the role of shearwise and transverse …marrella.meteor.wisc.edu/martin_2006.pdfmotions throughout...

The Role of Shearwise and Transverse Quasigeostrophic Vertical Motions in theMidlatitude Cyclone Life Cycle

JONATHAN E. MARTIN

Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, Madison, Wisconsin

(Manuscript received 14 March 2005, in final form 25 July 2005)

ABSTRACT

The total quasigeostrophic (QG) vertical motion field is partitioned into transverse and shearwise cou-plets oriented parallel to, and along, the geostrophic vertical shear, respectively. The physical role playedby each of these components of vertical motion in the midlatitude cyclone life cycle is then illustrated byexamination of the life cycles of two recently observed cyclones.

The analysis suggests that the origin and subsequent intensification of the lower-tropospheric cycloneresponds predominantly to column stretching associated with the updraft portion of the shearwise QGvertical motion, which displays a single, dominant, middle-tropospheric couplet at all stages of the cyclonelife cycle. The transverse QG omega, associated with the cyclones’ frontal zones, appears only after thosefrontal zones have been established. The absence of transverse ascent maxima and associated columnstretching in the vicinity of the surface cyclone center suggests that the transverse � plays little role in theinitial development stage of the storms examined here. Near the end of the mature stage of the life cycle,however, in what appears to be a characteristic distribution, a transverse ascent maximum along the westernedge of the warm frontal zone becomes superimposed with the shearwise ascent maximum that fuelscontinued cyclogenesis.

It is suggested that use of the shearwise/transverse diagnostic approach may provide new and/or sup-porting insight regarding a number of synoptic processes including the development of upper-level jet/frontsystems and the nature of the physical distinction between type A and type B cyclogenesis events.

1. Introduction

The midlatitude cyclone is a propagating baroclinicwave disturbance characterized by the generation, am-plification, and deformation of a lower-troposphericthermal wave. The vertical motions that accompanythese storms represent an important link between theirunderlying dynamics and associated sensible weather,manifest in the characteristic comma-shaped cloud andprecipitation distribution associated with the cyclone.Given their direct relationship to the sensible weatherassociated with cyclones, the distribution of cloud andprecipitation features and diagnosis of their generativevertical motions have been topics of active research formany years. More than 80 yr ago, Bjerknes and Solberg(1922) provided the first insights into the nature of this

distribution by drawing attention to the frontal struc-ture of the midlatitude cyclone. They hypothesized thatupgliding motions along the warm edges of both thecold and warm fronts in the cyclone produced the linearbands of cloud and precipitation associated with each ofthese features. Some years later, Sawyer (1956) andEliassen (1962) provided a solid dynamical explanationfor these frontal upgliding motions demonstrating thatelongated couplets of vertical motion that straddle thegeostrophic vertical shear are a direct consequence of aparticular type of deformation of the lower-tropo-spheric thermal wave—namely, frontogenesis.

In work concerning diagnosis of surface development[i.e., the intensification of a sea level pressure (SLP)minimum], Sutcliffe (1947) demonstrated that a signifi-cant portion of the synoptic-scale vertical motion couldbe attributed to cyclonic vorticity advection by the ther-mal wind (�VT · ��g). Given the nondivergence of thegeostrophic wind on an f plane, this is equivalent to theflux divergence of the vector VT�g, which, by definition,is aligned parallel to the geostrophic vertical shear.

Corresponding author address: Dr. Jonathon E. Martin, Depart-ment of Atmospheric and Oceanic Sciences, University of Wis-consin—Madison, 1225 W. Dayton Street, Madison, WI 53706.E-mail: [email protected]

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Consequently, this portion of the vertical motion isdistributed in couplets aligned along the thermal windvector.

In a pioneering study using output from a frictionless,f-plane, primitive equation channel model of the evo-lution of a baroclinic wave to finite amplitude, Keyseret al. (1992) examined the quasigeostrophic (QG) ver-tical motion in the mature and postmature phases of anidealized cyclone. They demonstrated that the total QGvertical motion is composed of two components, whichthey termed �s and �n.1 The �s component was cellularin structure and attributed to the along-isentrope com-ponent of Q (Qs). The �n component was banded instructure and attributed to the across-isentrope compo-nent of Q (Qn). They concluded that the characteristiccomma-shaped vertical motion distribution of the mid-latitude cyclone arises from a modification of the cel-lular (�s) dipole pattern by the banded (�n) dipolesassociated with frontal zones. Changes in the magni-tude and direction of the geostrophic vertical shearthroughout the midlatitude cyclone life cycle are tied tothe evolution of the cyclone’s thermal structure viathermal wind balance. To emphasize their orientationsrelative to the thermal wind, the present study will referto �s and �n as the shearwise (along shear) and trans-verse (across shear) QG vertical motions, respectively.

Synoptic experience supports the notion that the ex-istence of these two separate components of the verticalmotion field is more than an intellectual curiosity. It isoften observed, for instance, that a transverse (frontal)circulation, while quite capable of producing significantsensible weather, is usually incapable of producing sys-tematic surface development (e.g., Martin 1998). Con-versely, significant surface cyclogenesis is almost alwaysaccompanied by the growth of the “cloud head” portionof the comma cloud structure (e.g., Reed and Albright1986; Bader et al. 1995) whose morphology is oftenunrelated to the evolving frontal structure. Such obser-vations suggest that the transverse and shearwise ver-tical motions may play fundamentally different roles inthe life cycle of the midlatitude cyclone.

