2298 MONTHLY WEATHER REVIEW VOLUME II5The Role of Low-Level Convergence and Latent Heating in a Simulation of Observed Squall Line Formation BRUCE B. ROSSGeophysical Fluid Dynamics Laboratory/NOAA, Princeton University, Princeton, N.108542(Manuscript received 13 February 1986, in final form 25 March 1987) . ABSTRACT The eff~ts of mesoscale forcing and diabatic heating on the development of convective systems have beeninvestigated using a simplified numerical model to simulate the squall line and the convective system precedingit that occurred over Texas and Oklahoma on 10-11 April 1979. A simulation run without including latentheat showed both systems to be initiated and maintained by convergence produced by larger-seale forcing. Thefirst cloud system formed downwind of the convergence zone that was produced by the confluence ofai~treamsalong a do/line. A cloud front approaching from the west then merged with this dryline, destroying its horizontalgradients through diffusive effects and replacing it with a frontal convergence line that was aligned with the lowlevel flow. This new configuration was then favorable for the formation of the squall line that developed in thesimulation. When latent heat was included, the continuous cloud in the first convective system broke down into isolatedcells which moved downstream'from the convergence zone. In the non-latent heat case, the priraary mechanismfor providing moisture to this cloud was vertical diffusion from the moist surface layer. When latent heat wasadded, vertical advection within cell updrafts provided a more efficient means to supply raoisture to the convectivesystem. In the simulated squall line, latent heat release produced a deeper cloud system while intensifying and main~dning the low-level convergence. However, unlike the earlier system, the squall line did not break into convec~vecells when latent heat was included in the simulation.1. Introduction The issue of whether low-level convergence exists inthe prestorm environment prior to the developmentof many mesoscale convective systems has importancenot only for our understanding of how these systemsfirst develop but also for the potential predictability ofsuch systems by meso-alpha-scale numerical models.The Preliminary Program Design (UCAR, 1984) forthe proposed STORM-CENTRAL Experiment citesthe determination of whether such convergence precedes storm development as one of the primary research objectives relating to the preconvective environment. A number of observational' studies (Fankhauser, 1974; Ogura, 1975; Ogura and Chen, 1977;Koch and McCarthy, 1982) have found evidence toindicate mesoscale lifting to be present up to severalhours prior to the first development of convective activity. For such cases in which convergence is an identifiable precursor, the prediction of the resulting convection will be considerably easier. In fact, one canexpect deterministic forecasts of the timing and locationof convection to require that the triggering mechanisminitiating this convection either be resolvable by themodel or be able to be effectively represented by themodel's subgrid-scale parameterizations. The extent to which preexisting low-level convergencc is important to the development of a given systemwill be highly case dependent. When it is present, however, one would expect it to play a major role in deretraining the structure of.the convective system thatresults. In particular, if the lifting zone has a predominantly linear form such as occurs in a surface coldfront, one might expect that the resulting convectivesystem would take the form of a squall line. In the casestudied here, however, we will find that the direction,relative to the convergence line, of winds in the middletroposphere as well as near the surface may also playa role in determining whether the resulting convectionforms an organized line structure or breaks down intoisolated cells. The extent to which latent heat release influencesthe subsequent development of the storm is also important in determining how much the external forcingwill affect further storm development once free convection has occurred. If the atmosphere is conditionallystable, as is the case for most winter storms, the onlyway to produce and maintain precipitation is throughexternally forced lifting, usually caused by baroclinicinstability. On the other hand, for conditionally unstable cases, such as those typical of the springtimestorm environment, the convective system will becomeself-sustaining once free convection is achieved as longas the moisture supply to the 'system can be maintained.OCTOBER 1987 BRUCE B. ROSS 2299When strong large-scale convergence is present, however, this external forcing may continue to influencethe storm's development in competition with thesediabatic processes. In analyzing observed storm systems, it may be difficult to separate the contributions to the storm's deVelopment from these two effects. A crude but potentially viable way to do this would be to assume stationarity of the prestorm lifting and to attribute anyadditional parcel lifting to diabatic effects. On the otherhand, the process of identifying the influence of latentheat release is quite straightforward in the context ofa numerical simulation ofa mesoscale convective system, amounting only to the modeler's choice of thevalue of the heat of condensation to be used. The importance of latent heat release in producingmesoscale circulations within subsynoptic systems hasbeen demonstrated in several meso-alpha-scale studiesof springtime situations involving intense convectiveactivity (Chang et al., 1982; Anthes et al., 1982; Benjamin, 1983). In the case ofmeso-gamma cloud modelstudies, however, "turning off" latent heating wouldusually be quite uninteresting, since such models typically rely upon diabatic effects to maintain the convection once the system has been initially perturbed.A middle range exists between these two extremes,namely that