452 MONTHLY WEATHER REVIEW VOLUMI/!14 REVIEWA Review of the Structure and Dynamics of Upper-Level Frontal Zones DANIEL KEYSERLaboratory for Atmospheres, NASA/Goddard Space Flight Center, Greenbelt, MD 20771 M. A. SHAPIRONOAA/ERL/Wave Propagation Laboratory, Boulder, CO 80303(Manuscript received 28 March 1985, in final form 3 September 1985) This article presents a review of upper-level fronts wi~h the intent of synthesizin~ observational and modelingstudies into a conceptual and dynamical description of these fronts and their evolution relative W the life cycleof midiatitude baroclinic waves. The discussion be~/ns by tracing present-day concepts concerning the suuaureof upper-level frontal systems, which are based on compoaite analyses of radiosonde and aircraft da~a, fromtheir origins in the pioneering analyses of upper-air de~a in the 1930s. Perspectives from scales both smallerand la~er than upper-level frontal systems are provided respectively by considering the effect~ of turbulentprocesses on frontal s~ruaure and dynamics and by relating variations in frontal structure to the evolution ofthe baroclinic waves that provide the dynamical environment for upper-level fronto~enesls. The dynamic~ of upper-level fronts are shown to comprise the interactions between the primary (~eostrophic)and secondary (a~eostrophic) circulations. To elucidate the mechanisms and feedbacks contributing to theevolution of upper-level fronts in relation to their setting within baroclinic waves, the two-dimens/onal theoryof forced secondary drculafions in the cross-front plane developed by Sawyer and E!iassen is presented andinterp~x~ed, and theoretical and numerical examples of the formation of upper-level fronts in ideal/zed twodimensional flows are reviewed. In th9 three~mensional case, the presence ofalong-front ageostrophic circulationssuperimposed upon the cross-front agaostrophic circulations treated by the two-dimensional theory is discussedin terms of the gradient wind. The relative contribution of the along-front ageostrophic circulation to upperlevel frontngenesis is considered in the context of the results from three-dimensional ~-plane channel modelsof baroclinic wave growth. Directions for future observational, diagnostic and theoretical investigation are identified, including the scaleinteractions between upper-level fronts, their environmental baroclinic waves and related low-level cyclones,and between upper-level fronts and mesoscale convective systems. The review concludes with a discu,~ion ofthe potential role of recent innovations in remote-sensing technology and trend~ in numerical weather predictionusing me~cale models in motivating continuing interest and future advances in frontal r~,arch.CONTENTS PageI. Introduction ....................... 4522. Observations of Upper-Level FrontalStructure .......................... 454a. Historical overview ............... 454b. The contemporary structural model ofupper-level frontal systems ......... 458c. The effects of turbulent processes onupper-level frontal systems ......... 461d. The relationship of upper-level frontalsystems to baroclinic wave structure 4663. Diagnosis of Transverse Ageostrophic Circulations in Upper-Level Frontal Zones 470a. Dynamical equations for absolute momentum and potential temperature .. 472 b. The Sawyer-Eliassen equation for the transverse ageostrophic circulation .. 4734. Dynamical Models of Upper-Level Frontogenesis ............................ 479a. Two-dimensional processes ........ 479b. Three-dimensional processes ....... 4855. Directions of Future Research ......... 4916. Conclusion ........................ 495List of Symbols and Acronyms .......... 4961. Introduction A fundamental property of baroclinie wave distur- 'bances is the tendency for synoptic-scale variations inthe thermal and wind fields to become concentratedinto narrow transition zones referred to as fronts.Fronts are characterized by large horizontal temperature gradients, static stability, absolute vorticity andvertical wind shear. When viewed on surfaces of constant pressure or height, fronts appear as long, narrowfeatures with the along-front scale typically an orderFEBRUARY 1986 DANIEL KEYSER AND M. A. SHAPIRO 453of magnitude larger than the cross-front scale (10002000 km compared with 100-200 km). Because of thisgeometrical configuration, horizontal variations in thethermal and wind fields tend to be much greater in thecross-front than in the along-front direction. When depicted in vertical cross section, fronts appear as slopingzones with a vertical thickness typically on the orderof 1 to 2 km. Although fronts have been identified atall levels in the troposphere and lower stratosphere,their formation is favored by the presence of the naturally imposed quasi-horizontal boundaries consistingof the Earth's surface and the tropopause. Since frontsgenerated by processes based at the surface and at thetropopause exhibit differences in structure, are generated by distinct dynamical processes, and may occurindependently of each other, the respective designationsof "surface" or "low-level" and "upper-tropospheric"or "upper-level" serve as a convenient classificationfor frontal phenomena and processes. Fronts owe their existence in a kinematic sense (Petterssen, 1936, 1956; Miller, 1948) to spatially differential advection of the thermal and wind patterns resulting from sheared horizontal and vertical velocityfields associated with baroclinic waves. For example,in the absence of diabatic processes, horizontal potential temperature gradients are modified following parceltrajectories by horizontal confluence and convergencealong with tilting of vertical gradients of potential temperature (static stability) into the horizontal plane according to = oo (1.1) dt ~On] On On On Op'In this equation, 0 is potential temperature, n is a horizontal coordinate oriented normal to the isentropesdepicted on a constant pressure surface (positive towardcolder air), v, is the component of velocity in the ndirection, and w is the vertical velocity in the pressure(p) coordinate system (symbols and acronyms appearing in this paper are listed in the Appendix). In theabsence of frictional processes, absolute vorticity measured on pressure surfaces is generated along parceltrajectories by horizontal convergence and the tiltingof vertical wind shears into the horizontal plane according to OVd(~';f)= -(~'+ f)Vv.V- k' (Vvw X ~p). (1.2)In (1.2), ~'is the relative vorticity evaluated on surfacesof constant pressure and fis the Coriolis parameter.The horizontal wind velocity is denoted by V, and thehorizontal gradient operator for surfaces of constantpressure by Vv. Spatially differential advection is responsible notonly for generating frontal properties consisting ofhorizontal and vertical gradients of the thermal andwind fields, but also for the long, narrow geometricalconfiguration of frontal zones. Shears in the three-dimensional velocity field are associated with deformation in horizontal and vertical planes, which has theproperty of stretching and constricting broad regionsof a fluid into narrow zones. A classic demonstrationof this "scale-contraction process" is given by Welander(1955) in numerical simulations with a barotropicmodel of the evolution of a passive tracer in a flowfield typical of those observed in the midtropospherewithin midlatitudes. Further evidence for the frontogenetical role of deformation is found in the appearanceof impressively realistic front-like features in the laboratory experiments of Fultz (I 952) and Failer (1956),in which baroclinic eddies resembling midlatitude cyclones develop in a differentially heated, rotating fluid.The dynamics of frontogenesis, which account for themutual interactions among the thermal and wind fields,are strongly influenced by the Earth's rotation throughthe Coriolis force. The significant role of rotation infronts distinguishes them from a number of relatedphenomena in which divergence is dominant, such asinternal gravity waves, gravity or density currents andsquall lines. Furthermore, lineal phenomena generatedprimarily through localized surface-based differentialheating rather than synoptic-scale deformation (e.g.,sea-breeze fronts) usually are excluded from dynamicalconsiderations of fronts. The time scale in which frontsform from "smooth" synoptic-scale variations in thethermal and wind fields is on the order of several days,although rapid intensification may be focused intoshorter, mesoscale periods of 6 to 12 h. The meteorological significance of both surface andupper-level fronts stems from their relationship to thestructure and evolution of midlatitude baroclinic wavesand cyclones. Although fronts occupy only a relativelysmall fraction of the atmospheric volume affected bybaroclinic waves, they contribute a substantial fractionof the dynamical forcing for the irrotational part of theageostrophic circulation, which contains the divergenceand vertical motion fields. The divergence patterns associated with upper-level frontal systems and their accompanying jet streaks~ play an active part in midlatitude cyclogenesis by contributing to low-level geopotential height (mass) changes. The vertical circulations associated with upper-level and surface frontal zones also are a component in the development andorganization of midlatitude cloud and precipitationsystems, which assume a diversity of forms rangingfrom areas of widespread slant convection, organizedsystems of upright convection, and individual convective storms. Upper-level fronts are of further interestbecause they are preferred regions of small-scale mixingby a variety of phenomena including gravity waves, ~ Palm6n and Newton (1969, p. 199, pp. 206-212) use the term"jet streak" to describe a wind speed maximum situated along theaxis of a jet stream at the level of maximum wind.454 MONTHLY WEATHER REVIEW VOLUME 114Kelvin-Helmholtz billows and patchy turbulent eddymotions, all of which are labeled generically as clearair turbulence (CAT). The location and intensity ofupper-level fronts and jets are of considerable relevanceto aircraft operations not only for avoiding regions ofCAT and its'potential safety hazards, but also for economical flight routing in terms of fuel consumption.Finally, upper-level fronts are regions of significantmass exchange between the stratosphere and troposphere, including radioactive debris and chemical traceconstituents. This review is intended to document the present levelOf knowledge and understanding of upper-level fronts,with an emphasis on their relationship to the structureand life cycle of midlatitude baroclinic waves? An examination of low-level fronts is considered beyond thescope of this review, as this topic is of sufficient extentand depth to be treated separately.3 The motivationfor a review of upper-level fronts derives from the contention that observational research, which in the pasthas been based substantially on operationally availableradiosonde data and in recent times supplemented byresearch aircraft measurements, has matured to a pointof diminishing returns. Nevertheless, emerging remotesensing technologies such as ground-based wind profiling systems and satellite-derived soundings of temperature, moisture and ozone offer the possibility offilling some of the gaps in spatial coverage, temporalresolution and data uncertainty characteristic of radiosonde instrumentation. Parallel advances in computingtechnology are leading to limited-area mesoscale models with sufficiently fine horizontal and vertical resolution to resolve upper-level frontal systems explicitlyfor the first time. By providing temporally continuous,high-resolution, dynamically consistent datasets, numerical models offer the potential of conducting realistic diagnostic investigations and of testing hypothesesthrough systematic, controlled experimentation. It istempting to speculate that research on upper-levelfronts is on the threshold of major advances comparable with those realized in the past from radiosondeand aircraft observations. Consequently, an objectiveof this review not only is to place current knowledgeand thinking into perspective by tracing its evolutionfrom previous concepts, but also to identify unresolvedproblems and controversies in order to establish contexts and directions for future research. - Section 12 documents the evolution of structural 2 This review is restricted to upper-level frontal systems foundwithin midlatitude baroclinic waves. The structure of upper-levelfrontal systems associated with the subtropical jet stream is reviewedby Palm6n and Newton (1969, pp. 212-227). Recent examples ofupper-level frontal systems observed in arctic regions are providedby Shapiro et al. (1984b) and Shapiro (1985). 3 Readers interested in recent reviews of surface fronts from anobservational perspective may consult Palm6n and Newton (1969,pp. 259-263), Shapiro (1983) and Keyser (1986); theoretical aspectsare covered by Hoskins (1982) and Bluestein (1986).models of upper-level frontal systems, beginning withearly applications of upper-air data in the 1930s andconcluding with present concepts based on analysescombining radiosonde and aircraft observations. Perspectives from scales smaller and larger than frontsthemselves are provided respectively by considering theeffects of turbulent processes on frontal structure anddynamics and by relating variations in frontal structureto the stages of development of the baroclinic wavesthat provide the frontogenetical environment duringtheir life cycle. Section 3 presents the two-dimensionaltheory for determining the ageostrophic, vertical circulations associated with frontal zones that was introduced by Sawyer (1956) and extended by Elie~ssen(1962). In Section 4, theoretical and numerical evidence is presented for dynamical processes involved inthe formation of upper-level fronts in idealized twodimensional flows and in three-dimensional barrx:linicwaves. Unresolved issues.and problems awaiting fi~tureresearch are identified and discussed in Section 5, andthe review is concluded in Section 6.2. Observations of upper-level frontal structure The first descriptions of the three-dimensional thermal structure associated with midlatitude baroclinicwaves and cyclones resulted from analyses of observations taken over northern Europe with lightweight,retrievable, balloon-borne meteorographs that recordedtemperature and pressure. These instruments wereconstructed during the late 1920s by Jaumotte in Uccle,Belgium (Bjerknes and Palm6n, 1937), and set the stagefor the introduction of the radiosonde and systematicupper-air observations in the 1930s. The early investigations revealed narrow zones Of concentrated thermal contrast extending through the middle and 'appertroposphere, resulting in the generalization of previousfrontal concepts based on surface observations alone.The modification and evolution of structural modelsand interpretations pertaining to upper-level fronts andthe tropopause are discussed in this section. The discussion begins with the schematic in Fig. I from Reedand Danielsen (1959) illustrating several models foranalyzing upper-level fronts and tropopauses.a. Historical overview A representative example of the investigations of thestructure of upper-level fronts and the tropopause basedon meteorograph ascents is that of Bjerknes and Palm6n (19 37).~ Figure 2 consists of vertical cross sectionsof temperature and potential temperature extendingnortheastward across Europe from Spain to Sweden.Prominent features include the familiar vertical lapseof temperature in the troposphere and the ow,'rlying n Additional references are cited and summarized by Palrn6n andNewton (1969, pp. 131-133).F~BRUARY 1986 DANIEL KEYSER AND M. A. SHAPIRO 455(-1 F~G. 1. Schematic diagrams of models used in the past for analyzing upperlevel fronts and tropopauses: (a) Bjerknes and Palm6n (1937); (b) Palm6n andNagler (1949); (c) Berggren (1952); (d) Reed and Danielsen (1959). See section2a for detailed discussion. From Reed and Danielsen (1959). FIG. 2. Cross sections from Spain to Sweden of temperature (-C, top) and potential temperature (K, bottom) for the evening of 15 February t935,depicting the structure of the tropopause and an upper-level frontal zone analyzed to extend to near the Earth's surface. Thin solid lines denoteisotherms or isentropes, thick solid lines depict frontal and tropopause boundaries, and thick dashed lines represent bases of temperature inversions.From Bjerknes and Paim6n (1937).456 MONTHLY WEATHER REVIEW VOLUMI:, 114nearly isothermal stratosphere, which slopes downwardtoward the north. A deep frontal layer, characterizedby enhanced static stability and horizontal gradientsof temperature, extends from the surface to the uppertroposphere. This type of frontal zone was envisionedto separate polar from tropical air at all altitudes, andcan be considered a vertical extension of the polar frontidentified by the Bergen School in Norway in theirclassic conceptual model of the structure and evolutionof midlatitude cyclones (Bjerknes, 1919; Bjerknes andSolberg, 1921, 1922). At the upper extent of the frontal zone in Fig. 2,where the horizontal temperature gradient becomesdiffuse, the tropopause is folded into a characteristic"S" shape (Fig. la). The analysis of the fold is derivedfrom soundings in the vicinity of upper fronts thatcontain an upper-tropospheric layer of pronouncedstatic stability with potential temperatures at its basesimilar to those along the adjoining northern tropopause surface. The separation between the upper extension of the front and the folded tropopause inhibitsthe exchange of mass between the stratosphere andtroposphere in the region of the fold. Nevertheless,quasi-horizontal transport between the stratosphereand troposphere is permitted in regions such as thatsouth of the frontal zone where the tropopause risesdiscontinuously in a series of steps consisting of overlapping leaves. The analysis of the tropopause in Figs.1 a and 2 is compatible with the then-current thinkingconcerning stratospheric-tropospheric exchange, whichheld that the tropopause insulates the troposphere fromthe stratosphere except for slow leakage through thebreaks in the tropopause and diffusion across the tropopause itself. According to Palm6n and Newton (1969, pp. 181182), the structural model in Fig. la eventually fellinto disuse because of limited observational evidence,and was replaced by that illustrated schematically inFig. lb and applied in a cross-section analysis basedon radiosonde data in Fig. 3 (Palm6n and Nagler,1949). In this model, the folded tropopause is replacedby a "break region" separating the tropospheric frontallayer and the tropopauses overlying the polar and tropical air masses. As in the analysis of Bjerknes and Palm,n, the tropospheric frontal zone is considered toseparate polar from tropical air and is discontinued inthe upper troposphere where the horizontal temperature gradient diminishes. The tropospheric frontal layeris also a zone of concentrated cyclonic and verticalshear of the component of the geostrophic wind normalto the cross section, which is computed from thermalwind considerations. Although the front is not analyzedabove the tropopause break, the cyclonic shear is extended into the lower stratosphere within a broaderzone than in the troposphere. Finally, the geostrophicwind analysis contains a jet core at the level of thetropical tropopause situated above the position of thefrontal layer in the midtroposphere. The extremely ,.. )/ ~,/ ? * ,..,~ tO. /~ ,' ~ xxx ~ ,t t "~ .... I [14 Yg?r,g., _ ~r~ [' ~[ I~ rrrTl-;~;~ %.4s-.~ ~ i~...... 2: 7,........ r___ % K~ ~ 7~ zt~ i~ rt ~;;.~- ~:~---~ ~~ ~7-~--~ .... ~ ..... ~ :~. ?.~ ~ ~ ~ j-~ _ ... ~-.~ [P~ _. ~-*-~. ~__~ '~ .... ~.... ;~ "~,-~r-~= ->-7o~'~ :--= ~a~ ~ ~ ~um , ~ ~ ~t00 5O, ~50 - 0 2~ --'~"~-'~ 2~0 ~.~- -~s ~o -- 4~ P~~~ ~ .~ ~~~ T- - --~ . ~ --~ 0 --~ ~ ~ .,~. ~ ~ F~o. 3. No.h-south cross so.ion ~rom Bu~alo, New York, toHavana, Cuba, od~mcd nodal to an up.r-level ~rontal zonecm~dcd within a d~p up~r trou~ ~or 1~00 OMT 5 ~cb~a~1P47. Thin solid lines arc ~h~ com~ncm o~ the ~costrophk: ~ndno~ ~o the cross ~ion (m s-~), dashed lines a~ isothc~,s (-C)and the thick ~lid lin~ are tro~pau~ or fron~ ~un~fi~ (dm~dashed when relatively indistinct). From Palm~n and NaSer ( 1949),large geostrophic wind speeds in the jet core reflect theorientation of the cross section through a well-cleveloped trough characterized by cyclonic curvature. Berggren (1952) proposed an alternative structuralmodel of upper-level fronts and the tropopause, whichis shown in Figs. l c and 4. This model differs fromthat used by Palm6n and Nagler in that the troposphericfrontal layer is continued upward through the regionof the tropopause break into the stratosphere. Withinthe tropopause break in the vicinity of the level ofmaximum wind (LMW) and in the lower stratosphere,where the horizontal temperature gradient becomesnegligible and reverses in sign from that in the troposphere, the frontal zone is defined by strong cyclonicwind shear. The extension of the frontal zone high intothe stratosphere could not be confirmed observationallyand was discontinued in a later application of thismodel by Palm6n (1958). As noted by Shapiro (1976),direct evidence for the narrow (~ 100 km) cross-frontscale in the vicinity of the LMW was provided by theEuropean sounding network, characterized by 100 kmstation spacing and a 6 h sampling frequency. The greater spatial and temporal resolution afl?ordedby the European radiosonde network in comparisonwith that of North America (400 km station spacing,12 h sampling interval) probably contributed to thedifferences between the analyses of the cyclonic: shearzone in the vicinity of the LMW and in the lowerstratosphere by Berggren and by Palm6n and Nagler,the latter of which is broader and more diffuse (compareFEBRUARY 1986 DANIEL KEYSER AND M. A. SHAPIRO 457 lqG. 4. Cross section oriented east-west across northern Europefrom Hannover, West Germany, to Valentia, Ireland, of potentialtemperature (K, thin dashed lines) and observed wind speed (m s-I,thin solid lines) for 0300 GMT 9 November 1949. Thick solid linesdenote frontal boundaries, tropopauses and inversions; thin verticallines give location and vertical extent of wind soundings. From Berggren (1952).Figs. 3 and 4). The spatial resolution of the radiosondenetwork is less of an issue for the tropospheric part ofthe frontal zone than for the region of the tropopausebreak and lower stratosphere. The tropospheric portions of upper-level frontal zones contain significantvertical wind shear and static stability by virtue of theirslope. Consequently, the cross-front horizontal scalecan be determined from the detailed vertical resolutioninherent within sounding data and knowledge of thefrontal slope from adjacent soundings passing throughthe frontal layer. Spatial resolution becomes a significant factor where the frontal zone assumes a nearlyvertical orientation, which occurs in the region of theLMW and lower stratosphere. Contemporary with Berggren's approach for analyzing upper-level fronts was that introduced by anumber of investigators including Newton (1954) andReed (1955) and advocated by Reed and Danielsen(1959). In this approach (Figs. ld and 5), the polar andtropical tropopauses are respectively joined with thelower (cold) and upper (warm) boundaries of the tropospheric frontal layer. In contrast to Berggren's model,the cyclonic shear zone in the stratosphere occupies ascale of hundreds of kilometers (Fig. 5a), a likely consequence of the limitations in North American radiosonde data referred to before. The Reed-Danielsenmodel explicitly accounts for stratospheric-tropospheric exchange through the hypothesis that upperlevel frontal systems resuR from a process known astropopause folding (Reed and Sanders, 1953; Reed,1955), in which upper- and midtropospheric subsidencetransports lower stratospheric air downward into thetroposphere, occasionally reaching 700 to 800 mb inparticularly intense cases. This hypothesis was basedon the use of potential vorticity,5 o0 (2.1)P = -(~'0 + f) ~pp,where t0 + fis the absolute vorticity measured on isentropic surfaces, as a dynamical tracer for distinguishing between stratospheric and tropospheric air,which is valid to the extent that adiabatic, inviscid conditions prevail along parcel trajectories. The compositecross section in Fig. 5b shows the frontal boundariesseparating potential vorticity values in the stratosphereof at least an order of magnitude greater than those inthe troposphere, which is evidence of air of recentstratospheric origin within the tropospheric part of thefrontal zone. The decrease of potential vorticity withdecreasing altitude within the frontal layer is suggestiveof turbulent-scale mixing of tropospheric and stratospheric air across the frontal boundaries. The Reed-Danielsen frontal model represented abreak from previous thinking in several respects. Basedon earlier work by Reed and Sanders (1953) and Reed(1955), this model no longer required upper-level frontsto separate polar from tropical air. Rather than formingas a result of confluence between polar and tropical aircurrents through a deep tropospheric layer, upper-levelfronts were hypothesized to develop primarily throughthe effects of tilting [in the prognostic equations forthe horizontal potential temperature gradient (1.1) andvorticity (1.2)] due to differential subsidence associatedwith tropopause folding. According to this view, upperlevel fronts were considered to separate stratosphericfrom tropospheric air rather than polar from tropicalair. Furthermore, upper-level fronts were not requiredto extend to the surface, but could arise independentlyof low-level fronts and frontogenetical processes, apoint emphasized by Sanders (1955) in connection withsurface fronts. As referred to earlier, the tropopausefolding process provided for the transport of stratospheric air toward the middle and lower troposphere,where it could mix with tropospheric air and eventuallyreach the Earth's surface. Interest in this particular exchange process in the 1950s and 1960s stemmed fromthe concern that stratospheric radioactivity generatedby the atmospheric testing of nuclear weapons couldreach the surface, exposing the biological risks of sucha practice. 