2004 MONTHLY WEATHER REVIEW VOLUME 122Location and Interaction of Upper- and Lower-Troposphere Adiabatic Frontogenesis FRANCOIS LALAURETTE* AND CLAUDE FISCHERMdtdo France, Centre National de Recherches Mdtdorologiques, Toulouse, France JEAN-PIERRE CAMMASLaboratoire d'Adrologie, Toulouse, France(Manuscript received 28 June 1993, in final form 26 January 1994)ABSTRACTBoth upper-air and surface frontogenesis have often been depicted as processes whose dynamics could bereduced to 2D balanced problems in which "self-sharpening" configurations could be highlighted. This paper reports on a 3D adiabatic simulation of a baroclinic wave life cycle. Great care has been devotedto the vertical resolution, allowing for a good description of both surface and upper-air frontogenesis. The authorsintroduce a kinematic diagnostic (Q' vector) that permits the identification of frontogenetic areas in such complex 3D flows where classical, low-Rossby number balance conditions can be violated. Relations and specificitywith respect to frontogenetic forcing diagnostics are discussed. First, Q' is used for surface frontogenesis, whereit describes well the actual frontal activity, including the complex warm-frontal seclusion process. Upper-airfrontogenesis is also investigated, both in terms of this kinematic diagnostic or in terms of potential vorticitydisplacements on isentropic surfaces. Both types of diagnostics clearly distinguish between dynamics of theentrance zone of the northerly jet--where 2D concepts may usefully be applied--and those of the stronglycurved zone near the trough axis. Classical cyclogenetic terms (stretching and tilting) as well as the separationof ageostrophic circulations in terms of natural components of the wind also lead to a clear dynamical separation. The cold front is shown to extend from the surface far into the troposphere. This is shown to be related to asingular property of the 3D flow. Parcels undergoing frontogenesis in the northwesterly upper-air flow areadvected on top of those that were forced at the surface cold front in a southwesterly flow. The occurrence of afeedback process between these upper-air frontogenesis processes and the surface ones is then investigated.Stepwise vertical profiles of horizontal diffusion are used to force local frontolysis. The resulting upper-airfrontolysis, despite its local efficiency, does not have any remote effect on the surface front, whose frontolysisin turn has no effect on the upper-air front. The feedback process is thus not occurring in our simulation.1. Introduction The dynamical processes associated with surfacefront self-sharpening phenomena were first exhibitedby Hoskins and Bretherton (1972). They showed, in a2D context, that if geostrophic advections of momentum and potential temperature become importantenough, their frontogenetic effect can be relayed byageostrophic cross-front circulations, leading to a nonlinear increase of the forcing. Although the strongest thermal gradients are foundnear the ground, important frontogenetic processes alsoact at higher levels. [See Keyser and Shapiro (1986)for a review.] Their practical importance comes fromthe creation of a large slope of the isentropic surfaces[a process that Newton and Trevisan (1984a,b) designated as clinogenesis], which allows high-potential Corresponding author address: Franqois Lalanrette, MrtroFrance, CNRM/GNRM/RECYF, 42, av. G. Coriolis, F-31057, Toulouse Cedex, France.vorticity (PV) air to be advected down to unusuallylow levels on a fairly large scale. This advection isthought to be partly responsible for strong surface cyclogenesis events (Uccellini et al. 1985; Hoskins andBerrisford 1988). The success encountered in surface frontogenesis leddifferent authors to apply the geostrophic-ageostrophic partition to upper-air frontogenesis. This technique was again successful in describing the "catastrophic'' character of upper-air frontogenesis at theentrance of jet streaks advecting cold air (Shapiro1981; Keyser and Pecnick 1985a,b). This thermal, geostrophic advection was shown to change the forcedageostrophic circulation from a classical, thermally direct circulation (air rising on the warm side and sinkingon the cold side of the jet) to a pattern in which strongsubsidence was found just beneath the jet axis [ascentsneeded for mass balance are found either on the warmair side (Keyser and Pecnick 1985a) or on both sides(Shapiro 1981 )]. This displacement of the subsidencewas found to be a key factor for (i) the tilting of thehorizontal vorticity toward the vertical and (ii) the flitc 1994 American Meteorological SocietySEPTEMBER 1994 LALAURETTE ET AL. 2005ing of the isentropes (clinogenesis). The feedback loopis closed since both effects increase the ageostrophiccirculation forcing, which in turn increase the cyclogenesis and clinogenesis. However, this is not the whole story. Owing to thehigh wind speeds typically encountered, air parcels donot remain long in the jet entrance area. It seems ratherunlikely that they can stay there for the 24-48-h periodnecessary for a strong upper-level front to be createdin 2D models. If a rather small average speed of 30m s-~ is postulated in the entrance area, parcels will bedisplaced by about 2600 km in a day! On the otherhand, some authors (Newton and Trevisan 1984a,b)have stressed the efficiency of strongly curved flowsfor upper-level frontogenesis. The complexity of the processes associated with upper-level frontogenesis, which seems to support notonly different geometries (straight jet entrance area andcurved trough base) but also different dynamical balances (semigeostrophic in the former--gradient windin the latter), forced upon us the idea that a kinematicdiagnostic, free from any dynamical and geometricalhypothesis, could be of value. The aim of such a frontogenesis diagnostic would be to point out those areasthat are really efficient and for which a conceptual effort should be made to better understand the dynamicsinvolved. This diagnostic is introduced in section 2. The 3D, nonlinear development of normal-modetype perturbations superimposed on simple zonal jetswith meridional and vertical variations (crudely reproducing the westerly midlatitude jet) has received agreat deal of attention from modelers since the pionneering work of Mudrick (1974). [See Polavarapu andPeltier (1990) and Sch'fir and Wernli (1993) for a review of the scientific advances in this area.] This isbecause such experiments, despite the highly idealizedinitial condition from which they start, bear a strongresemblance to real extratropical perturbations. This isthe reason why we performed one such simulation asa test bed for our diagnostic. To parallel other studies(Hoskins and West 1979; Davies et al. 1991), we usean f-plane, hydrostatic framework, with full representation of the tropopause and a weak upper-level jet. Thenumerical treatment is presented in section 3. The description of surface frontogenesis in our experiment is presented in section 4. Upper-air frontogenesis is discussed in section 5. The existence of afeedback loop between these two processes is investigated in section 6. A summary of the results and themain conclusions are found in section 7.2. A kinematic, three-dimensional frontogenesis diagnosisa. Definition Frontogenetic forcing was introduced by Petterssen(1936) in terms of the kinematic action of the nondivergent components of the flow on a passive scalar(taken as 0) at a rigid lid (the ground). Important dynamic insights with respect to this problem have thenbeen developed by making a distinction between theprimary and secondary forcings, the latter being implicit through quasigeostrophic or semigeostrophic balance assumptions (Hoskins and Bretherton 1972; Hoskins and Draghici 1977). Nevertheless, it should benoted that such a distinction is useful mainly in 2Dgeometry (negligible surface front curvature), although Keyser et al. (1989) recently proposed a distinction in terms of irrotational and nondivergent components making 3D concepts easier to interpret. Miller (1948) stressed that for upper-air frontogenesis, vertical velocity gradients should be of crucial importance in tilting strong vertical gradients of potentialtemperature into the horizontal (his Fig. 3). Straightaccelerating jet streaks advecting cold air have beenidentified by Shapiro (1981) and Keyser and Pecnick(1985) as configurations for which upper-air frontogenesis could be described as a "catastrophe," whereimplicit ageostrophic frontogenetic circulations act askey terms of the nonlinear development. This processis fairly similar to the one occurring for surface frontogenesis, even if (due to the importance of verticalmotions) the dynamical processes differ (cf. section5d). Such configurations are nevertheless quite singular: the point here is that we want to draw a generalpicture of the frontogenetic processes in order to locatethe areas where the dynamics should be carefully examined. That is why any dynamical separation will beavoided so that no presumption will be made as to theimportance of the frontogenetical processes involved.The following Miller (1948) formulation is introducedin fully 3D geometry: for any scalar a whose Lagrangian tendencies are noted b~, it can be written d dtwhere tVu is the transposed tensor of the velocity gradient: its Cartesian components are (Ouj/Oxi We define the Q' frontogenetic vector as the totaladiabatic frontogenetic forcing that occurs in the flow(a = O, & = 0): Q' = -tV~.V0 = .vo . (2)Under adiabatic assumption, frontogenesis (i.e., tightening of isentropes) occurs every time Q' points toward warm air (d]]VO2/dt = 2Q' .V8). This is apurely kinematic result, as no assumption such as rigidlid (zero vertical displacement) or nondivergent primary flow is being made. An interesting formulation may be found if (2) isexpanded following a quite classical approach in kin2006 MONTHLY WEATHER REVIEW VOLUME 122ematics. [See Germain (1962) for an academic reference or Davies-Jones (1982) for a recent applicationto tornadogenesis.] When the partition of the velocitygradient tensor between its symmetric and antisymmetric parts is introduced, and when all these are translated in terms of rotational and rate of strain tensors, itturns out that1_ I=~AV0-- V.uV0- D.V0.