Such a suggestion is consistent with simple theoreti-cal expectations concerning the likely cyclogenetic in-fluences of these two components of vertical motion.According to the QG vorticity equation, any localmaximum in upward vertical motion promotes an in-crease in geostrophic relative vorticity (via columnstretching) and, thus, geopotential height or pressurefalls as well. It is fairly clear, however, that the distri-

bution of such upward vertical motion maxima withrespect to the thermal wind vector determines their cy-clogenetic potency to a large degree. For instance, asolitary, purely transverse, thermally direct vertical mo-tion couplet will produce opposing bands of positiveand negative vorticity on the warm and cold sides of theassociated baroclinic zone as shown in Fig. 1a. Notethat none of the hypothesized meridional flow (thinarrows) associated with the intensified circulation willadvect temperature in such a way as to promote cre-ation of a thermal wave.2 A purely shearwise verticalmotion couplet, on the other hand, is clearly associatedwith the development of a thermal wave through col-umn stretching and attendant vorticity production (Fig.1b). Such a thermal wave is an essential component ofthe cyclogenetic environment as viewed from either theQG height tendency (Holton 1992) or potential vortic-ity (PV; Hoskins et al. 1985) perspectives. Thus, theorysupports the notion that shearwise ascent is inherentlyand consistently associated with cyclogenesis.

The purpose of this paper is to consider the validityof this suggestion by means of examining the evolutionsof the separate shearwise and transverse QG verticalmotions throughout the life cycles of two observed mid-latitude cyclones. The paper is structured in the follow-ing way. In section 2 a review of the decomposition ofthe QG vertical motion field into its separate shearwiseand transverse components is given. A synoptic de-scription of the two example cyclone life cycles is of-fered in section 3. In section 4, the separate shearwiseand transverse components of the vertical motion fieldare traced through the life cycles of the two cyclones.Finally, a discussion of the results and some conclusionsare offered in section 5.

2. Isolation of the shearwise and transversecomponents of the vertical motion

a. Quasigeostrophic omega equation

To separate the shearwise and transverse verticalmotions, their respective dynamical forcings must beisolated. Currently, there is no such method availablefor partitioning the full primitive equation vertical mo-tion field. Consequently, we shall consider only the QGvertical motion in this study. Use of the Q vector formof the QG omega equation provides a convenient andrigorous means to isolate the transverse and shearwise

1 Similar reference is made to these two components of QGvertical motion by Pyle et al. (2004) in their study of jet streaks.

2 The isobaric thermal advection by the secondary circulationsimplied in Figs. 1a and 1b is not included in the QG framework.Thus, the conceptual basis for Fig. 1 is conjectural.

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components of the QG vertical motion. FollowingHoskins et al. (1978), the QG omega equation can bewritten as

��2 � f o2

�2

�p2�� 2� · Q, �1�

where Q is defined as

Q � �fo��Vg

�x· ��i � ��Vg

�y· ��j�, �2�

with � � (R/fopo)(po/p)(c/cp). The static stability, , isgiven by � �(RTo/p�o)(��o/�p), where To and �o arethe domain-averaged temperature and potential tem-perature at each level, respectively. For adiabatic, geo-

FIG. 1. (a) Effect of a purely transverse, thermally direct vertical circulation on a zonallyoriented baroclinic zone. Dashed black lines are isotherms at some initial time. Dark (light)shading represents upward (downward) vertical motion [UVM (DVM)]. UVM (DVM) pro-duces cyclonic (anticyclonic) vorticity tendencies, and bold black arrows represent the inducedhorizontal winds. Light gray dashed lines represent the isotherms after exposure to the in-duced circulation. Lighter arrows represent the induced circulations at the ends of linear bandsof ascent and descent. (b) Effect of a shearwise vertical motion couplet on a zonally orientedbaroclinic zone. UVM and DVM regions, initial and final isotherms, and induced circulationsindicated as in (a). Note how the induced circulation produces a thermal wave only in the caseof shearwise vertical motions.

FIG. 2. Schematic describing the natural coordinate partitioningof the Q vector used in this study. Thick dashed lines are isen-tropes on an isobaric surface. Qn (Qs) is the component of Q is then (s) direction, and its divergence is associated with transverse(shearwise) QG vertical motion.


strophic flow the Q vector represents the rate of changeof the vector �p� following the geostrophic wind;

Q � fo�d

dtg�p�, �3�

where d/dtg � �/�p � Vg · �p (the subscript g denotesgeostrophic). Thus, the Q vector contains informationabout the rate of change of both the magnitude and

direction of �p�. As shown in Fig. 2, for any arbitrary Qvector, only the component of Q perpendicular to theisentropes (Qn) can change the magnitude of �p� whileonly the component parallel to the isentropes (Qp) canchange the direction of �p�. The present vector decom-position of Q into components along the direction ofthe potential temperature gradient vector (n) and 90°counterclockwise from that direction (s, s � k � n)follows that outlined in Martin (1999a) and is illustrated