of the meso-beta simulation, for whichdiabatic effects and external forcing may have similarimportance in the formation of a convective system.In fact, Fritsch and Maddox (1981) have used a mesobeta simulation to demonstrate the possible effect oflatent heating in organizing a mesoscale convectivesystem, but external forcing was not included in theiridealized study. Ideally, a model would resolve thestructure of the storm system while at the same timemaintaining a realistic representation of the subsynoptic forcing which initiates and may help to maintain it. In the present study, we will attempt to do this bysimulating the development of an observed convectivesystem using a relatively simple meso-beta-scale numerical model. The case to be studied is that of 10-11April 1979, the first observing day of the SESAME Experiment. The convective outbreak which occurredduring this period over Texas and Oklahoma representsone of the most intensively studied events in the historyof mesoscale meteorology. (See Barnes, 1985, for acomprehensive bibliography.) The advantage of thiscase, in addition to the fact that several intense andstructurally different convective systems developedduring the period, is the availability of upper-air dataat 3-h intervals with an average network-spacing ofroughly 250 kin. This dataset, with its high temporalresolution, is needed to provide the lateral boundaryconditions which will force the simulation. A number of mesoscale numerical modeling studieshave been carried out for the 10-11 April case. Ross(1986) has identified at least ten different simulationsor forecasts of this period. These represent results fromseven different numerical models employing severaldifferent types of data sources. Most of these studiestend to concentrate on the formation of the convectively unstable environment which preceded the firstconvective outbreak that developed prior to 0000 UTC11 April, The squall line which occurred several hoursafter this time over central Texas received little attention and generally seems to have been poorly simulatedby these models. However, Kuo and Anthes (1984)show precipitation maps which indicate the presenceof a convective system over northern Texas, apparentlyrepresenting the squall line in a somewhat diffuse form.Also, Kalb (1985) shows an increase in relative humidity at 700 mb suggestive of the squall line. Both ofthese are meso-beta-scale simulations in which the upwind boundaries are relatively close to the region wherethe squall line developed. Out of all of the meso-alphastudies, only the forecast of Orlanskl et al. (1984), usingFirst GARP Global Experiment (FGGE) data in theirhost spectral model, produced a distinct line-type precipitation pattern oriented from southwest to northeastover Texas. From these results, it appears that the coldfront that produced the convergence which was ultimately responsible for the squall line formation wasoverly weak in most of these simulations; evidently theclose proximity of prescribed upwind boundaries inthe meso-beta studies as well as the more intense windsthat were apparently present in the meso-alpha forecastof Orlanski et al. improved the squall line representation. Regarding the boundary proximity, althoughthe nearness of lateral boundaries will usually tend toincrease the local noise level due to model adjustment,the imposition of intense low-level winds near thesquall line may also tend to intensify convergencewhere the confluent air streams intersect. The numerical simulations presented here will notinclude all of the physical processes which have beenincorporated in many other model studies. Rather, wewill attempt to simulate the convective developmentusing a model in which some potentially importantfeatures, such as terrain and detailed boundary-layerphysics, are absent. This approach does not conflictwith the findings of Carlson et al. (1983) and Benjaminand Carlson (1986) that these effects are important forthe development of the potentially unstable prestormenvironment. Rather, we will assume here that theirinfluence has already produced features important tothe preconvective environment such as the capping inversion and the differing air masses that force the simulation through their specification on the model inflowboundary conditions. Section 2 provides a description of the developmentof the observed convective systems. Section 3 includesa brief description of the numerical model and thepreparation of the dataset used for the initial andboundary conditions. Also, a discussion is given of howthe meso-beta model produces and enhances mesoscale230OMONTHLY WEATHER REVIEWVOLUME 115features from the coarser observational data. Section4 presents results from the numerical simulations.Cloud features from the basic simulation are shownand compared with corresponding satellite imagery.Then a comparison is made of the effects of low-levelmesoscale convergence and latent heating on development of the convective systems by comparing simulations without and with latent heating included. Ananalysis is also presented of the evolution of the simulated surface fro .nt and its effect on the dryline structure as the two lines merge. A discussion of results isgiven in section 5, including a trajectory analysis of airparcels flowing into each storm system. Finally, conclusions are presented in section 6.2. Observed Conditions The synoptic conditions associated with the 10-11April case have been described by several authors (seee.g., Moore and Fuelberg, 1981) and will only be reviewed briefly here. Primary emphasis in this paperwill be concerned with development of the squall lineover central Texas during the period from 2300 UTC10 April to 0600 UTC 11 April and a comparison between this and the convective .system that developedprior to it over northern Texas and southwestern Oklahoma. At 1200 UTC 10 April, a deepening surface low waslocated over Colorado with a surface front extendingsouth into