5 An extensive review of meteorological applications of potentialvorticity from observational and theoretical perspectives, includinghistorical developments, is presented by Hoskins et al. (1985).458 MONTHLY WEATHER REVIEW VOLUME 114mb250400 -500~600700/0~ $0 (a)-50 \ \40 50- 50 ~ O-:50 ~SCALE- ~ I00 km50 -60 200~ - 50~---40.~. -2050 (b) ~ 6o ~ ,,~@ 4~ 3o80~80 $0 ,~o ~o 70250604005050020'~ 40\ %700 % / \ / \ '%'30/ \ \ SCALE- ~' ~ IOO #m FIG. S. Composite cross sections of upper-level frontal and tropopausc structure. Frontal boundaries and the tropopause arc indica~ted byheavy solid lines; axis of warm air in lower stratosphere is denoted by a heavy dashed line: (a) isotachs of the component of geostrophicwind normal to cross section (ms-', light solid lines) and isotherms (-C, light dashed lines); (b) isoplcths of potential vorticity (10-6 K mb-Is-I, light solid and dash-dot lines) and isentropes (-C, light dashed lines), From Reed and Daniclscn (1959). Perhaps as a result of their novelty, coupled withthe limitations of radiosonde data, the interpretationsconcerning upper-level frontogenesis derived from theReed-Danielsen model remained controversial untiladditional independent observational evidence couldbe produced. Aircraft measurements of tracers such aswater vapor, ozone and radioactivity (e.g., Briggs andRoach, 1963; Danielsen, 1964, 1968) confirmed thepresence of stratospheric air within tropopause folds.Extensive diagnostic studies based on radiosonde datasuch as those of Staley (I 960), Bosart (1970) and Shapiro (I 970) demonstrated the importance of tilting effectsdue to differential subsidence in generating cyclonicvorticity and horizontal potential temperature contrastscharacterizing upper-tropospheric fronts. The use ofmeteorologically instrumented aircraft to observe upper-level frontal systems directly in conjunction withconventional radiosonde data was to result in observational and conceptual advances culminating in thepresent-day structural model of upper-level fronts,which forms the subject of the following subsection.b. The contemporary structural model of upper-levelfrontal systems The direct probing of upper-level fronts with instrumented aircraft has resulted in refinements and e. xtensions of concepts based on radiosonde data. In the firstof a series of studies of upper-level frontal structureusing aircraft measurements to supplement conventional radiosonde observations, Shapiro (1974) pointedout that earlier aircraft studies in the 1960s were limitedby uncertainties in extracting horizontal winds usingDoppler navigation techniques. The introduction ofinertial navigation systems provided a degree of precision in the winds sufficient for sensing horizontal andvertical air motions within frontal zones down to thespatial and temporal scales of turbulent motions. Majorresults from the application of aircraft measurementsto frontal research include the direct documentationof the -~ 100 km cross-front scale at the LMW as proposed by Berggren (1952), and a clearer appreciationof the nature and effects of CAT on the structure ofupper-level fronts.FEBRUARY 1986 DANIEL KEYSER AND M. A. SHAPIRO 459 In reexamining upper-level fronts with mesoscaledata from the European upper-air network, Shapiro(1976) reproduced Berggren's finding that the cyclonicshear in the lower stratosphere is confined to a scaleon the order of 100 km rather than spread across alarger distance on the order of 500 km characterizingthe Reed-Danielsen model (Fig. 5a). Direct wind measurements taken during horizontal traverses across thecyclonic shear zone in the vicinity of the LMW provided further confirmation of the mesoscale structureof upper-level fronts at the LMW and in the lowerstratosphere. Figure 6 is a schematic illustration of thestructural model derived from the results of aircraftflights combined with conventional radiosonde data,an example of which is shown in Fig. 7a. The schematiccontains elements from both the Berggren and ReedDanielsen models. As in the Berggren model (Fig. 1 c),the frontal zone extends into the lower stratospherewhere it slopes in the opposite sense as it does in thetroposphere. Unlike the Berggren model, the tropopauses overlying the cold and warm tropospheric airmasses do not break at the front, but are connectedrespectively with the lower and upper boundaries ofthe upper-tropospheric portion of the frontal zone, asin the Reed-Danielsen model (Fig. I d). The dynamical quantity absolute momentum,m= ug -fy, (2.2)introduced by Eliassen (1962), can be used to defineupper-level frontal zones. In (2.2), ug is the along-front(x) component of the geostrophic wind, F~G. 6. Schematic diagram of the present-day model for analyzingupper-level fronts and tropopauses. Solid lines denote frontal andtropopause boundaries; dashed line depicts the boundary of cyclonicshear zone in the lower stratosphere. Vg=yk X XTv~b= + ~~xjj, (2.3)fis the Coriolis parameter, which is taken to be constant, and y is the cross-front coordinate, positive toward colder air. In (2.3), ~ is the geopotential of a pressure surface. The quantity rn is termed absolute momentum since it is the Cartesian (tangent-plane)analogy to absolute angular momentum for the rotatingEarth. A property of rn is that it describes the absolutegeostrophic vector vorticity in the cross-front plane according to the relationship 0m o 0rn ~g2: -i X V2m: - ~pp] - ~yy k, (2.4)where V: --- O/Oy j - O/Op k is the two-dimensionalgradient operator in the cross-front (y, p) plane.6 Thevalidity of (2.4) requires the frontal zone to be sufficiently straight and along-front variations to be sufficiently small to be considered two-dimensional (lOvg/Oxl ,~ IOudoyl). According to (2.4), the absolute geostrophic vector vorticity lies along lines of constant m.Application of the thermal wind relationship 0V~=_~k x Vp0= ,~ ~+ -'~xxl (2.5)allows the vertical gradient of m to be expressed interms of the cross-front gradient of potential temperature; i.e., Om Op - ~ Oy' (2.6)Equations (2.5) and (2.6) are based on (2.3) and thehydrostatic equation in the form -- = -f~O, (2.7)where -~ =f~ (2.8)is a function of pressure alone (for the assumption ofconstant f), Po is a reference pressure (1000 mb), R isthe ideal gas constant for dry air, and cv and % are thespecific heats for dry air at constant volume and pressure, respectively. Inspection of (2.2) and (2.6) showsthat the vertical component of absolute vorticity andthe degree of baroclinicity characterizing a frontal zoneare described respectively by the cross-front and verticalgradients of m. The vertical cross section in Fig. 8adisplays the rn field for the frontal zone in Fig. 7a. It 6 Defining the gradient operator in terms of -O/Op allows the useof pressure as the vertical coordinate while preserving the familiarproperties ofa righthanded Cartesian coordinate system. Consistentwith this definition of the gradient operator, the three-dimensionalvector velocity is defined as ui + vj - -0k. This approach is equivalentto utilizing -- as the vertical coordinate, as in Bluestein (1986).460 MONTHLY WEATHER REVIEW VOLUME !14150 250p~4O0I000150ZOO~,004O06007O080O900000 I i I IXNW/?2374 TUS/72274 FRC/76256 INW/72574 TUS/72Z74 FRC/T6256 (~) (b) FIo. 7. Cross sections for 0000 GMT 17 April 1976 based on radiosonde observations at Window, Arizon,'i (INW), Tucson, Arizona(TUS), and Fraccionamicnto, Mexico (FRC), supplemented with NCAR Sabrelincr aircraft data in the layer between 250 and 300 rob: (a)Potential temperature (K, solid lines) and wind six~l (m s-', dashed lines). Winds are plotted with respect to north at the top of the 'figure;flags, full barbs and half barbs respectively indicate speeds of 25, 5 and 2.5 m s-L (b) Potential vorticity (10-? K rob-' s-I, solid lines) andarray of dots formed by the intersection of (m, 0) coordinates displayed in Fig. 8b. From Shapiro (1981).20030060I00J 150200 2~0 30Op~4OO $00 $00 ?OO 80~ 90~I00~ 2O 40! I 60 I I INW / ?25?4 TUS / 72274 FRC/76256 ! NW / 72 ~74 TUS / 72274 FRC f 76256 (a) (b) Fro. 8. Cross sections as in Fig. 7, except for (a) absolute momentum, m = u~ -fy, (m s-', solid lines) with y = 0 at left side of figure,decreasing toward the right; (b) (m, ~) coordinate grid from patterns in Figs. 7a and 8a, with contour intervals of 10 ms-' and 4 K. Heavydashed lines in (a) and (b) indicate first-order discontinuities in rn. From Shapiro (1981).FEBRUARY 1986 DANIEL KEYSER AND M. A. SHAPIRO 461is readily apparent that (i) the entire frontal zone isdescribed by the region of large gradients of m in the(y, p) plane, (ii) the frontal zone is characterized bylarge magnitudes of the absolute geostrophic vectorvorticity (2.4), and (iii) the frontal boundaries can berepresented as discontinuities in the gradient of m.Thus, absolute momentum is a single parameter capable of describing two-dimensional frontal zones provided that the along-front component of the wind isapproximately geostrophic. For those situations where frontal zones satisfy theconditions for two-dimensionality alluded to following(2.4) and the along-front component of the wind isapproximately geostrophic, the potential vorticity (2.1)can be expressed entirely in terms of the variation ofquantities in the cross-front plane (denoted by subscript2). Replacing ~'0 + fwith -Om/Oyo and transformingto pressure coordinates yields the expressionwhereP2 = J~,(m, 0), (2.9) ~40~LOS ~e~EL-S FIG. 9. Analyses of wind speed at 287 mb (m s-I, solid) and ozoneconcentration (pphm vol-', heavy dashed lines) derived from Sabreliner data taken between 0615 and 0700 GMT 16 April 1976. Flighttracks are indicated by light dashed and dot-dashed lines. Line AA'is the projection for the cross section in Fig. 10. From Shapiro (1978).Jyp(m, 0)=-i. (V2m X V20) Om O0 Om O0(2.10)The Jacobian form of P2 dictates that its magnitude isdirectly proportional to the areal density of intersections between contours of m and 0, or inversely proportional to the size of the solenoids formed by theintersections of adjacent pairs of rn and 0 contours.These interpretations are illustrated respectively in Figs.7b and 8b. [In these figures the areal proportionalitydoes not hold exactly because the vertical axes of thecross sections are drawn with respect to In(p)]. Potentialvorticity is largest in the zone of stratospheric cyclonicshear, where the m lines and isentropes are concentrated and oriented nearly perpendicular to each other.This configuration may be contrasted to the tropospheric portion of the frontal layer where m lines andisentropes are closely spaced but nearly parallel to eachother. The structure of the cyclonic shear zone in thelower stratosphere turned out to have a significantimplication concerning the effect of turbulent mixingon upper-level frontal structure. As cited earlier, theReed-Danielsen model assumed more-or-less uniformdistributions of stratospheric and tropospheric potentialvorticity, which are discontinuous at the tropopausefrontal boundaries. The --~500 km horizontal scale ofthe cyclonic shear zone is consistent with the assumption of nearly uniform potential vorticity within thestratosphere and the upper-tropospheric portion of thefrontal layer. In particular, reference to (2.1) and Fig.5 reveals that large values of potential vorticity in the.tropospheric part of the frontal zone are associated primarily with large static stability. Absolute vorticitiesare relatively moderate because isotachs coincide approximately with sloping isentropic surfaces. In the region of the LMW and lower stratosphere, the staticstability is similar to that in the tropospheric part ofthe front, but the isentropes have a much smaller slope.Consequently, the isotachs must spread apart and occupy a larger cross-front scale to maintain values ofpotential vorticity comparable with those in the tropospheric part of the frontal zone. In the case of the Berggren model, the ~ 100 kmscale of the stratospheric cyclonic shear in the vicinityof the LMW implies much greater values Of absolutevorticity on isentropic surfaces compared with the upper-tropospheric portion of the frontal layer and thestratospheric portion sloping over the jet core (Fig. 8b).Therefore, the potential vorticity at the LMW must beanomalously large relative to background stratosphericvalues rather than slowly varying, as evident fromcomparing Figs. 5b and 7b. The question that immediately arises concerns the source of the anomalouspotential vorticity maximum in the LMW. If potentialvorticity were conserved, this maximum would not beanticipated. Consideration 'of the hypothesis that potential vorticity is generated locally at the LMW ledShapiro (1976, 1978) to examine the roles of diabaticand frictional processes associated with turbulent mixing in upper-level frontal zones.?c. The effects of turbulent processes on upper-level frontal systems Figures 9 and 10 respectively display horizontal andcross-sectional subjective analyses of an upper-level jet ~ A comprehensive summary of the results of earlier investigationsof turbulent processes in upper-level frontal zones is given by Reiter(1969, pp. 191-220).462 MONTHLY WEATHER REVIEW VOLUME i14 200 rnb $00400 500600700800900 ~I000 ~4070300290IIII I0AK/72493 MFR/72597 FIG. 10. Composite cross-section analysis based on aircraft and radiosonde data for 0000 GMT 16 April1976 along line AA' in Fig. 9. Heavy dashed lines indicate wind speed (m s-t); solid lines are potentialtemperature (K). Flight path is denoted by light dashed lines; solid circles are times (GMT). Horizontaldistance between OAK and MFR is about 500 km. From Shapiro (1978).streak, and its associated frontal zone, based on radiosonde data and supplemented by aircraft data. The aircraft traverses confirm the upward extension of the~ 100 km scale cyclonic shear zone into the lowerstratosphere. The cross-sectional distributions of po.tential vorticity and ozone (Figs. 1 la and 1 lb), thelatter of which can be considered a conservative quantity over the time scale of the generation of an upperlevel front, suggest that potential vorticity is producedlocally. If potential vorticity were conservative, its distribution would be expected to match that of the ozonemuch more closely. The lack of potential vorticityconservation,~ proposed previously by Eliassen andKleinschmidt (1957) and Staley (1960), should not betaken as contradictory of earlier inferences on tropopause folding and upper-level frontogenesis by Reed(1955) and Reed and Danielsen (1959), which are confirmed by the downward-directed tongue in the ozonepattern. The development of the potential vorticity maximum in the vicinity of the LMW evident in Figs. 7band 1 la can be discussed quantitatively in terms of theprognostic equation for the potential vorticity [as de' fined in (2.1)], which is -(~'o + f) ~pp + ~pp k. Vo~ X O0 - -- [k- (XTs X F)]. (2.11) In the above expression, ~'0 is the horizontal.gradient operator for isentropic surfaces, and F and 0 are theFEBRUARY 1986 DANIEL KEYSER AND M. A. SHAPIRO 463~5020C300400500600?00800900$000 , ' 900 500~ ~__ I00 \ I I 0AK/72493 MFR/7~597150200mb300~005006007O08009O0000I00~ ~I00O&K/?Z493 MFR/?Z597(b)150~00mb3004005006O0?00800~00I000MFR/?~597(c) FIG. 11. Analyses for the cross section appearing in Fig. 10: (a)potential vorticity (10-7 K mb-~ s-t); (b) ozone concentration (pphmvol-', dashed) and potential vorticity isopleth (100 x 10-7 K rob-'s-I, solid) indicative of the tropopause; (c) Richardson number. FromShapiro ( 1978).frictional and diabatic contributions to the prognosticequations for the horizontal vector wind and potentialtemperature. Detailed discussion of(2.11) can be foundin Staley (1960) and Gidel and Shapiro (1979). Shapiro(1976) applied (2.11) at the LMW in the stratosphericzone of cyclonic shear (approximately 355 mb in Figs.10 and 11), which removed the middle term on theright from consideration. On the basis of the results ofa scale analysis, Shapiro further neglected frictionalprocesses and focused on the first term, describing theeffect of the vertical distribution of diabatic heatingdue to vertical mixing by CAT. The diabatic heatingrate may be expressed as b = (pw'O'), (2.12)where g is gravity, p is the density of dry air, w is thevertical velocity in terms of height, z, primed quantities464MONTHLY WEATHER REVIEWVOLUME 114denote turbulent eddy motions and the overbar indicates an ensemble average. With the above assumptions, (2.11) reduces to dP 02 -~ = g(fo + f) ~p2 (-pw'O'). (2.13) The vertical eddy flux of potential temperature,w'O', is expected to be 'large and negative (downward)in regions of CAT, which is favored by small values ofRichardson number,Ri = 0 azl ~zz (2.14)The cross-sectional distribution of Ri is shown in Fig.11 c for the frontal zone in Fig. 10. As evident fromthese figures and the schematic illustration in Fig. 12,Ri is minimized in kidney-shaped patches of large vertical wind shear situated above and below the jet core,implying maximum positive values Of -w'O' in theseregions. The postulated vertical profile of-w'O' in Fig.13, applicable to the cyclonic shear side of the jet core,reflects the vertical distribution of the Richardsonnumber described above, and indicates static stabilization and potential vorticity generation at the LMW,.where the curvature of the -w'0' profile is maximized.This inference is based on the approximated form ofthe potential vorticity equation (2.13). The overall effectof CAT is to produce warming (cooling) in the --- 1 kmthick layer above (below) the LMW through a convergence (diverge.nce) of the vertical eddy flux of potentialtemperature [0 ~ -O(w'O')/Oz]. The vertical distribution of diabatic heating due to CAT acts to inhibit thevertical spreading of the isentropes at the LMW thatwould be required if potential vorticity were conservedduring the frontogenetical scale contraction of the cy150p~$O04 IO00 km ) FIG. 12. Schematic illustration of regions of clear-air turbulence(stippled) in the vicinity of an upper-level jet core and frontal zone,Solid and dashed lines respectively indicate potential temperatureand wind speed. From Shapiro (1976).+1 ,/~ ..,,-- ~-t = +17Kday-!km 0 ~ LEVEL OF MAXIMUM WIND-.B - 4'// '1 I I O 0.1 0.2 0.$-w8~ FIG. 13. Vertical profile of the downward eddy flux of potentialtemperature (-w"~ in m s-t K) expected on the cyclonic shear sideof an upper-level jet. Circles enclosing x's indicate observed :fluxesfrom Kennedy and Shapiro (1975). From Shapiro (1976).clonic shear zone to --- 100 km. Direct measurementsof the eddy flux of potential temperature using researchaircraft indicate that the described mechanism is sufficiently intense to account for an exponential ",doubling'' time of about 10 h for the potential vorficity(Shapiro, 1978). The mechanism responsible for enhancing the .,,taticstability within the LMW can also be shown to dimifiish the static stability within the frontal shear layers,as apparent from the curvature of the -w'O' profile 1km above and below the LMW in Fig. 13. Browningand Watkins (1970) and Browning ( 1971) documentedthe occurrence of such a decrease in static stability inan upper-tropospheric frontal layer as a result of anepisode of Kelvin-Helmholtz billows, which were detected by radar. Time-height sections illustrating thewind speed along with its vertical shear and the staticstability are respectively shown in Figs. 14a and 14b.The statically stable layer marking the upper-tropospheric frontal zone is shown to split as a consequenceof vertical mixing during the billow event. The profilesof vertical wind shear, Richardson number and staticstability immediately before and after the billow ,event(Fig. 15) indicate an overall decrease in the wind shearand increase in the Richardson number. The static stability is diminished within the shear layer and enhancedat its top and bottom, as Would be .expected from considering a vertical profile of -w'O' similar to that inFig. 13 below the LMW. The bulk effect of CAT is to limit the horizonttd andvertical scale contractions of sloping upper-tropoFEBRUARY I986 DANIEL KEYSER AND M. A. SHAPIRO 465128 18 16 14 12 (13) TIME GMT) 12J i i- I I I I f 18 16 14 12 (b) TIME (GMT) ~o. 14. (a) Time-height cross section of wind speed and the magnitude of the vertical wind shear for an upper-level jet on 6 February1970, derived from balloon-borne targets tracked by radar at thetimes indicated by vertical arrows. Solid lines are isotachs (contourinterval 10 m s-~); hatched, cross-hatched and solid shading respectively indicate shears of 8-12, 12-16 and >16 m s-~ over 400 m. (b)Time-height cross section of the vertical gradient of potential temperature determined from radiosonde ascents at the times indicatedby vertical arrows. Hatched, cross-hatched and solid shading respectively correspond to O0/Oz > 1.5, 2 and 2.5-C (100 m)-L Thin dashedVENTICAL -1ND SHEAR0 4 I (m/t ptt ZOOm) Q I Z 3( Cper ~OOm) VERTICAL GRADIENT OF ( ,OT[NTt~L TEH,E~ATU~E-7 O.