FIG. 3. (a) SLP and 900–500 hPa thickness analyses from the 0-h forecast of the NCEP Eta model valid at 1200UTC 12 Nov 2003. Solid lines are sea level isobars labeled in hPa and contoured every 4 hPa. Dashed lines are900–500 hPa thickness isopleths labeled in dam and contoured every 4 dam. Conventional frontal symbols mark thesurface cold and warm fronts. Thick dashed line is a leeside trough and “L” indicates location of the SLP minimum.(b) 850 hPa geopotential and temperature analyses from the 0-h forecast of the NCEP Eta model valid at 1200 UTC12 Nov 2003. Solid lines are geopotential heights labeled in dam and contoured every 3 dam. Dashed lines areisotherms labeled in °C and contoured every 3°C. (c) 500-hPa geopotential, temperature, and absolute vorticityanalyses from the 0-h forecast of the NCEP Eta model valid at 1200 UTC 12 Nov 2003. Solid lines are geopotentialheights labeled in dam and contoured every 6 dam. Dashed lines are isotherms labeled in °C and contoured every3°C. Absolute vorticity is shaded in units of 10�5 s�1 and contoured every 5 10�5 s�1 beginning at 20 10�5 s�1.


with the aid of Fig. 2. The unit vector in the direction of�� is given by

n ��

|��| . �4�

The component of Q in the direction of n will be de-noted as Qn and is equal to

Qn � �Q · ��

|��| � ��

|��| or Qn � �Q · ��

|��| �n. �5�

Recalling that the QG frontogenesis function is givenby Fg � (Q · ��)/|��| (Hoskins and Pedder 1980), theexpression for Qn reduces to Qn � �Fgn. Thus, Qn islarge (small) where Fg is large (small). By virtue of thedefining orientation of the Qn vectors to isotherms, the

QG forcing of vertical motion associated with Qn (i.e.,�2� · Qn) forces elongated, banded regions of verticalmotion that are parallel to, and associated with, regionsof concentrated baroclinicity (frontal zones) within theflow (Keyser et al. 1992). In other words, the across-isentrope component of Q relates to the forcing oftransverse vertical motions that are uniquely associatedwith frontogenetic and frontolytic processes.

The component of Q along the isentropes will bedenoted as Qs and is equal to

Qs �Q · �k ��

|��| ��k ��

|��| �. �6�

Keyser et al. (1988) demonstrated that, following thegeostrophic flow, the potential temperature gradient

FIG. 4. Same as in Fig. 3, but for 0000 UTC 13 Nov 2003.


vector is rotated in the direction of Qs to a degree pro-portional to the magnitude of Qs (the reader is referredto that work for the complete derivation of this rela-tionship). Keyser et al. (1992) found that the pattern ofvertical motion associated with �2� · Qs was cellularand distributed on the synoptic scale (which theytermed wave scale). A similar result was reported byKurz (1992). By virtue of the orientation of Qs vectorsto the isentropes, the resulting vertical motion coupletsare distributed along, or shearwise to, the thermal wind.Therefore, a precise partitioning of the total QG omegainto shearwise and transverse components is possibleby separately considering the divergence of the Qs andQn components of Q, respectively. Throughout the re-mainder of this paper the shearwise vertical motion willbe understood to be associated with �2� · Qs, while thetransverse vertical motion will be understood to be as-sociated with �2� · Qn.

b. Calculation of QG omega

In the subsequent analysis, gridded model outputfrom the National Centers for Environmental Predic-tion’s (NCEP’s) Eta and Global Forecast System (GFS)models is used in the calculation of the QG omega.These gridded data are first bilinearly interpolatedfrom their original output grid to a 1° 1° latitude–longitude grid at 12 isobaric levels (1000, 900, 800, 700,600, 500, 400, 300, 250, 200, 150, and 100 hPa) using aninterpolation program included in the General Meteo-rology Package (GEMPAK). Employing the techniqueof successive over relaxation (SOR), we then solve thef-plane version of the QG omega equation using a spa-tially averaged static stability that varies for each timewith fo set equal to the central latitude (45.5°N) of thedomain for each of the two cases we examine. Withgeostrophic forcing corresponding to the divergences of



Q, Qn, and Qs, the total, transverse, and shearwise QGvertical motions, respectively, are returned in units ofPa s�1. In the next section we present a brief synopticoverview of two observed cyclones before tracing theevolution of the separate modes of QG vertical motionthroughout the life cycle of these storms.

3. Synoptic description of two case studies

a. The 12–14 November 2003 cyclone

On 11 November 2003, a weak Alberta Clipper wasresponsible for distributing heavy snows in portions ofwestern Canada. From 12–14 November, that initiallyweak storm underwent vigorous and prolonged cyclo-genesis over the northern United States. During that48-h period, the storm deepened explosively (1.11 berg-erons from 1200 UTC 12 November to 1200 UTC 13

November) and traversed the Upper Great Lakesstates in association with the migration of an intenseupper-level front over the same region.

At 0000 UTC 12 November a local minimum in SLPwas located along the Montana/North Dakota borderto the north of a rather featureless lower-troposphericbaroclinic zone spanning the eastern two-thirds of theUnited States (not shown). By 1200 UTC 12 November,the surface cyclone had intensified slightly while mi-grating eastward to northwestern Wisconsin (Fig. 3a).An intense lower-tropospheric thermal contrast had de-veloped by this time as evidenced by the 900–500 hPathickness (Fig. 3a) as well as the substantial tempera-ture gradient at 850 hPa (Fig. 3b). During this sameinterval, an upper-tropospheric baroclinic zone that ex-tended from central Iowa to northern Alberta had alsointensified (Fig. 3c).