New Mexico. A stationary front was positioned in an east-west orientation near the Gulf Coast.Also, a southerly low-level jet was located over easternTexas and Oklahoma. During the next 12 h, the coldfront to the west moved into the Texas Panhandle,while the front along the Gulf moved north as a warmfront to a location at 0000 UTC along the Texas-Oklahoma border (Fig. la). A jet streak moved from NewMexico into west Texas around the upper-level troughlocated to the west (Fig. lb). The low-level jet, apparently acting in response to this jet streak passage (Carlson et al., 1980), intensified during this period. An inversion also formed over the lower terrain of easternTexas as a result of differential advection of dry airfrom the Mexican plateau passing over moist low-levelair moving northward from the Gulf (Carlson et al.,1983). A dryline over western Texas marked the western edge of the moist southerly flow. This drylinemoved east to meet the southern edge of the cappinginversion by 0000 UTC 11 April (Fig. 1 a). Convection first developed after 1800 UTC (1200CST) as a line of thunderstorms (oriented from southeast to northwest) just south of the Texas Panhandle.By 2100 UTC (1500 CST), the line had moved east tothe vicinity of the Red River Valley. Behind this convective line, a more isolated, intense storm developedto the west-southwest of Witchita Falls, Texas, before2200 UTC. This storm moved to the east-northeasttoward the Red River Valley (see Fig. 2a and 2b) producing the most damaging tornadoes of the SESAMEI period from 2300 UTC (1700 CST) to 0400 UTC,11April (2200 CST) (Alberty ~t al., 1979). During thisperiod, satellite photographs showed the upwind(southwest) portion of the storm cloud shield movingto the northeast into Oklahoma (Fig. 2a-2c). While this system was developing, a narrow line ofconvection formed over west-central Texas just prior(a) SURFACEt-Z~)/~. ~.96 ~ ~ 8 12 -.. 16' ..2024 FIG. 1. Synoptic charts of 0000 UTC 11 April 1979. (a) Surface conditions, including sea level pressure (solidcontours, in units of mb with only last two digits shown) and surface isotherms (dashed contours, in units of deg.C). Dryline is indicated by the dash-dot line. (b) The 500-mb winds (dashed contours indicate isotachs, in units ofm s-l). Figure adapted from 'Figs. 17 and 18 ofAnthes et al. (1982).OCTOBER 1987 , BRUCE B. ROSS 2301(a) 2300GMT (1700CST) (b) 0101GMT (1901CST)(c) 0303GMT (2103CST) (d) 0545GMT(2345CST)I~G. 2. Satellite photographs showing (a) visible and (b-d) infrared imagery. A reference line has been added at the same location in each frame to indicate the position of the initial development of the cloud system.to the 2300 UTC (1700 CST) satellite photograph. Figure 2a shows this initial development as a thin bandof clouds between Midland and San Angelo, Texas,just east of the southern end of the reference line shownin the figure. (The reference line, which is used in thisand subsequent figures, is the approximate westernborder of the squall line clouds in the satellite photographs.) As shown by the first two frames of the satellite photographs in Fig. 2, convection initially developed fromsouthwest to northeast along a line that correspondedto the orientation of the dryline over west-central Texas.Comparison of the cloud development with the reference line indicates a slight southwestward growth andan extensive northeastward development between 2300UTC 10 April and 0101 UTC 11 April. However, during this period, there was essentially no motion perpendicular to the reference line. Convective intensitywas also quite weak initially, as indicated by the factthat the Midland, Texas radar, located 110 km to thewest, did not observe any reflectivity signature fromthe line until approximately 0130 UTC. Thereafter,the storm developed rapidly, producing the first severeweather report of damaging hall northwest of San An2302 MONTHLY WEATHER REVIEW VOLUME I15gelo at 0216 UTC (Alberty et al., 1979). Also after 0130UTC, the line began to move eastward at a speed ofroughly 10 m s-l. This behavior suggests that the earlierclouds along the lin~ shown in frames 2a and 2b weredue to weaker forcing which produced shallow convection oriented along the dryline. The later explosivegrowth observed from radar data (not shown) resultedfrom the arrival of a stronger forcing mechanism, apparently the eastward-moving cold front, that producedmuch more intense low-level convergence. By 0303 UTC (Fig. 2c), the deep convection occurring parallel to the reference line produced a cloudshield associated with the earlier convective system overcentral Oklahoma. At 0545 UTC (Fig. 2d), the majoraxis of the squall line continued to move eastward withits cloud shield merging with the clouds of the systemto the northeast. The southwestern portion of the cloudsystem lagged behind somewhat, possibly due to localized effects of orography.3. Modeling approach The present study will employ a rather simple numerical model in an effort to simulate the essentialfeatures of the squall line and the environment in whichit developed without including many of the complicating features which were present at the time of itsformation. The effect of the larger-scale forcing uponthe development of this system is provided by an analysis of the SESAME rawinsonde observations whichwere used to prescribe the conditions on the upwindinflow boundaries of the model domain. However,these observed data are still relatively coarse comparedto the meso-beta-scale structure of the squall line andthe convergence zone which produced it. It is thereforeessential for the mesoscale model to enhance the largerscale features imposed at the model boundaries in orderto produce the required mesoscale structure as will bedemonstrated in subsection 3c. This model enhancement of the mesoscale features will also be discussed.a. Brief description of the model The mesoscale model used here is quite similar tothat described by Ross and