$ I $ IOLAYER NICHAROSON NOI'IBEK , RIK: 6 5VE~C~. vmo ~t,i.RAU~A\AZj0 4 8 (m/s per ZOOm) ~ ~:.~ &u ~hS:H~l/~ a. I~r'::...~~' :::i::::l'l" .... ======================= / /m :Xq I; .., .......... ] // :k:~Et ECHOES I:~:::::j AT I~00 GHT h;:::~o ~ 2 3 (oc per zOOm)V[~ICAL ~AOIENT OF [Ae~~TENTIAL TE~ATURE ~/NUH6ER, Ri FIG. 15. Vertical profiles of static stability, vertical wind shear andRichardson number derived from radiosonde ascents on 6 February1970 immediately before (top, 1207 GMT) and after (bottom, 1309GMT) a large-amplitude billow event. All oftbe above quantities areevaluated over a 200 m height increment. The clear-air radar echoescorrespond to the vertical extent of the Kelvin-Helmholtz billows at1245 GMT (top) and to the two-layer structure in the static stabilityprofile at 1300 GMT (bottom). From Browning and Watkins (1970).spheric frontal layers to the observed minimum valuesof approximately 100 km and 1.5 km (100 mb)(Browning et al., 1970; Roach, 1970). The limitinghorizontal scale can be related to the Richardson number according to the expressionlines indicate isotherms (-C). The thick dashed contours reveal theboundaries of dry air (relative humidity of 50% with respect to ice).Stippling denotes region of cirrus. The large X indicates the time andlocation of a Kelvin-Helmholtz billow event, which is followed bythe splitting of the stable frontal layer. From Browning (1971).466 MONTHLY WEATHER REVIEW VOLUME 114 by = \---f-j Ri, (2.15)where by is the cross-frontal scale, ta0 is the slope ofisentropes (bp/~yo) within the frontal zone and ~0 is thepotential temperature difference across the front.Equation (2.15) is derived from the expression for Riin pressure coordinates with the assumption that 0V/Op can be replaced by the vertical shear of the alongfront component of the geostrophic wind, Oug/Op.Taking values typical of the 500 mb level in midlatitudes (3' = 4.71 x 103 m2 s-~ K-~ mb-~, ~0 = (100 mb)(100km)-~, ~0 = 10K, f= I x 10-4 s-~) and Ri'between0.25 and 0.3, which is compatible with the measurements in Fig. 15, yields by between 120 and 140 km.This estimate of the cross-frontal scale is comparablewith observed values. An implication of the nonconservation of potentialvorticity is that the folded tropopause associated witha well-developed upper-level frontal zone is not a material surface, but is a region of active systematic transport of air between the stratosphere and troposphere.In particular, the generation of potential vorticity atthe LMW provides a mechanism by which trajectoriesfollowing the mean motion may enter the stratospherefrom the troposphere. Further discussion of the stratospheric-tropospheric exchange process with respect toupper-level frontal zones appears in papers by Shapiro(1978, 1980). At the time of their publication, thereexisted widespread interest among the scientific community in identifying processes by which chlorotluoromethanes could enter the stratosphere from the troposphere and participate in the chemical consumptionof ozone, which is required to filter the ultraviolet portion of the spectrum of incoming solar radiation. Thisfocus may be contrasted with the emphasis 20 yearsearlier on the transport of radioactivity from thestratosphere to troposphere. A more general perspectiveon the stratospheric-tropospheric exchange problemis provided in the review by Reiter (1975).d. The relationship of upper-level frontal systems to - baroclinic wave structure Although a rather complete description of the structural characteristics of well-developed upper-levelfrontal systems has emerged over the past 50 years,progress has been limited in describing and understanding the temporal evolution of upper-level frontsin the context of structural changes ofbaroclinic wavesthrough their life cycles. The slow rate of progress canbe attributed primarily to restrictions in spatial coverage, temporal resolution and accuracy of radiosondedata. A consequence of limited coverage and temporalresolution is that upper-level frontal zones cannot betracked continuously throughout their entire life histories. Significant structural changes often occur overdata-sparse regions or between upper-air observingtimes (typically separated by 12 h). As a result, observational documentation of the initial development ofupper-level fronts, as well as details of the frontogenesisprocess, has been virtually nonexistent or at best fragmentary. Restrictions in horizontal resolution have notbeen as much of a problem as temporal resolution,because the detailed vertical resolution in radiosondeobservations can be converted into horizontal resolution finer than that anticipated from the station spacingin regions of sloping tropospheric frontal layers, as alluded to in Section 2a and discussed by Shapiro (1970),Shapiro and Hastings (1973) and Petersen (1986).. Observational uncertainties in radiosonde data havebeen emphasized regarding winds, especially within andabove the upper troposphere under strong-wind conditions, where balloon elevation angles become smalland errors in differences in balloon position becomemagnified. As a result, direct measurement of jetstream winds is not always possible and estimates ofageostrophic winds are subject to uncertainty. Consequently, the results of observational studies of dynamical interactions between the primary (geostrophic) andsecondary (ageostrophic) circulations in upper4evelfrontal systems often have been controversial. Finally,the role of aircraft data has been to augment the spatialresolution of radiosonde observations and also to reduce uncertainties in radiosonde-derived winds. Investigation of upper-level frontal systems with aircraftobservations has been limited, however, to documenting the structure of upper-level fronts over short 'timeintervals; it has not been feasible to deploy aircraft tomonitor upper-level fronts continuously through asegment of (let alone all of) their life histories. A case study of the evolution of a baroclinic waveover North America during a 48 h period by Newton(1958) contains many of the salient aspects knownconcerning the relationship of upper-level frontal systems to the synoptic-scale baroclinic waves in whichthey are embedded. In Fig. 16, depicting the dewdop'merit of an upper-level trough at a relatively early stage,the upper-level frontal zone and jet are clearly definedin the northwesterly flow upstream of the trough axis.Downstream of the trough axis, frontal structure ismost apparent at the surface, whereas it is diffuse aloft.One day later (Fig: 17), the upper trough has ampltifiedand the surface cyclone has intensified, while the frontalstructure has become more-or-less .symmetric relativeto the trough axis. At the final time shown (Fig. 18),the frontal system On the downstream side of the troughaxis is more distinct in comparison with that on theupstream side, so that the asymmetry is essentiality reversed from its configuration two days earlier. A similarchain of events is described by Palmtn and Ne'~on(1969, pp. 335-338). Questions concerning the interpretation of the sequence of events in Figs. 16-18 centeron the details of the process by which the upper-.levelfrontal system becomes established on the downstreamside of the trough between Figs. 16 and 17. Data limFEBRUARY 1986 DANIEL KEYSER AND M. A. SHAPIRO 46715kin-.-60 ~O-tOkm*$ k m-'~ .0Okra-' I __ o~c)~ 394 386 486 476 576 66~ 764 74? 6~5 553 445 3~0 ~48 Z31 STH LAS ELY 6JT LND RAP SIS INL STC 0M~ C81 LIT SHV ~Y ~220- ~1~330~ I ~ ,eso o, (b) ~G. 16. Synoptic analy~s over Noah America for 03~ G~T 4 April 1950. (a) Su~acc fro~ts, ]0~ mb heistcontoum (thin lines, contour int-~ ~00 ~) a~d 500 mb heist contou~ (thicker lines, contour inte~ ~00 fi).Sfipplin8 indicates continuous precipitation; cro~ hatchi~8 reprc~ms well~efincd fron~ zones at 500 rob. (b) Cro~~mion aloes thin double lines in (a). Hea~ lines de.me tropopau~s and boundaries of fro~ a~d s~b]- ]ayem. To~~nd s~ed (kt) is depimcd by thin solid lines, tem~mturc (-C) by d~h~ lines. ~lcctcd ~n~ ~c plowed ~th ~es~tto noah at the top of the fi8u~e; fiass, full barbs and half barbs rcs~tivcly i~dicatc 50, 10 and 5 kt. Three~i~tnum~m are pom~ti~ tem~ratum (K). From No.on (]958).itations of the type referred to above prevent establishing the degree to which the frontal structure is advectedin from the west relative to being generated locally,and the extent to which the upper-level and surfacesystems merge as indicated relative to remaining structurally independent. Various investigators have examined the structureof upper-level fronts during particular stages of the se468MONTHLY WEATHER REVIEWVOLUME 1 1415kin-~0 -5 -60 - -50 -- -IOkm-405 krn~ I0- -55' /17~ ~0~0#~".--220- 03 Z/~BQ 6JT LND 8iS INL SS~ MTC 8UF PiT 040-~ 310-APRIL 1950 ol soo, . ~o~m.~ Ro. 17. As in Fig. 16, except for 0300 GMT 5 April 1950.SHiP"H" 130-.-,. (b)quence of events illustrated in Figs. 16-18. The majority of case studies have focused on the stage in Fig.16, where an upper-level front is embedded in thenorthwesterly flow upstream of a trough axis, includingthose of Reed and Sanders (1953), Newton (1954),Staley (1960), Shapiro (1970) and Uccellini et al..(1985). A consistent outcome of these studies is thedominance of tilting, due to a cross-stream gradient ofvertical motion such that subsidence is maximized onthe warm side of the frontal zone, in generatinlg thecross-frontal poiential temperature gradient (1.1) andcyclonic vorticity (1.2). A more general case study byReed (1955) describing the development of a naajortrough over North America also documents the importance of differential subsidence in producing upperlevel frontogenesis and associated tropopause foldingFEBRUARY 1986 DANIEL KEYSER AND M. A. SHAPIRO 469APRIL 19,50)Skin-6.o- eo -$o ;.50~ coo // ~-~"~I t ! \\IOkm.O- 265 ~53TUL I~S WlS O~C FV~*--2~0oO3Z 6 APRIL 1950 445FLV CBI53~ 5~7 528 520 ~O~ ~RAN MTC BUF PIT SWF I~L ~ (HEr~ 050o ,~3~0o 0 500 I~0 km I ~ ~I~G. 18. As in Fig. 16, except for 0300 GMT 6 April 1950.SHIP "H"K:O-~'O- -70 200--o-- 700 - ,000I~A~ 30~---(b)in the northwesterly flow upstream of the trough axis.In Reed's case, the upper-level frontal system eventuallyattained its greatest intensity and the tropopause foldreached its maximum downward penetration in theconfluent southwesterly flow downstream of the troughaxis. The outcome of this study suggests that the upperlevel front was generated in the northwesterly flow upstream of the trough axis by tilting processes, and was470 MONTHLY WEATHER REVIEW VOLUME 114 subsequently transported around the base of the trough into the southwesterly flow where its intensity was maintained or augmented by horizontal confluence. A progression of events similar to that in Reed's casestudy is evident in the case examined by Bosart (1970),who considered upper-level frontogenesis in terms ofthe migration of a short-wave trough comprising thefrontal zone through a major long-wave trough. Temporal resolution of 3 h was available through a specialradiosonde network situated over the southeasternUnited States.. The upper-level front intensified initiallyas a result of tilting in the northwesterly flow upstreamof the axis of the long-wave trough. The frontal zonethen reached its maximum strength in the southwesterly flow downstream of the axis of the long-wavetrough as a result 0fhorizontal confluence. At this stage,tilting effects were found to be frontolytical, with thereversal in sign having occurred as the upper-level frontpropagated around the base of the long-wave trough. Shapiro (1983) synthesized the preceding observational evidence into a hypothetical schematic depictingthe migration of an upper-tropospheric jet-front system8 through a synoptic-scale baroclinic wave situatedover North America (Fig. 19). The stages representedin this schematic correspond closely with those identified by Riehl et al. (1952, Fig. 15), Riehl et al. (1954,' Fig. 2.7) and Kfishnamurti (1968) for the passage of ashort-wave trough through a long-wave trough. Theprogression of events begins over western Canada withthe confluence between a polar trough and a midlatirude ridge (Fig. 19a), a flow configuration hypothesizedby Namias and Clapp (1949) to be conducive to theformation and intensification of upper-level fronts andjets. Roughly a day later (Fig. 19b), the jet and fronthave progressed to the inflection in the northwesterlyflow upstream of a diffluent trough exhibiting a northwest-southeast tilt. The thermal wave lags the heightwave by one-quarter wavelength, which places the frontin a region of cold-advection. The tilt in the heightfield is a sign ofbarotropic amplification provided thatthe background (zonally averaged) zonal wind becomesincreasingly westerly with latitude in the vicinity of thedeveloping short-wave disturbance (Haltiner and Williams, 1980, pp. 72-75), while the separation betweenthe thermal and height waves is optimal for baroclinicamplification (Holton, 1979, pp. 134-135, 223-227).The flow configuration in Fig. 19b reflects the sense of s The schematic depictions of upper-tropospheric jet-front systemsin Fig. 19, as well as in Figs. 21 and 23, apply at a level that issufficiently low for the horizontal temperature gradient to be welldefined and sufficiently high for the jet structure in the wind field tobe apparent. The choice of such a "compromise level" (~400 mb)is dictated by the observed structure of upper-level jet-front systems(see Fig. 7a), in which horizontal temperature gradients are best defined in the midtropospbere, while the jet pattern is most distinct inthe vicinity of the tropopause (LMW), a level at which the horizontaltemperature pattern is typically diffuse.the asymmetrical trough structure in the early stagesof development identified by Newton (1958) in ]Fig.16, and is consistent with previous descriptions of upper-level frontogenesis due to differential subsidenceoccurring in the northwesterly flow inflection. At the following time (Fig. 19c), the jet-front sysl:emhas reached the base of the long-wave trough and assumed a curved orientation. The absence of asymmetries in terms of the disappearance of the latitudinaltilt and phase separation between the thermal andheight fields indicates the cessation of barotropic andbaroclinic amplification. At the final time (Fig. l'gd),the jet and front have migrated to the inflection in thesouthwesterly flow' downstream of the long-wavetrough, which has taken on a confluent configuration.The southwest-northeast tilt of the trough axis and thethermal wave leading the height wave respectively signal barotropic and baroclinic damping. The sense ofthe asymmetry is reversed from that in Fig. 19b, andcorresponds to the stage of upper-trough developmentillustrated in Fig.'l 8 and the observational descriptionsof upper-level fronts maintained by confluence in thesouthwesterly flow downstream of a long-wave troughaxis. The preceding discussion underscores the relationship between upper-level frontal evolution and the environmental baroclinic wave. The synoptic-scale wavestructure provides the dynamical setting in which processes involving the interplay between primary andsecondary circulations lead to scale contractions resulting in and maintaining fronts. The following sectionwill introduce and interpret a theoretical approach fordiagnosing the vertical (secondary) circulations, gj~venthe geostrophic (primary) flow field, that is applicableto idealized, two-dimensional flow configurations. Thisdiagnostic approach will establish a quantitative basisfor examining upper-level frontogenesis in Section 4in relation to the conceptual description provided byFig. 19.3. Diagnosis of transverse ageostrophic circulations in upper-level frontal zones The results of scale analyses of the adiabatic, inv~scidmeteorological equations (Eliassen, 1962;~ Shapiro,1970; Hoskins and Bret. herton, 1972; Emanuel, 1985)indicate that provided a frontal zone is sufficientlystraight9 and along-front variations are sufficientlysmall, the along-front componen.t of the wind can beapproximated by its geostrophic value. As a conse 9 The condition that a frontal zone is straight does not necessarilyrequire that the isentropes are oriented parallel to the zone (O0/Ox= 0). A frontal zone consists of a region in which the horizontalpotential temperature gradient is maximized, and is not necessarilybounded by isentropes. The schematics in Figs. 19b, 19d and 21bprovide examples of along-front potential temperature variation.FEBRUARY 1986 DANIEL KEYSER AND M. A. SHAPIRO 471 ~ .o..~/~:~.% - -~ ..'%D'-. ( '"-'. t', "at / :. ..-"-'.? '~...<:,%..:f i ~/ ". / /'.- .... ',.,)~"~t/ : ..... :,, ?<.~.r--('q'-.ill "...-~ '-~ ~ ".. i~,.'L~ 'ti '.>. , ~,~ .... ',. ~ ~ 'C'.~j ~ '.. ~. '- ... ~~ ~ ...... ,, ..,:,. '--,~ ...~ ~ .-~ ...... -~~_-.......~ ~ ~%< ~ ~;"~c.. ~ ~ ~%~ ~~,~- .~~ ~ X~ ~ ~ ~: ~'~, F'"~ 0 ..~ ~'~~/~'~'"~-~- n.., / ~ _j' /~.d ........ '~ / ~ ,~ ~ '.. t, ; ~,_~ .A~-~~/ ~ V ~' ~.? ) ~., %. ~.~... ~ ~ -' ; ~,.. ,:' ~;~ / 4~ ........ . ;: (CI) t'to t* t' ~...-a ..-....fV ..... ., .., ...: ...... -, ~. ) ~. ..'"' L/ .... -. ":::.-..5 '.. ~ i3 ",, ....... '.. \.., t'~'... .!:' .... - ........ . ~ \ ",.;...'. "~ ..~,_ '"'-.: t--~ '"'".:....i ',,5 ".: .... .: "'... ....... i~'x\: .." "..., i--~.-_.-'~X ..,-" _::':~ ?..,~.%X ~w- ~", ........-%,. .>_L_-5.\\X', ..'/~'.~,7..,.>k''.'5' ', hX~,~? % ~.-- _\: \ / . xX,%7~ /~'~-" ',.~-- ~~ -( ..'~ ~ %~ % - :~ - :~ \ / ~',,..' '-.%...:/' I'~ (b) 1 ' to + 24h FIG. 19. Idealized schematic depiction on a constant pressure surface of the propagation of an upper-tropospheric jet-front system througha midlatitude baroclinic wave over a 72 h period: (a) formation of jet-front in the confluence between mid- and high-latitude currents;b) jet-front situated in the northwesterly flow inflection of amplifying wave; (c) jet-front at the base of the trough of fully developed wave;(d) jet-front situated in the southwesterly flow inflection of damping wave- Geopotential height contours, thick solid lines; isotachs, thickdashed lines; isentropes or isotherms, thin dashed lines. From Shapiro (1983). ....,. ~:.i ...... - .... j " ........ x.. / , ,. i~ ...... ,, ,.~:....~ ',, - .~'" :Z' ',.;... i ,..( ......... :.. '.. t ".~'.......: i \ ".,c... ".. 'x. k. I - ~' ~_ ..'" ~ ....... 7''~ I ? ":4, ! '"..j'"'.... ;,:: "-. \ k ' ......... :~.~: .._ '-.,....X ? ,.~,~j,~,~~/'":----'"'---- '%x\\ ....... i"\$'~ /Z-""~ :__---- ~ ,::,....,> , ....... ~...-~ - '~ .~i ~.~ .&-.. ~--...__~-----.J :,& ,....:./'>~'A~ : ..'"-~--_t ?'.~/7~'_.~L -_._-'-7---,':-"7 -,' i d) J ~"tG +?2h472 MONTHLY WEATHER REVIEW VOLUME. 114quence of this approximation, the ageostrophic circulation is confined to the cross-front (transverse)plane. This approximation is often referred to as "crossfront geostrophy," which describes the near balance ofthe Coriolis and pressure gradient forces in the crossfront direction, and is a special case of the geostrophicmomentum approximation (IdVag/dtl ~ IdVg/dtl),leading to the semigeostrophic equations (Hoskins,1975). The two-dimensionality of the ageostrophic circulations in straight frontal zones provides a considerable conceptual simplification in understanding thedynamical processes producing vertical circulations.a. Dynamical equations for absolute momentum and potential temperature For a straight frontal zone oriented in the east-westdirection, the approximation of cross-front geostrophyimplies lUagl ~ lugl, (3.1a)dt I~ ' (3.1b)Txl41ayl~ ~(3. I c)These relations are a consequence of the geometricalproperties of fronts, i.e., that the cross-front length scaleis much less than the along-front scale and that thecross-front component of velocity is much less thanthe along-front component. As a consequence of(3.1),the prognostic equations for m (2.2) and 0 aredm Or).... + Fx, (3.2)dt OxwheredO = b, (3.3)dt d 0 0 0 0 dt - Ot + ug ~x + (vg + vaO Ty + o, ~. (3.4)In the above equations, F~, is the along-front componentof the friction term in the equation of motion, F, andthe subscript ag denotes ageostrophic. I.n (3.2) and (3.3),it is implicitly assumed that F~ and 0 are sufficientlysmall in magnitude so as not to invalidate the approximation of cross-front geostrophic balance. As a consequence of (3.1c) and the assumption ofconstant Coriolis parameter, the mass continuityequation reduces to ava~ + Ow ay ~pp = 0. (3.5)This form of the continuity equation permits definitionof an ageostrophic streamfunction, -, such that~- 0- 0- Va~2 = -i x VErb = - ~ppj ~y k, 1',3.6)where V~2 = v~j - wk and ~2 is as defined in Section2b. As defined in (3.6), when facing toward the positivex direction, the ageostrophic circulation is clockwise(counterclockwise) around maxima (minima) in ~ (Fig.20). Additional equations to be used with.