Further surface development occurred in the 12 hending at 0000 UTC 13 November, at which time thesurface cyclone center was located near Sault St. Marie,Michigan, and had a well-developed cold front stretch-ing southwestward to central Texas (Fig. 4a). At 850hPa, a strong cold frontal signature was clearly evident,whereas a weaker warm frontal temperature contrastattended by a diffluent geostrophic wind field suggestedmodest frontogenesis over the eastern Great Lakes(Fig. 4b). The upper-level front had greatly intensifiedby this time as it exhibited a 12°C temperature contrastat 500 hPa over approximately 225 km above centralIowa (Fig. 4c). A potent upper-tropospheric short wavehad also developed by this time at the eastern end ofthe upper frontal baroclinic zone over central lowerMichigan as evidenced by the 500-hPa absolute vortic-ity (Fig. 4c).

In association with the continued intensification ofthe upper-tropospheric wave, the surface cyclone also

continued to strengthen, reaching an SLP minimum of981 hPa by 1200 UTC 13 November (Fig. 5a). The cy-clone appeared occluded by this time as the SLP mini-mum was disconnected from the peak of the warm sec-tor. A deep, coherent cold frontal structure also char-acterized the storm at this time as evidenced by the900–500 hPa thickness (Fig. 5a), as well as the 850- and500-hPa potential temperatures (Figs. 5b and 5c). Theprimary upper-level low center was well defined at thistime and the upper front had maintained its consider-able intensity while continuing its eastward migration(Fig. 5c). Evidence of the occluded thermal ridge ap-peared in the 900–500 hPa thickness as well as the tem-perature fields at both 850 and 500 hPa.

Finally, at 0000 UTC 14 November, the cyclone, hav-ing undergone some reorganization in the intervening12 h, was located over northwestern Maine and haddeepened slightly further to 977 hPa. The frontal struc-ture remained robust along the cold front (Figs. 6a and

FIG. 7. Same as in Fig. 3, but from the NCEP GFS analysis valid at 1200 UTC 6 Oct 2004.


6b), and a better-defined warm front and thermal ridgeconnecting the geopotential height minimum to thepeak of warm sector were evident at 850 hPa (Fig. 6b).A similar thermal ridge signature, displaced to thenorth of its counterpart at 850 hPa, was also evident at500 hPa where the upper shortwave was now embeddedwithin a negatively tilted larger-scale trough (Fig. 6c).

b. The 6–8 October 2004 cyclone

At 1200 UTC 6 October 2004 a weak surface cyclonewith a central SLP of 1010 hPa was located well southof the Aleutian Islands (Fig. 7a). The baroclinic zonealong which this cyclone was developing was sharplydefined both in the 900–500 hPa thickness field and the850 hPa isotherms (Fig. 7b) at which level a weak butdiscernible geopotential height trough was clearly evi-dent. At 500 hPa, a shortwave embedded in general

northwesterly flow was characterized by a well-devel-oped thermal perturbation (Fig. 7c).

By 0000 UTC 7 October 2004, the surface cyclonehad progressed eastward and deepened dramatically to995 hPa (not shown). Additional rapid deepening leftthe SLP minimum at 982 hPa by 0600 UTC 7 October(Fig. 8a). By this time, the cyclone also exhibited anascent occluded thermal ridge in the 900–500 hPathickness field. This thermal ridge structure was re-flected at 850 hPa as well (Fig. 8b), where equally im-pressive geopotential height falls characterized the de-velopment. Continued intensification of the upper vor-tex, both in terms of curvature and shear vorticity, wasalso evident at 500 hPa (Fig. 8c), where a well-developed upper front was now located at the base of anegatively tilted, diffluent upper trough.

By 1200 UTC 7 October the central SLP of the sur-face cyclone had dropped to 971 hPa, and a fully de-

FIG. 8. Same as in Fig. 7, but for 0600 UTC 7 Oct 2004.


veloped occluded thermal structure characterized thestorm not only at sea level (Fig. 9a) but also at 850 hPa(Fig. 9b), where, as before, the development was asimpressive as it was at sea level. Even at 500 hPa, wherethe upper vortex and shortwave had further intensified,there was a hint of a thermal ridge wrapping into thegeopotential height minimum (Fig. 9c).

In the 12-h period between 1200 UTC 7 October and0000 UTC 8 October, the minimum SLP of the surfacecyclone oscillated within 2 hPa of 972 hPa as the stormcontinued to wrap up off the Washington/British Co-lumbia coast (Fig. 10a). The occluded thermal ridgelengthened considerably during this wrapping-up pe-riod as evidenced in the all three panels of Fig. 10. Asappears to be characteristic in such wrapped-up storms,

the northern and eastern edges of the vorticity maxi-mum at 500 hPa were nicely coincident with the posi-tion of the surface cold and occluded fronts (Fig. 10c) asdiscussed in Martin (1998).