Orlanski (1982). The modeluses an anelastic, hydrostatic formulation of the equations of motion on a Cartesian coordinate system withthe height z as vertical coordinate. The horizontal gridresolution is 20 km and the vertical grid spacing isnearly 1000 m, with the model lid located at 15 km;the finite-difference grid staggering is type C under theArakawa convention (Arakawa, 1972). The limitedarea domain has open lateral boundary conditionswhich use the local normal velocity to determinewhether inflow or outflow conditions exist. Surfacewinds are controlled by a simple bulk aerodynamicdrag with the drag coefficient, Cz>,'equal to 0.25 x 10-3.1The surface temperature is prescribed from observations in order to provide some effect of surface heating.The vertical gradient of water vapor is set to zero atthe surface, implying no water vapor flux across thelower boundary. Fourth-order diffusion is used in thehorizontal to reduce high wavenumber noise. The vertical diffusion coefficient employed in the model depends primarily upon the local Richardson number,as was described in Ross and Ofianski (1982). The model uses an explicit formulation of moistconvection with a latent heating term included in theenergy equationl The equation system contains a prognostic equation for cloudwater. Rainwater is not predicted prognosfically but rather is generated by autoconversion when cloudwater exceeds a threshold value,specifically when the cloudwater per unit volume exceeds 1.5 g m-3; this rainwater is then removed immediately from the system and added to the total accumulated from the atmospheric column. (The inclusion of falling rainwater in the model, which isimportant in providing evaporative cooling below thecloud, is difficult to incorporate in a consistent way inthe present model with its 20-km grid increment andwill be postponed to a later study.) Finally, because ofthe smaller horizontal grid size used in this modelcompared to earlier simulations (e.g., Odanski andRoss, 1984; Odanski et al., 1985), saturation is assumedhere to occur at 100% relative humidity rather than95% as was used in these earlier simulations. A major simplification of the model lies in the absence of orographic effects iri the equation formulation.The result of this is to eliminate the mean effect of theterrain slope from northwest to southeast in the simulation. If the goal of this study were to simulate thedevelopment of the different air masses which interactin the storm region, the lack of orography as well asthe simplified treatment of the surface heating usedhere would be a serious limitation of the model (Benjamin and Carlson, 1986). However, because these airmasses are already formed by the time they reach thedomain (inflow) boundaries, their characteristics arebelieved to be represented adequately by the observedboundary conditions without requiting direct terraineffects within the model. The extent of the model domain as well as the heightof the actual terrain are shown in Fig. 3. The primaryregion of interest in this study will be confined to thesouthwestern portion of this domain, consisting ofnorth-central Texas and southern Oklahoma. This region is strongly controlled by the inflow boundaries tothe south and west. The extension of the model domainto the north and east, as shown in the figure, is done ~ This relatively small value has been chosen because the largevertical grid spacing would produce an overly deep layer of large.shear if larger values of Co were used.OCTOBER 1987 BRUCE B. ROSS 2303 I~G. 3. Map of model domain with contours indicating heightabove sea level, in meters, of actual terrain. Heavier dark contourcorresponds to constant height of model surface.tO reduce the influence of disturbances along thesedownstream boundaries. The height of the model's lower boundary was chosen as 400 m, which corresponds to the heavier contourin the figure. This contour roughly bisects the domainand represents the approximate surface height at whichthe squall line reached maturity. The low-level windsapproaching the squall line from the Mexican plateaugenerally followed the contours of the terrain, whilethe winds from the west boundary tended to movemore downslope after the cold front entered the domainand thus were more influenced by the absence of terrainin the model. The assumption made here is that thesesteeper downslope effects were of only secondary importance for the dynamics of the flow within the modeldomain. In fact, for a wind speed of 20 m s-I followingthe surface, these slopes (less than or of order 1:400)over west Texas upwind of the region of interest wouldproduce a vertical velocity at the surface of only 5 cms-1, which will be found to be quite small comparedto vertical velocities produced above the convergencezone, even without latent heating effects.b. Preparation of initial and boundary data The dataset which was used for initial and boundaryconditions in the numerical simulations was kindlyprovided to the author by Dayton Vincent and ThomasCarney of Purdue University. The procedures whichthey employed in the preparation of this analysis ofthe SESAME rawinsonde and surface observationshave been described by Vincent et al. (1981) and Vincent and Carney (1982). Their approach involved anobjective analysis of the surface data and the rawinsonde soundings at 25-mb increments onto a 1 - latitude-longitude grid over the SESAME domain. Thedata were then vertically smoothed to pressure surfacesat 50-mb increments. These gridded data, which were provided at 3-h intervals for the period 1200 UTC 10 April to 1200 UTC11 April, were then interpolated to the present modelgrid using the techniques described by Ross and Orlanski (1982). Because the model surface is located ata height of 400 m above sea level, it was necessary toprovide bogus data at model grid points located belowthe physical surface. As Fig. 3 shows, the region requiting such a procedure was primarily confined to thenorthwestern