(3.2)-(3.6)are the components of the geostrophic wind (2.3) andthe thermal wind (2.5). Prognostic equations may be developed for the crossfront and vertical gradients of m and 0, which describeabsolute vorticity (Om/Oy), the components of crossfront thermal wind balance (Om/Op = 3,00/Oy) and l~taticstability (O0/Op). Taking O/Oy and O/Op of(3.2) and (3.3)results inThe Jacobian operator is that defined in (2.10). In (3.9),the term involving d ln3,/dp [= -(cdcv)/p] is usuallyneglected, which is a form of the Boussinesq approximation for the pressure coordinate system. Equations (3.7) and (3.10) reveal that the vorticityand static stability changes involving the motion fielddepend only on the ageostrophic circulation. On the ~o Use of V~2 in (3.6) to denote the transverse ageostrophic circulation should be distinguished from the more conventional notation, V~, which refers to the horizontal ageostrophic wind (unl + vnd).The latter usage is intended, for example, in the inequality describingthe condition for the geostrophic momentum approximation, appearing at the beginning of this section.FEBRU^RY 1986 DANIEL KEYSER AND M. A. SHAPIRO 473other hand, (3.8) and (3.9) indicate that in the absenceof frictional and diabatic processes temporal changesin the components of cross-front thermal wind balancedepend on both geostrophic and ageostrophic processes, which are partitioned among the first and secondJacobian terms [aside from the "non-Boussinesq" termin (3.9)]. The geostrophic Jacobian term common to(3.8) and (3.9) shows that geostrophic motions contribute to temporal changes of Om/Op and 3~O0/Oy alongparcel trajectories at rates that are equal in magnitudebut opposite in sign. Therefore, ageostrophic circulations are required to preserve thermal wind balance[d(Om/Op)/dt and d(3,00/Oy)/dt must be everywhereequivalent], which cannot be maintained by geostrophic motions alone, a paradox noted by Hoskinset al. (1978). The principle of preserving thermal windbalance leads to the formulation of a diagnostic equation for the transverse ageostrophic circulation (v,g, ~o)from (3.8) and (3.9). In this equation, the transverseageostrophic circulation will be viewed as a responseto frontogenetical processes, with respect to Om/Op and'~O0/Oy, involving the geostrophic flow along with frictional and diabatic processes.b. The Sawyer-Eliassen equation for the transverse ageostrophic circulation Since the left sides of(3.8) and (3.9) are assumed toremain equal, a diagnostic equation for (v~, w) can beformed by subtracting the two equations, yielding Om d ln3,~o- Op-~~' (3.1 l)The definition of ~ (3.6) allows the transverse ageostrophic circulation to be expressed in terns ofa sin~evariable at the expense of obtaining a hi~er-orderequation. Separating ~e Jacobians into their indihdu~components and using (3.6) leads to a linear, secondorder pani~ differential equation in ~ with variablecoefficients:Equation (3.12) was fomulated ofi~n~ly by Sa~er(1956) for the speci~ case of the absence of~ong-frontvariations in potential temperature [Jyn(~, ~ reducesto -(Ou~Op)(Ov~Oy)], which were subsequentlychided by Eliassen (1962). The coefficients of the second-order terns on thele~ of (3.12) respectivdy quantify the static s~bility,baroclinicity and inertial stability. The distributions ofm and 0 as well as the right side of (3.12) (the forcing)are assumed known, so that ~ (the response) can bedetermined uniquely provided that boundary conditions are specified and an ellipticity condition, Om O0 (Om'~2 '~ Oy 0.D ~-~--~] = ~P2 ~ 0, (3.13)is satisfied everywhere in the (y, p) domain. The equality within (3.13) can be verified by referring to (2.9)and (2.10) along with (2.6). The condition of positivepotential vorticity ensures that transverse ageostrophiccirculations will arise only in response to the forcingterms on the right of(3.12), rather than to self-excitinginstabilities of the zonal current containing the frontalzone. In particular, symmetric baroclinic instability[detailed descriptions and references are given by Hoskins (1974), Orlanski and Ross (1977) and Emanuel(1979)] is possible in regions of negative potential vorticity. This instability can lead to significant magnitudesofduaddt, which are not considered in the formulationof (3.12). Under such circumstances, a more generalformulation for f must be developed that incorporatesthe time history of f through terms involving its temporal derivatives and specified initial conditions. Thetheories of forced frontal circulations and symmetricbaroclinic instability may be considered complementary in the sense that frontal circulations are treated inthe absence of symmetric baroclinic instability throughthe constraint of positive potential vorticity, whilesymmetric baroclinic instability occurs in the absenceof frontal circulations through the assumption of astraight zonal current in which vg is constant (typically zero), eliminating the geostrophic forcing termin (3.12). Since the Sawyer-Eliassen equation (3.12) is secondorder and the coefficients of the 02/Oy2 and 02lOp2 termsare typically positive, positive (negative) values of theforcing correspond to relative minima (maxima) in f(Fig. 20). According to the previous discussion of thedefinition off (3.6) and with the y axis pointing towardcolder air, relative minima (maxima) in f are associatedwith thermodynamically direct (indirect) circulations.For a thermodynamically direct circulation (Fig. 20a),cold air is sinking and warm air is rising, which contributes to decreasing the cross-front thermal contrast.At the same time, westerly and easterly momentumare created respectively at upper and lower levels[through the inviscid % momentum equation, duddt--fVag, obtainable from (3.2)], which contributes toincreasing the vertical shear of the along-front windcomponent. Conversely, for a thermodynamically indirect circulation (Fig. 20b), the cross-frontal thermalcontrast is enhanced and the vertical shear of the alongfront wind component is diminished. In addition to estimating the sense of the transverseageostrophic circulation from the sign of the forcing,474 MONTHLY WEATHER REVIEW VOLUME i14FORCING-p(a) FORCING < 0 I -p ' W %%% C , y . (b) DG. 20. Schematic illustration of sign of forcing and sense oftransverse ageostrophic circulation from diagnostic Sawyer-E!iassenequation. Ageostrophic circulation is denoted by solid.lines; dashedlines depict an isentrope separating potentially colder from warmerair. Small circles enclosing x and dot respectively indicate along-frontwind into and out of the cross section. Transverse ageostrophic circulation is thermodynamically direct in (a) and indirect in (b).it is possible to infer qualitatively the shape of the circulation, which for a given forcing depends on the relative magnitudes and distributions of the coefficientson the left side of (3.12). Such inferences can be determined from the properties of the Green's functionfor (3.12), which physically describes the response (~b)to forcing consisting of a point source (8-function) fora given choice of lateral boundary conditions. The results of such an analysis (Eliassen, 1962) indicate thefollowing: (i) large potential vorticity and small inertialstability inhibit vertical motions and favor horizontalageostrophic motions, resulting in an elliptical circulation with a relatively small aspect ratio; (ii) small potential vorticity and large inertial stability favor verticalmotions and inhibit horizontal ageostrophic motions,resulting in an elliptical circulation with a relativelylarge aspect ratio; (iii) the baroclinicity determines thetilt of the circulation from the vertical; (iv) for a givenforcing, the amplitude of ~ varies inversely with theinertial stability.Interpretation of the Sawyer-Eliassen equation is facilitated by considering its quasi-geostrophic courtterpart. The justification for such an approach is thal thesemigeostrophic equations, which include the same assumptions as those used in deriving (3.12), predict adistortion of solutions determined from the quasi-geostrophic equations, rather than leading to entirely different solutions (Hoskins, 1975). This behavior isunderstandable in that the dominant terms in thesemigeostrophic equations are those constituting thequasi-geostrophic equations. The quasi-geostrophiccounterpart to (3.4) is ,/ o ua+~ ~=O-~+ gax vg~y. (3,.14)Comparison with (3.4) shows that the transverseageostrophic circulation is neglected in determi:aingparcel trajectories. The effect of vertical motions is included in the thermodynamic equation (3.3), however,by accounting for adiabatic warming and coolingthrough the term, -~odO/dp, where O(p) is a referencedistribution of potential temperature. The quasi-geostrophic counterparts to (3.7)-(3.10) are d(O~_~) _fOw OFx (3.15) (.~p.p) Ov~ OF~, rtat om= -;%(u,, v~) +fop + op ' (3.16)d(a0) aOa~ a4~ ~y = s~(,~,~)-~T~Tyy+~y, (3.17) (3.18)It can be confirmed that (3.15)--(3.18) can be determined from (3.7)-(3.10) by approximating m by -fyand 0 by O in all terms involving the ageostrophic circulation. The quasi-geostrophic form of (3.12)is dO\ O2f OF~ OtJ = -22~(u., h) + -~ - * Ty' (S.19)The discrepancies between the ageostrophic circulations resulting from (3.12) and (3.19) are due entirelyto differences in response, since the forcing is identicalFEBRUARY 1986 DANIEL KEYSER AND M. A. SHAPIRO 475in both equations. A corresponding analysis of theproperties of the Green's function would show that fora given latitude only variations in static stability canaffect the aspect ratio of the elliptical circulation, andthat the circulation cannot tilt from the vertical, sincethe mixed-derivative term on the left of (3.12) does notappear in (3.19). The ellipticity condition for (3.19),which is the quasi-geostrophic counterpart of (3.13), isthat the static stability is positive, i.e., -f3, ~pp > 0. (3.20) The dynamical forcing to the Sawyer-Eliassen equation (3.12) and its quasi-geostrophic counterpart (3.19)can be expressed in four equivalent forms. The first is -2Jyp(ug, vg) = 2i. (~72Ug X ~72Vg) Oug ovg ovg~= -2(~yy Oug~.~~Oy/, (3.21a)which can be verified from the definition of the Jacobian operator in (2.10). This form is convenient forvisually evaluating the forcing from the solenoidsformed by the intersections of Ug and vg isotachs on a(y, p) cross section. Use of the thermal wind (2.5) andthe nondivergence of the geostrophic wind on an J:plane (OUg/OX = -OVg/Oy) in (3.21a) results in -23,Jxy(Ug, 0)=-23,k'(V~,ug x VpO) [ Oug O0 OUg = -23,k'~x ~yy Oy ~xx, ' (3.22a)This form is useful for estimating the forcing of thecross-front ageostrophic circulation from constantpressure charts of ug and 0. In natural coordinates(3.22a) becomes 23'100/0n10ug/0S, where n points towardcolder air and s is oriented along isentropes 90- to theright of n. Two additional forms of the dynamical forcing canbe obtained by substituting the expression for the nondivergence of the geostrophic wind into (3.21a) and(3.22a): Ou, aug aug Ovg] (3.21b) ,, 0% O0 , Ouz 00) -23'J,,,y(%, O) = z3'[~-yy ~yy ~- ~yy ~xx_ ' (3.22b)These expressions respectively correspond to the geostrophic contributions to d(Om/Op)/dt and d(-3'00/Oy)/dt, and will be used to demonstrate how the geostrophicwind differentially advects u, and 0 to disturb thermalwind balance in (3.8)-(3.9) and (3.16)-(3.17). The schematic patterns of u~ and 0 in'Fig. 21 allowthe interpretation of the dynamical forcing for thetransverse ageostrophic circulation in terms of modifications to the cross-front potential temperature graCON FLUENCE/DIFFLUENCE OU OO <0 OU 00 > 0(a) ~x Oy ~ ~HORIZONTAL SHEAR FIG. 21. Schematic depictions on a constant pressure surface ofstraight upper-tropospheric frontal zones characterized by (a) con~tluence and difiluence associated with a jet maximum and (b) horizontal shear in the presence of a positive along-front thermal gradient.Geopotential height contours, thick solid lines; isotachs of the alongfront geostrophic wind component (us, denoted by U), thick dashedlines; isentropes, thin dashed lines. Heavy arrows indicate the jet axisin (a) and the sense of cross-front shear of the along-front wind component in (b). Adapted from Shapiro (1983).dient through (3.22a) and (3.22b). Figure 2 la shows astraight upper-tropospheric jet maximum with isentropes parallel to its axis, which eliminates the secondterms in (3.22a) and (3.22b) from consideration. Thefirst terms in the expressions for the forcing are positiveand negative respectively in the confluent entrance anddiffiuent exit regions of the jet, implying direct andindirect circulations about the jet-front system in theentrance and exit regions (Fig. 20). These transversecirculation patterns are consistent with the four-quadrant pattern of upper-level convergence and divergenceimplied from considering temporal changes of alongfront momentum (dug/dt =fon) or vorticity [see (3.15)]for parcels migrating through the jet more-or-less parallel to the geopotential streamlines (e.g., Riehl et al.,1952, 1954; Cahir, 1971; Uccellini and Johnson,1979).1t Figure 2 l b illustrates the complementary sit "The cross-front ageostrophic wind component and horizontaldivergence associated respectively with the temporal rates of changeof along-front momentum and vorticity following parcel trajectoriestend to reach a maximum at the LMW in upper-level jet-front systems,since the along-jet relative flow and gradients of the along-front windcomponent and vorticity are largest at this level. On the other hand,the magnitude of the geostrophic forcing (3.22a) of the Sawyer-Elias'476 MONTHLY WEATHER REVIEW VOLUME 114 V = -5 m/secU=O(b) FiG. 22. Transverse ageostrophic circulations for an idealized frontal zone characterized by (a) confluence (OvslOy < 0, OvslOp = 0) and(b) horizontal shear (Ovs/Oy = O, Ovs/Op > 0). Dashed li.nes, isotachs of us (denoted by U); thin solid lines, isotachs of vs (denoted by V);thick solid lines, streamlines of ageostrophic circulation. Adapted from Eliassen (1962).uation in which the effects of confluence and diffluenceare eliminated by assuming us is uniform in the alongfront direction. The second terms in (3.22a) and (3.22b)are negative, implying an indirect circulation (Fig. 20b)for this case of cold advection (potential temperatureincreasing downstream) in the presence of cyclonicshear (Ous/Oy < 0). This part of the geostrophic forcingis referred to as the horizontal shear effect. Finally, thenatural-coordinate form of the geostrophic forcing, introduced following (3.22a), can be used to determinethe sense of the ageostrophic circulations in Fig. 21. InFig. 21 a, us increases along the isentropes (in the direction such that cold air is to the left) in the entranceregion of the jet, yielding positive forcing and a directcirculation. Indirect circulations in the exit region ofthe jet in Fig. 2 la and the frontal zone in Fig. 2 lb areassociated with decreases in us along the isentropes. The patterns 'in Fig. 22 from Eliassen (1962) are~suitable for interpreting the geostrophic forcing in termsof (3.21a). In Fig. 22a, Ovg/Op is taken to be zero, negating the first term in (3.21a). The configuration ofOus/Op < 0 [colder air to the north according to (2.5)]and Ovs/Oy < 0 (confluence) implies positive forcingand a direct circulation. This pattern corresponds to across section ~hrough the entrance region of the jet inFig. 21a. In Fig. 22b, the confluence effect is eliminatedthrough the assumption that vs varies only with pressure, which isolates the horizontal shear effect. Withsen equation tends to be relatively small at the LMW relative to midand upper-tropespheric values, since horizontal potential temperaturegradients are typically indistinct at the LMW. Nevertheless, the upperhorizontal branch of the transverse ageostrophic circulation, whichis effectively bounded by the large increase in static stability at thetropopause, is usually maximized at the LMW, consistent with theabove expectations from the momentum and vorficity equations.Consequently, evaluating the Sawyer-Eliassen forcing at the LMWalone can give the misleading impression that there is little or noforcing of transverse ageostrophic flow associated with upper-leveljet-front systems.Ovg/Op > 0 (O0/Ox < 0, the opposite of that in Fig. 21b)and cyclonic shear (OuS/Oy < 0) within the frontal zone,the forcing is positive and the circulation is direct. Outside the front, the sense of the lateral shear of us isanticyclonic and the circulations are indirect. The frictionless, adiabatic forms of the quasi-geostrophic equations for the vertical shear of the alongfront wind component (3.16) and the cross-front potential temperature gradient (3.17) will be used in conjunction with Figs. 21 and 22 to illustrate in detail howdifferential advection by the geostrophic wind disruptsthermal wind balance. Inspection of the first term in(3.21 b) shows that confluence tends to reduce the magnitude of the vertical wind shear (decreased negativevalues of Ous/Op), since larger positive values of us atupper levels compared with lower levels (Ous/Op < O)differentially advect less positive values of US (OUS/Ox> 0) at a greater rate at upper levels than at lowerlevels. From Fig. 21a and the first term in (3.22b) itcan be seen that confluence tends to enhance the magnitude of the cross-front potential temperature gradient(increased negative values of OO/Oy) by compressing isentropes in the y direction. Consequently, the contributions of geostrophic advection to d(Orn/Op)/dt andd('vOO/Oy)/dt are respectively positive and negative. Thistendenc3/toward imbalance in the thermal wind iscounteracted by a direct circulation (OvadOp < 0,Oy > 0;. Fig. 20a), which simultaneously increases themagnitude of the vertical wind shear by contributingpositively to us at upper levels and negatively at lowerlevels (3.16), and decreases the magnitude of the crossfront potential temperature gradient by adiabaticallywarming the cooler air to the north of the front andcooling the warmer air to the south of the front (3,. 17). In the case of the horizontal shear effect illustratedin Fig. 22b, reference to the second term in (3.21b)'shows that the vertical shear in vs (Ovs/Op > 0) tendsto tip the us isotachs into the vertical where the horizontal shear is Cyclonic (Ous/Oy < 0), diminishing themagnitude of the vertical wind shear. Examination ofFEBRU^RY 1986 DANIEL KEYSER AND M. A. SHAPIRO 477the second term in (3.22b) reveals that cyclonic shearin the presence of along-front decreases in potentialtemperature (O0/Ox < 0) tends to augment the magnitude of the cross-front potential temperature gradient,since larger positive values of us south of the front relative to north of the front differentially advect highervalues of potential temperature at a greater rate southof the front relative to north of the front. A direct circulation in the same sense as in the confluence case isrequired to preserve thermal wind equilibrium. The above interpretations of (3.12) and'(3.19) bringout the importance of accounting for the contributionsof differential geostrophic advection of both the windand thermal fields when considering the forcing for thetransverse ageostrophic circulation. Qualitative interpretations often emphasize the effects of confluenceand horizontal shear on the cross-front potential temperature gradient (3.22b), while neglecting their corresponding effects on the vertical wind shear (3.21b),which are more difficult to visualize. The given interpretation is believed to be appealing because it placesthe secondary circulation in the physically familiarcontext of an adjustment to a continuously imposedimbalance, which may be viewed as a negative feedback. Figure 23 displays various configurations of the potential temperature field relative to a straight uppertropospheric jet maximum, which is revealed by theus field. The sign of the geostrophic forcing and senseof the transverse ageostrophic circulation can be determined from (3.22a) or its companion formulationin natural coordinates. Figures 23a and 23b exhibitpatterns of potential temperature that respectively isolate the effects of confluence (O0/Ox = 0 as in Fig. 2 la)and horizontal shear (O0/Oy = 0). Figures 23c and 23ddepict straight isentropes rotated at an angle from thejet axis, respectively resulting in cold and warm advection in the along-front direction. These examplesshow the effect of combining the confluence and horizontal shear mechanisms. The influence of confluenceand diffiuence in forcing direct and indirect transversecirculations in the entrance and exit regions is apparent.The superimposed effect of horizontal shear is to shiftthe direct and indirect circulations laterally toward thecyclonic or anticyclonic shear sides of the jet axis, depending on the orientation of the isentropes relativeto the jet and the resulting sign of the along-front thermal advection. For example, in the confluent entranceregion of the cold advection case (Fig. 23c), the directcirculation is shifted toward the anticyclonic shear sideof the jet, so that the region of maximum midtropospheric subsidence is located beneath the jet axis ratherthan the cyclonic shear side, as in the case of confluencealone (Fig. 23a). Figures 23e and 23f permit the senseof the along-front thermal advection to change sign atthe jet maximum by placing the jet in a thermal ridgeand trough, respectively. In the case of the thermalridge (Fig. 23e), the entrance and exit regions are respectively characterized by cold and warm advection.The transverse circulations are shifted to the anticyclonic shear side of the jet, as in the entrance and exitregions of Figs. 23c and 23d. The discussion of Fig. 23 illustrates the importanceof considering the modifying influence of along-frontthermal variations on the four-quadrant distributionof midtropospheric vertical motion in straight jets (Figs.21a and 23a), which is based on deductions from themomentum or vorticity equations. This idealized pattern of vertical motion has been shown to hold onlyfor the special case in which the isentropes are parallelto the jet axis. A weakness of qualitatively inferringthe vertical motion pattern from the cross-front ageostrophic wind component due to parcel accelerationsor from the sign of the divergence due to vorticitychanges along a parcel trajectory is that the effect ofalong-front thermal variations is not taken into account. The above analyses and interpretations of the Sawyer-Eliassen equation can be extended in a number ofdirections. The influence of frictional and diabaticforcing associated with CAT has been analyzed byShapiro (1981); a similar analysis of nonconservativeforcing due to deep convection appears in Shapiro(1983). It is possible to transform the Sawyer-Eliassenequation into alternative coordinate systems. Replacingy with m in (3.12) (Eliassen, 1962) reduces the left sideto a form similar to the quasi-geostrophic version(3.19). The baroclinicity term is absorbed into thetransformation from y to m and physically reappearsin the tilted m coordinate lines. Absolute momentumis a stretched coordinate in the sense that contours ofconstant m are concentrated in regions of large absolutevorticity, affording enhanced horizontal resolution infrontal regions (Fig. 8). The transformation from (y,p) to (rn, p) is the two-dimensional counterpart to thatleading to the three-dimensional semigeostrophicequations developed by Hoskins (1975). It is also possible to transform the vertical coordinate from pressureto potential temperature; the Sawyer-Eliassen equationexpressed in (y, 0) coordinates is given by Hoskins andDraghici (1977). Although an obvious extension wouldbe to combine the horizontal and vertical stretchingproperties of m and 0, a version of the Sawyer-Eliassenequation in (rn, 0) coordinates has not to our knowledgeappeared in the literature. Hoskins and Draghici (1977) and Hoskins et al.(1978) generalized the two-dimensional theory leadingto the Sawyer-Eliassen equation to apply to three dimensions, an approach that accounts for contributionsto the horizontal divergence by the along-front component of the ageostrophic flow. This approach is basedon the geostrophic momentum approximation, whichis justifiable if the time scale of momentum changefollowing a parcel is much greater than f-t (Hoskins,1975). For adiabatic, frictionless flows, this conditionshould be satisfied if (i) the temporal rate of change of478MONTHLY WEATHER REVIEW ':3~+A~ ~)+A~ ~)+A~(o) (b)VOLUME 114~+~ (1= I- ~+A~ ~) +/t~ (1: -15- ~.