(3)X In the latter expression, ~ is the 3D vorticity (twice the rotational vector) and the strain tensor is separated into- its divergence/convergence and deformation D parts; D may be reduced to the canonical form on the principal directions (ei)~i<_3. Locally, D trans forms a material sphere into an ellipsoid of the same volume. The principal directions (el)t~i_<3 are the prin cipal axes of this ellipsoid, and (hi)~<~_<3 are the rates of linear dilatation on these axes. Such a formulation indicates~ that only deformation (most efficient when the isentropes are normal to the maximum contraction axis) and convergence may be frontogenetic, while vorticity only rotates the isentropes keeping their spac ing constant. In practice, only projections of Q' will be displayed (on either the horizontal or vertical plane). These vi sualize the evolution of 0 gradients in the plane in ques tion: dt ' (4) where Q~', is the. e~-orthogonal projection of Q', and Vx, is the gradient operator with xi being kept constant. The cross-isentropic component of Q~'~ measures the frontogenesis/frontolysis in the e/-orthogonal plane, while its along-isentropic component measures the ori entation changes. Further separation in terms of the vertical and hori zontal velocity contributions to frontogenesis may eas ily be recovered. They are 00 Q'~ = - -- Vw (5) 0z Q',, = Q' - Q'w (6) O0 Vu - O0 = -~xx ~yyVV. (7) Figure 1 illustrates Q' for some 2D (x, z) flow pat ~ A 2D, quasigeostrophic version of this treatment has been independently derived by Schfix and Wemli (1993); a part of it alsoappears in Mudrick (1974)._1 ~i0x /// /-&/ / / / ///lo~/// /// / X FIG. 1. Some 2D (x, z) frontogenetic flow patterns and associatedQ' vectors: (a) horizontal confluence (typical of surface frontogenesis), (b) tilting of isentropes through vertical velocities shear (typical of upper ffontogenesis), (c) vertical stability increase throughvertical velocities confluence (this is responsible for strong inversions occurring near the ground under anticyclonic, subsident conditions), and (d) vertical stability increase through tilting of isentropes (typical of frontogenetic cross-frontal circulations).terns. Even if the Q' formulation allows a full 3D picture of the frontogenesis (including static stability evo-.lution, cf. Figs. lc and ld), it should be kept in mindthat clinogenesis is felt to be the most important dynamical process, because it allows the advection ofhigh PV from stratosphere to troposphere, for example.b. Relations of Q ' With frontogenetical forcing vectors Even if horizontal projections of Q~ look a bit likeclassical Q vectors (Hoskins et al. 1978), it should beremembered that Q retain only the primary part of thefrontogenetical function (i.e., the geostrophic, horizontal frontogenesis). Even if the secondary circulationscan be determined from the primary circulationsthrough the quasi- or semigeostrophic balance assumption, it is not straightforward to infer the total frontogenetical tendencies from a display of Q and isentropes.SEPTEMBER 1994 LALAURETTE ET AL. 2007 Davies-Jones (1991, hereafter DJ91) introduced anice primitive equation discussion in terms of the 3Dpseudovorticity vector. The horizontal component ofthis vector reduces to the horizontal thermal gradientunder the thermal wind balance assumption (with opposite sign, and after some rescaling). A generalized,but still 2D, Q vector [Q*, Eq. (3.17) in DJ91] couldbe shown to be the mean of two vectors: one is a measure of thermal frontogenesis, and the other is a measure of vertical wind shear generation. This generalization is quite illuminating when it makes possible aprimitive equation discussion of the necessary generation of (ageostrophic) thermal, wind imbalance in frontogenetic flows starting from geostrophic equilibrium(D J91, section 5). However, a generalized version ofthe quasigeostrophic w equation forced by the divergence of the Q* vector [Eq. (7.4) of DJ9I] was possible only through both a new balance hypothesis anda further approximation O of the Q* vector; Q is thehorizontal projection Q'~ of our Q', [cf. Eq. (7)] except for the divergent part of the wind field (which isomitted in D J91, as required by a formulation of thefprcing of an w equation). As demonstrated in DJ91,Q (and so our Q '~) is the Keyser et al. ( 1988 ) versionusing a rigid-lid hypothesis of the vector frontogeneticfunction F, whose Q' is the 3D generalization. Xu (1992) proposed the 3D C vector as a quasigeostrophic (QG) forcing of secondary circulations.The vertical component2 was defined by Xu [1992, Eq.(2.3.c)] as a geostrophic forcing of the ageostrophicvorticity. Thus, the information about the barotropicpart of the ageostrophic circulation, which is lost byHoskins et al. (1978) Q-vector formulation, may berecovered. The C vector should not, however, be confused with our Q'. The vertical component of Q' is ameasure of the Lagrangian evolution of the static stability. It is shown later [Eq. (11 )] that it is associatedwith the baroclinic part of the ageostrophic circulation-quite at variance with the vertical component ofthe C vector that is associated with the barotropic ageostrophic circulation. Moreover, C is a forcing for QGageostrophic circulations, while Q' is a kinematic measure of the 3D action of the flow on the 0 distribution.3. The numerical model and the experimenta. Numerical techniques The model comes directly from the mesoscale numerical weather prediction PERIDOT (Prrvision hEchrance Rapprochre Intrgrant des Donnres Observres et Trlrdrtectres) system, which has been operationally mn by Mrtro France between 1985 and 1993.[Imbard et al. (1986) describe it in detail, while J. Stein(1992) and -. Ducrocq (1993) show recent researchThe horizontal projection C= is Q A k.undertaken with it.] It is a limited-area model, forcedon its lateral boundaries using a simplified form of theDavies (1976) relaxation method. Some aspects havebeen modified for the simulations described in this paper. To allow free development in one direction, periodic conditions were introduced at the so-called zonalboundaries (channel-like geometry). The governingequations are the primitive equations, solved on an Arakawa C-type horizontal grid, with cr = P/Ps as verticalcoordinate. An implicit treatment is adopted for bothgravity waves and vertical advection. The only diabaticparameterization used here is a Laplacian diffusion applied to 0 and psU, mainly to counter numerical noiseproduction. No spherical effect is introduced (f-planeapproximation, to allow comparison with semigeostrophic models). The water vapor content is kept atzero everywhere. We used a horizontal grid of 98 x 52 points, withAx = Ay = 83.33 km spacing (maximum zonal lengthresolved: 4000 km). Only 74 points (6000 km) in thenorth-south direction will be displayed; extra space tothe north and to the south is kept only to prevent spurious reflection. Using the zonal periodicity, 1.5 timesthe maximum wavelength (again 6000 km) will be displayed in the west-east direction. The vertical grid includes 41 levels, with the tightest spacing in the PBL(7 levels from the ground to cr = 0.84), about 500-mspacing in the troposphere and lower stratosphere, anda model top at cr = 0.005. It should be noted that sucha vertical resolution near the tropopause is a significantimprovement over previous studies. The time step is1200 s, and the horizontal viscosity ~, = 83.33 x 103m2 $-1 leads to an e-damping time of 2.5 h for a 2Axwave.b. The basic state and initial perturbation The basic state (Fig. 2) is a zonal jet with smoothmeridional and vertical variations. Our reference is the(z) e ~ ~ ~_=_~__ _--~_ _ __ ___~_~ __ ___-~__, _-_z~___~$__-,_~ ~ 1 0-~--~- ~-~' -- -~-~~ 5 :- .........~-~ ~ ~ =.~-~- ...... ?-7-~-~ q~'7~,~,2125 2125(km) 6875 4375de/ds U- PV DAY 0 RUN 552125187521.