part of the domain. The vertical gridspacing in the model is roughly 1 km, and the gridstaggering requires a half-grid increment displacementof thermodynamic variables and horizontal windsabove the model surface. Therefore the only pointsrequiring special treatment of horizontal winds andwater vapor are located where the earth's surface isabove a height of 900 m. However, potential temperature must be extended down to the actual model surface at 400 m above sea level for use in the temperatureboundary conditions; Fig. 3 shows this region to berestricted to an area immediately adjacent to the westboundary. The extrapolation method is straightforwardand assumes a well-mixed layer. Horizontal winds areassumed to have zero vertical shear. Potential temperature is extrapolated adiabatically to the model surface,while water vapor is assumed to have a constant mixingratio.c. Model enhancement of mesoscale features The SESAME dataset provides a considerable improvement in both spatial and temporal resolution overthat of the standard operational rawinsonde network.With an average station spacing of roughly 250 kmand a nominal time interval of 3 h between balloonreleases, these data offer nearly a twofold improvementin station separation and a fourfold increase in thenumber of soundings per day. This resolution is stillnot sufficient to resolve many of the mesoscale featuresof interest here, including the squall line and the mesoscale convergence which precedes it. We must therefore rely upon the considerably higher resolution ofthe model and its associated dynamics to enhance thelarger-scale forcing imposed at the lateral boundariesand therefore to produce the necessary meso-beta features of interest here. Although the present model was initialized at 1200UTC 10 April, sensitivity studies performed by Orlanski et al. (1984) suggest that cases such as the presentsolution, with its relatively small domain, will be dominated by lateral boundary conditions rather than initialconditions at the time when the squall line is developing. Using a meso-alpha model for a limited-areadomain of roughly 5000 by 3000 km, Orlanski et al.demonstrated that solutions with the same lateralboundary conditions but with different initial conditions converged to very similar solutions after only 1day of integration. Similar results that indicate the po2304 MONTHLY WEATHER REVIEW VOLUME II5tentially dominant influence of lateral boundary conditions in limited-area simulations have also been reported by Anthes et al. (1985). It is reasonable to expectthat the time required for boundary conditions todominate should be on the order of the transit time ofan air parcel through the model domain. In the presentcase, this time is approximately 10 h, suggesting thatlateral boundary forcing will dominate the current solution prior to 0000 UTC 11 April, which is well beforethe time of squall line development. Figures 4 and 5 show comparisons, respectively, ofhorizontal and v~rtical fields between observations andthe model simulation at 0300 UTC 11 April. In eachfigure, the left frames are taken from observations andthe right frames from the model simulation with latentheat effects excluded. The region shown in Fig. 4 isroughly the southeastern two-thirds of the completemodel domain and represents the primary region ofinterest in this paper. At low levels (the lower two frames of Fig. 4), themodel wind field indicates a considerable intensification of the wind gradient, compared to the analyzed 'winds, along a line in the western half of the domain.This increased gradient is created in the model as thecolder air from the west encounters the warmer airfrom the south and southwest. In the observationalanalysis, the cyclonic turning of the air entering fromthe west occurs more gradually over a distance of several hundred kilometers, which roughly correspondsto the separation of the rawinsonde stations, as onemight expect. The low-level temperature fields also reflect this convergence of airstreams. In the observations,a broad tongue of warm air enters the domain fromthe southwest between the cold front to the northwestand the moist air to the east; however, in the model,this warm air is squeezed between these two airstreamswith stronger temperature gradients separating the different regions. In contrast to the lower levels, the winds in the middle troposphere (the upper row of Fig. 4) show littledifference between observations and simulation. Theonly significant differences appear in the model resultsANALYSIS OF OBSERVATIONSMODEL SIMULATION~20m/s FIG. 4. Comparison of winds (vectors) and potential temperature (contours, in deg. C) for twoheights, 887 and 5753 m, at 0300 UTC between simulation without latent heat and analysis ofobservations. Line segment, AB, indicates position of vertical cross section used in Fig. 5.OCTOBER 1987 BRUCE B. ROSS 2305(a) OBSERVATIONAL ANALYSIS (b) SIMULATION( 1.OOms-t ~ 20ms-l) ~'~ DIVERGENCE xtO40 200 4O0 DISTANCE (kin)(t l.OOms-I ~ 20ms-l) , ,',I, , ,~ 20o 4o0 DISTANCE (km) FIG. 5. Comparison between observations and simulation without latent heat, both at 0300UTC, for vertical cross section, AB, indicated in Fig. 4, showing potential temperature (solidcontours, in deg. C), winds in the plane (vectors), and wind speed normal to plane (dashedcontours, in m s-I). Lower plots show corresponding distributions of divergence and vorticity,in s-l, at 887 m height.as an eastward deflection of the wind; this deflectionindicates a divergent flow acting at this level in responseto the line of convergence at the 887-m level. The potential temperature field in the simulation indicatesthe adiabatic cooling associated with this line of upwardmotion. The mesoscale features appearing in the simulation occur not only as smaller-scale effects such asa more intense convergence zone but also as increasedgravity wave structure which has been largely filteredby the observational analysis. Some of these waves