~A~(c) (d) ~+A~ THERMAL RIDGE ~+A~ ~+A~ THERMAL TROUGH(e) FiG. 23. Schematic illustration on a constant pressure surface of various idealized configurations of potential temperature and along-frontgeostrophic wind for a straight upper-tropospheric jet maximum. Thick solid lines, gcopotential height contours; thick dashed lines, isotachsof the along-front wind component; thin solid lines, isentropes, or isotherms; thick solid arrows, sense of cross-front ageostrophic windcomponent at level of maximum wind; plus and minus signs, sense of midtroposphcric pressure-coordinate vertical velocity, o~. (a) Pureconfluence and diflluencc in the absence of along-jet thermal advection (o~O/Ox = 0); (b) pure horizontal shear with ~O/Ox > 0 in the absenceof the effect of confluence and difflucnce (O~/Oy = 0). (c)-(f) Mixed cases of confluence/di/fluence and horizontal shear: (c) along-jcI: coldadvection, (d) along-jet warm advcction, (c)jet in a thermal ridge, (f)jet in a thermal trough. From Shapiro (1983).horizontal wind speed along a parcel trajectory is muchless than the Coriolis acceleration ([dV/dt[ ,~ 73) and(ii) the radius of parcel trajectory curvature, Rt, is nottoo small (V/f IR, I '~ 1). The ageostrophic streamfunction (3.6) becomes a vector, ~k, defined such that= -O~bx/Op, v~s = -O~k~,/cgp and co = Vp- ~k, which satisfies the three-dimensional continuity equation inpressure coordinates. A coupled system of second-orderelliptic partial differential equations for the ageostrophic circulations in the (x, p) (~,) and (y, p) (~y)planes replaces (3.12) or its quasi-geostrophic counterpart (3.19). This system of equations can be combined into a single diagnostic equation for the verticalmotion, co, with the dynamical forcing expressed in arevealing way that links vertical circulations directlyto frontogenesis. The quasi-geostrophic version of theF~BRU^RY 1986 DANIEL KEYSER AND M. A. SHAPIRO 479diagnostic co equation will be reproduced because ofits relatively simpler mathematical form. The form of the quasi-geostrophic co equationthat results from combining the diagnostic equationsfor the ageostrophic circulations in the (x, p) and(y, p) planes is dO\ 2 ,-02co co + o? ( OF)- 7Vf0. (3.23) k. V, XThe terms on the right of (3.23) respectively quantifythe dynamical, frictional and diabatic forcing of thevertical motion. The dynamical forcing is proportionalto the horizontal divergence of the so-called "Q vector,"consisting of the temporal rate of change following thegeostrophic motion of the horizontal potential temperature gradient; i.e., d Q = ~ V~ = -Jxy(vs, 0)i + Jx~(%, 0)j (3.24)and d/dt is defined in (3.14). The components of Q inthe x and y directions respectively contribute to theforcing of the ageostrophic circulations in the (x, p)and (y, p) planes. Hoskins et al. (1978) and Hoskinsand Pedder (1980) showed that the dynamical forcingof(3.23) comprising the Q vector is equivalent to theconventional form involving the vertical shear of thevorticity advection and Laplacian of the thermal advection (Holton, 1979, pp. 136-140): O -2~(V,. Q) = ~p (Vs- Vn~g) + 3,V~(-s- V,0). (3.25)The expression of the dynamical forcing for the verticalcirculation in terms of frontogenetical processes associated with the geostrophic wind field leads to the significant interpretation that the forcing of vertical motions within midlatitude baroclinic flows is most concentrated and pronounced in frontal regions. Thisperspective emphasizes the important role of fronts inthe dynamics of midlatitude baroclinic waves and cyclones.4. Dynamical models of upper-level frontogenesis This section considers time-dependent modelingstudies of upper-level frontogenesis in two and threedimensions with the intent of isolating and elucidatingsignificant physical mechanisms and processes ratherthan focusing on mathematical aspects, which will beleft to individual references. Results of two- and threedimensional model simulations will be used to confirmand illustrate the schematic representations of ageostrophic circulations associated with upper-level jetfront systems proposed in Fig. 23, which, in turn, canbe related to the conceptual model of the progressionof a jet-front system through an evolving baroclinicwave presented in Fig. 19. In two dimensions, the interpretations are simplified considerably, since ageostrophic circulations are 'confined to the cross-frontplane and the Sawyer-Eliassen equation developed inSection 3b is applicable. In three dimensions, the interpretations are more complicated because of the possible contribution of the along-front component of theageostrophic flow to the horizontal divergence andvertical circulations. Considerations of the along~frontcomponent of the ageostrophic flow will be based ongradient wind concepts.a. Two-dimensional processes The first time-dependent studies of upper-levelfrontogenesis were performed with the adiabatic, frictionless semigeostrophic equations in two dimensions,and are physically described in Hoskins (1971, 1972)and mathematically formulated in Hoskins and Bretherton (1972). The initial conditions consist of a baroclinic troposphere separated from a barotropic stratosphere by a sloping tropopause, and the troposphereand stratosphere are characterized by relatively smalland large static stabilities. The cross-front variation ofpotential temperature is specified in terms of an arctangent function, and the frontogenesis is driven byconfluence in the nondivergent basic-state wind fieldin which v = -ay, u = ax and a is a constant (= 1X 10-s s-~). In this specification, which describes a hyperbolic deformation field, the isentropes are orientedparallel to the axis of dilatation for the basic-state windfield (the x axis), a configuration which is kinematically optimal for frontogenesis (Petterssen, 1956, pp.200-205). Figure 24 illustrates the structure of the frontal zoneafter considerable development has taken place. A jethas formed along the.tropopause, which has folded intothe midtroposphere and has extended downward nearlyto 450 mb. The frontal structure at upper levels is quiterealistic in comparison with the wind (Fig. 5a) and potential temperature (Fig. 5b) patterns analyzed by Reedand Danielsen (1959). Features realistically reproducedby the model include the jet core along the tropopause,and the barotropic structure of the cold air and baroclinic structure of the warm air separated by the frontalzone in the middle and upper troposphere. The mainshortcoming of the model is that the folded tropopausedoes not extend to the 600-700 mb levels as documented observationally for well-developed cases (e.g.,Reed, 1955). Related to this deficiency is that the cyclonic shear and cross-front potential temperature gradient defining the frontal zone are maximized near thebase of the tongue of stratospheric air, and do not extend into the midtroposphere. In fact, these quantitiesare most diffuse at this level. A frontal zone also develops at the surface in response to the initial specification of the cross-front variation of potential temper4801:55MONTHLY WEATHER REVIEW ,VOLUME 11420O:500 ! !I !400E ~600 800- ~ --~ ! ~ ~' '~% ! - % 1000 ,500km~ ,~ *- , ~ ~ FIG. 24. Analytically derived cross section indicating tropopau~ folding and frontogenesis atthe tropo~ause and surface due to the effect of confluence in a two-dimensional ~migeostrophicmodel. Solid lines, i~ntro~s (contour inte~al 7.8 K); dashed lines, iso~chs of ~ong-front ~ndcomponent (contour inte~al 10.5 m s-~). The tropopause is indicted by a ~lid line ~pamtingre~ons of hi~ and low potential vonicity. V~tor a~ows within the figure reveal sho~-te~parcel trajecto~es; tho~ ~neath the lower surface depict the basic-state geostrophic defo~ationfield. The ordinate in this figure and in Figs. 25-28 is linear in the ~-c~led p~udohei~t, z,introduced by Hoskins and Brethe~on (1972), which is propo~ional to ~. From Hos~ns(1972).ature, which is invariant with height in the troposphere.The development of the unrealistically strong jet at thesurface can proceed because of the free-slip lowerboundary condition. The frontogenesis at upper levelsis affected little by that at the surface (Buzzi et al., 1981). Keyser and Pecnick (1985a) generalized the abovetwo-dimen~ional problem by including the effects ofthe along-front variation of potential temperature in aprimitive equation model formulation, allowing for thesimultaneous treatment of the confluence and horizontal shear mechanisms referred to in Figs. 21 and23. Figure 25 displays cross sections of the initial conditions for potential temperature and cross-front geostrophic wind, %, for the pure confluence case (Fig.25a) discussed above and for cases in which the alongfront variation of potential temperature is respectivelypositive (upper-level cold advection, Fig. 25b) andnegative (upper-level warm advection, Fig. 25c). Accordingly, the configurations in Figs. 25a-25c correspond to infinitely long jet entrance regions (an artifactof the two-dimensional nature of the model formulation) for the potential temperature patterns respectivelyshown in Figs. 23a, 23c and 23d. The 48 h evolutionof the along-front wind component and potential temperature in Fig. 26a confirms the results of the semigeostrophic model appearing in Fig. 24 and providesa benchmark for considering the results of the "coldadvection" and "warm advection" cases in Figs. 26band 26c. The presence of upper-level cold advectionresults in a well-defined zone of cyclonic shear andcross-front potential temperature gradient apparentdown to the 600 mb level. The upper-level and surfacefronts are clearly distinct, structurally separate features.The presence of upper-level warm advection also leadsto the generation of frontal properties in the upper andmiddle troposphere, but the upper-level and surfacefrontal zones are "connected" in the sense that a s:ingleenvelope of isentropes defines both fronts, similar tothe pure confluence case. The temporal history of the transverse circula~fionsfor the above three cases is revealed in the back trajectories displayed in Fig. 27 for parcels originating at 0h immediately above the initial tropopause and. terminating at 48 h within the respective frontal zones.The effect of confluence is apparent as parcels on thecold and warm sides of the frontal zones migrate towardconfluent asymptotes within the frontal zones. Thetrajectory patterns for the pure confluence (Fig. 27a)and warm advection (Fig. 27c) cases are qualitativelysimilar, with the frontal zones separating descer~tdingcold air from ascending warm air. In contrast, in thecold advection case (Fig. 27b), the frontal zone comprises sinking air and the strongest descent appears onits warm side. Parcels originating just above the: tropopause and terminating within the frontal zone approach the 700 mb level. The dramatic vertical excurFEBRUARY 1986 DANIEL KEYSER AND M. A. SHAPIRO 481 (a) v g PURE CONFLUENCE CASE 0 h (b) vg COLD ADVECTION CASE O h 135 FcmTiTqTmTmTynrm.~rqTrTmmjTT~rmTiTTnnTrll~mr~Trrl~mm~_~ 100 13~ ~mnlrTJ~m~mTJTTrITTTrqT~rnmTpnmTlrJm'ln~lTJnnn'lTqTTmrlrr] I00 ~: ......... ~ ........... t .......... ~ ........... .~ ........... r .......... ~ ........... ~-:-:---:--:~ -=~!!~_.'~:------~ :-.- ---- --- .-~.. ~:--~-~-~~~:=~'.-~ -:::::::::: :::i~::::::-::::'i?,~;_~'i.:::.'L:~L:~i .::'-~i.:.!L:~!! ?_'2~X.:~ :':' :'~ .L:L: ?-::~.~!:L:~ ~ ::~iiiiii: i:-_~Siii!:: :iii:,~?_: ::!5-':::!!: :::-.i5~!~[:-::,'~':::' :.:.-'.i::":'"" :~::'-'-': ....... "~ '-"' =-~~~' ~~- _ :~;~. =="~-=--'~-' ~ 6.2 "' ". 'x. ',,, ',.. '* ,~ 485 "-,,, '",,, ' ',. 'x "--..~ - "'* F~ '~'-~'"'~~, "'I~... %-. ',\~\ '".~.\, "- ..., -..., 1.9 "",.., '\ ", .., ', ' -,, 78020~ 15~0 lffiO 500 0 - 600 - 1000 - 1500 - 2000 2000 1500 1000 500 0 - 500 - 1000 - 1500 - 2000y (km) y (km)(c) vg WARM ADVECTION CASE 0 h 13.5 JIIIIIIlllJlllllllllJlllllllllJlllllllllJlllllllllJllllllllJlllllllllJlUllllll 10011.610.26,5 1.81452O526O372 ~8~2000 1500 1000 ~ 0 -500 -1000 -1500 -2000y (kin) FIG. 25. Cross sections of the cross-front geostrophic wind component (contour interval 5 m s% solid) and potential temperature(contour interval 5 K, dashed) at the initial time of the numericalintegration of a two-dimensional primitive equation model of frontogenesis due to pure confluence (a), and confluence in the presenceof upper-level cold advection (b) and warm advecfion (c). The slopingthin solid line immediately above the lower boundary denotes surfacepressure. Arrows indicate direction of cross-front geostrophic windcomponent. Adapted from Keyser and Pecnick (1985a).sions of parcels in the cold advection case are indicativeof realistic tropopause folding and reflect the importance of vertical motions in the upper-level frontogenesis process. The instantaneous transverse ageostrophic circulations at 24 h indicate thermodynamically direct patterns for the pure confluence (Fig. 28a) and warm advection (Fig. 28c) cases, with sinking and rising motionsituated respectively to the cold and warm sides of thedeveloping frontal zones. A thermodynamically directcirculation also occurs for the cold advection case (Fig.28b), but its center is shifted laterally toward the warmair to such an extent that subsidence is maximizedwithin and to the warm side of the developing frontalzone at upper levels. A consequence of this lateral shiftin the ageostrophic circulation is a change in sign ofthe cross-stream gradient of vertical motion within thefrontal zone from the thermally direct sense (&o/Oy> 0) in the pure confluence and warm advection casesto thermally indirect (&o/Oy < 0) in the cold advectioncase. Nevertheless, the overall circulation pattern inthe cold advection case is in the direct sense, as requiredfor the respective generation of westerly and easterlymomentum at upper and lower levels (Fig. 26b). The shift in the transverse ageostrophic circulationin the cold advection case relative to the pure conflu482 MONTHLY WEATHER REVIEW VOLUME i14(a)PURE CONFLUENCE CASE 135 FlTrrmT~Trr~rrhm HHi,,h. mlm,H n q dlTh mlnHn,~ '-::='!ii~i:.'-:i:-i: i:i:'~:i!::!iiiiiii~.~!iii:~ii!ii: ".:;ii~i::~iii:..:i!ii:iii~,,,,o~ ~::~'~iiiii:,:i~'-;':'~~:i[VT: :-~ ~iiii!i:i~::::.%-i:i!~i_: :!~':-!!:-~;:'"'~";:;~'-""':~:~~ u ~i~i~!i:ii:-.:.:ii:~:~i_-'.':.:,~.~: ' . ~ : ....... ............ ,,-~ :::.:.~:~ ....................... :~ " ......... :"i'~ ~// -" I "r ............. '~~~~ .~~~,~ ........... x"~ . ~ '-. ~,~-.. ........ ~,~ - 'M) .............. ' \ ............ ~:. ..................... :. / (b)48 h u COLD ADVECTION CASE 48 h 1961,.5 '::,-./f ~'[~' / %"~=' "'"' "-~':-" "~ "'"-"~'~~~!:.~;~'"'7~'"'"""f ~~'-' ' '"'" ' "~' :' ~~~~'" 2~5 10.2 20~ 280 8.5 28il ~ ~ - ~ ,.., ~,~ ~~ ~M I~ 485 5.2 4~5 620 3.6 6~0 780 1.9 ]TO ............ ,~.~.. 967 0.3 9(172o0o 1500 1000 5oo 0 -soo -iooo -1500 y (km)2900 1500 1000 500 9 - 960 - 1~0 - 1500 y (km)(c) 13.5 f~?tiiiiHiiiiiHi,,, !--'~L:; :i~ii!::L:! lo.2 ~::ii~iii:-:~ =-: .......... :~;:::::.:~;~:;~::;- .--..~8.5 '-~:;"C"~"ii?-'~=============~==~~=====~ . F::!~!~!:i?~~.~ ................... 1~ ..................... [ U WARM ADVECTION CASE ' 48 h II II [lllll II I1111~111111 H IIIII III IIIIIII IIIII Ill IIIllllf_.I 196 :::::::::::::::::::::::::: ....... ~;: ~(~'~: t::: '" ~ ~ *" '-' ~:::~%'' -':4 :::' ';::::::::::~~? iL:L:~i.: _:~Jig.:_: :-.;:=:;:- ':::::::-:: :;; - - ~%'-"": --:;: '*: ' :2 ::.' ..* :;:: :::;~i: '~* '~:'i-~";::~:;22:'*;'_'-._*~ :~.'_* ~ L*; 2 .'.': 2 .'.L; .; 145 "2' ;; ::;::::--':.* ':.':::: :: .~q-..::.':.*: :;....~:;2::.~:. :*'- '-~ ............ :: .......... ~.'i ~'/g' '~' '"-'"'*"*~ ....... ::'--'-:::: ........ ":i i:L:: 'i~::.:-;::Ei~.:~:;:::::::-:--.~:::: -- ......;'. :.'. :z~':;~.~r--....;;::;;;;;;:Z...':; "r~'"'"~~ !tJ~. .:~i.'~'''''/'::'''-.:.'.~, ::::::::::::::::::::::::::::::::::::::::::::::::::' ~'""r~, , ......... ....... ,,*-~ ~. ~ ~ ", / . ~ ,.. . ,,. . , ,?..-... ............ : %, ............. ~.'.,, , - ~ $~n ......... ,: o ~' ,~~ ::,,,:::"::':ii,,,,,,1a~ I~ 1~ ~ ~ -~ -1~ -1~o -a~ y (kin)ence case is compatible with the qualitative predictionsfrom the two-dimensional Sawyer-Eliassen equation(3.12) applied to the entrance region of a straight jetmaximum. In particular, in the cold advection case(Fig. 28b), midtropospheric subsidence is maximizedbeneath the jet core, as indicated in Fig. 23c, comparedwith the pure confluence case (Fig. 28a), where midtropospheric subsidence is maximized to the cyclonicshear side of the jet axis, as indicated in Fig. 23a. Inthe warm advection case, the predicted shift of theageostrophic circulation toward the cyclonic shear sideof the jet core (Fig. 23d) is suggested in the model circulation pattern in Fig. 28c. There is an indication ofmid- and upper-tropospheric ascent beneath the jet core F]o. 26. Cross sections of the along-front wind component (contourinterval 5 m s-~, solid) and potential temperature (indicated as inFig. 25) after the 48 h numerical integration of a two-dimen~;ionalprimitive equation model of frontogenesis due to pure confl~aence(a), and confluence in the presence of upper-level cold advection (b)and warm advection (c). Adapted from Keyser and Pecnick ( ! 985a).in the warm advection case, which is absent from thepure confluence case. An analysis of the prognostic equations for vorticity(3.7) and cross-front potential temperature gradient(3.9) partitioned between horizontal and vertical motions reveals fundamental dynamical differences inupper-level frontogenesis for the pure confluence: andwarm advection cases compared with the cold a(lvection case. Under adiabatic, ,frictionless, Boussinesqconditions, the above-mentioned equations reduce tod Om~_ OmOva~ OmOw (4.1)~; ~ Tyy / oy oy o, ~ 'F"EBRUARY 1956 DANIEL KEYSER AND M, A, SHAPIRO 483(a)13.511.6 I0,,2 8,.5N $2 .a3 13 r3 PURE CONFLUENCE CASEJll III II1~ HI Ill II1~ HIll IIHII II II IH I~111111111~1111111111 I IIII III1~ III1'11111 100............................................................................................ ::.~!!i.:*:.:L:~!~:~iii.~.:i~!!L:!!i-~;~:~i~i~.:*~i:+:L...:~...ii.5iiiiL.:i~.;5 5~i!ii~5~::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 145:2::2 ....................... 3~O. -.';.':.'.'.~..':;~---:.-:::::.':_-:::_'_ ..::: :-'::::.',L':.';: .........;:::::!i F !!E iiL:!!iiii L:!! L:!!!! !::::::!EZ:E::.:L:i.:L:-: .-'.: ~ F~,- .:.: .:L-'.-' .::: :.::::: ::~? F i E :' ?'.-':~:z:: :z:%::: ........... ~~===================~ 7: ::: .-; ::::::::::::::::::::::::: :2a::.'TM .............. .............. :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::.... :%::.' ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: .........:%: .............. ' :.'::': ....... :.*::'.L.-;:.-;;.~ ................ aa. - -- --'-': '-'~' -' -'C -'.'L'~' '-' "";:::::::::::::::::::::::::::::::::::::::::: ............ . ................... :?:-:-:i!i!i!!::.:'r::-5::iii~.:'~.:~:: ..... .,. ' .............~_ ........._......-.... _........~.-.... :-_~...-_. _ -~~~~~~~.~~~~ - -- ..,.,, ..........=. .............. ...~ ,% ',.~~'x,~ , ' ................ ~. -'-.,...'%. ',, '\, % ',... -,,,, ,,~x, ,,, \, ,.,.,. .~ .... ~ ,,, ,~ ,,~ x. ............. sod.-' ............. "--.. '"'~ ",X, "' "~ '"~. '-,.,.,.% ',, ~ \', ,~ ',\' ",,, ", 'x ,, ',\ '~ '%, i.... , ',,\~ ~ ..... - 789......................... --. ,- , ,,,,\ ..................' '"'~, .. ",. '"-."',"N\- ~,.., ~,, -.,',,'%\ \- .~.~ --,.. ,.~..,2 , ...., ....! ..... ~,1,,,;~ .... z; 1500 1000 560 0 - 5OQ - 1000 - 1500 - 3OOOy (km)312 ~ ~.8~(b)11.8 $21303 2000COLD ADVECTION CASE 100 145 2O5.0 372 -~ ~ ~;, ,,----~ '"'"" ,~' x ....................... 485 m. -%. -.,, ',,,,; ............. ~:, ............ ,,.. .....: ... ' ........ "'..?-.~i'..~'.i:,~ 1 ~. - ............ -.. ,. -. -,,~,:,\ ......i ......... ~.. --. '-. x.... *-.~ ~ ..... 967'::::!:::.!;;;:'~! .... ~,,,~,,I .... I.,.,-1 15g) 1000 6GO 0 - 500 - 1000 - 1509 - 2000y (km)(c) WARM ADVECTION CASE13.5, I Illl I Illllllllllll[ I IIIIII1 Ill IIIlllfl[lllllllll[lllllllll] IIIlllllll IIIIIIlll. .......... ~:C;::- :.'.':; :.';.'.'" :::' '"'2:;;; ;:;:; :;;;:'-: ;::; ;;:: ': .......... ::: -;::..---- ...._..2113 :~i!..-i.:~:-~i~iiii~ii~!.~i:~i~:!iii::iiii::iii::iiiii i:iiiiiii:_:i~i~i:_..~iliiiii_:i~)_:i_:~i~ ;:::::: ::::::::::::::::::::::::::::: :i-:i!:'-;~;?-_'C-.-":-::--:~-L:?i~;i-;L:E:::::::::::::::--.---: '-::: :: '-: :: '-':i'.' ! ::!~ '-'-': -'; - - - - ~. ==~=====================~====== ........ :::::::::::::::::::::::10.2 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ii:' ............. :'":'"*'::;~':'"":::" ::::::::::::::::::::::::: ':: ...... ' ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ....... ;-... .. .-:__ ::~ .-:~.~ .---: Z !Z :'F:::::~!:':::::::' ~ ':-<5.:5.--.-,, .................... ;,'**= .......~;::: ........ ;:;;:'---;: '--- 2" ~'.-**'./ . _ -... ,::.:'.--.,,, '-,,. -. ............................ ,; - * ........... "C:."-. % "% : - ,,%,,,,, ',% '-,,~ - . ..... %?',, '% .... ..... . \ '* \ '--.-. ............. ,; -~'~'-' "-~~* ' "~'~-* * ' -*~i*~ ','*~,,.-- ~"~ .......... 7~,, .._. ..................................... : - ..,... ...... ',,',,:. ,,~;~., ::.~?:,,~ ~1.9 ........................... '" <'' '~',-X '~~. '~-J - ~ ................ "<:~i~~::'~ ................... ~ . -.. .. ~-3 : ....~ ....~ :-TTi'""~---~-T"~F~,,,, t ,~d. .... I,, ~ - 2000 1500 1000 500 0 - 50~ - 1000 - 1500 - 2000~ 63!"~$210014520528037Z -~48~820?8fl~7y (km) FIG. 27. Back trajectories ending at 48 h at x = 0 km and originatingat 0 h near the tropopause (thick solid line) from a numerical integration of a two-dimensional primitive equation model of frontogenesis. The small x's marked along the trajectories indicate 12-hourlyparcel positions- The cross sections depict y-z projections of trajectories ending at (a) 5.6 km (458 rob) for case of pure confluence, (b)2.8 km (692 rob) for case of confluence in the presence of upperlevel cold advection and (c) 4.4 km (550 mb) for case of confluencein the presence of upper-level warm advection. The potential temperature background (indicated as in Fig. 25) is for the respectivecases at 48 h. Adapted from Keyser and Pecnick (1985a).*)=r ,r*,* **) ao'r (4.2) Op Oy 'where the first term in (4.1) and the bracketed term in(4.2) consist of horizontal frontogenetical effects, and(3.22b) has been used to replace the Jn,(%, %) termin (3.9). In the pure confluence and warm advection cases,the terms in (4.1) and (4.2) involving horizontal motions are frontogenetical in the mid- and upper-tropospheric portions of the frontal zone and dominatethe tilting terms, which are frontolytical because of thedirect sense of the cross-frontal gradient of vertical motion (OodOy > 0) in the presence of increasing westerlywinds with height (Orn/Op < 0) and a statically stablestratification (O0/Op < 0). The situation is essentiallyreversed in the cold advection case. In this case, horizontal motions are frontolytical and are dominated bythe tilting terms, which are frontogenetical because ofthe "locally indirect" sense of the cross-frontal gradientof subsidence (OodOy < 0). The dominance of the tiltingterms in the cold advection case compared with the484 MONTHLY WEATHER REVIEW (la3!5 (Vag,W)PURE CONFLUENCE CASE 24h'~oo (b) (v.w) 13.5 11.8 145 11.8 10.2 205 10.2 8.5 280 8.5 ~ 6.9 972 ~ ~ 6.~ ~ ~ N ~. ~ 5.2 485 ~' 5.2 . ~&a:b~ 3.6 620 3.6 L ...... ' 1" ~ . .... ~ j ~ '~, ~ , , , 1.9 ~ /'~';'*"'-,--:,,-&.: 7~ ~ 1.9 10 m s-~ 0.3 2~ 1~ 1~ ~ 0 -~0 -1~ -15~ -2~ 2000 1~0 1~0 5~ y (kin)VOLUME l 14COLD ADVECTION CASE24 h 1001452O5280 0y (kin)372 ~485 620 , 780 ~ g 967 mL~ lore s-~-500 -1000 -1500 -2000(c) (v~w) WARM ADVECTION CASE 24 h13.5 100 .... :'--:::.4::.- ....... :::::::::::::::::::::::::::::::::::::::::::::::::::: 8.5 '::::--""::'::-': .......... *--'**-:-'~"~:*'*~:*~:-'"~ - ........... : .................. 280 I: ................... ~~ - "~' ~"L~" ~ '~- ''" ~ ~x-~ - -- ~ - .~~~:""~'-~ 8.~, [:..-:,--f-:~::.~",--~".'.~.,~..'._ - -, ,,,.: ~., ..... ,.- ',,\',, %, ..... ~37~, ~ 1.9 I- ..... ,, 4%,,~,~'~?,, ..,,.,,~ ,/.~ ,.;., ,, ~ - ,~ 780 - ' 1:: .... .,' '~- ~ 4,,. ~?..., .'.~_ _ x' ..~,.',,;/% .... ~ E ~- ................. -'"'"'"~ ~'q'""~".-. '.'. zZ...... '._.... ~'; ....... ---'~1 0.3 ....... -', ~-.._~.' ....... ~t_.. . . . , , 'x ........ "~'"?'