-625 FIG. 2. Meridional cross section of the basic state: zonal wind(solid line at intervals of 5 m s-~), and potential temperature (dashedlines at intervals of 4 K). The short dashed contour is for O0/cgs = + 1K (100 km)-~ (s being distance along the section). The tropopauseis shaded for PV values between 1.5 and 2.5 PVU (1 PVU = 10-6K m2 s ~ kg-~). Horizontal tick marks are each 250 km (equal tothree model grid spaces). The X and Y refer to the horizontal axes(Fig. 3 and subsequent figures).2008 MONTHLY WEATHER REVIEW VOLUME 122Hoskins and West (1979) formulation in the troposphere. A stratospheric thermal extension is formulatedin order to introduce a realistic tropopause definitionand a decrease of the wind. The maximum intensity ismoderate (a "jet" maximum of 28 m s-l) and the surface wind is zero (uniform surface pressure).The temperature field is computed to be in thermal wind balance with the jet profile. The most unstable 4000-km-wavelength mode forthis basic state was found by using an iterative procedure starting from a random noise perturbation.3 Thenormal-mode character of the perturbation after 15days of quasi-linear run was verified from the almostuniform zonal phase speeds and growing rates in thedomain. For example, the phase speeds and growingrates of the meridional wind have a respective meanvalue of 8.3 m s-I and 4.4 x 10-6 s-~ and a respectivestandard deviation of 0.3 m s-~ and 0.3 x 10-6 s-l, ifweighted by the perturbation amplitude of each wave.The initial state for the life cycle experiments describedin the following sections was the sum of the basic stateand of this normal-mode perturbation scaled to have1.7 m s-t maximum amplitude for the meridional windat ground level.4. Surface frontogenesisa. Frontal pattern The results obtained (Fig. 3) are in good agreementwith previously mentioned simulations using primitiveequations (Mudrick 1974; Newton and Trevisan 1984;Takayabu 1986; Keyser et al. 1988). The main pointsare the following: - A very strong4 cold front that forms from thesoutheast of the cyclone and then bends around the anticyclone to appear as a weak warm front on its westernpart (Fig. 3). This extension was already described interms of advection of frontogenetic forcing in Hoskinsand West (1979) and Takayabu (1986). Other aspectsof this front are in agreement with 2D, semigeostrophicpredictions: vertical tilting toward cold air of the direct,cross-frontal circulation (Fig. 5) and strong vorticitygeneration on the warm side of the front. - A frontogenetic area that appears as a warm fronton the north-northeastern part of the cyclone. Duringthe first stages of the frontogenesis, this is more intensethan the cold front (see Fig. 3a). But as the alongfrontadvections become more important [Fig. 4 and Taka 3 The initial perturbation was taken to be monochromatic with a4000-km wavelength, only amplitudes and phases being specified atrandom. From the Hoskins and West (1979) results, it was felt computer-time consuming and unuseful to excite the 2000-km and following subharmonics. 4 Thermal gradients go from 0.8 K ( 100 km) -~ in the initial stateto a local maximum of 5.63 K (100 km)-~ at day 10.yabu ( 1986, Fig. 11 )], particles undergoing frontogenesis are quickly removed from the warm front. This isin contrast with the situation near the cold front, whererelative winds are quite weak. All this is in good agreement with Takayabu's (1986) and Sch'~ and Wernli's(1993) findings. At the end of the simulation, this frontis finally less marked than in the cold one (Fig. 3b),with an important curvature around the cyclone thatseems far from being tractable in a classical, 2D context.b. Frontogenesis diagnostics using the Q' vector Keyser et al. (1988) introduced, at a rigid lid, a 2Dnatural partition of the frontogenesis function Q'm= dVfl/dt into its magnitude and direction components. Their results may be recovered through 2D vector analysis similar to (3): Q '.~ = -tV~u. VzO (8) 1 ~k ^ V~0 - 1 ~ = ~ ~Vz-UVfl - D~.Vz0, (9)where ~ is the ve~ical component of vo~icity and Dzis the 2D isosufface derogation tensor. Such p~itioning of frontogenetical forcings in natural components- of ~e velocity tensor (namely vonicity, divergence, and derogation) ~e much more meaningfulthan the classical, 2D-originated p~ifoning betweenshe~ and derogation-induced frontogenesis. Frontogenetical processes occur at ground level bothat the cold front and at the w~ front (see 300- and304-K isothe~s, Fig. 3). However, frontogenesis ismore active at the cold front in the later stages of thesimulation (see the cross-isentropic Q~ component inFig. 6a).s Between day 8 and day 9, the maximumsurface the~al gradiems go from 3.39 to 4.78 K ( 100~)-~ at the cold front, while they go only from 2.77to 3.02 K (100 ~)-~ at the w~ front. ~is is anindication that the w~ front, unlike the cold front,does not really proceed from a "self-sheening" process but rather quic~y secludes. ~is impo~ant distinction between frontogenesis at the cold and w~front was first depicted and expl~ned in te~s of ~ong~ont advections by T~ayabu (1986). Keyser et al.(1988)~ could create patterns loo~ng much like oursat day 7 with a purely ~nematic model of passive scal~derogations (their Fig. 8). ~e impoaant point, neve~heless, comes from ~e fact that at day 9 the ~nematic symmet~ is quite broken down in te~s of frontogenetic vectors Q~ (Fig. 6a)~this being due to thepositive frontogenefic feedback that occurs at the cold 5 Note that due to the lower boundary condition w = 0, Q~ = Q '~z,and so may be interpreted as Davies-Jones's Q w forcing. 6 Keyser et al. (1988) referenced Doswell (1984) as the originalwork.SEPTEMBER 1994 LALAURETTE ET AL. 200962505000375025001250(KM) 0 862505000375025001250 0(KI~)1250 2500 3750 5000 6250 SIP ~/fo DAY 10 RUN 55 ' ' ' ' ~ ' ' ' ' ~ ' ' ' ' ~ ' ' ' ' ~ ' ' 'B' ~-. -~ ~' xx~ ~.~---~ ~ ~ ~ t ~--- ~ I '~ "~ ~ ~l ~--- ~ - " ~ , ".~c_.~;~X,.~x~.., ~ t ['~ ,. ~Xx X X ~ ~ I ~ X I ~~,,~ ~ ~Mk~(m ~5: ~ ,"-~ ~, ~' "~c;~ % .~ ~' , ~1 I~'x ~t ~ ' iI I IIZ~;x,, ,,,'%~,~Z~ Y/~L~ ~ I t I ~ ~ ..~ ~ ~ ~::~-~', ~ ._ .-~M~ %~:? ~j~,k~, ,. -.. '.~ ~.~ - , '~IL;%Lff ~ ; % ~'oo ~A~ ,, ' '", % ," .~'~X,.-~'~,~ ~~~''"-~)' ' ~'5~ ~::?~ x~ ..... . ~ - . , t . , , , ~ . , , , ~ , ~ ~ ~ i , , , , 1250 2500 3750 5000 6250 FIG. 3. Pressure (dashed lines at intervals of 6 hPa) and potentialtemperature (solid lines at intervals of 4 K) at the surface for (a) day7 and (b) day 10. Grid points at which relative vortJcJty is more than0.S fare shaded (heavy shades beyond f).front and not at the warm front in our dynamical simulation. The influence of frontogenesis on static stability iseasily depicted in terms of the vertical component ofQ', which may be written from (4) as Q, _ Q~, = d~~00 k (10) dt Oz - V0k, (l~) Ozshowing that only ageostrophic circulations can modifydry static stability. The most striking feature of our simulation (Fig. 6b)is the increasing stability behind and at the cold front.This has an Eulerian influence on the static stability inthis part of the system, as relative winds are small (Fig.4). A residence time of 1.5 x 105 s can be estimatedin the 1500-km area behind the cold front where relative winds are no stronger than 10 m s-~ and the vertical frontogenesis larger than 70 x 10-9 K m-~ s-t.This leads to an increase of the vertical stratificationO0/Oz by an amount of 0.01 K m-l. (This value is inagreement with those that can be deduced from Fig.5a.) Destabilization is noticeable only at the northernmost part of the warm sector. The asymmetry betweenpositive and negative efi%cts may easily be interpretedin terms of the secondary ageostrophic circulations thatbecome increasingly important at the front during thesimulation. The cross-front ageostrophic winds converthorizontal gradients of potential temperature into staticstability at the front (Fig. ld), while the vertical spacebetween isentropes is compressed by the subsidencebehind the front (Fig. lc). Only ahead of the front isthe ascent stretching the isentrope spacing.5. Upper-air frontogenesis Surface and upper-air processes cannot be dynamically separated at the synoptic scale, as baroclinic instability has been convincingly described as a vortexinteraction process between an upper-air potential vorticity anomaly and a surface temperature anomaly5$.M/S ~ U62505000375025001250 0(~) o~-(7,0)M/S W zsoou DAY 9 RUN 55:;::: i i i i ~: i :: :. :: i ~ i i~ iii i i ! :: :: :.. i :~ i :: i :~ :: :~ i-- - --'- - --: ..... : .~: : -~--"-'"'-'-"~~-~~~. - ~ ::-~!~' '.-'~15~ ~ ~ ~ ~ ~ ~ i i ii~.~.--~'~.~.~, ~1 ,. ii ii ii !i ii 1 i ! tl-~ 1"-'~'lJi~' ::::,,'~'~:L~.~:"' t~ii iX_:; l 1 iI!! ! J'? ;I~ ~'~: : -,~"~-'~,:,;'"' '~ ~":':;; , ~,,~.~_..:~:~,~-~,, ,.:" ~,,~.*_ ; i !' i. . ! i i- ,.: :::',~.,~zz;;;;~--.-. '(!~.~:',',~.~ ~.. ....... .... ..... :...%,,, ~.....~i!!!!!!!~'~' -~_ _--'_;~! ! i'~.~! ! !!-~-~t.: .....::::~ ~-----___"'-'-~c':.c:: ~,~-"'-'-~~, ~~::::: .". ~. -L'-z 1250 2500 3750 5000 6258 FIG. 4. Relative surface winds together with 1500-m vertical velocities (negative dotted, positive solid lines at intervals of 0,5cm s -~ ). The average system speed is 7 m s -~ eastward.2010 MONTHLY WEATHER REVIEW VOLUME 122(z)lO o 3042(kin) 34588 W PV DAY 9 RUN 55~ ~ ~ ~-~---.'L-:~,~ ~ ~ .... ~--~~ ~ ~ ~,~ .... .~ ~ ~./-- ~~ -,' ~~ ~ -~342. ~:. ....' ( ' ~, ~ 330. ~~ X ~' > ~ / -~~~ . ~ ~ -~ /'. ,.~ - ,~~ ~ s. ~ / "-- -.. ~ t 1.~ - .? ~.~ .~, ~,~ ~(Z) U1 dO/ds PV DAY 9 RUN 55 15 .... ~, , .