4. Evolution of the QG omega in the cyclone lifecycles

In this section, we examine the evolution of theshearwise and transverse QG omega for the cyclonesdescribed in section 3. Though omega was available ata variety of vertical levels as described in section 2c,700-hPa omega is most consistently representative ofthe distribution of vertical motions in the lower tomiddle troposphere throughout the life cycle, and we



chose to employ 700-hPa omega in the subsequent pre-sentation. We begin by examining the QG omega evo-lution in the November 2003 storm.

a. Partitioned QG omega for November 2003 case

The total 700-hPa QG vertical motion field at 1200UTC 12 November 2003 is shown in Fig. 11a. As mightbe expected in association with a developing surfacecyclone, a broad region of modest ascent occurs overand to the northeast of the SLP minimum while equallymodest descent occurs to the west. Evidence for na-scent frontal circulations is apparent in the transversecouplets associated with the cold front and less-organized warm front (Fig. 11b). The transverse verti-

cal motions were related to regions of QG frontogen-esis (not shown) as expected. At this early stage indevelopment, however, the essential character of thecyclone’s vertical motion field is better represented bythe shearwise vertical motions (Fig. 11c).

The distribution is rather similar at 0000 UTC 13November at which time a much more robust couplet ofvertical motion characterizes the cyclone (Fig. 12a)with the greatest ascent nearly directly above the SLPminimum. The cold frontal circulation had intensifiedby this time, as had that associated with the barocliniczone centered over the Upper Peninsula of Michigan(Fig. 12b). Both of these locations were local maxima ingeostrophic frontogenesis (not shown). Evidence for aquadrapole distribution of omega around the upper-



level jet/front feature, albeit with a weak right exit re-gion component, also appears in the transverse verticalmotion field from Lake Erie to western Nebraska.Once again, however, the predominant component ofQG vertical motion was the solitary shearwise coupletwhose ascent branch was located directly above theSLP minimum (Fig. 12c).

By 0000 UTC 14 November, a more highly amplifieddistribution of stronger QG vertical motions was evi-dent in association with this developing storm (Fig.13a). Note that, at this time, the maximum QG ascent inthe cloud head portion of the cyclone was aligned along

a narrow band roughly parallel to the 900:500 hPathickness ridge axis with the SLP minimum locatedslightly southwest of the maximum. The transverseomega field also displays a number of interesting char-acteristics (Fig. 13b). First, a strong cold frontal circu-lation is particularly evident over the southern Appa-lachians where geostrophic frontogenesis was strongest.The secondary maximum in transverse ascent, locatedover the Canadian Maritimes, combined with the as-cent portion of the Appalachian couplet forms a coher-ent band of ascent associated with the cold front. Itappears that the northern piece is associated with the

FIG. 11. (a) Total 700-hPa QG omega and 900–500 hPa thickness derived from the NCEP Eta model analysisvalid at 1200 UTC 12 Nov 2003. Dark (light) shading is negative (positive) omega labeled in dPa s�1 and contouredevery �2 (2) dPa s�1 starting at �1 (1) dPa s�1. The 900–500 hPa thickness (thin solid lines) is labeled in dam andcontoured every 4 dam. Frontal symbols and “L” indicate surface frontal positions and location of the SLPminimum, respectively. (b) Same as in (a), but for 700-hPa transverse QG omega at 1200 UTC 12 Nov 2003. (c)Same as in (a), but for 700-hPa shearwise QG omega at 1200 UTC 12 Nov 2003.


cold front aloft portion of the robust warm occludedthermal structure exhibited by this storm at this time.Though the shearwise vertical motions are still charac-terized by a single, dominant couplet with ascent overQuebec and the Maritime Provinces and descent con-centrated to the southwest over eastern Kentucky (Fig.13c), a couple of characteristics of that couplet are dif-ferent at this stage in the life cycle as compared to priorstages.3 First, the SLP minimum is not directly beneath

the maximum in ascent. Second, the ascent is domi-nated by a narrow band of large vertical motionsaligned nearly along the 900–500 hPa thickness ridge,rather abruptly ending at the peak of the warm sector.

b. Partitioned QG omega for October 2004 case

At 1200 UTC 6 October, a modest couplet of QGvertical motion straddled the trough in the 900–500 hPathickness (Fig. 14a). As might be expected in associa-tion with a developing surface cyclone, the ascent oc-curred over and to the northeast of the surface cyclonewhile the slightly stronger descent occurred to the west.Very little evidence for frontal circulations is evident inthe transverse component of the QG omega (Fig. 14b)at this time as almost no geostrophic frontogenesis was

3 The QG � field appears to be more structured than the flowitself in Fig. 13c. Since Q is the product of derivatives of thethermal and geostrophic momentum fields, each of which has awavelike character, the multiplication of the two tends to halvethe wavelength.



occurring at 700 hPa (not shown). In fact, at this na-scent stage of development, the QG omega is almostentirely manifest in the shearwise couplet (Fig. 14c).

The distribution is essentially the same 12 h laterwhen the cyclone had just entered an extended periodof rapid development. The total 700-hPa QG omegadisplays a wavelike distribution with the ascent portionof the couplet centered just to the northeast of the sur-face cyclone center (Fig. 15a). The more linear descentregion stretches along the cyclonic shear side of thedeveloping upper front discussed previously. Indeed, athermally direct transverse circulation along that baro-clinic zone appears in Fig. 15b, along with a weak ascentregion associated with the western edge of the devel-oping surface warm front. The majority of the middle-tropospheric QG omega is, however, associated withthe shearwise component (Fig. 15c).