areexcited by adjustment in the model fields that occurnear the left inflow boundary. Temperatures along thewestern and southern inflow boundaries in the simulation have been prescribed from the observations;hence, while the interior temperature exhibits thesewaves, the net temperature gradient spanning this region between the western and southern boundariesmust be determined by these prescribed boundaryconditions. Figure 5 shows a comparison between observationsand model results at the same time but in the verticalcross section defined by the line segment AB which isroughly perpendicular to the convergence line evidentin Fig. 4. This figure shows potential temperature (solidcontours), wind component perpendicular to the crosssection (dashed contours), and wind vectors within theplane. Below each contour map is a plot of relativevertical vorticity and horizontal divergence at 487 mabove the model surface, which is the first interior gridpoint. The structure of the surface cold front is evidenton the left side of the frames with the jet stream ineach frame exhibiting a similar value of maximumcross-plane wind; however, the strong jet stream windextends further to the right in the simulation. As was evident in Fig. 4, the major differences between the simulation and the observations occur in the.lower levels below 5 km. This disparity is caused bythe substantial increase of both convergence and vorticity near the surface cold front in the simulation. Theplots of these fields show this intensification quiteclearly. The observed fields exhibit a broad region (250km wide) of weak vorticity and convergence with acorresponding layer of weak upward motion extendingup to 7 km. On the other hand, the model produces anarrow band of intense convergence and vorticity having a width of roughly 100 km.2 As in the observations,the associated layer of upward motion extends to aheight of 7 km; however, because this upward motionin the model is much more intense (over 80 cmthe contours of both potential temperature and crossplane winds show considerable vertical displacement.This structure is similar to that shown in other frontalsimulations involving intense vertical motion (Rossand Ofianski, 1978; Ofianski and Ross, 1984). Thedramatically increased low-level convergence in themodel is due to the strong low-level wind componentwithin the cross-sectional plane to the left of the updraft 2 The vorticity and divergence in the present frontal system havea similar structure to that shown by Ross and Orlanski (-1984, seetheir Figs. 3 and 4), in which the maximum convergence is locatedat the zero vorticity node ahead of the region of positive vorticity.The larger convergence compared to vorficity in this case probablyreflects the more intense mesoscale forcing from the boundary.2306 MONTHLY WEATHER REVIEW VOLUME II5zone (compare wind vectors in Fig. 5). Reference toFig. 4 indicates that this larger wind component di~rected along AB is caused by a clockwise rotation ofthe model winds from their direction in the observations with the total Wind speed being comparable toobservations. Another feature of this case is the stron~ restraininginversion which is evident below 2 km on the right sideof each frame in Fig. 5. While the stability of this layerremains fairly intense from the right border to the surface front in the observations, it is weakened considerably in the simulation, apparently due to the frontallifting as well as the relatively coarse vertical resolutionin the model.4. Development of the squall line The simulation of the squall line, which will be seento be quite realistic within the limitations of the model'sresolution and simplified physics, provides a better understanding of the development of this system. It willbe most instructive to compare the formation of thisconvective line with that of the more cellular convection associated with the first convective outbreak whichpreceded it. In order to distinguish the dynamic forcingmechanisms which initiated these convective systemsfrom the diabatic effects which later intensified them,we will compare solutions without and with latentheating included, in the numerical model. However,before considering these differences, we will first lookat the cloud structure of the full simulation with diabatic effects included and compare it with observations.a. Cloud features of the full simulation The basic simulation with latent heating includedwas run, as in the non-latent heat case, for the periodfrom 1200 UTC 10 April, when no convection waspresent in the observations, to 0600 UTC 11 April,when the first convective outbreak had moved well intoOklahoma and the Texas squall line was well developed. In this simulation, the first convection occurredas an isolated system in the Texas Panhandle adjacentto the western border at around 1900 UTC 10 Apriland moved to the northeast. A second region of-clouds,involving a more continuous generation of convectiveelements, then developed in the region somewhat tothe south of this, beginning around 2300 UTC. Thefirst convective system, indicated by the letter "A" inFig. 