~ , , ,(kmJ 3458 2431 1403 375 FIG. 5. Vertical CC' cross section through the surface front at day9 (see Figs. 4 and 6). (a) Potential temperature (solid lines at intervals of 4 K) and vertical velocities (positive dashed, negative dottedlines at intervals of 0.5 cm s-~ ), and (b) normal wind (solid lines atintervals of 5 m s ~ ) and positive O0/Os [dashed lines at intervals of1 K (100 km)-~, s being distance along CC']. Tropopause, axes,and tick marks as in Fig. 2.this quasi-rectilinear trajectory, at the end of which acutoff occurs. The respective properties of baroclinicwave life cycles that lead to such cutoff processes aftera cyclonic or anticyclonic deviation have recently beendiscussed in detail by Thorucroft et al. (1993). Oursimulation clearly is of their "cyclonic" type.375025001250 0(~) 0 ~-~K~/s O ou ' ~ q'. 0 M DAY 9 RUN 556250 , ,, .... , .... , .... ,,,,5000 I::.'.'. ' ...... &l ~"-~%.'121.. .iii ...... iii~. ~ ~;'iiiiiii"ii';';~ ~ ~ -~~..i~ii ~ I, ....... x-~/ ~l.~ ...... X[[~:-~" ~' ~lA~ -' ~ ~ ~ :~ ....... %~.~.. ,,-. -.,)' ),, :~ :~ ::: z, :~::::~ :::::::: ::.: ~ ..... ,/l , ~~ ~ ~ .... tt ~ illlli[lllllliillltli'ill 125~ 2500 3750 5000 625~ [5-~SU,j62505000 3750(Hoskins et al. 1985). Such an interaction, however,occurs at a fairly broad scale, which is confirmed bythe sensitivity experiment described in section 6. That 2500is the reason why upper-air mesoscale processes produced by scale contraction frontogenesis phenomenawill be treated in a separate way from surface fronto- 1250genesis.a. Description A southeastward extrusion of stratospheric air withhigh PV occurs on the 325-K surface (Fig. 7), with avery marked anisotropic character--the cross-flowscale is much smaller than the along-flow one. A sudden and dramatic cyclonic change in direction follows0 0M Q'-Q', DAY 9 RUN 55~ ,..,. ,..,. , .,. ,..~. ~..,. ,..,. ,..,. , .,. ,..,. ~..,. ,..,. ,. 151 ............... ' ~5-~ t~. -r~ .............. ~. ~\~. I ~~ t ........ ~ .~ .~ t ~ ~ o ~'.~~~ ...... t / ~lll ' ' ' %~ ,, ,, ~ ~%~' ...... ,, ~" .... :: ,z ~"~''':' ; '' ,,Z I ' ~ ~ z ..... ,Z ~ z .....~ ~ /,~:1: '. , z,'.~::: ~:::~ ~:~,. 2~ ...... ~ ~ .....~ ~Z].-,--:5:-. '~2~~~/I~.~-:-:~:~~>/~t:~'~ ~: :~:: ' "~>~~7~;~'.~ ~: :~ 4~ XX~. . ,/// k X~x. ' ~% ~ -~//Z L ~ ~ ~ F" ~ -'~~~~~~~~~~tX~_~.... ~::-~ -.o::~~~;x~~~:. ~5.-o:~% 1250 2500 3750 500B 625~ FIG. 6. Day 9, at the surface: (a) potential temperature at intervalsof 4 K and horizontal frontogenetic Q~ vector (arrow centered at gridpoints), and (b) ageostrophic winds and vertical component of theQ' frontogenetic vector (at intervals of 25 x 10-9 K m-~ s ~).SEPTEMBER 1994 LALAURETTE ET AL. 20116250 ......... , ......... r ......... , ......... ~ ....... r. I:~i! :: :: :: :: :': i :: i !>:15000 .... :-- ". :::~i'"xx.i '_:ii.i;:i:~ ':i: _~~..~ ~ .... .-. ~.~. ~. \ ~ ', ~ , ~ ~ ' ' ' '.~',~''' ~ ~ ~ooou P~uoou ~tttlt/, ' ~X~ 6250 ~,,. .... ~,~~~~~~~~ ~~~ ,~'.~;~: ~ I ..... I '~ ' '~~~~~ '~~~~~/~ ~ I t ~ t; J~5o~ ~ ................ ~~~~~~~~~~~~~/~ '<~; ~ ~- ........ .. ~ ~~~~~~~~//~ ? ~;;;; L- .......... / -~~~~~~~~<~d~ '~ ~ ~ ~: ] ~ -"" -~~~, ,~~.'/, > u x, ;: ~ f~ .......... ~~~~,~~~~.;~;f;;~ s~,,,~ ~::'~0'~~;;~i~;:;:?~ [5 :~':::::::~::::::/x~;/:::::::~: - -~~--~' '"~ ...... ''~~:;:':'"S~O];'~;]::];:~];:'' '~~ 375-PV~.x 5o.~1/S~ lJa~-( ?,0)M/8 DAY 10 RUN 55 If frontogenetic processes have been thoroughly studied in the quasi-2D entrance of the northwesterly jets [see Keyser and Shapiro (1986) for a review; more recent results are in Reeder and Keyser ( 1988, hereafter RK88) and Moore (1987)], it seems important to stress again that the story is far from being complete at the end of the quasi-2D regime in our simulation. The DAY 10 RUN 55 , ' ' , I , , , , I , , , , I ' ' ' ' I ' , 'A/ ~, /~ "~ ~ --'~o.' ' - \ I % ~ t' ' % I ~ I 5",A~.,,~%"', ', ,~ ~ ~x ~ ! / - / .;---~ it N~X ~_-./I ill IIII ] ///'.__ ~.~._ ~ --,.: /' q eO/' ,, d ~/ /' ~x /~~ .' / ~~ ..~ I ' ' ' I , , , , I i , ~, I , , ~ , I , , , , 125~ 25~ 375~ 5~- 62581258 2500 3750 5880 6250 FiG. 7. Potential vorticity (at intervals of 0.25 PVU) and relativewind field on the 325-K isentropic surface (day 10; the average system speed is 7 ra s -~ eastward). The frontogenesis linked with this high-PV extrusionalso appears in Fig. 8 with the tightening of both isentropes and isotachs on the cyclonic side of the northwesterly jet, where a well-marked descent occurs. Theimportant change of regime between the very anisotropic, quasi-2D regime upstream of the trough and thevery curved regime in the trough again appears; important frontogenetic processes also occur in and leadto maximum tightening of isentropes just downstreamof the trough. Numerous cross sections and 3D visualizations have been made using a z vertical coordinate,which also show that the maximum downward extension of the 1-PVU surface also occurs at the troughbase, with an absolute height of 7000 m (not shown).b. Frontogenesis diagnostic using the Q' vector Again, a synoptic view of all frontogenetic processes(including ageostrophic and vertical advections) at7000 m can easily be captured from a display of Q~'and 0 (Fig. 9). Frontogenesis occurs in the quasi-2Dand northwesterly part of the flow, but it is clearly moreactive just upstream of the trough base. Frontolysis thenhappens downstream of the trough, which is fully consistent with the observed location of maximum isentropic gradients. These frontogenesis processes are, however, much less intense than at the surface. (The acrossisentropic component of Q' is about 1.5 x 10-mK m-~ s -~ at 7000 m, one tenth of the surface value.)The along-isentropic component of Q ~ indicates an important Lagrangian change in the isentropic orientationat the trough.25001250(~) 0 W 7ooou U uooou DAY 10 RUN 556250 .... , .... , .... , .... , , , ,., /5000 / .... _-.... ,... .-..~ ...... .... , . - -- '.',~ %~."/k ~'. q '-.','~. ,~ ,, ,O'~X.'.. .. ,.~ ,,,375~ -, x~x x x x ~%'.'.. - ~ ~ x x , . ,,~ ',,,~', ~ ,,,~f~ x, 4 ,1,~', ', . ,, / ~ ~ / ~ ,' ,.:.~,~. ,~ ,,~~.~..~ ,:~/~/ ,, ~ x~..~'O ~ ~ .::~,.__... - ,,~.::~:~ -, ..... . u ~(~M) ~ 125~ 258~ 375~ 5~8 625~ Era. 8. Day 10: (a) potemial temperature (solid lines a[ Jnle~alsof 4 K) a~d pressure (dashed lines at imcrvals of 5 hPa) at ?000 m;(b) recital rdociti~s al ?000 m (positive ~as~ed, ~gati~c dottedlines at intervals of 0.5 cm s-~) and wind speed at 9000 m (solidlines at Jn[ervals of 5 m s-~ st~Jng at 25 m s-~).2012 .MONTHLY WEATHER REVIEW VOLUME 12262505000375025001250 0(KU) 0'87ooou grad~?ooou DAY 10 RUN 55 , ' , , I , , , , I , , , , I , ' , , I , , , ~,.. ,%, L. ~/~ ~, , '(''ij~ ', ~ ~ / / t . , , , , m i m m m I m m m I i I m I m m m m 125~ 25~ 375e 5~- 625B 97ooo~ q', 7000 M DAY 10 RUN 555!]00(KM) - 1258 250e 375e 5eee 625e F~G. 9. Day 10, 7000 m: potentiat ~empemture (at inte~als of 4K) and (a) live011 [solid lines at intervals of 0.5 K ( lO0 ~)-~], and(b) Q~ (centered at the data location). ~e jet stre~ at 9000 m isreproduced as the dotted line (25 m s-~ isotach in Fig. 8). The frontogenesis at the trough is easily discernible here.dynamics associated with these two frontogenetic regimes are further investigated in the next sections.c. A simple partition between different contributions to the subsidence patterns Some controversy exists about upper-air frontogenesis between concepts underlining the importance ofthe very anisotropic entrance zone of the northwesterlyjets (Keyser and Pecnick 1985a,b; RK88) and thosestressing the strong curvature effects at the trough axis(Newton and Trevisan 1984a,b). Cammas and Ramond (1989) introduced a partition of the ageostrophicflow between along-flow (U,s~) and cross-flow (u,,n)components. They can be easily interpreted using thedissipation-free horizontal momentum equation du -- +f0k ^ u. = 0 (12) dt[cf. Holton (1979), Eqs. (3.2) and (3.3)]. Assumingquasi-horizontal trajectories and using natural components we get 1 dU u,, = ---- (13) fo dt U2 u,s = - --, (14) for,where r, is positive (negative) for cyclonic (anticyclonic) trajectory curvature: As expected (Fig. 10a),the entrance and exit zones of the northwesterly jet areassociated with cross-isobaric components of the ageostrophic winds, while the strong curvature near thetrough axis has upflow signature. No trace of inertialoscillation downstream of the ridge can be found here.7 Following Cammas and Ramond (1989), we introduce these natural ageostrophic components in the expression for the divergence of the flow again expressedin terms of natural components [this is an essential distinction from the Keyser et al. (1989) formulation]'~7.U = ~7.U.(b) Ou.s Ou.. Oq, u.. ' (15) Os + -b--~-n + U"s on r~ ' % wr - (c) (d) (r)where - is the angle between the flow and some constant direction, and rs is the streamline curvature radius. The spatial correlation between the .total divergencefield (b) at 9000 m and the vertical velocity patterns at7000 m is always very good, especially in the north-'westerly jet zone, up to the trough base (see Fig. 10band Fig. 8b at day 10). In this zone, most of the divergence is explained by the terms (c) and (d) in ( 15 ):the residual (r) term appears to be negligible (Fig.10b). Term (c) (Fig. 10c) is the diffiuence of thealong-flow ageostrophic wind; we may associate it with"'the along-flow ageostrophic circulation created by cur 7 Sanders et al. ( 1991 ) stressed the importance of such unbalancedoscillations in the development of observed intense upper-levelfronts.SEPTEMBER 1994 LALAURETTE ET AL. 20135000375025001250 5_~/s U.