~ - "~ 867 10 2000 1500 1000 500 0 -500 -1000 -1500 -2000y (km)pure confluence and warm advection cases is relatedto the magnitude of the subsidence in the former, whichapproaches a value of 10 cm s-~, as also noted in severalobservational case studies (Reed and Sanders, 1953;Staley, 1960; Shapiro, 1970). The strong subsidence inthe cold advection case is frontogenetical not only inthe sense that it generates frontal properties along parceltrajectories, but also in that it transports these propertiesdownward as they are generated. The Sawyer-Eliassen equation (3.12) can be used toidentify interactions between the transverse ageostrophic circulation and its geostrophic forcing. Consideration of the geostrophic forcing in the form of(3.22b) reveals that feedbacks in a two-dimensionalmodel formulation are restricted to modifications tothe cross-front potential temperature gradient, O0/Oy,and the relative vorticity, -0%/Oy, since Ovs/Oy andO0/Ox are specified externally. Thus, (4.2) and (4.1) canbe used to determine how the ageostrophic response FIo. 28. Cross sections of the transverse ageostrophic circulation(v~, w) and potential temperature (indicated as in Fig. 25) after the24 h integration of a two-dimensional primitive equation model offrontogenesis (Keyser and Pecnick, 1985a) due to pure confluence(a), and confluence in the presence of upper-level cold advection (b)and warm advection (c). Location of the upper-level jet in the ~dongfront velodty component is indicated by J; magnitudes ofcomlxmentsof transverse ageostrophic circulation are represented by vector scaleson lower-right margins of figures.respectively affects the confluence and horizontal shearforcing, which, in turn, can lead to changes in~ theageostrophic response through the Sawyer-Eliassenequation. As an example, in the cold advection casethe differential subsidence within the upper-level lrrontal zone reinforces the horizontal shear forcing termin (3.22b) by increasing the cyclonic vorticity through(4.1). As suggested in the interpretation of the ageostrophic circulation pattern in Fig. 28b and de~nonstrated in an analysis of the Sawyer-Eliassen equation(3.12) for the cold advection case by Keyser and Pecnick (1985b), the cyclonic horizontal shear is responrsible for shifting the ageostrophic circulation towardthe warm air, so that the cross-frontal gradient of subsidence is frontogenetical with respect to the vorticityfield. The resulting increases in cyclonic vorticity leadto increases in the horizontal shear forcing and thefrontogenetical subsidence, establishing a positivefeedback loop.FEBRUARY 1986 DANIEL KEYSER AND M. A. SHAPIRO 485 The results of the preceding analysis of two-dimensional frontal models can be applied to interpret dynamically the schematic representation of the progression of an upper-level jet-front system through a baroclinic wave presented in Fig. 19 (Section 2d). Severallimitations of the two-dimensional frontal modelsshould be kept in mind. First, their formulation describes an infinitely long confluent entrance region ofa jet, rather than a finite-length jet maximum. Second,the sign of the along-front thermal variation cannotchange with time during the frontal evolution, as suggested from the sequence of events in Fig. 19. Despitethese restrictions, the pure confluence, cold advectionand warm advection cases may correspond respectivelyto the stages illustrated in Figs. 19a, 19b and 19d, forwhich the jet-front systems are reasonably straight. Themodeled transverse ageostrophic circulations for thethree cases (Figs. 28a, 28b and 28c) conform fairly wellto those in the jet entrance regions diagnosed qualitatively from the two-dimensional Sawyer-Eliassenequation (Figs. 23a, 23c and 23d), which correspondto the respective stages under consideration in Fig. 19.Furthermore, the change in dominance of vertical motions over horizontal motions in contributing to upperlevel frontogenesis in the northwesterly flow inflection(Fig. 19b) to horizontal motions over vertical motionsin the southwesterly flow inflection (Fig. 19d), documented observationally in Section 2d, is consistent withthe preceding two-dimensional dynamical descriptionsfor the cold and warm advection cases.b. Three-dimensional processes Conspicuously absent from the above interpretationof the stages of the progression of an upper-level jetfront system through a baroclinic wave in terms of twodimensional considerations is that of the jet-front system situated at the base of the long-wave trough (Fig.19c). The thermal advection patterns for the configuration in Fig. 1% correspond to the case of a jet in athermal ridge shown in Fig. 23e, with the major exception that the jet in Fig. 19c is cyclonically curved.The purpose of this subsection is to discuss three-dimensional modifications to the two-dimensional vertical circulation patterns in Fig. 23e introduced by significant curvature in the flow. For this discussion,curved flows may be defined as those in which the curvature component of the relative vorticity is greaterthan or comparable with the shear component, whichmay be contrasted to straight flows where the curvaturecomponent is much less than the shear component.The discussion begins with Fig. 29, which respectivelyillustrates idealized cases of pure cross-contour andalong-contour ageostrophic flow considered in the absence of frictional and diabatic processes. The designations cross- and along-contour will be used as thethree-dimensional counterparts of the two-dimensional terms cross- and along-front. Upper-level fronts(a)TROUGH (b) FiO. 29. Schematic representation of the aeostrophic motions(heavy arrows) and associated patterns o- convergence (CON) anddivergence (DIV) in the vicinity of (a) a straight jet streak in theabsence of along-contour thermal advection and (b) a uniform jetstream within a stationary synoptic-scale wave. Both representationsare assumed to apply at or near the level of maximum wind, wherethe horizontal wind distribution is most distinct and the flow is approximately horizontal. Solid lines indicate geopotential height of aconstant pressure surface; dashed lines are isotachs (maximum windspeed shaded). Adapted from Shapiro and Kennedy (1981).and jet features typically are oriented approximatelyparallel to the geopotential height contours. The case of pure cross-contour ageostrophic flowshown in Fig. 29a consists of a straight jet streak in theabsence of along-contour thermal variations, treatedtwo-dimensionally in the descriptions of Figs. 21 a and23a. In terms of the frictionless u momentum equationsubject to the geostrophic momentum approximation(dug/dr = fVag), cross-contour ageostrophic flow is associated with accelerations in ug, as parcels tend tomigrate through the jet approximately parallel to thegeopotential streamlines. The case of pure along-contour ageostrophic flow shown in Fig. 29b consists of awave pattern in which the wind speed is uniform alongthe height contours (height contours correspond to isotachs). The wave is assumed to be stationary and steady,state, and horizontal flow is assumed at the level of thewave, so that streamlines and parcel trajectories coincide. With these restrictions, wind-speed accelerationsfollowing parcels vanish, eliminating cross-contour486 MONTHLY WEATHER REVIEW VOLUME 114ageostrophic flow. In this special case, parcel accelerations are confined to the cross-contour direction andare. required to change the direction of parcels as theymigrate through the wave. Under these conditions, theassumptions leading to the gradient wind are satisfiedexactly, so that it .may be used to quantify the contribution of centripetal accelerations induced by flowcurvature to along-contour ageostrophic motions andthe related patterns of convergence and divergence. The gradient wind, V~, is given by (e.g., Dutton,1976, pp. 311-315) KI/~\-' V~ = (l + --~--~ V,, (4.3)where K is the curvature parameter, defined as the inverse of the radius of parcel trajectory curvature (K-- 1/R~). Equation (4.3) confirms that the gradient windis oriented parallel to the height contours. Consequently, its ageostrophic part, t KV~X V~r- Vg = -~--~-/V~r, (4.4)is in the along-contour direction and is proportionalto the square of the wind speed and the magnitude ofthe trajectory curvature. As illustrated in Fig. 29b, thealong-contoui- ageostrophic wind is directed against thegradient wind in the trough (K > 0, subgeostrophicflow) and along the gradient wind in the ridge (K< 0, supergeostrophic flow). The along-contour ageostrophic flow is zero at the inflections in the wave pattern, where the curvature vanishes. As a consequenceof the specification of uniform wind speed along theflow, the required variations ofgeostrophic wind speedalong the flow result in confluence and diffiuence ofthe height contours upstream and downstream of thetrough axis, respectively. This pattern of confluenceand diffiuence, associated with along-flow variationsin curvature, should be distinguished from that in thestraight-jet case (Fig. 29a), which is associated withalong-flow variations in wind speed. The horizontal divergence of the gradient wind (4.3)for the special case of uniform along-contour windspeed in Fig. 29b is -- -(1 + -7-/ L? + ' (4.5)The above expression contains two contributions,which are respectively suppressed and amplified in thepresence of cyclonic and anticyclonic trajectory curvature. The contributions comprise (i) the /g-effect,which produces divergence and convergence in thenorthwesterly (v~ < 0) and southwesterly (v~ > 0) flowsupstream and downstream of the trough axis, and (ii)the advection of curvature weighted by the gradientwind speed. For the example in Fig. 29b, the curvatureeffect results in maximum convergence and divergenceat the flow inflections upstream and downstream ofthe trough axis along the contour channel containingthe highest wind speed (the jet stream). The/g-effectopposes, but is subordinate to, the curvature effecT: except for very long (planetary) waves. It should be emphasized that the horizontal divergence and con. vergence in the wave pattern in Fig. 29b are associatedprimarily with along-flow variations in curvature. Furthermore, the ageostrophic wind field (4.4) may havea significant nondivergent component, which does notcontribute to the vertical circulation. As an extxemeexample, a symmetric circular vortex, characterizedby constant curvature on an jZplane, is nondive~gentaccording to (4.5) but contains significant ageostrc,phicflow acco~ding to (4.4). The above analysis of curvature effects based on theconcept of gradient flow has been extended by Ne~onand Trevisan (1984a) to include propagating waves inwhich the wind speed is uniform along streamlines ofthe geostrophic flow relative to.the motion of the wave.On the basis of earlier work by Palm~n and Napier(1949), they kinematically infer vertical circulationsand associated frontogenesis for parcels migratingthrough such waves, which they refer to as "gradientwaves." The outcome of their analysis is that for purposes of qualitative interpretation, it is possible to viewthree-dimensional ageostrophic circulations as a combination of cross-contour (tranverse) ageostrophic flowassociated with along-contour variations in wind speedand along-contour ageostrophic flow associated withalong-contour variations in curvature. Stated alternatively, for a cyclonically curved jet maximum (i'n theabsence of along-contour thermal variations) situatedin the base of a trough, the ageostrophic flow and convergence/divergence patterns in Figs. 29a and 29b maybe linearly superposed, with the implicit assumptionthat the two patterns are independent of each other ina dynamical sense. In a conceptual sense, this approachis based on a partitioning of the three-dimensionalageostrophic circulation that is linked to identifiablestructural features within baroclinic flows. Specifically,the cross-contour component of the ageostrophic circulation is associated primarily with the upper-leveljet-front system and the along-contour component isassociated primarily with the baroclinic wave in whichthe jet-front system is embedded. This approach wouldappear to permit the two-dimensional interpretationsbased on the Sawyer-Eliassen equation to carry overto describe the vertical circulations associated withcross-contour ageostrophic flow in the three-dimensional case, while using reasoning based on the gradientwind to describe the vertical circulations associated withalong-contour ageostrophic flow. It needs to be emphasized that the above viewpointis considered appropriate only'for qualitatively interpreting and understanding three-dimensional ageostrophic flow patterns in upper-level jet-front systems.FEBRUARY 1986 DANIEL KEYSER AND M. A. SHAPIRO 487Nevertheless, we choose to proceed with this hybridapproach of synthesizing deductions based on theSawyer-Eliassen equation and the gradient wind in viewof the paucity of examples in the literature of the quantitative diagnosis of three-dimensional ageostrophiccirculations associated with upper-level jet-front systems. Such diagnoses appear to require an approachsuch as the three-dimensional generalization of theSawyer-Eliassen .equation introduced by Hoskins andDraghici (1977), alluded to near the conclusion of Section 3b. This diagnostic method yields ageostrophicvertical circulations in orthogonal planes, i.e., a vectorstreamfunction, which can be partitioned into crossand along-contour components. Although we are unaware of such an interpretation, it may be possible inprinciple to relate the forcing of the along-contourcomponent of the vector streamfunction to dynamicalprocesses linked to flow curvature. An alternativequantitative approach would be to solve a diagnosticequation for the vertical velocity, such as that formulated in terms of quasi-geostrophic theory (3.23) orsemigeostrophic theory (Hoskins and Draghici, 1977),but with the vertical velocity expressed in terms of avelocity potential (Eliassen, 1984). Solution of such adiagnostic equation would allow inference of the extentto which the irrotational part of the horizontal ageostrophic flow is oriented in the cross- versus the alongcontour direction, as well as determination of the vertical velocity field. In view of the preceding arguments based on thegradient wind, the vertical circulations associated withthe cyclonically curved jet-front system located in thebase of the long-wave trough illustrated schematicallyin Fig. 19c may be inferred qualitatively. The orientation of the isotherms at the base of the trough resultsin a pattern of along-contour thermal advection similarto that depicted in Fig. 23e. Therefore, the cross-contour (transverse) ageostrophic circulations can be anticipated to be respectively direct and indirect in thejet entrance and exit regions, but shifted laterally toward the anticyclonic shear side of the jet. The influenceof curvature should be to force a dipole pattern consisting of midtropospheric subsidence and ascent belowthe jet axis in the entrance and exit regions, which aresituated respectively within the northwesterly andsouthwesterly flow inflections in Fig. 19c. As a result,the anticipated effect of curvature is to reinforce thedownward branch of the direct transverse ageostrophiccirculation in the entrance region and the upwardbranch of the indirect transverse ageostrophic circulation in the exit region along the jet axis. The corresponding vertical branches of the transverse ageostrophic circulations situated below the anticyclonicshear side of the jet axis are weakened by the curvatureinduced ageostrophic circulations. The favorable superposifion of the upward branches of the cross- andalong-contour ageostrophic circulations that occursbeneath the axis of a cyclonically curved jet when itsexit region coincides with the inflection in the heightcontours downstream of a trough axis explains whythe flow configuration in Fig. 19c is predisposed to lowlevel cyclogenesis beneath the jet exit region. The above expectations on the nature of the verticalcirculations associated with a cyclonically curved jetfront system in the base of a trough are confirmed bythe results of numerical simulations ofbaroclinic waveamplification using/5-plane primitive equation channelmodels under adiabatic, frictionless conditions. Theinitial conditions for these models typically consist ofa small-amplitude disturbance (in the cases .to beshown, an anticyclone-cyclone couplet extendingthrough the depth of the troposphere) superimposedupon a longitudinally uniform jet possessing lateral andvertical shear and in thermal wind balance with themeridional potential temperature gradient. As the wavedisturbance amplifies, a midtropospheric frontal zoneforms in the base of the trough, as shown from theresults of Buzzi et al. (1977)~2 in Fig. 30a. The temperature field at the base of the trough assumes thecharacteristic thermal ridge configuration shown in Fig.19c, and the upper-level jet (not shown) is cyclonicallycurved approximately along the height contours. Thecross sections for the vertical velocity field for the jetentrance (Fig. 30b) and exit (Fig. 30c) regions respectively reveal direct and indirect circulation patterns.The circulations are shifted toward the warm (anticyclonic shear) side of the frontal zone, and the strongervertical motions are found within the frontal zone,which is situated beneath the jet axis. This asymmetrical character of the vertical motion patterns issuggestive of the influence of an along-contour ageostrophic circulation associated with curvature variationsin augmenting the "two-dimensional" transverseageostrophic circulations in the jet entrance and exitregions.' Diagnostic calculations of frontogenesis with respectto the horizontal potential temperature gradient forthis numerical simulation reveal the dominance ofvertical over horizontal motions for parcels migratingaround the base of the trough through the frontal zone.The orientation of the subsidence pattern relative tothe frontal zone in the entrance region of the upperlevel jet-front system indicates a frontogenetical rolefor tilting (1.1) on the horizontal potential temperaturegradient, arising from the locally indirect sense of thecross-contour variation of subsidence within the frontalzone (Fig. 30b). Similarly, tilting is frontolytical in theexit region, where the orientation of maximum ascentnear the jet axis results in a locally direct sense of the ~2 The numerical model used by Buzzi et al. was formulated interms of isentropic coordinates in the vertical direction by E!iassenand Raustein (1968, 1970). The ability of isentropic coordinates torepresent the structure of upper-level frontal systems was demonstrated in a subsequent application of this type of model by Shapiro(1975).488MONTHLY WEATHER REVIEW A' B'VOLUME 114A - B(b)(c) FIG. 30. Analyses illustrating the results of a 48 h numerical simulation of a baroclinicallyunstable wave in a fi-plane primitive equation channel model using potential temperature as thevertical coordinate: (a) 500 mb geopotential (m2 s-2, solid)and temperature (K, dashed); crosssections of pressure-coordinate vertical velocity (10-I ~b s% dashed) and potential temperature(K, solid) along lines AA' (b) and CC' (c) shown in part (a). From Buzzi et al. (1977). cross-contour variation of ascent within the frontal zone (Fig. 30c). Both the shift of the transverse ageo strophic circulation toward the warm side of the frontal zone and the dominant frontogenetical role of vertical- motions in the entrance region of the jet-front system in the three-dimensional channel model are consistent with the corresponding results from the two-dimen sional model of upper-level frontogenesis' forced by a combination of cold advection and confluence (Sec tion 4a). Further documentation of the nature of the vertical circulations associated with an upper-level frontal systern situated at the base of a trough of a baro,elinicwave is found in the numerical results of Newton andTrevisan (1984b), which are derived from a/g-planechannel model very similar to that ofBuzzi et al. (! 977).The idealized case simulated by Newton and Trevisanconsists of the evolution of an upper-level jet sl:reamand its associated frontal structure, which is best definedat the base of the trough. This case should be contrastedwith that ofBuzzi et al., which contains a jet maximumat the base of the trough (as treated schematic,tlly inFigs. 19c and 23e). The case considered by Newtonand Trevisan reflects the schematic representati~on ofFEBRUARY 1986 DANIEL KEYSER AND M. A. SHAPIRO 489a curved jet stream in Fig. 29b, and thus isolates thefrontogenetical influence of an along-contour ageostrophic cimulation in the absence of transverse ageostrophic circulations in the entrance and exit regionsof the frontal zone. Figure 31 illustrates the midtropospheric vertical motion pattern relative to the heightfield and the orientation of the jet-stream axis simulatedby Newton and Trevisan. In agreement with qualitativeexpectations based on gradient flow (Fig. 29b), subsidence and ascent are maximized near the flow inflections along the jet-stream axis, which corresponds tothe warm boundary of the frontal zone (not shown).This orientation of maximum vertical motions relativeto the midtropospheric frontal zone is consistent withparcel frontogenesis and frontolysis in the frontal entrance and exit, respectively, as described previouslyin the discussion of Fig. 30. Vertical cross sections of the total (geostrophic plusageostrophic) transverse flow for the inflection in theflow coinciding with the frontal entrance region (Fig.32) exhibit subsidence along a confluent asymptotecorresponding to the jet axis. The confluent asymptoteseparates a region of widespread descent on the cyclonicshear side of the jet' axis from descent in the warm airon the anticyclonic shear side of the jet axis. That thistransverse flow pattern is frontogenetical for parcelsmigrating from the upstream ridge through the inflection to the base of the trough is reflected in the betterdeveloped midtropospheric frontal structure in the isentropes at the trough compared with the ridge (Fig.32b). The similarity is striking between the transverseflow pattern in Fig. 32 and the trajectory pattern fromthe two-dimensional model of upper-level frontogenesisdue to a combination of cold advection and confluencein Fig. 27b, despite the association of subsidence withan along-contour ageostrophic circulation in the formerand a cross-contour ageostrophic circulation in the latter. The similarity between both of the above, numerically derived patterns involving the total transverseflow and the idealized schematic of transverse Circulations accompanying tropopause folding in Fig. 33(Danielsen, 1968) suggests the possible general connection between these transverse flow patterns and upper-level frontogenesis. Identification of frontogenetical feedbacks betweenthe three-dimensional vertical cimulations and theirforcing is limited to the interpretation of upper-levelfrontogenesis in a primitive equation/~-plane channelmodel by Mudrick (1974). In this case, a positive feedback is postulated between the subsidence and vorticitypatterns for the entrance region of a jet-front systemin the northwesterly flow inflection between a ridgeand downstream trough (the stage in Fig. 19b). Subsidence beneath the jet axis (Fig. 23c) enhances thecyclonic and anticyclonic shear vorticity on the respective sides of the jet in the midtroposphere through50 \w p.b s FIG. 31. Analysis at 500 mb illustrating the results of a 72 h numerical simulation of a baroclinically unstable wave in a fi-plane primitive equation channel model similar to that referredto in Fig. 30. Thick solid lines are height contours (contour interval 100 m, 50 denotes 5000 m),thin solid and thin dashed lines are pressure-coordinate vertical velocity (contour interval 1 ~bs-~), and thick dashed arrow represents axis of intersection of jet stream with the 500 mb level.From Newton and Trevisan (1984b).490 MONTHLY WEATHER REVIEW VOLUME 114 'mb276 ~68 I~(a) (b) F~o. 32. Total transverse circulation for the northwesterly flow inflection, FF, shown in Fig.31, indicated by streamlines in (a) and vector arrows in (b). Potential temperature (K) for theinflection, FF, is represented by dashed lines in (a). Potential temperature (K) for the ridge axis,RR, and trough axis, TT, shown in Fig. 31, is represented respectively by dashed and solid linesin (b). The circled plus signs denote the location of the jet at 500 mb within the flow inflection,FF. From Newton and Trevisan (1984b).tilting (1.2), since the wind speed in the jet increaseswith height. The tilting thus results in an enhancedcross-contour gradient of vorticity. Mudrick then invokes an argument based on an extension of the quasigeostrophic ~0 equation (3.23) to the primitive e, quations. The "primitive" o~ equation consists of a morecomplicated response (left side) than its quasi-geostrophic counterpart, but its forcing (right side) is theFIG. 