6, developed at 1900 UTC; its initiation time wasclose to that of the first observed convection, but itslocation was too far south into Texas. The second system, indicated by the letter "B", occurred several hourstoo late in its development compared to the corresponding observed storms which moved into the RedRiver Valley around 2300 UTC. The time period, 0100 to 0500 UTC, of the cloudfields shown in Fig. 6 corresponds to the interval in which the squall line develops in the simulation. The algorithm used to show the structure of the cloud pat terns in this figure is the same as that employed by Ofianski and Polinsky (1984), namely that stippling intensity is used to indicate the total amount of cloud water in the column. At 0100 UTC, a line of convection is predicted to occur along the southwest border of' Oklahoma, while an older, more isolated system has moved into southcentral Kansas. Comparison of this field with the satellite image of Fig. 2b shows general similarity between the simulated and observed cloud shields within the field shown in Fig. 23 but with the simulated clouds displaced to the west of observations. This displacement seemed to be caused by a delay in the development of the simulated storm, possibly be~ cause of the slow development of the cold front in the model .as discussed in section 4c. However, both the- simulated and observed storms developed in the TexasPanhandle west of the Red River Valley and thenmoved eastward as a system (although individual convective "cells" moved to the northeast). A weaker cloudsystem also developed near the center of the easternborder, apparently due to upgliding motion associatedwith the warm front which extended east from Oklahoma. At 0300 UTC the primary convective system in the simulation had moved to the northeast, although new convective elements developed over southern Okla homa. Also the first indications of squall line devel opment are evident over northern Texas. While this convection beghn over 1 h later than in the observed case, it occurred at approximately the same position, relative to the reference line, as the observed squall line (Fig. 2c). By 0400 UTC, this line convection extended to the southwest, parallel to the reference line. This tendency to develop new convection on the upwind end Of the line is characteristic 0f "back-building" squall lines, as referred to by Bluestein and Jain (1985). As in the observed case, the cloud shield extended northeastward but had not reached the northern system in the simulation by this time, probably because of the delay in its initial development. However, the distance of the convective line from the reference line and' the shape of the cloud shield are quite similar to that of the observed system. Clouds associated with the warm front formed a denser solid line normal to the eastern boundary by 0500 UTC. Neither these clouds nor those that had formed in the southeast comer were convectively ac tive. Both of these features may have been affected by the artificially elevated terrain to the southeast and by interaction with the eastern boundary. 3 The general absence of clouds downwind over Missouri in thesimulation is not supported by observations, possibly because theexcessively elevated terrain in this area does not permit sufficientmoisture from the Gulf to reach this region in the model.OCTOBER 1987 BRUCE B. ROSS 23070100 GMT0400 GMT ~ii%~i~i!!" ...........,,iii?' C~J!i'0300 GMT ............. ~t; ~-~ii!ii:~i::i-~-ii);~:. :);j~ig:~q~~m~": ': .. , ~~:;iii~i:i~iii~iiiii :: :: ~]jij:jj]jjjij~,jjjj]~Jljj~J~j~jii]Lii?iiiiiiiiiiiiiiiiiiiiiiiJ~JiiiJiii,~~%.'ii:' :i]ii]iiii!iiJ2'~ii~JiJ~~~iJiJiJJJJiJJ!!0500 GMT .................~:~mJ~!~il~J ~i~'~i~J~J~~J~i[~B'~J~J~J~iJi~CJ~J~~J~JJJ~J~JiJ~ijiijijiijiiRj~i~-i~iij '~J[J~iJJJ~JJ~J+~ tr~l~JJ~! i~] j~jj~]J~i~] ji~[J~J~iJLii]iJi]EJJT]~iJJ]JJJ~i][~J ] J~~j~Jh~[~j:~]j ........... ~:~t~r ""~:::;[A~J~[~~j~'~ '~BB]~i?'":'~i~ ~]~j~i~J~d'"!~*~'~[JJJ[~,,,-~:,~J~J~b,,~J]JJ[JJ~Ji~ ...... ~JJJJ[J[~[]~J~JJJJ~[l~[~~+;;P '"'t~'~~f~~~?~JB~:~iL~]f~i~J[~[[~]~~t~[;:l~JJJ~ti~i~B~l~~ ;~~j~~~ ~'~B~Ei~!iiiii~i~iiiiiii~ii~Bi;i~iliiil~i'~i~i~;E ' '~il~[;~i~"x;~ii[~il~l~l~J~i'~;; F~G. 6. Plots of vertically integrated cloudwater amounts at four different times from simulation with latent heat included. The letter X shows position of maximum total cloudwateramount. Letters A, B, and C designate different convective systems. Reference line is at thesame position as that in Fig. 2.b. Effect of low-levd convergence without latent heating The cloud structure from the simulation without latent heating (Fig. 7) and the corresponding structurewhen latent heating is included (Fig. 6) show a numberof similarities. Each of the major convective systemsoccurring over Texas, Oklahoma, and Kansas in thelatter figure is also identifiable in the former. The totalcolumn-integrated cloudwater amount in Fig. 7 is considerably less than in Fig. 6, reflecting the shallowercloud depth in the case without latent heat. This reduced cloud penetration also causes a reduction in thedownstream extent of the cloud shield or anvil in Fig.7 because of the reduced wind speed occurring at theselower heights. However, the similar location of thedense cloud regions in each figure suggests that themechanism creating these source regions in the casewith latent heating is also present in the solution without latent heating. Figure 8 shows the correspondence between thecloudwater field (stippled area) at 1860 m height andthe wind and moisture fields at 887 m, which are shownfor the same times as in Fig. 7. A region of maximumconvergence (solid contours) occurs upstream of eachcloud zone. This convergence is also aligned with thedryline interface, which is indicated in the figure bythe line of large gradient of water vapor mixing ratio(shown primarily by the dashed contours of 6 and 9gm kg-~). In fact, the moist, cooler air east of this lineflows almost due north and provides a low-level barrierto the more westerly flow from the west. Trajectoryanalyses (presented in section 5) of the origin of airparcels within the southern portion of each cloud forthe times shown indicate that inflow from low levels2308 MONTHLY WEATHER REVIEW VOLUME II50100 GMT0400 GMTI~G. 7. As in Fig. 6 except taken from case without latent heat.occurs along a path from the southwest, defined approximately by the indicated line segments AB andCD. These line segments are parallel to each other andreflect the persistent flow direction of the weakly stratified warm air mass originating over the Mexican plateau. Finally, note that the inflow direction for AB isoriented at an angle to the major axes of both the cloud'and the convergence zone at 0100 UTC; however, at0400 UTC, the corresponding inflow for CD is inalignment with the cloud and the major axis of theconvergence zone. This change in orientation seemsto explain the structure of the resulting cloud system,particularly the "dog-leg" turn at the Texas-Oklahomaborder which is evident in the cloud pattern at 0400in Figs. 7 and 8. Vertical cross sections (Fig. 9) taken along the linesAB and CD for the corresponding times indicate moreclearly the different way in which the low-level convergence produces clouds for the two different times.A comparison of the horizontal wind speeds within theplane (the horizontal component of the vectors) andperpendicular to the plane (dashed contours) showsthe flow below 4 km and ahead of the zone of upwardmotion to remain roughly within the plane in both0100 GMTI",, ........ 