~ 9000M Peooou DAY 10 RUN 556250 6250 "" 5 i~'i i'iii i~)i: 55' i~i~i i i i i i%t ....... ;' ;,~,; S .'~ :~Z', ;;; ......... ~ 5~e , ~ ~ ~ f///~. ......... ~, , ~ ~ ~ t z///~.~ , ~ ~ / ~ l/////--~. ...... ~ , , ~ - ... zll///~--I zz ~ ...... .~ ........... ~..~ ~ ~/ ... ', ~ //~ ~5~. ?., 9'~~%--~ ~~--~. -, ,z~~ ~ ~ - . / ~ /~ ~ / ~ : ~%~-~/f ~ ~ ~ , ~ ~ ~ 2500 1250 ~~::::::;:'.'.::'.::~:: .................... , ................ ..................................... .................. ~ ................. ~ i '~' i -,. ~ ,,- ~ .,. ~ '1' ~ 'F i ',. ~ ',' ~ ',' ~ '1' i '~' i '~' ~(K~) - 125~ 25-8 3750 5eee 6250 (K~)dU~./dsoooo., DAY 10 RUN 5,5~":~:,'~/ Z/ ) ~ ',, ",,, ..... '::'.;/'. .:;,~/ ~/ ?:' .~"...-..>..:;:~,: ~. : 1 ~50 2500 3750 5000 625-62505-00375-1250divU.ooou RES.diVU.ooou DAY 10 RUN 55(KM) 0duma/dnaooou DAY 10 RUN 555000 % ' // /.'2500 . / ,,.,',-.~ ........ ' - .....: ?-.:L/o 1250 2500 3750 5000 6250 (KM) 0 1250 2500 3750 5000 6250 Fro. 10. Day 10, 9000 m: (a) pressure at intervals of 5 hPa and ageostrophic winds, (b) total divergence, (c) along-, and (d) cross-flowageostrophic diffluence (positive solid, negative dotted lines at intervals of 2 x 10 a s-I). The residual field b - (c + d) is (heavily) shadedin panel (b) for absolute values beyond 10 6 s-~ (2 x l0-6 S-I).vature effects. The convergence maximum (7.6X 10-6 S -4 ) appearing just upstream of the trough axisis mainly the result of this effect. Term (d) (Fig. 10d),on the other hand, is the diffluence of the cross-flowageostrophic wind. Its signature is maximum in the entrance and exit jet areas, with characteristic dipoles.(Refer to Fig. 8b for the jet position.) The first convergence maximum (8.43 x 10-6 s-I) is mainly theresult of this curvature effect. Clearly, Cammas and Ramond's (1989) diagnosticpermits an objective separation between the two kindsof ageostrophic circulations, which gives a confirmation of the role of both the strongly curved parts of theflow and the linear acceleration area in the tropopausefolding process. Such a diagnostic of the curvature effects following the streamlines is more in accordancewith the "gradient wind thinking" than partitions inorthogonal planes. However, the smallness of the residual term (d) hasto be verified each time such a separation is made. Ourtreatment in natural components does not separate between the rotational and divergent part of the ageostrophic wind; this is done to represent vertical circulations among orthogonal vertical planes without internal cancellation of vertical velocity components(Keyser et al. 1989). Difficulties involved with retain2014 MONTHLY WEATHER REVIEW VOLUME 122ing the nondivergent part of the ageostrophic wind inour treatment do not seem to be crucial as far as onlythe interpretation of the divergence field is concerned.There is a straightforward similarity of Figs. 10c and10d with the divergence associated with the gradientwind and a straight jet streak, respectively, which givesless importance to internally canceling contributionproblems in this case.d. Dynamical diagnostics 1) ROSSBY NUMBERS The importance of ageostrophic advections of momentum has been stressed in several studies of upperair frontogenesis (Shapiro 1981; RK88). These termsare neglected in QG equations and retained in semigeostrophic ones (Hoskins 1975 ). An expansion of themomentum equation in terms of a Lagrangian Rossbynumber (hereafter, ROL) was introduced in this latterreference, as opposed to the Eulerian classical expansion in terms of the advective Rossby number (Ro,)leading to the QG equations (Snyder et al. 1991 ); ROLis defined using the rate of change of momentum, whileRoa retains only the momentum advections. (See theappendix for more details.) The differences betweenthe Ro, and ROL fields are quite important in the elongated jet-entrance zone (Fig. 11 ).8 Characteristic values for Rot are 0.05 on the cyclonic side, while theyare 0.15 for R%. On the anticyclonic side, these valuesare 0.15 and 0.3, respectively. This indicates both thatthe geostrophic momentum approximation is better justified than the QG one in the jet-entrance zone and thatthe flow is in approximate geostrophic balance there.This is in agreement with numerous results from 2Dmodels (e.g., RK88). The occurrence of nonsmall Rossby numbers (Roam 0.4 and ROL m 0.3) near the trough has to be stressed,which makes the separation between primary and secondary flow difficult, at least on the basis of geostrophic balance. Such a result is in agreement withKeyser et al. (1989). This (geostrophically) unbalanced situation has to be contrasted with what has beenencountered in the jet-entrance zone.2) VORTICITY DIAGNOSTICS The partition of the ageostrophic flow in naturalcomponents that is introduced in section 5c indicatesthat most of the upper-air divergence in the jet-entranceregion comes from the cross-flow ageostrophic wind.Such symmetric configurations have been extensivelystudied in recent years by 2D simulations (Keyser and 8 Singularities in Fig. 1 lb occur at points where u --~ 0. At suchpoints, u-Vu -~ 0 but du/dt usually approaches nonzero values,which explains why singularities occur in Fig. 1 lb but are not foundin Fig. 1 la. Ro. 90001/ -gradW^dU/dz DAY 10 RUN 556250 .... , .................. ~ ~ ./5000 ~ ./ - ,o',,b,~'~ -_v- / N x \ ,-.x :.3 hS! 9',,5 X,, :;M ?',5 ~ ~ ~ ~x ~ ' ~ kV~'~z.'x~",. ~ ,,, ~Vllk~X , ~, ,. , %, . , ~ / x ' % ' / / I~. )',4] J J~ "( % /) ,"1~ ~ '~-~17 X /x, ~ ~1~ ,, x ~ j, ~ ,..~~u.>;, .125- / / ; & ~ , ~ , , i ~ i ~ ~ , .... ~ , , , , ~ , , , ,(~) ~ 125~ 2500 3750 50~0 625~ RoL 9000,1 -(-+f)divU?ooo. DAY 10 RUN 5562505000375025001250 0(K'M) 0 1250 2500 3750 5000 6250 FIG. 11. Day 10. Rossby numbers at 9000 m (contours every 0.15)and vorticity generation at 7000 m (light shading larger than10-~-s ~; heavy shading larger than 2 x 10-~-s-~): (a) Ro,,= Ilu-Vull/f01lk A ul[ and tilting of horizontal into vertical vorticity,and (b) Roc = [Idu/dtll/follk ^ ull and stretching. Jet streak as in Fig.9b. Note that the maximum of the tilting occurs in a zone where thestretching is minimum.Pecnick 1985a,b; RK88; Moore 1987). The authorshave proposed an interesting feedback process to explain the. dramatic tropopause folding occurring inthese regions: . 1 ) a displacement of the subsidence beneath the jetcore due to the differential cold advection forcing term(OUg/Oy)(OO/Ox) in the Sawyer-Eliassen (SE) diagSEPTEMBER 1994 LALAURETTE ET AL. 2015nostic equation [ see section 3b of the Keyser and Shapiro (1986) review], and 2) an efficient vorticity generation by tilting fromthe horizontal to the vertical component, leading tostrong shears on the cyclonic side of the jet that in turnreinforces the subsidence by an increase of the SE forcing term (point 1 ). This strong localized subsidence is also a key factorin upper-air clinogenesis, which seems mainly inducedby horizontal shear in vertical velocity (Keyser andPecnick 1985b). The displacement of the subsidence pattern towardthe jet core clearly happens in our simulation (Fig. 8b).Weak cold advection also can be detected in the enitive coupling between surface and upper-air frontogenesis. After some depiction of the vertical signatureof both upper-level and surface frontogenesis (section6a), a dynamical proof of their noninteraction will begiven (section 6c).a. Q' in vertical cross sections The vertical extension of frontogenesis can be explored using Q' displays in vertical cross sections[Q~, where n designates the coordinate normal to thecross section; see Eq. (4)]. Two such cross sectionstrance area of the jet (Fig. 8a). Therefore, following (z)RK88, the vorticity generation terms were investigatedin order to get some insight into the possible feedbackprocesses occuffing in our simulation (point 2). Theinviscid, hydrostatic vo~icity equation used isd(~ +f) _ (~ +f)V'Uh dt -k' V~WA +k' ~2 . (16)The first rhs te~ is the stretching terns; the second oneis the tilting te~. We verified that the last (solenoidal)te~ was negligible for the case shown. RK88 have ,,,,shown that the tilting term was clearly overriding thestretching term when the feedback processes were acting in the jet-entrance area (their Fig. 7). This clearlyis not the case in our simulation (Fig. 11 ). Maxima are1.3 x 10-~- and 2.7 x 10-1- S-I, respectively, for thetilting and stretching cyclogenetic terms in this area.This is not too surprising, since we are dealing with arather modest upper-level frontogenesis and RK88(their Fig. 7) found the feedback process for strongcold advections only. The upstream part of the trough base is another areaof vorticity generation. Tilting terms are importantthere. They are acting on the cyclonic side of the jet,with values of about 2 x 10-~- s-2 in a 800 km x 200km area, where there is almost no vorticity generationby stretching. This is in accordance with the Rossbynumbers in this area (Fig. 11) and confirms that thedynamics of this very curved and frontogenetic part ofthe flow is far from QG.6. Some investigation into upper-air-surface frontogenesis interaction A striking feature when comparing surface and upper-air frontogenesis patterns is that they appear to belinked, since the maximum tropopause descent occursdirectly over the surface cold front, with a tilt towardthe cold air. This is reminiscent of results obtained with2D models. Therefore, one might expect to see a pos,4292 3431 2569 1708 /yX/(kmj 5292 4403 3514 2625(Z) 0 W 1E-9_~K/r~/SQ,,~a PV DAY 10 RUN 5515 : ' 414 ~ ~ ''-,', ~_ '~~~.j~:- :~:~:: ' %3~~ %" ~: :~ - -%"~ ~. ~ ...... %5, . ~ ~ ---. _ , .