vertical wind shear dueto the anomalous friction torque. The third and fourthterms on the rhs of (8) involve the anomalous zonalmean surface wind field. These terms are primarily dueto the thermal wind adjustment as a result of the anom-alous eddy heat and momentum flux forcing, as de-


FIG. 10. The anomalous mass streamfunction regressed against the LOD tendency at (a) lag 211 days, (b) lag 26 days,(c) lag 21 days, and (d) lag 14 days. The contour interval is 5.0 3 108 kg s21. Solid contours are positive, dashed contoursnegative, and the zero contour is omitted.

scribed earlier in this section. Thus, the dominance ofthese terms implies that the anomalous friction torqueis driven by the anomalous Coriolis torque.

As the surface winds and drag coefficient are notreadily available quantities in the NCEP–NCAR re-analysis dataset, it is not possible to precisely determinethe value of each term on the rhs of (8). Instead, theapproach we adopt is to estimate the surface wind withthe NCEP–NCAR reanalysis wind field at the lowestmodel sigma level, and to estimate the surface dragcoefficient following the procedure in Weickmann et al.(1997), where CD is assigned a constant value of 1.5 31023 over water and 6.5 3 1023 over land. A comparisonof this estimate of the anomalous friction torque (seeFig. 11c) with that shown in Fig. 3a indicates that theseare reasonable approximations.

The zonal mean and eddy wind contributions to theanomalous friction torque are shown in Figs. 11a and11b. It can be seen that the zonal mean contributionaccounts for the vast majority of the Southern Hemi-sphere friction torque. On the other hand, in the North-ern Hemisphere, the extremes of the zonal mean con-

tribution to the anomalous friction torque are typicallyabout twice that of the eddy contribution. These resultsreveal that it is indeed the anomalous meridional cir-culation that is the primary contributor toward the driv-ing of the anomalous friction torque.

There still remains the important question of whetherit is the anomalous eddy fluxes or zonal mean heatingthat drive the anomalous meridional circulation. Theanswer to this question requires the solution of an in-homogeneous elliptic partial differential equation for themass streamfunction, in which the forcing term is afunction of the zonal mean heating and eddy fluxes. Thisquestion will be fully addressed in a separate paper.Nevertheless, there are hints from Fig. 9, which showsthe anomalous eddy AAM flux convergence, that thisquantity is indeed important for driving the anomalousmeridional circulation.

If the anomalous eddy AAM flux is an importantfactor in driving the anomalous meridional circulation,one expects that 1) the latitude at the center of the anom-alous mass streamfunction cells should approximatelycoincide with that of the anomalous eddy AAM flux


FIG. 11. The contribution to the anomalous zonal mean frictiontorque from its (a) zonal mean wind component, (b) eddy component,and (c) the sum of (a) and (b). The contour interval is 3.0 3 1017 kgm2 s22. Solid contours are positive, dashed contours negative, andthe zero contour is omitted. See the text for details describing howthese quantities are approximated.

convergence and 2) the anomalous low-level Coriolistorque must be of the same sign as the anomalous eddyAAM flux convergence. This is because it is found thatthe anomalous eddy AAM flux convergence is confinedto the upper troposphere, and an adjustment to thermalwind balance by the anomalous meridional circulationwould require the above characteristics. Upon exam-ining the anomalous eddy AAM flux convergence, onecan see that at lag 26 days, there are regions of negativeanomalous eddy AAM flux-convergence between 158and 458S and poleward of about 58N. Furthermore, thereis a positive anomalous eddy AAM flux convergence

between 158S and 58N. The corresponding anomalousmeridional circulations that would lead to a thermalwind adjustment are two thermally direct anomalouscells, one between 58 and 358N, the other between 158and 458S, and two thermally indirect anomalous cells,straddling either side of the equator between 158S and58N. Comparison with Fig. 10b reveals a very goodmatch outside of the deep Tropics. Within the deep Trop-ics, where the vertical extent of the meridional circu-lation is shallow due to the small Rossby depth scale,the match is reasonably good in the Southern Hemi-sphere and poor in the Northern Hemisphere. However,given the fact that the anomalous friction torque is neg-ligible inside the deep Tropics (Fig. 3a), these resultssuggest that the driving of the anomalous friction torqueby the eddy AAM fluxes is indeed an important process.With regard to the anomalous eddy heat flux (notshown), large values are found only in the SouthernHemisphere, centered at 458S. Such eddy heat fluxeswill drive anomalous meridional circulations at the samelatitude. However, as large anomalous friction torquesare not found at this latitude, it is likely that the anom-alous eddy heat flux does not play an important role inthe LOD variability.

One can get an appreciation of the role of the zonalmean heating by comparing Figs. 7 and 10. As expected,the latitude of the negative OLR extremes closely co-incides with that of the maximum anomalous verticalwinds as inferred from the anomalous mass stream-function. This relationship is apparent between lag 211and lag 14 days as both the negative OLR extrema andthe center of the two tropical cells move northward to-gether. Furthermore, because the above eddy flux anal-ysis suggests that the eddies do not directly drive theentire anomalous deep tropical meridional circulation,it is likely that at least the low-latitude anomalous me-ridional circulation is in part driven by the anomalouszonal mean heating. However, because the present anal-ysis cannot distinguish whether or not the zonal meanheating is itself driven by the eddies, it is not possibleto speculate whether a zonal mean heating anomaly,independent of the eddy driving, plays an important rolein driving the anomalous friction torque.

d. Eddy surface pressure

In order to investigate the relationship between theanomalous eddy streamfunction field and the anomalousmountain torque, it is useful to examine the anomalouseddy surface pressure field. This is illustrated in Fig. 12at lag 14 days, the time of the maximum anomalousglobal mountain torque. It can be seen that the anom-alous mountain torque at South America is associatedwith a surface anticyclone on the eastern side of theAndes that extends over a large fraction of the continent.The anomalous mountain torque at the Himalaya is as-sociated with a weak surface cyclone on the westernside of the mountains.