Continued rapid deepening of the cyclone through0600 UTC 7 October was coincident with a more thandoubling of the 700-hPa QG omega by that time (Fig.16a) as compared to 6 h earlier. As before, the strongascent was located just northeast of the position of theSLP minimum. The partitioned QG omega at this time,however, revealed that the frontal circulations associ-ated with the cyclone had become more robust withclear transverse couplets of omega associated with theelongated surface cold front and the stubbier surfacewarm front (Fig. 16b). Note that the ascent maximumassociated with the warm frontal circulation is nearlycentered on the surface cyclone center. This is relatedto the presence of a maximum in 700-hPa geostrophicfrontogenesis directly north of the position of the sur-face low (not shown). Despite the clear structure evi-dent in the transverse vertical motions, the lion’s share



of the QG omega is still contained in the shearwisecomponent (Fig. 16c). At this time, however, the shear-wise ascent maximum lies just to the north of the SLPminimum.

By 1200 UTC 7 October, at which time the explosivedeepening was finally coming to an end, the total 700-hPa QG omega was at its most intense with the ascent(descent) maximum at �25 dPa s�1 (17 dPa s�1)(Fig.17a). At this time, the surface cyclone was locatedslightly northward of the boundary between a north–south-oriented couplet of vertical motion. The robusttransverse couplets, first identified 6 h earlier, were stillclearly identified in the transverse omega (Fig. 17b).The most intense transverse circulation remained re-lated to quasigeostrophic frontogenesis along thenorthwest edge of the occluded thermal ridge [in theregion of strongest geostrophic winds in the lower tomiddle troposphere (see Fig. 9b)] and helped to pro-

vide strong transverse ascent just north of the surfacecyclone. In fact, that ascent maximum accounted forjust over 40% of the total QG omega near the cyclonecenter at this time—a much larger fraction than at anyprior time. The majority of the QG omega was still,however, associated with the shearwise component(Fig. 17c). After this time, the QG vertical motionsweakened rapidly and development ceased. By 0000UTC 8 October, the total QG omega was again splitabout 40/60 between the transverse and shearwise com-ponents (not shown).

5. Discussion

Keyser et al. (1992) were among the first to considera partition of the QG omega into along- and across-isentrope components. They found that the character-istic comma-shaped vertical motion distribution of the

FIG. 14. Same as in Fig. 11, but derived from the NCEP GFS model analysis valid at 1200 UTC 6 Oct 2004.


midlatitude cyclone resulted from modifications of acellular dipole pattern in �, associated with along-isentrope Q divergence, by banded dipoles associatedwith across-isentrope Q divergence concentrated nearthe frontal zones. Their analysis was restricted to themature and immediate postmature phases of an ideal-ized, primitive equation, channel model cyclone andemphasized the pattern separation between the twocomponents of vertical motions rather than their re-spective physical roles in the cyclone life cycle.

The Keyser et al. (1992) study prompted a number ofsubsequent efforts that have employed partitioned QGomega diagnostics to investigate a variety of canonicalsynoptic structures [i.e., cold fronts as in Barnes andColeman (1993) and occlusions as in Martin (1999a,b)].To our knowledge, however, the only examinations ofobserved cyclone life cycles employing a similar parti-tion of the Q-vector forcing for omega, prior to thepresent paper, were those undertaken by Kurz (1992,

1997).4 In these studies emphasis was placed upon therespective cyclogenetic and frontogenetic processesrepresented by the partitioned Q-vector forcings. Kurz(1992) concluded that a QG frontogenetic circulationoften leads to the first stages of lower-tropospheric cy-clogenesis but that it must be supported by ascent as-sociated with the passage of an upper-troposphericshortwave trough in order to sustain development.Careful consideration of the evidence he presents (seehis Fig. 8), however, suggests to the author that eventhe initial cyclogenesis proceeds only when the shear-wise forcing for ascent arrives in the vicinity of thesurface development. Thus, a plausible alternative in-terpretation of his evidence is that shearwise ascent

4 Martin (1999a) examined the Qs/Qn partition in real cyclonesbut at only one time. Additionally, Martin (1999b) considered asubstantial portion of a cyclone life cycle but only with regard toa further partition of Qs.



dominates the cyclogenesis throughout the develop-ment. It is important to note that the Kurz studies showonly the forcing for QG omega from each componentof Q, not the actual inverted omega. This can some-times complicate interpretation in synoptic settingscharacterized by weak forcing and may underlie thedivergence of opinion in this case.

In the present study we have referred to the twocomponents of QG omega as transverse and shearwise,corresponding to those associated with the across- andalong-isentrope components of Q, respectively. Thetransverse omega is associated with processes that in-tensify or weaken |��| (i.e., QG frontogenesis), whilethe shearwise omega is associated with processes thatrotate ��.