~j .~,.~ :~', :::::: ::-,_. ,%~ .....(kml 5292 4403 3514 2625 FIG. 12. Day 10: AA' cross section (jet entrance, see Fig. 8) showing 0 every 4 K together with (a) positive O0/Os [dotted lines atintervals of 1 K (100 kin)-~] and Q,' vectors (s being the distancealong AA ', n across AA' ). Note that clinogenesis occurs only at highlevels. (b) Vertical velocities at intervals of 0.5 cm s-~ and theirfrontogenetical contribution Q~'.,. The vector orientation is consistentwith the horizontal and vertical distance scales. Only vectors greaterthan -20 of the plotted scales are plotted. Tropopause, axes, and tickmarks as in Fig. 2.2016 MONTHLY WEATHER REVIEW VOLUME 122have been produced at day 10. The first one (AA ', Fig.12) crosses the quasi-2D entrance zone of the northwesterly jet (see Fig. 8b), while the second one (BB',Fig. 13 ) crosses the area where a strong subsident pattern is created by the along-flow ageostrophic wind(see Fig. 10c). On both cross sections, clinogenesisoccurs since Q,', points horizontally to the warm side(the right side in the troposphere on Figs. 12 and 13).The vertical component gives information as to thestatic stability that particles are undergoing. Since thepotential vorticity is conserved (d/dt)[((o + f)O0/Oz] -- 0 , such variations of static stability must becompensated for by isentropic vorticity variations ofthe opposite sign. The Q' pointing down can thus beinterpreted in terms of isentropic vorticity generation. Frontogenetical processes are nascent only in the jetentrance zone (Fig. 12) and are confined to the uppertroposphere (8000-9000 m). The Q; show that isentropes are tilted clockwise in this zone (clinogenesis),while a strong isentropic vorticity generation can befound from the downward Q~' orientation. The formereffect is mainly the result of the vertical velocity action(Fig. 12b) transforming static stability into barocliny[Q'~,. ~- = -(Ow/Os)(OO/Oz) where ~-, s refer to thecross section horizontal direction]. Such a process hasmaximum efficiency just under the tropopause whereboth static stability becomes strong and vertical velocities keep their large tropospheric signature. Things look much different at the jet exit, just upstream of the trough (BB' cross section, Fig. 13). Particles arriving there have been frontogenetically forcedfor a longer period of time, and both the tropopausefolding and the baroclinic zone are better defined. Thevertical extent of the frontogenetical process is striking.The Q~' points to the right from the tropopause to theground. This is an important fact that must be relatedto the large vertical extension of the baroclinic zone atthe surface cold front, just downstream of the upperlevel trough (CC' cross section, Fig. 5). Hoskins andHeckley (1981) and Keyser and Pecnick (1987) havepostulated that 2D processes are responsible for thischaracteristic. These authors have stressed that this isa fundamental difference between cold and warmfronts. Both studies underline the importance of thecold advection on the frontogenetic processes that takeplace at the cold front. However, the frontogeneticaldiagnostic reported in Fig. 13a traces back the originof the upper-level and midtropospheric barocliny to theclinogenesis in the curved jet exit. Again, these processes are mainly the result of the action of verticalvelocities (Fig. 13b). Yet the effect of the total wind(Fig. 13a) is smaller than this vertical velocity contribution. This shows that even if it is not dominant, theaction of the horizontal wind cannot be neglected in theclinogenesis process. Conceptual models convincingly depicting the fron togenetical dynamics in such baroclinic, curved zones are still lacking, the problem being not only to adapt(Z) 0 d0/dsTM K---?/Sq'n PV DAY 10 RUN 55lO 54708 4292 3875 3458 [yX/(km) 4042 2875 1708 542(Z) O W -'--> Q wn PV DaY 10 RUN 55 '_---i5110 ,,~ ~ ! ~ ~i~ B ~ ' ' --~~~ o 47~8 4292 3875 3458 ~(km) 4~42 2875 17-8 542 F~G. 13. Same as Fig. 12 for BB' cross section (entrance of thetrough, see Fig. 8). Note that clinogenesis occurs throughout thetroposphere.the concepts derived from the usual balance approximations to these curved geometries but also to find newbalance conditions for these large-Rossby numberzones. An important fact that would be explained bysuch a conceptual model is, for instance, the verticaltilt of the vertical subsidence pattern (Fig. 13b), whichis very reminiscent of the vertical tilt of the secondarycirculations and which were well accounted for by thesemigeostrophic theory in 2D geometry. The upper- and lower-troposphere-filling frontogenetic processes occurring in the BB' cross section appear to feed one another. To prove that this is not thecase, we will use the horizontal viscosity as an effective(even if quite artificial) frontolytical process whose efficiency will be demonstrated in the next subsection.This frontolytical effect will then be used in a selectiveSEPTEMBER 1994 LALAURETTE ET AL. 2017way, either in the upper (above 4000 m) or in the lowertroposphere (below 4000 m). In case of a feedbackprocess, a remote effect should be felt by the other frontogenetical process (section 6c).b. The frontolytical impact of horizontal diffusion To test the impact of the horizontal diffusion on thesimulation, we have run the model without it from day5 to day 9 (experiment 552). It should be rememberedat this point that hyperdiffusion is introduced in numerical models not only to conteract numerical noiseproduction but also to parameterize the large-scale impact of the turbulent cascade going to molecular scales(viscous dissipation). The complete suppression of diffusion can thus be expected to lead to small-scale energy production, especially at fronts (Gall et al. 1987 ),which would be compensated for by viscous dissipationin a "perfect" model (i.e., without truncation effect).This is the reason why we present only results from run552 up to day 9. Surface fields indicate that the fronts are more vigorous at this date (Fig. 14a) than one day later in thereference run (experiment 55, Fig. 3b). This shows thatfrontogenesis is largely reduced by diffusion at day 10in the reference simulation. The dift%rence remainsquantitative, however, since all qualitative features(relative position of fronts and of action centers, relative importance of the two observed fronts) remain thesame. This is equally true for the upper-air (325 K)fields (Fig. 14b, to be compared with Fig. 7); PV isbest conserved in the nondissipative case, but the aspectof the stratospheric extrusion is not fundamentally different. The 0.5-PVU line, for example, still undulatesin a reversible way (no cutoff), indicating that confinement of the PV rearrangement north of this line isnot an artifact of diffusion (Thorncrofi et al. 1993). The CCl cross section intersects both the surfacecold front and the point of the maximum tropopausedescent (Fig. 14). The flow there (Fig. 15) is veryreminiscent of 2D studies, with a baroclinic zone extending from the ground throughout the entire troposphere, with a marked tilt toward cold air, its upper partbeing associated with a tropopause fold that can be seenclearly on the PV contours. The differences introducedby diffusion appear to be more quantitative than qualitative. Both the surface and upper-air fronts are dramatically enhanced when diffusion is removed, whichis evident by comparison with all fields in Fig. 5: thePV contours show a greater descent of stratosphericvalues on a smaller horizontal scale; velocities normalto the cross section show a more pronounced contrastbetween the cyclonic and anticyclonic part of the jet,and more surface shear; and potential temperaturesshow greatly enhanced barocliny. Particular attentionshould be devoted to the vertical velocity pattern, evenif it becomes somewhat noisy in the case without dif62505000375025001250O o~ S~ ~/fo DAY 9 RUN55~ ' ~---,, .... d,--',, '-~-~ ~ , ~-----~.~ ~ 7~ ', ~ \ ' ..---.. .., ~ x ~x t ~ / ~ ~ xx I %~ x_~:~ ~,~~ ~ ** t I %~ 9 I[I I ~~5~,, .,~',~ cFm~%~ ,, )~ i~, ', ','~ ~%~P~.~,~) ;~,' ~27 ll~.4& ~ ',)< ~;~1~1 / - -7 ~.~' ,. "-. '~-~,~4~ i5 5~,~' % ~ ~'~',l~'/;~ t x :~-~ '~-'~~~~~.' '~ ~ x ~ x~ ',., ~-~~~~~ ~ O. ~ , , ~ ~ I , , ~ ~ I ~ i , , ~ .... ~ , , ,(~) 0 1250 2500 3750 5000 625~ . .B 50.M/S PV aesJr '~* Ua~5~-( 7,O)M/S DAY 9 RUN552"~: :. :-:~i~'i~': :-'~ i. ~.~ :. :~ ~ ~.~'j: ~'~ ~/'-~~1250 0(Kid) 1250 2500 3750 5000 6250 FIG. 14. Day 9, run 552 (no diffusion): (a) is as Fig. 3b, and (b) is as Fig. 7 for the reference simulation at day 10 (run 55). /Ill /lilt ,,.. ll/ll I//Itl, .... ~'//lit ,, ..... x\ l/trill ....