33. Schematic illustration of transverse circulations conducive to upper-level frontogenesis and troIx)pause folding. Note that orientation of figure is reversed from that in Fig. 32. From Danielsen (1968).FEBRUARY 1986 DANIEL KEYSER AND M. A. SHAPIRO 491same as in the quasi-geostrophic form (3.25) exceptthat the vertical shear of the vorticity advection andLaplacian of the thermal advection involve the totalhorizontal wind rather than the geostrophic wind.Consequently, the presence of a thermodynamicallydirect cross-contour ageostrophic circulation in the jetentrance region results in a vertical increase in anticyclonic vorticity advection by the cross-contour component of the ageostrophic wind in the frontal zone.The increase of anticyclonic vorticity advection withheight can be expected to be most intense in the vicinityof the jet axis, where the cross-contour gradient of shearvorticity is greatest. The result is midtropospheric subsidence maximized along the jet axis on the warm edgeof the frontal zone, which is favorable for frontogenetical tilting and thus doses the positive feedback loop. Although this subsidence-vorticity argument appliesto a three-dimensional flow pattern, it appears to betwo-dimensional in the sense that it involves the production of shear vorticity and its advection by the crosscontour component of the ageostrophic circulation. Noreference is made to the along-contour component ofthe ageostrophic circulation, nor its forcing. It is possible that this feedback process is related to that identified in the two-dimensional cold advection case (Section 4a) involving the horizontal shear forcing of theSawyer-Eliassen equation and subsidence. Nevertheless, the differing forms of the diagnostic equations forthe vertical circulation on which the two- and threedimensional interpretations are based renders theirreconciliation problematical.5. Directions of future research The preceding sections have presented an overviewof current knowledge and perspectives on the structureand dynamics of upper-level frontal zones. The application of synoptic-scale radiosonde observations supplemented by those from research aircraft has led tothe synthesis of conceptual models of the structure ofupper-level frontal systems. The application of twoand three-dimensional dynamical models has reproduced this structure and elucidated mechanisms andprocesses involved in upper-level frontogenesis. Nevertheless, a number of unresolved problems and issuescan be identified and serve as the subject of discussionfor this section. Topics requiring further research include (i) observational documentation of frontal evolution throughout the life cycle ofbaroclinic waves; (ii)resolution of the relative importance of two- and threedimensional dynamical processes in upper-level frontogenesis and consideration of the potential importanceof dynamical processes excluded by the geostrophicmomentum approximation; (iii) investigation of theinteraction between upper-level frontogenesis andbaroclinic wave amplification and their effect on lowlevel cyclogenesis, along with the implications for required horizontal and vertical resolution for numericalweather prediction models; (iv) consideration of therelationship between upper-level frontal circulationsand low-level circulations, a process sometimes referredto as "coupling"; and (v) investigation of the interactionbetween mesoscale convective systems and upper-levelfrontal systems. A major shortcoming in our understanding of upperlevel frontal dynamics is due to the absence of temporally continuous observational documentation offrontal evolution throughout.the life cycle of a baroclinic wave. The schematic illustration of this processin Fig. 19 is based on fragmentary and incomplete observational evidence, and thus awaits further confirmation. The primary reasons for the incomplete documentation of frontal evolution are the gaps in thespatial coverage and temporal resolution of operationalradiosonde observing networks. These data gaps havelimited observationalists to focusing on only portionsof the frontal evolution with a few snapshots describingthe instantaneous structure. Another "gap" consists ofthe debatable accuracy of ageostrophic circulations derived from radiosonde data, which is primarily a consequence of uncertainties in the winds, especially atupper levels. These observational uncertainties havehindered progress in documenting three-dimensionalvertical circulations within frontal regions. As a result,the application of diagnostic approaches and consideration of dynamical processes involving the ageostrophic part of the flow have been restricted primarilyto datasets produced by idealized numerical models intwo and three dimensions. Rapid developments in progress in the field of remote-sensing technology have the potential of fillingsome of the data gaps in observational descriptions ofupper-level jets and fronts. For example, the capabilityexists of remotely measuring patterns of vertically integrated ozone from satellites, which permits the detection oftropopause folding and the position and perhaps the. intensity of upper-level jet streaks (Shapiro etal., 1982; Uccellini et al., 1985). Related advances inground-based wind-profiling technology based onDoppler radar [see Larsen and Rtttger (1982) for areview] offer considerable promise for examining thetemporal evolution of the wind field in upper-levelfrontal regions. Vertical profiles of the horizontal windfield from near the surface to the 100 mb level can beobtained with vertical resolution on the order of severalhundred meters and temporal resolution of an hour orless. The accuracy of the one-hourly averaged winds istypically several meters per second, which surpassesthat of radiosonde data, especially in the upper troposphere and lower stratosphere. A recent example of the application of wind profilermeasurements to describe upper-level frontal structureis given in Figs. 34-36 (Shapiro et al., 1984a). Figure34 consists of a subjective analysis of radiosonde observations for the 300 mb level supplemented by severalprofiler observations over Colorado, depicting a north492 MONTHLY WEATHER REVIEW VOLUME 114300 mb WI~ND SPEED ms-~)STREAMLINES1200GMT 13JUNE 1983 FIG. 34. Wind speed analysis at 300 mb for 1200 GMT 13 June1983, Profiler wind vectors, open circles; wind speed (m s-t), dashedlines; streamlines, thin solid lines. Winds are plotted according tothe standard convention (see caption for Fig. 7a). MSG denotes missing radiosonde wind observations. From Shapiro et al. (1984a).1200 GMT 13 JUNE t~ FIG. 35. Cross-section analysis of wind speed (ms-~, dashed lines)and potential temperature (K, solid lines) for 1200 GMT 13 June1983 along the projection AA' in Fig. 34. Analysis is a composite ofradiosonde and radar wind profiles (designated by letter P on theabscissa). From Shapiro et al. (1984a). ~17- 16- 15 14 13 12 11 ~o ~ S ? $-$ LAY CREEK, COLORADORADAR WINDPROFILER 13-14 JUNE, 1983 WIND SPEED (ms-l) Time' -t (GMI~ '~7 5 3 1 23 21 19 16 I I I I I I I I FiG, 36. Time-height cross section of wind speed (m s-~) fbr 1314 June 1983 with distances scaled as in Fig. 35. Vector winds areplotted at 2 h intervals at the indicated times; dotted lines i~adicatefrontal boundaries. From Shapiro et al. (1984a).westerly jet approaching the southwestern corner ofColorado. Figure 35 consists of a southwest-northeastoriented cross section through the jet derived subjectively using a composite of conventional radio:sondewinds and temperatures and profiler winds. The struc,ture of the upper-level frontal zone conforms 'to theexpectations from previous analyses based on a combination of radiosonde and aircraft data (e.g., Fig. 7aand 10). The time-height cross section in Fig. 36, drawnfrom wind profiler data alone, reproduces the stnactureof the jet in the spatial-cross section in Fig. 35 withremarkable fidelity. Frontal research could benefitsubstantially from the degree of temporal informationcontained within profiler observations of the wind field.Not only could time-space conversion techniques beapplied to extract mesoscale detail from individualwind profiles as in the above example, but the temporalFEBRUARY 1986 DANIEL KEYSER AND M. A. SHAPIRO 493evolution of upper-level jet systems could .be monitoredcontinuously from a profiler network possessing mesoscale horizontal resolution. Another group of increasingly attractive tools forupper-level frontal research consists of numericalweather prediction models possessing mesoscale spatialresolution (see Anthes, 1983, for a recent review ofmesoscale models). If computing technology continuesto advance, numerical models with domains sufficientlylarge to cover the area affected by a synoptic-scalebaroclinic wave during its life cycle and with horizontaland vertical resolution capable of explicitly resolvingfrontal systems could become a reality. Observationalcase studies could be supplemented with model simulations benefiting from dynamical consistency and theassimilation of data from a variety of sources includingsatellites, profilers and aircraft as well as conventionalradiosondes. On the theoretical side, there is a need todesign approaches for modeling the evolution of upperlevel fronts in the context of the life cycle ofbaroclinicwaves. The/~-plane channel models describing baroclinic wave amplification (Section 4b) produce an upper-level jet-front system that remains at the base ofthe trough, which fits only one of the stages (Fig. 19c)envisioned during the evolution of baroclinic waves.Theoretical approaches must be devised to simulatethe migration of a short-wave feature containing theupper-level jet-front system through a long wave inorder to complement numerical simulations of thisprocess anticipated using observational data. A number of issues related to the evolution of upperlevel frontal systems within baroclinic waves requireinvestigation. One question concerns the origin of jetstreaks and upper-level fronts, or, alternatively, theinitiation of the chain of events represented schematically in Fig. 19. Namias and Clapp (1949) hypothesized that large-scale confluence established betweenpolar and midlatitude airstreams could lead to the initial development and intensification of upper-levelfrontal systems. To our knowledge, this hypothesis hasnever been demonstrated, presumably because of thesparsity of radiosonde data in the northern midlatituderegions where the confluence process appears to bepreferred (e.g., the Gulf of Alaska and western Canada for upperdevel frontal systems affecting NorthAmerica). An issue of diagnostic interest identified in Section4b is determining the relative contributions of the crosscontour (transverse) and along-contour componentsof the ageostrophic circulation to upper-level frontogenesis as a function of the stage of baroclinic waveevolution. Related questions concern the suitability ofthe geostrophic momentum approximation in thecontext of the quasi- and semigeostrophic equationsfor describing the three-dimensional ageostrophic flowpatterns in flow regimes possessing substantial parceltrajectory curvature and where wind speeds are large.Shapiro and Kennedy (1981) and Uccellini et al. (1984)cite observed cases where adopting the geostrophicmomentum approximation can lead locally to errorsin the magnitude and even the direction of the crosscontour component of the ageostrophic circulation derived by considering accelerations of the along-contourwind component following parcel trajectories. Systematic comparisons between quasi-geostrophic, semigeostrophic and primitive equation formulations, as wellas the additional "intermediate models" proposed byMcWilliams and Gent (1980), through the integrationof prognostic models of idealized baroclinic flows [asin Mudrick (1974)] would be useful for assessing thegeneral validity and accuracy of these approximations.A related but complementary approach consists of utilizing diagnostic formulations based on the above setsof approximations to solve for the three-dimensionalageostrophic circulations from the output of primitiveequation model simulations, for which the "true"ageostrophic circulations are known exactly. A question of considerable practical significance isthe extent to which upper-level frontal systems andfrontogenetical processes must be resolved in numericalweather prediction models to improve the accuracy offorecasts~3 involving significant midlatitude cyclogenesis and precipitation. A related consideration isthe extent to which upper-level jet-front systems mustbe resolved in initial datasets. These questions are reflected in the closing comments of the synoptic meteorology textbook by Palmrn and Newton (1969, p.585):Although some of the principal mechanisms governingcyclogenesis have been exposed, it cannot be said thatthe process is completely understood. For example, ithas been possible to produce replicas of cyclones innumerical prediction experiments without taking intoaccount the existence of fronts (although in some casesthese develop in rudimentary form). Since well-developed fronts are characteristic of the real atmosphereand much of the available potential energy and kineticenergy are concentrated in their vicinity, there is stillto a certain extent an open question about the fundamental physical relationships between frontogenesisand cyclogenesis.Although published over 15 years ago, the conflictingviewpoints raised in this passage questioning the extentto which upper-level frontogenesis is a passive consequence or an active causal mechanism for cyclogenesisrequire reconciliation. The opposing views concerning the relationship between upper-level frontogenesis and cyclogenesis maybe related to differing perspectives on the nature of thecyclogenesis process between the observational and 23 The concept of"improved forecast accuracy" takes on a precisemeaning only when the needs or requirements of a particular userare taken into account, and is, of course, open to considerable inoterpretation and debate.494 MONTHLY WEATHER REVIEW VOLUME 114theoretical disciplines. The typical sequence of eventsassociated with cyclogenesis identified observationally(e.g., Petterssen, 1955; 1956, pp. 334-338; Palm6n andNewton, 1969, pp. 316-324) conforms to the schematicin Fig. 19, with cyclogenesis favored during the stagesdepicted in Figs. 19b and 19c. In particular, a surfacecyclone begins to develop beneath the diffiuent (delta)region in the upper-level height contours as a jet-frontsystem propagates from the northwesterly flow inflection toward the base of the trough. The deepening ratethen increases as the jet rounds the base of the trough,assuming a cyclonically curved orientation, and migrates toward the southwesterly flow inflection. Theimplication of this synoptic viewpoint of cyclogenesisis that the upper-level jet-front system plays an activerole in the process by organizing and focusing the patterns of upper-level divergence necessary for low-levelpressure falls. This viewpoint suggests that in somecases forecasts of the timing, location and intensity ofcyclogenesis in numerical weather prediction modelsmay demonstrate a significant degree of sensitivity tothe resolution of upper-level jet-front systems. Most contemporary theoretical perspectives onmidlatitude cyclogenesis derive from the original formulations of' baroclinic instability theory by Charney(1947) and Eady (1949). These classic theoretical developments, along with the extensive elaborations andgeneralizations they have inspired, collectively describethe exponential growth to finite amplitude of an infinitesimal wavelike disturbance (referred to as a normalmode) superimposed upon a basic state consisting ofa zonal jet possessing vertical (and sometimes lateral)shear and in thermal wind balance with the temperature field. The horizontal scale of the initial disturbanceis selected to be that yielding the most rapid growthrate. This theory isolates the dynamical mechanismsand feedbacks involved in the intensification of midlatitude cyclones, referred to as the "self-development"process by Sutcliffe and Forsdyke (1950). By focusing on the growth process, classic baroclinicinstability theory does not treat the complete life cycleof midlatitude cyclones. In particular, the details of theprocess by which cyclogenesis is initiated are not considered, and are irrelevant in the sense that the structureof the cyclone and its growth rate are determined bythe basic state alone, rather than by a combination offactors including the initial conditions (a characteristicof the so-called normal-mode approach). Although realistic reproductions of upper-level and surface frontsare found in the context of baroclinic instability theory,they arise as a consequence Of upper-level wave amplification and low-level cyclogenesis, rather than appearing in advance of these processes. The implicationof the normal-mode approach to baroclinic instabilitytheory for numerical weather prediction is that the detailed resolution of upper-level jet-front systems doesnot appear to be required, because the cyclogenesisprocess depends upon the properties of the large-scaleflow pattern, which corresponds to the basic state inthe theory. Reconciliation of the conflicting observational andtheoretical viewpoints concerning the active comparedwith the passive role of upper-level jet-front systemsin cyclogenesis appears to require determining the relative influence of the initial conditions compared withthe basic state on the baroclinic growth process. Recently, Farrell (1982, 1984) has fit baroclinic instabilitytheory into the mathematical construct of an initialvalue problem. This approach produces a group of solutions referred to as "nonmoral," required to accountfor the specification of arbitrarily general initial conditions, in addition to the conventional, but structurallylimited, normal-mode solutions. The overall result isthat the nonmodal solutions dominate in the earlystages of baroclinic growth, while the normal modesare of increasingly greater importance later on in theprocess. These idealized results may be interpreted assuggestive of an active role for upper-level jet-front systems in the initiation phase in the life cycle of :midlatitude cyclones. As stated in the introduction, this review has focusedfor organizational necessity on upper-level jet-frontsystems at the expense of virtually ignoring their lowlevel counterparts. From the standpoint of Dines'compensation, the divergence patterns forced by jetfront systems at upper levels may be considered 'to beassociated with convergence patterns forced by frontogenetical processes at lower levels. Consequently, although upper-level and lower-level fronts and jets mayappear to be structurally separate from each 6ther, under suitable conditions they may be viewed as coupledthrough their vertical circulations. This interpretationhas been applied by Uccellini and Johnson (1979) andUccellini (1980) to connect upper- and lower-lew,q jetsdynamically and relate this coupled jet configurationto the organization of an environment conducive tothe initiation and organization of severe convectivestorms. Shapiro (1983) presents hypothetical schematics of superposed upper-level jets and surface frontsand their associated transverse ageostrophic circulations respectively unfavorable and favorable for thedevelopment of severe convective storms. Further observational research is needed to link the establishmentof the preconvective environment, as well as the initiation and organization of convective storms, to thethree-dimensional ageostrophic circulation pmternsforced by coupled ~upper- and lower-level jet.,; andfronts. Upper-level jet-front systems may not only contribute to the development of convection, but may in turnbe influenced by its presence. Organized convectionmay contribute to the frictional and diabatic forcingterms in the Sawyer-Eliassen equation (3.12) big vertically transporting momentum and heat, as well asthrough the direct heating and cooling effects of condensation and evaporation. Shapiro and KennedyFEBRU^RY 1986 DANIEL KEYSER AND M. A. SHAPIRO 495(1982) suggest that their aircraft measurements of crosscontour ageostrophic flow toward lower heights in thevicinity of the core of a straight jet, for which speedaccelerations and curvature effects may be considerednegligible, can be accounted for by the nearby presenceof a line of deep convection. If frictional effects alsocan be ignored in the jet core, this cross-contour component of the ageostrophic flow is in the appropriatesense to result in the intensification of the jet. Observational studies (e.g., Ninomiya, 1971; Maddox, 1979;Fritsch and Maddox, 1981; Fuelberg and Browning,1983; Wetzel et al., 1983; Keyser and Johnson, 1984)and mesoscale numerical model simulations (e.g.,Maddox et al., 1981; Anthes et al., 1982) have shownthat an organized mesoscale convective system cancontribute to the enhancement of a preexisting upperlevel jet or even the formation of a new jet throughcross-contour ageostrophic circulations associated withthe anticyclonic, divergent outflow found at the tropopause level above the convective storm system. Thelonger-term impact of the convectively generatedmodifications to upper-level jets over time scales extending beyond the lifetime of the convection has beenquestioned by Wetzel et al. (1983), who point out thatenhancements in jet wind speeds are confined to a relatively shallow layer near the tropopause and do notappear to be in dynamic balance with the thermal field.Additional research is necessary to document furtherthe patterns of the three-dimensional ageostrophic circulations and their forcing involved in the scale interactions between upper-level jet-front systems and mesoscale convective storms.6. Conclusion Our knowledge and understanding of the structureand dynamics of upper-level frontal zones and theirinteractions with larger- and smaller-scale phenomenaand processes have advanced considerably since theirdiscovery and initial observational description with theadvent of upper-air data over 50 years ago. Observational descriptions have evolved to the point of thoroughly documenting the structure of upper-level jetfront systems at particular stages in their life histories.Dynamical descriptions of the associated vertical circulation patterns have been established through theapplication of two-dimensional theoretical models anddiagnostic approaches, and mechanisms involvingfeedbacks between the primary (geostrophic) and secondary (ageostrophic) circulations have been identified.The theoretical basis has also been introduced for extending two-dimensional diagnostic concepts to threedimensions. When surveying the results of research into upperlevel frontal systems during the past 50 years, one maybe impressed by the significant influence of technological innovations on changes in observational and theoretical thinking. The discovery of upper-level frontswas a consequence of interest in exploring the atmosphere above the Earth's surface and documenting itsthree-dimensional structure, rather than continuing torely on the limited methods of indirect aerology, whichconsisted of inferring the upper-air patterns from surface data, cloud observations and air-mass types. Interest in probing the three-dimensional structure of thetroposphere must have been heightened by the operational requirements of the fledgling aviation industry.The application of upper-air data eventually led toquestioning of the inferences of the Bergen Schoolconcerning the existence of a deep polar front encirclingthe globe at midlatitudes, separating polar from tropicalair. By the late 1940s, the development