FIG. 12. The anomalous surface pressure regressed against the LOD tendency at lag 14days. The contour interval is 20.0 N m22. Solid contours are positive, dashed contoursnegative, and the zero contour is omitted.

A comparison between the anomalous eddy stream-function and eddy surface pressure fields at lag 14 daysreveals a complex relationship between these two fields(see Figs. 8c, 12). However, in general, the eddy surfacepressure anomalies tend to occur in similar geographicallocations as the eddy streamfunction anomalies. An ex-amination of the signs of the anomalies of both fieldssuggests a baroclinic structure in the Tropics, and anequivalent barotropic structure in middle and high lat-itudes. For example, east of the Andes, the 200-mb eddystreamfunction field consists of a relatively strong(weak) upper-tropospheric anticyclone (cyclone) thatoverlaps with the southern (northern) half of the surfaceanticyclone. This indicates that the Andean mountaintorque is associated with a disturbance of both baroclinicand barotropic characteristics. In the Himalaya region,where most of the mountain torque occurs at a lowerlatitude than in the Andes, the eddy surface pressureand streamfunction anomalies have opposite sign, re-vealing that this particular mountain torque is linked toa baroclinic disturbance.

These results imply that one cannot simply infer thesign of the anomalous mountain torque by assumingthat the anomalous surface pressure field resembles theanomalous upper-tropospheric streamfunction. Presum-ably an understanding of these properties can be ob-tained with the aid of potential vorticity inversions (Hos-kins et al. 1985).

5. Conclusions

The primary aims of this study are both to documentthe spatial and temporal properties of the friction andmountain torques and to investigate several of the basicatmospheric dynamical processes associated with intra-seasonal LOD variability during the austral winter. Forthis purpose, we use the LOD timeseries, the NCEP–NCAR reanalysis dataset, and OLR, and regress a num-ber of different quantities against the LOD tendency.

It is found that the anomalous global friction torqueleads the anomalous global mountain torque by abouteight days. The largest contributions to the anomalousglobal friction torque occur at Australia and the adjacentIndian and Pacific Oceans, and southeast Asia, whilethe largest anomalous mountain torque is mostly due tothe Andes. A closer examination of the anomalous fric-tion torque reveals that the dominant contribution comesfrom ocean surfaces, implying that ocean dynamics mustrapidly transfer angular momentum to the solid earthduring the austral winter.

The regression analysis yielded results that suggestthat the friction and mountain torques are both drivenby the response of the atmospheric circulation to thediabatic heating field associated with the MJO. Thisresponse to the MJO heating includes an anomalousmeridional circulation, which excites the anomalousglobal friction torque via an anomalous Coriolis torque,and a direct eddy response to the diabatic heating, whichhas the appropriate phase relative to the topography togenerate a large mountain torque. Although this analysisdid suggest that the anomalous meridional circulationis forced by the anomalous eddy AAM fluxes, and thatthe anomalous eddy AAM fluxes were in turn drivenby the MJO heating, the analysis also points to possibleforcing of the anomalous meridional circulation by zon-al mean heating, as suggested by Hendon (1995).

The results of this study raise several important ques-tions on intraseasonal LOD variability. However, thesequestions are not limited to the austral winter, as theyare equally relevant for the boreal winter. For example,both the present investigation and the intraseasonal bo-real winter LOD–GAAM study of Weickmann et al.(1997) find relationships to tropical convection. To placethis relationship on firmer grounds, it would be nec-essary to use either a barotropic or a multilevel baro-clinic model and examine the response to diabatic heat-ing anomalies resembling those found in observations.Furthermore, the link between the anomalous upper-


tropospheric eddy streamfunction field and anomalouseddy surface pressure field, and hence the anomalousmountain torque, is found to be rather complex. Last,there remains the question of whether the anomalousfriction torque is driven by the zonal mean eddy angularmomentum flux or the zonal mean diabatic heating. Thisquestion is also particularly relevant for the boreal win-ter, as the analysis of section 4c as applied to the borealwinter also reveals that the anomalous friction torqueis driven by the anomalous meridional circulation. Thelatter of these three questions is a subject of ongoingresearch.

Acknowledgments. This research was supported bythe National Aeronautics and Space Administrationthrough Grant NAG5-6207. I would like to thank Drs.Sukyoung Lee, Richard Rosen, Klaus Weickmann, andthree anonymous reviewers for their beneficial com-ments. I would also like to thank the NOAA ClimateDiagnostics Center for providing me with the NCEP–NCAR reanalysis dataset, and Dr. Peter Nelson of theAtmospheric and Environmental Research, Inc., for pro-viding me with the LOD time series.

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