~,t~,,, ..... ,~x% ~''~''' .....::::::::::::::::::::::::::::::::::::~.. ....................... N., , ,~? ..... i i, iii, iii,iii,ii,~ii,?ii,iii,?ii, ii3, ii~.ii,ii3fusion. In both cases, two dipoles of ascent/descent canbe defined: one associated with the surface front, andthe other with the upper-air front. The same could besaid about the baroclinic zones that, rather than extending from the ground to the tropopause throughoutthe troposphere, seem to extend from both the groundand the tropopause in two distinct bands that marginally join. This reinforces us with the idea that each phenomenon supports its own dynamics without beinggreatly influenced by the other. This rather subjectiveopinion has already been proposed by many authors(Hoskins and Bretherton 1972; Buzzi et al. 1981; Key2018 MONTHLY WEATHER REVIEW VOLUME 122(z)lO o 3[542(km) 34580 W PV DAY 9 RUN552i:-~-~ :~ ~~~~~ ~ '~, ;~~,. .,~ ~:.,, ::~/~ ~ i '~~_ .~~ ~4~, ' . ; ;~, ,,, ',,;.,, ,,' ;,' ,,~ ;,~xk',~ ~ , r~-- 3:~ ~ ';~___~q~.~': ...'.~ ~, , ~. ~ ?.~ o!? -:;~ ::~,,~,~~~... ,,` ..?~ 2~k ,~+~___ ', - ,.: ~..i ;_-~w-. ~..~.',,~o ' ,~ ~ ~%,%4~ .... ~ , ;,~,. __...-~%%,~ iii~.' ' ,~x'~%'-;- -~~-"~_ .... ', '. ' 373~ 4431 5~5 t~/ 2431 14~3 375the applied diffusion (Fig. 16). The remote (surface)front keeps all its activity (cf. vertical velocity, thermal,and wind signatures) exactly as if it did not feel theupper-air change. This is confirmed by the horizontalpatterns (not shown) that are dependent only on thelocal diffusion that we used and not on what happensin the other layer. A companion experiment was run (experiment 553)in order to test the remote impact that the surface frontogenesis might have on the upper-air front. The surface frontogenesis was reduced by application of diffusion at levels where cr > 0.611, diffusion being keptat zero elsewhere. The results (Fig. 17) again indicatea local influence of the weakening of the surface front,without any remote influence on the upper-air frontthrough a feedback process. If the surface front resultsfrom a quasi-2D, local process, the upper-air one is theresult of a more complex 3D evolution. As was shown(z) uj. dO/ds PV DAY 9 RUN552 ~ 5 b (z)~ 5 lO3042(km) 3458 ~473316 14z~1~ 53100 tyX/ 0 FiG. 15. Vertical CC' cross section through the surface front atday 9 when diffusion is suppressed (run 552; see Fig. 5 for the samecross section in the reference run). (a) Potential temperature (solidlines at intervals of 4 K) and vertical velocities (positive dashed,negative dotted lines at intervals of 0.5 cm s-~), and (b) normal wind(solid lines at intervals of 5 m s-~) and positive O0/Os [dotted linesat intervals of 1 K (100 km)-~, s being for distance along CC'].Tropopause, axes, and tick marks as in Fig. 2.ser and Shapiro 1986; Sanders et al. 1991); we aregoing to reassert it in a more objective manner in thenext subsection.c. Has frontogenesis a remote impact? Having shown the sensitivity of frontogenesis to diffusion, we used it to reduce the upper-level frontogenesis while allowing the lower-troposphere dynamics tooperate with zero diffusion. From day 5 to day 9, diffusion was applied at levels Where rr < 0.611 (z ~>4000 m) and kept at zero at lower levels (experiment554). The upper-air frontal pattern alone is affected by(km) 3458 2431 14~3 375(Z) UI de/ds PV DAY 9 RUN55415105(km) 3458 2431 1 403 FIG. 16. Same as Fig. 15 but with diffusion acting at rr < 0.611 (run 554).SEPTEMBER 1994 LALAURETTE ET AL. 2019(Z) U- dS/ds PV DAY 9 RUN55315 , 3042 3736 4431 5125(km) 3458 2431 1403 375 FIG. 17. Same as Fig. 16b but with diffusion acting for a > 0.611 (run 553).in section 5, the origin of the upper-air baroclinic zoneobserved in CC' lies far upstream, in the quasi-2D region just downstream of the ridge. The frontogeneticalprocess is continuous from this point and includes thestrongly curved region in the trough (Fig. 9). If a"meeting point" between the surface and upper-airfrontogenesis exists, this appears to be almost fortuitous. The fact that frontogenesis has been shown to berather insensitive to remote effects might be relatedwith the well-known property of small-scale featuresthat they have only a marginal vertical penetration("Rossby height"; e.g., see Hoskins et al. 1985). Inthat sense, the self-sharpening process might bethought of as a small-scale phenomenon whose influence cannot go very deep in the vertical. Such arguments start from the Poisson equation form of the forcing equation. [See, e.g., Gill (1982), Eq. (12.8.14), orHoskins et al. (1985), Eq. (29), for the invertibilityequation, or Keyser and Pecknick (1985b), Eqs.(2.5) - (2.7), for the Sawyer-Eliassen equation.] It isthen easy to show that the response to the forcing isanisotropic in space, the aspect ratio of the vertical tothe horizontal scale being crudely f/N. However, thisis not the whole story, because there is no reason whythe horizontal scale of the response should be the sameas that of the forcing. A limit example is nicely illustrated by a Dirac 6 functionlike forcing, which inducesa remote response (Green function) far beyond its position and so on a scale that is infinitely larger than itszero-width support? The intrusion of stratospherichigh-PV air in a folding tropopause may be seen as anintermediate situation between a Dirac distribution 9 The analogy between electrostatics and the invertibility problemwas recently discussed in detail in Bishop and Thorpe (1993).(where the scale of the response depends only on the"dielectric" properties of the basic state) and a sinuslike distribution (where the horizontal scale of theresponse is constrained to be that of the forcing, thevertical scale being related to it by the Rossby heightrelation).7. Summary and conclusions Further insights into fully 3D, geostrophically unbalanced frontogenesis is gained in this study by theuse of a kinematic diagnosis. Using the adiabatic assumption, the Q' vector was defined to be the Lagrangian rate of change of the potential temperature gradient. It was shown to have a diagnostic expression [Eq.(2) ]. An intrinsic separation of Q' into the local rotation, divergence, and deformation part of the velocitygradient tensor was recovered. This indicates that anyfrontogenetic process can be reduced to convergenceand/or deformation processes. An alternative anisotropic separation of Q' into the vertical and horizontalwind velocity contributions to the velocity gradient tensor also was introduced. The standard problem of the nonlinear evolution ofthe most unstable normal mode of a zonal jet with realistic vertical and meridional structure was then revisited. The vertical numerical treatment (a -- P/Pso~ coordinate, with 500-m grid spacing at most) enabled aprecise description of both surface and upper-air frontogenesis, together with their possible interaction. Both upper-air and surface frontogenetic processesoccurring in this experiment were highlighted by thisdiagnostic. At the surface, cold and warm frontogenesiswere found to be of quite different character. Cold frontogenesis was found to be in good agreement with 2D,semigeostrophic Eady simulations. Warm frontogenesis, on the contrary, was occurring at a curved front(substantial alongfront Q' component) where selfsharpening processes were not found to be strongly active. The vertical frontogenetic signature (static stability evolution) was found to be most important at thecold front, which resulted in an increased stability (thisresult is, however, suspected to be very sensitive to theadiabatic assumption). The Q' diagnostic revealed that most of the upperair frontogenesis occurred in the very curved zone atthe trough base, even if the area highlighted by many2D simulations or diagnostics (Shapiro 1981; Keyserand Pecnick 1985a,b) was found to have some actionin the entrance zone of the northwesterly jet, upstreamof the trough. Some key factors revealed by these 2Dstudies were recovered, such as a strong subsidenceoccurring just beneath the jet-entrance axis in a coldadvection zone. Following Cammas and Ramond(1989), we have separated the divergence in terms ofnatural components of the ageostrophic wind, therebyproving that the ageostrophic circulation in the entrancearea of the jet could be described within a 2D frame2020 MONTHLY WEATHER REVIEW VOLUME 122work. Unlike what occurred in 2D simulations (Reederand Keyser 1988), vorticity was, however, shown tobe generated mainly by stretching processes, even iftilting of horizontal toward vertical vorticity proved tobe nonnegligible.. No clear feedback between subsidence forcing and cyclogenesis could therefore be invoked in our experiment. The frontogenetically efficient zone at the base ofthe upper trough was shown to be nongeostrophicallybalanced, with strong tilting of horizontal into verticalvorticity. Its frontogenetic character was also shown toact through a thick layer of the troposphere. This isproposed to be an alternative explanation to previous2D descriptions (Hoskins and Heckley 1981; Keyserand Pecnick 1987) for the deep baroclinic extension ofthe cold front that is downstream of the frontogenetictrough base for upper-air parcels. As both surface and upper-air frontogenesis occur inalmost the same vertical plane (with an upward tilt toward cold air), a constructive cooperation between thetwo, by ageostrophic transverse circulation, could beimagined. However, the uncoupled