In the foregoing analysis, we have traced the evolu-tions of the shearwise and transverse vertical motionsthrough the life cycles of two recent Northern Hemi-sphere surface cyclones. That analysis, as well as the

less thorough examination of a large number of othercases (not shown), has suggested the following dynami-cal picture of the cyclone life cycle. (Other cases aremonitored by daily perusal of a Web site on which par-titioned QG �, calculated using NCEP–NCAR modeloutput, is displayed each day; the address for this Website is http://marrella.aos.wisc.edu/omega/omega.html.)The origin and subsequent intensification of the lower-tropospheric cyclone appears connected to the columnstretching and lower-tropospheric vorticity productionassociated with the updraft portion of the shearwiseQG vertical motion, which displays a single, dominant,middle-tropospheric couplet at all stages of the cyclonelife cycle. The shearwise ascent is associated with along-isentrope Q-vector convergence that is consistent withthe simultaneous production of a thermal ridge in thelower troposphere (Martin 1999a). This set of circum-stances represents the canonical cyclogenetic environ-ment as described by Hoskins et al. (1985); one char-



acterized by ascent and a lower-tropospheric warmanomaly located downstream of an upper-troposphericpotential vorticity anomaly. It is worth noting that thetransverse couplets of vertical motion, unrelated asthey are to rotation of ��, are never associated with theproduction of such thermal anomalies. This restrictionis consistent with the repeated observation that thetransverse omega does not play a significant role in theincipient stages of cyclogenesis.

The transverse omega, associated with the frontalzones of the cyclone, appears only after those frontalzones have been established and plays little role in ini-tiating the development of the surface cyclones exam-ined here as a result of the absence of associated localmaxima in column stretching near the cyclone center.In fact, less careful examination of a large number of

cyclone life cycles over the Northern Hemisphere in theprior winter has revealed no case in which the trans-verse omega so influences surface cyclogenesis, con-trary to the suggestion of Kurz (1992). It does appear,however, that near the end of the mature stage of thelife cycle, a transverse response to QG frontogenesisalong the western edge of the warm frontal zone (wherethe geostrophic wind is often very large in the lowertroposphere) results in a local maximum of ascent co-incident with the shearwise ascent that fuels the con-tinued cyclogenesis (see Figs. 14b, 16b, and 17b). Thissame signal appeared in a large number of other cases,of varying intensities, in the course of this work andappears, therefore, to be a characteristic aspect of thelife cycle.

The present study’s persistent lack of evidence for



cyclogenesis events whose initial stages are character-ized by dominant transverse QG ascent seems at oddswith a large body of prior work concerning the natureof midlatitude cyclogenesis. In their examination ofcomposites of typical surface developments over theNorth Atlantic Ocean more than 40 yr ago, Petterssenet al. (1962) suggested that surface cyclogenesis comesin two basic types. Formally designated as type A andtype B by Petterssen and Smebye (1971), the distinctionbetween these varieties was based upon the two sepa-rate forcing terms in the traditional QG omega equa-tion. Type A cyclones were thought to develop in theabsence of any significant upper-level disturbance. Cor-respondingly, the influence of differential vorticity ad-vection (the first term in the traditional QG omegaequation) was considered much smaller than the influ-ence of the Laplacian of thermal advection (the secondterm in the omega equation) in such cases. Type Bcyclogenesis occurred when a preexisting upper troughapproached a low-level baroclinic zone. In such a case,the influence of vorticity advection overwhelmed thatof thermal advection in the initial cyclogenetic stage.

Petterssen et al. (1962) and Petterssen and Smebye(1971) both tacitly assumed that the vorticity advectionwas most significant at upper-tropospheric levelswhereas the influence of thermal advection was largestat lower-tropospheric levels. Deveson et al. (2002) re-cently noted, however, that the implicit assumption thatboth thermal advection forcing at upper levels and vor-ticity advection forcing at lower levels are negligible hasnever been suitably demonstrated. The resulting em-phasis on the levels at which these processes occur, in-spired by the assumptions made in the seminal workson this topic, has subsequently grown to eclipse an em-phasis on the processes themselves.

Equally troubling is the fact that these processes, rep-resented by the supposedly separate forcing terms inthe traditional QG omega equation, contain consider-able internal cancellation as pointed out by Trenberth(1978). The vector frontogenesis approach (Keyser etal. 1988), which considers the across- and along-isentrope components of the Q vector, casts this forcingin terms of changes in the magnitude and direction of��, respectively, and by so doing places investigation ofthe relationship between QG omega and the underlyingdynamics of midlatitude cyclones on a more physicallysatisfying foundation. We suggest that the shearwise/transverse perspective on QG omega, coupled with theheight attributable diagnostic method of Clough andDavitt (1994) and Clough et al. (1996) may provide newinsight by helping to refocus the type A/B debate onphysical processes while maintaining a respect for the

importance that the vertical distribution of those pro-cesses has on cyclogenesis.

The analysis presented here, in conjunction with alarge number of cases examined in lesser detail, sug-gests that, in many cases, cyclogenesis slightly precedesfrontogenesis and that the generation of a lower-tropospheric cyclone is initiated by shearwise coupletsof vertical motion. We expect that an emphasis onshearwise and transverse vertical motions might be use-fully employed to reconsider the physical processes thatunderlie the development of a number of canonical dis-turbances in the midlatitude atmosphere including up-per-level fronts, documented type A cyclogenesisevents [examples of which are included in Petterssen etal. (1962) and Plant et al. (2003)], and jet streak circu-lations. Future work will pursue investigation of suchfeatures from this perspective.