of baroclinicinstability theory and approaches for diagnosing cyclogenesis and vertical motions based on quasi-geostrophic theory revealed a shift away from the focuson surface discontinuities and kinematic treatments toa viewpoint of a three-dimensional, continuous atmosphere describable in terms of dynamical principles.With this change in emphasis, fronts were viewed aszones of transition rather than discontinuities, a description appropriate to upper-level fronts. In retrospect, the ideas of Reed, Sanders, Newton and Danielsen in the 1950s on the formation of upper-levelfronts through dynamically induced subsidence, ratherthan through the confluence of polar and tropical airmasses as in the case of surface fronts, represented aculmination of the shift in emphasis toward contemporary thinking in synoptic meteorology. The subsequent research involving aircraft measurements hasextended and refined modern views on the structureand evolution of upper-level fronts, rather than resulting in major, revolutionary changes. It may be argued that the implementation of electronic computers and the rapid development of numerical weather prediction as an established meteorological discipline during the 1950s may have lessenedinterest and slowed frontal research. The early baroclinic models primarily were intended to treat the longwave patterns on a hemispheric scale, so that upperlevel and surface fronts were subgrid-scale phenomena.Encouragingly realistic and accurate predictions couldbe interpreted to suggest that fronts are of lesser importance in the dynamics of midlatitude baroclinicwaves and cyclones than might have been anticipated.The emerging viewpoint was that baroclinic development is a large-scale process of which fronts are apassive consequence, consonant with the results ofnormal-mode approaches to baroclinic instability theory. Eventual limited improvements in the skill of numerical forecasts, coupled with substantial practicalinterest in quantitative precipitation forecasting, subsequently led to a focus on developing parameterizations of planetary boundary layer and convective precipitation processes. The development of finer-resolution, mesoscale models suitable for applicationsinvolving real data during the 1970s appears to have496 MONTHLY WEATHER REVIEW VOLUME 114 been governed by the widespread opinion that majorgains in forecast accuracy were to be made throughrefined treatments of boundary layer and convectiveprocesses. This approach reflects the view that baro- agclinic processes are synoptic-scale and more than ad- cpequately resolved in mesoscale models. Consequently, c~there was relatively little motivation to focus attention CATand effort systematically on resolving frontal-scale d( )/drprocesses in mesoscale models, which consists of emphasizing vertical resolution in objective analysis-ini- ffialization schemes and model grid systems. FIt is tempting to speculate that a practical context is Fxemerging for renewed interest in upper-level and sur- gface fronts. Mesoscale numerical weather prediction grmay be progressing to the point of diminishing returns iwith respect to increases in the accuracy of quantitative jprecipitation forecasts. It may be that the parameter- J,,y(fl, f2)ization of precipitation processes has advanced to thestage where,further improvements in precipitation Jyp(f~, f2)forecasts require explicit resolution of the vertical circulation patterns responsible for initiating and orga- knizing mesoscale convective systems. If such a conjec- Kture is correct, the resolution of fronts becomes important, since they are the primary seat for the forcing In( )of mesoscale vertical circulations. Computing tech- LMWnology now exists to resolve fronts in both mesoscale mmodels and their initial conditions. Novel observingtechnologies involving the remote sensing of winds nfrom the ground, and temperature, moisture and ozonefrom space offer promise in filling gaps in the temporal pseparation, spatial coverage and accuracy of data from P0conventional radiosonde networks. The likely necessity Pof explicitly resolving frontal systems in mesoscalemodels, coupled with the above advances in computing P2and observing technology, has the potential of renewinginterest and stimulating progress in frontal research. QSuch progress in frontal research should yield not onlyrefinements in mesoscale model forecast skill, but alsoimproved conceptual models of the life cycle of mid- Rlatitude cyclones in the spirit of the polar-front cyclone Rtmodel of the Bergen School in Norway, which un- Ridoubtedly served as a tremendous impetus earlier in sthis century for the intellectual and practical achievements documented in this review. t uAcknowledgments. The authors have benefited con- vsiderably from the advice, comments and reviews of VnDrs. R. A. Anthes, L. F. Bosart, K. A. Emanuel, B.F. VFarrell, J. M. Fritsch, B. J. Hoskins, R. A. Maddox, VC. W. Newton, R. A. Petersen, R. J. Reed, J. Simpson Va~and L. W. Uccellini. The contribution of the first authorto this paper was funded in part by the NASA Meso- V~2scale Atmospheric Processes Research Program and bythe Air Force Office of Scientific Research through wContract AFOSR-ISSA-85-00008. Ms. Mildred Birchfield expeditiously and accurately typed the numerous w'O'versions of the manuscript, and Mr. Lafayette Long xassisted in preparing the figures. APPENDIXList of Symbols and Acronyms subscript denoting ageostrophic specific heat for dry air at constant pressure specific heat for dry air at constant volume clear-air turbulence temporal derivative following a parcel tra jectory Coriolis parameter friction term in vector equation of motion component of friction term in x direction gravity; subscript denoting geostrophi~c subscript denoting gradient unit vector in x direction unit vector in y direction Jacobian operator in (x, y) plane defined as (0fl lax)(Of21oy) - (Of, IOy)(O~21,~x) Jacobian operator in (y, p) plane defined as (0fl/Oyl,)(Of2/Op) -- (0fl/OP)(Of2/Oy~) unit vector in vertical direction inverse of radius of parcel trajectory cur vature natural logarithm level of maximum wind absolute momentum parameter [detined by (2.2)] horizontal coordinate oriented normal to isentropes (positive toward colder air) pressure reference pressure general expression for potential vorticity in isentropic coordinates (2.1) two-dimensional (y, p) form for potential vorticity [defined by (2.9)] vector quantity constituting dynamical forcing of quasi-geostrophic w equation [defined by (3.24)] ideal gas constant for dry air radius of parcel trajectory curvature Richardson number [defined by (2.14)] horizontal coordinate oriented along is entropes 90- to the right of n time component of wind velocity in x direction component of wind velocity in y direction component of wind velocity in n direction horizontal wind speed horizontal wind velocity ageostrophic horizontal wind velocity de fined as Ua,i + Va~ j ageostrophic vector wind in the (y, p) '.plane defined in (3.6) as v~j - o~k vertical velocity in z coordinate system [=dz/dtl vertical eddy flux of potential temperature horizontal coordinate increasing eastward; along-front coordinate; subscript deFEBRUARY 1986 DANIEL KEYSER AND M. A. SHAPIRO 497 noting component of a vector in i di rectionhorizontal coordinate increasing north ward; cross-front coordinate (positive toward colder air); subscript denotingcomponent of a vector in j directionheight coordinate; in Section 4a and Figs. 24-28, pressure-dependent pseudo height introduced by Hoskins and Bretherton (1972)confluence parameter introduced in Sec tion 4a, equal to one half of the mag nitude of the horizontal deformation.latitudinal variation of the Coriolis pa rameterfunction of pressure (2.8) appearing in thermal wind (2.5) and hydrostatic (2.7) relationsoperator denoting incremental distance in ( ) directionrelative vorticity evaluated on a constant pressure surfacerelative vorticity evaluated on an isen tropic surfaceabsolute geostrophic vector vorticity in (y, p) plane [defined by (2.4)]potential temperaturediabatic heating ratepressure-dependent reference distribution of potential temperature introduced through quasi-geostrophic thermody namic equationslope of isentropes constituting a frontalzone [=bp/byo] appearing in (2.15)dummy variable used in defining Jacobian operatorsdensity of dry airgeopotential of a constant pressure surfaceageostrophic streamfunction in (y, p) plane [defined by (3,6)]vector streamfunction for three-dimen sional ageostrophic flow defined such that u~ = -&Px/Op, rag = -O~y/Op, o~vertical velocity in p coordinate system [=dv/dt]horizontal gradient operator on a constant pressure surfacehorizontal gradient operator on an isen tropic surfacegradient operator in (y, p) plane [defined following (2.4)1REFERENCESAnthes, R. A., 1983: Regional models of the atmosphere in middle latitudes. Mon. Wea. Rev., 111, 1306-1335.~, Y.-H. Kuo, S. G. Benjamin and Y.-F. Li, 1982: The evolution of the mesoscale environment of severe local storms: Preliminary modeling results. Mon. Wea. Rev., 110, 1187-1213.Berggren, R., 1952: The distribution of temperature and wind con nected with active tropical air in the higher troposphere and some remarks concerning clear air turbulence at high altitude. Tellus, 4, 43-53.Bjerknes, J., 1919: On the structure of moving cyclones. Geofys. Publ., 1(1), 1-8. , and E. Palm,n, 1937: Investigations of selected European cy clones by means of serial ascents. Geofys. Publ., 12(2), 1-62. , and H. Solberg, 1921: Meteorological conditions for the for mation of rain. Geofys. Publ., 2(3), 1-60.--, and --, 1922: Life cycle of cyclones and the polar front theory of atmospheric circulation. Geofys. Publ., 3 1), 1-18.Bluestein, H. B., 1986: Fronts and jet streaks: A theoretical perspective. Mesoscale Meteorology and Forecasting, P. S. Ray, Ed., Amer. Meteor. Soc., Chapt. 9 (submitted).Bosart, L. F., 1970: Mid-tropospheric frontogenesis. Quart. J. Roy. Meteor. Soc., 96, 442-471.Briggs, J., and W. T. Roach, 1963: Aircraft observations near jet streams. Quart. J. Roy. Meteor. Soc., 89, 225-247.Browning, K. A., 1971: Radar measurements of air motion near fronts. Weather, 26, 320-240. , and C. D. Watkins, 1970: Observations of clear air turbulence by high power radar. Nature, 227, 260-263. , T. W. Harrold and J. R. Start, 1970: Richardson number limited shear zones in the free atmosphere. Quart. J. Roy. Meteor. Soc., 96, 40-49.Buzzi, A., T. Nanni and M. Tagliazucca, 1977: Mid-tropospheric frontal zones: Numerical experiments with an isentropic coor dinate primitive equation model. Arch. Meteor. Geophys. Bio klirn., A26, 155-178. , A. Trevisan and G. Salustri, 1981: Internal frontogenesis: A two-dimensional model in isentropic, semi-geostrophic coor dinates. Mon. Wea. Rev., 109, 1053-1060.Cahir, J. J., 1971: Implications of circulations in the vicinity of jet streaks at subsynoptic scales. Ph.D. thesis, The PennsylvaniaState University, University Park, PA 16802, t70 pp.Charney, J. G., 1947: The dynamics of long waves in a baroclinic westerly current. J. Meteor., 4, 135-163.Danielsen, E. F., 1964: Project Springfield report. DASA 1517, De fense Atomic Support Agency, Washington, DC 20301, 97 pp. [NTIS AD-607980]. , 1968: Stratospheric-tropospheric exchange based on radioac tivity, ozone and potential vorticity. J. Atmos. Sci., 25, 502 518.Dutton, J. A., 1976: The Ceaseless Wind.' An Introduction to the Theory of Atmospheric Motion. McGraw-Hill, 579 pp.Eady, E. T., 1949: Long waves and cyclone waves. Tellus, 1, No. 3, 33-52.Eliassen, A., 1962: On the vertical circulation in frontal zones. Geofys. Publ., 24(4), 147-160. , 1984: Geostrophy. Quart. J. Roy. Meteor. Soc., 110, 1-12.--, and E. Kleinschmidt, 1957: Dynamic meteorology. Handbuch derPhysik, Vol. 48, S. Fliigge, Ed., Springer-Verlag, 1-154. , and E. Raustein, 1968: A numerical integration experiment with a model atmosphere based on isentropic surfaces. Meteor. Ann., 5, 45-63.--, and --, 1970: A numerical integration experiment with a six-level atmospheric model with isentropic information surface. Meteor. Ann., 5, 429-449.Emanuel, K. A., 1979: Inertial instability and mesoscale convective systems. Part I: Linear theory of inertial instability in rotating viscous fluids. J. Atmos. Sci., 36, 2425-2449.--, 1985: Frontal circulations in the presence of small moist sym metric stability. J. Atmos. Sci., 42, 1062-1071.Faller, A. J., 1956: A demonstration of fronts and frontal waves in atmospheric models. J. Meteor., 13, 1-4.Farrell, B. F., 1982: The initial growth of disturbances in a baroclinic flow. J. Atmos. Sci., 39, 1663-1686.498 MONTHLY WEATHER REVIEW VOLUME 114 ,1984: Modal and non-modal baroclinic waves. J. Atmos. Sci., 41, 668-67!t.Ffitsch, J. M., and R. A. Maddox, 1981: Convectively driven me soscale weather systems aloft. Part I: Observations. J. Appl. Me teor., 20, 9-19.Fuelberg, H. E., and P. A. Browning, 1983: Roles of divergent and rotational winds in the kinetic energy balance during intense convective activity. Mon. Wea. Rev., 111, 2176-2193.Fultz, D., 1952: On the possibility of experimental models of the polar-front wave. J. Meteor., 9, 379-384.Gidel, L. T., and M. A. Shapiro, 1979: The role of clear air turbulence in the production of potential vorticity in the vicinity of upper tropospheric jet stream-frontal systems. J. Atmos. Sci., 36, 2125 2138.Haltiner, G. J., and R. T. Williams, 1980: Numerical Prediction and Dynamic Meteorology, 2nd ed. Wiley, 477 pp.Holton, J. R., 1979: An Introduction to Dynamic Meteorology, 2rid ed. Int. Geophys. Ser., Vol. 23, Academic Press, 391 pp.Hoskins, B. J., 1971: Atmospheric frontogenesis models: Some so lutions. Quart. J. Roy. Meteor. Soc., 97, 139-153. , 1972: Non-Boussinesq effects and further development in a model of upper tropospheric frontogenesis. Quart. J. Roy. Me teor. Soc., 98, 532-541. ,1974: The role of potential vorticity in symmetric stability and instability. Quart. J. Roy. Meteor. Soc., 100, 480-482. , 1975: The geostrophic momentum approximation and the semi-geostrophic equations. J. Atmos. Sci., 32, 233-242.--, 1982: The mathematical theory of frontogenesis. Annual Re views in Fluid Mechanics, Vol. 14, Annual Reviews, 131-151.--, and F. P. Bretherton, 1972: Atmospheric frontogenesis models: Mathematical formulation and solution. J. Atmos. Sci., 29, 11 37.--, and I. Draghici, 1977: The forcing of ageostrophic motion according to the semi-geostrophic equations and in an isentropic coordinate model. J. Atmos. S-i., 34, 1859-1867.--, and M. A. Pedder, 1980: The diagnosis of middle latitude synoptic development. Quart. J. Roy. Meteor. Soc., 106, 707 719.--, I. Draghici and H. C. Davies, 1978: A new look at the ~o equation. Quart. J. Roy. Meteor. Soc., 104, 31-38.--, M. E. McIntyre and A. W. Robertson, 1985: On the use and significance of isentropic potential-vorticity maps. Quart. J. Roy. Meteor. Soc., 111, (October issue).Kennedy, P. J., and M. A. Shapiro, 1975: The energy budget in a clear air turbulence zone as observed by aircraft. Mon, Wea. Rev., 103, 650-654.Keyser, D., 1986: Atmospheric fronts: An observational perspective. Mesoscale Meteorology and Forecasting, P. S. Ray, Ed., Amer. Meteor. Soc., Chapt. 10 (submitted). , and M. J. Pecnick, 1985a: A two-dimensional primitive equa tion model of frontogenesis forced by confluence and horizontal shear. J. Atmos. Sci., 42, 1259-1282. - , and , 1985b: Diagnosis of ageostrophic circulations in a two-dimensional primitive equation model of frontogenesis. J. Atmos. Sci., 42, 1283-1305.Keyser, D. A., and D. R. Johnson, 1984: Effects of diabafic heating on the ageostrophic circulation of an upper tropospheric jet streak. Mon. Wea. Rev., 112, 1709-1724.Krishnamurti, T. N., 1968: A study of a developing wave cyclone. Mon. Wea. Rev.. 96, 208-217.Larsen, M. F., and J. Rtttger, 1982: VHF and UHF Doppler radars as tools for synoptic research. Bull. Amer. Meteor. Soc., 63, 996 1008.Maddox, R. A., 1979: The evolution of middle and upper tropospheric features during a period of intense convective storms. Preprints Eleventh Conf Severe Local Storms, Kansas City, Amer. Meteor. Soc., 41-48:.--, D. J. Perkey and J. M. Fritsch, 1981: Evolution of upper tro pospheric features during the development of a mesoscale con vective complex. J. Atmos. Sci., 38, 1664-1674.McWilliams, J. C., and P. R. Gent, 1980: Intermediate models of planetary circulations in the atmosphere and ocean. J. Atmos. Sci., 37, 1657-1678.Miller, J. E., 1948: On the concept of frontogenesis. J. Meteo.~., $, 169-171.Mudrick, S. E., 1974: A numerical study of frontogenesis. J. Atrnos. Sci., 31, 869-892.Namias, J., and P. F. Clapp, 1949: Confluence theory of the high tropospheric jet stream. J. Meteor., 6, 330-336.Newton, C. W., 1954: Frontogenesis and frontolysis as a three-di mensional process. J. Meteor., 11,449-461.--., 1958: Variations in frontal structure of upper level troughs. Geophysica, 6, 357-375.--., and A. Trevisan, 1984a: Clinogenesis and frontogenesis in jet stream waves. Part I: Analytical relations to wave structure. J. Atmos. Sci., 41, 2717-2734. , and ,1984b: Clinogenesis and frontogenesis in jet-stream waves. Part II: Channel model numerical experiments. J. Atmos. Sci., 41, 2735-2755.Ninomiya, K., 1971: Mesoscale modification of synoptic situations from thunderstorm development as revealed by ATS IIl and aerological data. J. Appl. Meteor., 10, 1103-1121.Orlanski, I., and B. B. Ross, 1977: The circulation associated ~dth a cold front. Part I: Dry case. J. Atmos. Sci., 34, 1619-163_~,.Palmtn, E., 1958: Vertical circulation and release of kinetic eoergy during the development of hurricane Hazel into an extratrc,pical storm. Tellus, 10, 1-23.--, and K. M..Nagler, 1949: The formation and structure of a large-scale disturbance in the westerlies. J. Meteor., 6, 227--242.--, and C. W. Newton, 1969: Atmospheric Circulation Systems: Their Structure and Physical Interpretation. Int. Geophys. Ser., Vol. 13, Academic Press, 603 pp.Petersen, R' A., 1986: Detailed three-dimensional isentropic analysis using an objective cross-sectional approach. Mon. Wea. Rev., 114 (in press).Petterssen, S., 1936: Contribution to the theory of frontogenesis. Geofys. Publ., 11(6), 1-27. - , 1955: A general survey of factors influencing development at sea level. J. Meteor., 12, 36-42.--, 1956: Weather Analysis and Forecasting, Vol. 1. Motion and Motion Systems, 2rid ed., McGraw-Hill, 428 pp.Reed, R. J., 1955: A study of a characteristic type of upper..level frontogenesis. J. Meteor., 12, 226-237. , and F. Sanders, 1953: An investigation of the development of a mid-tropospheric frontal zone and its associated vorticity field. J. Meteor., 10, 338-349. , and E. F. Danielsen, 1959: Fronts in the vicinity of the tro popause. Arch. Meteor. Geophys. Bioklim., All, 1-17.Reiter, E. R., 1969: Jet-Stream Meteorology. The University o17 Chi cago Press,. 515 pp. , 1975: Stratospheric-tropospheric exchange processes. Rev. Geophys. Space Phys., 13, 459-474.Riehl, H., and Collaborators, 1952: Forecasting in MiddleLatilludes. Meteor. Monogr., No. 5, Amer. Meteor. Soc., 80 pp. , M. A. Alaka, C. L. Jordan and R. J. Renard, 1954: Tt~e Jet Stream. Meteor. Monogr., No. 7, Amer. Meteor. Soc., 100 pp.Roach, W. T., 1970: On the influence of synoptic development on the production of high level turbulence. Quart. J. Roy. Meteor. Soc., 96, 413-429.Sanders, F., 1955: An investigation of the structure and dynamics of an intense surface frontal zone. J. Meteor., 12, 542-552.Sawyer, J. S., 1956: The vertical circulation at meteorological fronts and its relation to frontogenesis. Proc. Roy. Soc. London, A234, 346-362.Shapiro, M. A., 1970: On thd applicability of the geostrophic ap proximation to upper-level frontal-scale motions. J. Atmos. Sci., 27, 408-4202---, 1974: A multiple structured frontal zone-jet stream system as revealed by meteorologically instrumented aircraft. Mon. Wea. Rev., 102, 244-253.---, 1975: Simulation of upper-level frontogenesis with a 20-levelFEBR~J^R- 1986 DANIEL KEYSER AND M. A. SHAPIRO 499 isentropic coordinate primitive equation model. Mort. Wen. Rev., 103, 591-604.--, 1976: The role of turbulent heat flux in the generation of po tential vorticity in the vicinity of upper-level jet stream systems. Mon. Wea. Rev., 104, 892-906. ,1978: Further evidence of the mesoscale and turbulent structure of upper level jet stream-frontal zone systems. Mort. Wea. Rev., 106, 1100-1111.--, 1980: Turbulent mixing within tropopause folds as a mecha nism for the exchange of chemical constituents between the stratosphere and troposphere. J. Atmos. $ci., 37, 994-1004. ,1981: Frontogenesis and geostrophically forced secondary cir culations in the vicinity of jet stream-frontal zone systems, d. Atmos. Sci., 38, 954-973.--, 1983: Mesoscale weather systems of the central United States. The National STORM Program: Scientific and Technological Bases and Major Objectives, R. A. Anthes, Ed., University Cor poration for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307, 3.1-3.77. , 1985: Dropwindsonde observations of an Icelandic low and a Greenland mountain4ee wave. Mon. Wen. Rev., 113, 680-683. , and J. T. Hastings, 1973: Objective cross-section analyses by Hermite polynomial interpolation on isentropic surfaces. J. Appl. Meteor., 12, 753-762. , and P. J. Kennedy, 1981: Research aircraft measurements of jet stream geostrophic and ageostrophic winds. J. Atmos. $ci., 38, 2642-2652. , and ~, 1982: Airborne radar altimeter measurements of geostrophic and ageostrophic winds over irregular topography. J. Appl. Meteor., 21, 1739-1746. ., A. J. Krueger and P. J. Kennedy, 1982: Nowcasting the position and intensity of jet streams using a satellite-borne total ozone mapping spectrometer. Nowcasting, K. A. Browning, Ed., Ac ademic Press, 137-145.--, T. Hample and D. W. van de Kamp, 1984a: Radar wind profiler observations of fronts and jet streams. Mon. Wea. Rev., 112, 1263-1266. , R. C. Schnell, F. P. Parungo, S. J. Oltmans and B. A. Bodhaine, 1984b: El Chichtn volcanic debris in an arctic tropopause fold. Geophys. Res. Lett., 11, 421-424.Staley, D. O., 1960: Evaluation of potential-vorticity changes near the tropopause and the related vertical motions, vertical advec tion of vorticity, and transfer of radioactive debris from strato sphere to troposphere. J. Meteor., 17, 591-620.Sutcliffe, R. C., and A. G. Forsdyke, 1950: The theory and use of upper air thickness patterns in forecasting. Quart. J. Roy. Meteor. Soc., 76, 189-217.Uccellini, L. W., 1980: On the role of upper tropospheric jet streaks and leeside cyclogenesis in the development of low-level jets in the Great Plains. Mon, Wea. Rev., 108, 1689-1696.--., and D. R. Johnson, 1979: The coupling of upper and lower tropospheric jet streaks and implications for the development of severe convective storms. Mon. Wea. Rev., 107, 682-703. , P. J. Kocin, R. A. Petersen, C. H. Wash and K. F. Brifl, 1984: The Presidents' Day cyclone of 18-19 February 1979: Synoptic overview and analysis of the subtropical jet streak influencing the precyclogenetic period. Mon. Wea. Rev., 112, 31-55. -, D. Keyser, K. F. Brill and C. H. Wash, 1985: The Presidents' Day cyclone of 18-19 February 1979: Influence of upstream trough amplification and associated tropopause folding on rapid cyclogenesis. Mon. Wea. Rev., 113, 962-988.Welander, P., 1955: Studies on the general development of motion in a two-dimensional, ideal fluid. Tellus, 7, 141-156.Wetzel, P. J., W. R. Cotton and R. L. McAnelly, 1983: A long-lived mesoscale convective complex. Part II: Evolution and structure of the mature complex. Mon. Wea. Rev., 111, 1919-1937.