character of upperair and surface frontogenesis was confirmed by our sensitivity study, using vertically varying horizontal diffusion. As each of the two phenomena was quantitatively strongly influenced bY. the value 'of thisparameter, we forced a stepwise vertical modulation toact selectively On the net local frontogenesis. If eachfrontogenesis process was fed by the other in the reference experiment without any diffusion, an impact oflocal diffusion of one front should occur on the remotefront. This was not observed, and the noninteraction ofthe upper-air front with the surface One is thus proved.This demonstration is, Of course, limited to the adiabatic framework of our experiment. Coupling processes between the jet' streak dynamics and the lowlevel ones have been shown through diabatic processesby Keyser and Johnson (1984) or Sortais et al. (1993),among others. The limited strength of our jet streak (41m s-~) might also be recalled. Beyond the ad hoc introduction of diffusion that wasused artificially in order to modify the frontogeneticphenomena, a more fundamental problem is posed bythe strong quantitative influence of this dissipative process on the frontal scales, both at the surface and atupper levels. It is well known that a free-slip lowerboundary condition is very crude, and more or less realistic boundary layer parameterizations of momentumtransfers have long been introduced in atmosphericmodels. The intense response of upper-air frontogenetic flows to the horizontal diffusion reveals that muchwork also has to be done to improve our knowledge ofdissipating processes at higher levels, since the formulation introduced in the models greatly influencesthe results produced at the resolved scales. This pleadsthe case of an extensive study of dissipating processesin the 3D, frontogenetical context. Acknowledgments. We would like tO thank P. Bougeault, D. Ramond, and A. Joly for their friendly supportand scientific advice during this research, and P. Zwackfor discussion and improvement of the English text. Thiswork has been supported by Grants CNRS/PAMOY953176/7 and INSU/PAMOS 90/ATP/615/AP90. APPENDIX Advective and Lagrangian Rossby Numbers As stressed by Hoskins ( 1975 ), the semigeostrophic(SG) theory assumes only that "the Rossby number,defined as the ratio of the magnitudes of the rate ofchange of momentum and of the Coriolis force, issmall." We note RoL = Ildu/dtll/follk ^ ull--the "Lagrangian" Rossby number. Thus, SG makes a far lessrestrictive assumption than QG, which states that eachterm of the rate of change of momentum (namely, theEulerian tendency and the advection) is separatelysmall as compared to the Coriolis force (see Gill 1982,for example). This claim was recently claimed to be false in Snyderet al. ( 1991 ). The authors, using the same expansion interms of Lagrangian Rossby numbers RoL as Hoskins(1975), claim that the O(RoD expansion of the momentum equations leads to the QG, not the SG System. Suchexpansions often lead to nonunique solutions, depending0n the assumptions made by the different authors. In theSnyder et al. (1992) case, a rigorous expansion of boththe Eulerian velocity v field and the panicle position x isproposed. This should lead to an expansion of their Eq.(B5) different from their Eq. (B5 '):6tx0 = v0[xo(a, t), t] (A1)6,x~ = v~ [x0(a, t), t] + xl(a, t) - VV0[xo(a, t), t]. (A2)The implied modification of the approximate Eulerianmomentum equation is of the same order as the difference between QG and SG. So, we will refer in the following to the original Hoskins (1975) Lagrangian expansion. An advective Rossby number is introduced insection 5d as Ro, = (llu'Vull)/f011k ^ ull; QG (SG)requires Roa ~ 1 (Ro~ ~ 1). Both Rossby numbers aredisplayed in Figs. 1 la and 1 lb. The numerators werecomputed as I1-~11 ~ II-f0k ^ u~,ll Ilu. Vull ~ II-fok ^ ua - ~-II,where Eq. (12). was used. The time derivative wascomputed using finite differences between two consecutive model time steps ( 1200 s). The robustness of themethod was tested by computingSEPTEMBER 1994 LALAURETTE ET AL. 2021Ilu'Vull = [(u'Vu)2 + (u'Vv)2]":du 0uVertical advections of momentum were neglected inthe last equation. The fields computed using the lasttwo equations were almost indiscernible from Figs. 1 laand 1 lb (not shown).REFERENCESBishop, C. H., and A. J. Thorpe, 1994: Potential vorticity and the electrostatics analogy: Quasi-geostrophic theory. Quart. J. Roy. Meteor. Soc., 120, 713-732.Buzzi, A., A. Trevisan, and G. Salustri, 1981: Internal frontogenesis: A two-dimensional model in isentropic, semi-geostrophic co ordinates. Mon. Wea. Rev., 109, 1053-1060.Cammas, J.-P., and D. Ramond, 1989: Analysis and diagnosis of the composition of ageostrophic circulations in jet-front systems. Mon. Wea. Rev., 117, 2447-2462.Davies, H. C., 1976: A lateral boundary formulation for multi-level prediction models. Quart. J. Roy. Meteor. Soc., 102, 405-418. , C. Sch'fir, and H. Wernli, 1991: The palette of fronts and cy clones within a baroclinic wave development. J. Atmos, Sci., 48, 1666-1689.Davies-Jones, R., 1982: Observational and theoretical aspects of tor nadogenesis. Intense Atmospheric Vortices, L. Bengtsson and J. Lighthill, Eds,, Springer-Verlag, 175-189.--, 1991: The frontogenetical forcing of secondary circulations. 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Rep. 161, EERM, 70 pp. [Available from CNRM/DOC, 42 av. G. Coriolis, F-31057 Toulouse Cedex, France. JKeyser, D. A., and D. R. Johnson, 1984: Effects of diabatic heating on the ageostrophic circulation of an upper tropospheric jet streak. Mon. Wea. Rev., 112, 1709-1724.--, 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.--, and M. A. Shapiro, 1986: A review of the structure and dynamics of upper level frontal zones, Mon. Wea, Rev., 114, 452-499.--, and M. J. Pecnick, 1987: The effect of along-front temperature variation in a two-dimensional primitive equation model of sur face frontogenesis. J. Atmos. Sci., 44, 577-604.--, M. J. Reeder, and R. J. Reed, 1988: A generalization of Pet tersen's frontogenesis function and its relation to the forcing of vertical motion. Mon. Wea. Rev., 116, 762-780. , B. D. Schmidt, and D. G. Duffy, 1989: A technique for rep resenting three-dimensional vertical circulations in baroclinic disturbances. Mon. Wea. Rev., 117, 2463-2494.Miller, J. E., 1948: On the concept of frontogenesis. J. Meteor., 5, 169-171.Moore, G. W. K., 1987: Frontogenesis in a continuously varying potential vorticity fluid. J, Atmos. ScL, 44, 761-770.Mudrick, S. E., 1974: A numerical study of frontogenesis. J. Atmos. Sci., 31, 869-892.Newton, C. W., and A. Trevisan, 1984a: Clinogenesis and fronto genesis in jet-stream waves. Part 1: Analytical relations to wave structure. J. Atmos. Sci., 41, 2717-2734.--, and --, 1984b: Clinogenesis and frontogenesis in jet-stream waves. Part 1I: Numerical experiments, J. Atmos. Sci., 41, 2735 2755.Petterssen, S., 1936: Contribution to the theory of frontogenesis. Geofys. 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## Abstract

Both upper-air and surface frontogenesis have often been depicted as processes whose dynamics could he reduced to 2D balanced problems in which “self-sharpening” configurations could be highlighted.

This paper reports on a 3D adiabatic simulation of a baroclinic wave life cycle. Great care has been devoted to the vertical resolution, allowing for a good description of both surface and upper-air frontogenesis. The authors introduce a kinematic diagnostic (**Q**′ vector) that permits the identification of frontogenetic areas in such complex 3D flows where classical, low-Rossby number balance conditions can be violated. Relations and specificity with respect to frontogenetic forcing diagnostics are discussed. First, **Q**′ is used for surface frontogenesis, where it describes well the actual frontal activity, including the complex warm-frontal seclusion process. Upper-air frontogenesis is also investigated, both in terms of this kinematic diagnostic or in terms of potential vorticity displacements on isentropic surfaces. Both types of diagnostics clearly distinguish between dynamics of the entrance zone of the northerly jet—where 2D concepts may usefully be applied—and those of the strongly curved zone near the trough axis. Classical cyclogenetic terms (stretching and tilting) as well as the separation of ageostrophic circulations in terms of natural components of the wind also lead to a clear dynamical separation.

The cold front is shown to extend from the surface far into the troposphere. This is shown to be related to a singular property of the 3D flow. Parcels undergoing frontogenegis in the northwesterly upper-air flow are advected on top of those that were forced at the surface cold front in a southwesterly flow. The occurrence of a feedback proem between these upper-air frontogenesis processes and the surface ones is then investigated. Stepwise vertical profiles of horizontal diffusion are used to force local frontolysis. The resulting upper-air frontolysis, despite its local efficiency, does not have any remote effect on the surface front, whose frontolysis in turn has no effect on the upper-air front. The feedback process is thus not occurring in our simulation.