Acknowledgments. This research was supported by agrant from the National Science Foundation (NSF-0202012). Assistance with the computation of QGomega by Dr. Justin McLay is greatly appreciated. Dis-cussions concerning QG omega with Drs. Michael Mor-gan and Chris Davis are also appreciated. The carefuland insightful reviews of Dr. David Schultz, two anony-mous reviewers, and Dr. Juan Carlos Jusem are greatlyappreciated as well.

REFERENCES

Bader, M. F., G. S. Forbes, J. R. Grant, R. B. E. Lilley, and A. J.Waters, 1995: Images in Weather Forecasting. CambridgeUniversity Press, 499 pp.

Barnes, S. L., and B. R. Coleman, 1993: Quasigeostrophic diag-nosis of cyclogenesis associated with a cutoff extratropicalcyclone—The Christmas 1987 storm. Mon. Wea. Rev., 121,1613–1634.

Bjerknes, J., and H. Solberg, 1922: Life cycle of cyclones and thepolar front theory of atmospheric circulation. Geofys. Publ.,3, 1–18.

Clough, S. A., and C. S. A. Davitt, 1994: Development of an At-lantic frontal wave during IOP3 of Fronts92. The Life Cyclesof Extratropical Cyclones, S. Gronas and M. A. Shapiro, Eds.,Vol. 2, Geophysical Institute, University of Bergen, 151–156.

——, ——, and A. J. Thorpe, 1996: Attribution concepts appliedto the omega equation. Quart. J. Roy. Meteor. Soc., 122,1943–1962.

Deveson, A. C. L., K. A. Browning, and T. D. Hewson, 2002: Aclassification of FASTEX cyclones using a height-attrib-utable quasi-geostrophic vertical-motion diagnostic. Quart. J.Roy. Meteor. Soc., 128, 93–117.

Eliassen, A., 1962: On the vertical circulation in frontal zones.Geofys. Publ., 24, 147–160.

Holton, J. R., 1992: An Introduction to Dynamical Meteorology.3d ed. Academic Press, 511 pp.

Hoskins, B. J., and M. A. Pedder, 1980: The diagnosis of middlelatitude synoptic development. Quart. J. Roy. Meteor. Soc.,106, 707–719.


——, I. Draghici, and H. C. Davies, 1978: A new look at the�-equation. Quart. J. Roy. Meteor. Soc., 104, 31–38.

——, M. McIntyre, and A. W. Robertson, 1985: On the use andsignificance of isentropic potential vorticity maps. Quart. J.Roy. Meteor. Soc., 111, 877–946.

Keyser, D., M. J. Reeder, and R. J. Reed, 1988: A generalizationof Petterssen’s frontogenesis function and its relation to theforcing of vertical motion. Mon. Wea. Rev., 116, 762–780.

——, B. D. Schmidt, and D. G. Duffy, 1992: Quasigeostrophicvertical motions diagnosed from along- and cross-isentropecomponents of the Q vector. Mon. Wea. Rev., 120, 731–741.

Kurz, M., 1992: Synoptic diagnosis of frontogenetic and cycloge-netic processes. Meteor. Atmos. Phys., 48, 77–91.

——, 1997: The role of frontogenetic and frontolytic wind fieldeffects during cyclonic development. Meteor. Appl., 4, 353–363.

Martin, J. E., 1998: The structure and evolution of a continentalwinter cyclone. Part I: Frontal structure and the occlusionprocess. Mon. Wea. Rev., 126, 303–328.

——, 1999a: Quasigeostrophic forcing of ascent in the occludedsector of cyclones and the trowal airstream. Mon. Wea. Rev.,127, 70–88.

——, 1999b: The separate roles of geostrophic vorticity and de-formation in the midlatitude occlusion process. Mon. Wea.Rev., 127, 2404–2418.

Petterssen, S., and S. J. Smebye, 1971: On the development ofextratropical cyclones. Quart. J. Roy. Meteor. Soc., 97, 457–482.

——, D. L. Bradbury, and K. Pedersen, 1962: The Norwegiancyclone models in relation to heat and cold sources. Geofys.Publ., 24, 243–280.

Plant, R. S., G. C. Craig, and S. L. Gray, 2003: On a threefoldclassification of extratropical cyclogenesis. Quart. J. Roy. Me-teor. Soc., 129, 2989–3012.

Pyle, M. E., D. Keyser, and L. F. Bosart, 2004: A diagnostic studyof jet streaks: Kinematic signatures and relationship to co-herent tropopanse disturbances. Mon. Wea. Rev., 132, 297–319.

Reed, R. J., and M. D. Albright, 1986: A case study of explosivecyclogenesis in the eastern Pacific. Mon. Wea. Rev., 114,2297–2319.

Sawyer, J. S., 1956: The vertical circulation at meteorologicalfronts and its relation to frontogenesis. Proc. Roy. Soc. Lon-don, A234, 346–362.

Sutcliffe, R. C., 1947: A contribution to the problem of develop-ment. Quart. J. Roy. Meteor. Soc., 73, 370–383.

Trenberth, K. E., 1978: On the interpretation of the diagnosticquasi-geostrophic omega equation. Mon. Wea. Rev., 106,131–137.


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