1:' \ I / ~---12 .... -'' '..x ',,\ I /....' 1,4.9 .....0400 GMTI I / i 9.6I I I ', .....' ' .... ~ 20m/~ ~ 20m/s F~G. 8. Composite plots' from simulation without latent heat, showing cloudwater at 1860 m height (stippling);convergence (solid contours, in intervals of 25 X 10-s s-~); water vapor mixing ratio (dashed contours, in units ofg kg-~); and winds (vectors), all at 887 m height. Line segments, AB and CD, indicate positions of vertical crosssections, at designated times, in Figs. 9 and 15.OCTOBER 1987 BRUCE B. ROSS 23090100 GMTlg 2 [~[~[~i~i~i~!~!~!!!!!!!:'~!!!!!!!!!!!!!i!~E~i5~5~[~i~[~!![~!!!!! / ~ :::: :~::: :~ ~! :, .~ !:~::: :~: .~ :~: ,~ ~!::?~~ ~i~i~]~i~!:'~ ~!!!!~!!!!!:::::::::::::'""::::::q~!!!!!!!' x -~ ~ ::::::::::::::::::::: .......... :~:: ~ ~ ~ ~ ~ .:::: ....... ~ ~5~5~~ ~~ ~ ~ ~:.~5~5~]~:.~r'~" ~ ~ ~ ~?~? / ~ ~ ~ ~ ~ ::~:::~:::~::~: ~ ~ / - -~ -- / ~ ........ 2~L .... . .... I / .... ~u/~ ~ a '~2~ or ', ~,- ~t ~"~ ,-~ A 0d00 G~T10 ~.91 ~ C 100 200 300 400 500 D ~JSTANCE (km) ~ 2ms-i _,.. 20ms-~ FIG. 9. Maps for vertical cross sections, AB and CD, indicated inFig. 8, showing eloudwater (stippled regions, where lighter inner stippling indicates mixing ratios greater than 2 g kg-I), potential temperature (solid contours, in units of deg. C), winds in the plane (vectors), and wind speed normal to the plane (dashed contours, in unitsofm s-l).cases. At 0100 UTC, the upward motion is quite abruptas the low-level flow encounters sloping isentropes(solid contours) and strong cross-plane winds to thenortheast. Because the updraft is narrow, the cloudzone itself is also narrow at the base with a shallowanvil extending downstream at higher levels. Note thatthe stratification of the warm air mass below 5 km isweak ahead of the convergence zone, thus permittingdeeper penetration of air parcels when they encounterthe low-level convergence. At 0400 UTC, the zone of upward motion is shownin Fig. 9 to be much wider, thereby producing a broaderlow-level cloud zone within the cross section. At thesame time, both the isentropes and cross-plane windsvary more gradually in the horizontal due to the closeralignment of the cross section with the interface between air masses. Finally note that the magnitude ofthe maximum vertical speed at 0400 UTC is comparable (the maximum vertical velocity is around 70 cms-~) to that at 0100 UTC; however, it now extends overa region of several hundred kilometers compared withan extent of less than a hundred kilometers at the earliertime. The forcing mechanism producing the cloudwaterzone in the simulation develops through an interactionof different air masses within the solution. These airmasses are identifiable by their low-level temperatureand wind direction. Figure 10 summarizes the evolution of these fields in the solution without latent heatfor the period during which the squall line developed.The warm air mass moving into the domain from thesouthwest is indicated by shading inside the 33 -C contour of potential temperature (thin contours). Themoist air mass to the east can be identified by southerlywind flags (plotted at every fifth model grid point). Finally the cool, dry air behind the cold front appears tothe north of the warm air mass. The initial structureof the temperature contours and wind flags in the latterregion prior to 0300 UTC is not consistent with thatof a typical surface cold front. This apparently is dueto the artificial response of the model to the boundaryconditions associated with the entry of the frontal system; these features also reflect to some extent the factthat data at this level were extrapolated down from theactual earth's surface, which is roughly 800 m abovethe model surface in the most northwestern corner ofthe domain in Fig. 10. However, from 0300 UTC on,the frontal structure becomes more realistic at a timewhen it is becoming more important to the development of the convergence zone. Figure 10 shows clearly how the convergence zonerotates clockwise from a north-south orientation at0000 UTC to a southwest-to-northeast alignment at0300 UTC. This is accompanied by a similar rotationof the eastern border of the warm air mass. At the sametime, the northeastern border moves southeastward asthe cold front moves into the domain. As the surfacefront overtakes the dryline, the region of potentialtemperature greater than 33-C is reduced and finallyeliminated as the front and dryline merge. Note alsothat the peak convergence increases to a maximum of80 x 10-s s-~ at 0300 UTC as the lines first merge andthen decreases after the low-level region of warm airhas collapsed. This maximum apparently occurs because the frontogenetic convergence reinforces theprevious convergence zone that was produced by upgliding motion along the air mass boundary, i.e., thedryline.c. Influence of the coM front The evolution of the surface cold front and its influence on the flow field as the front merges with the dry2310 MONTHLY WEATHER REVIEW, VOLUME II50000 GMT 0100 GMT 0200 GMT0300 GMT0400 GMT0500 GMT F]G. 10. Comparison of convergence (heavy contours, in units of 10-5 s-l), potential temperature(light contours, in units of deg. C), and winds (flags, using standard meteorological convention)for simulation without latent heat at 487 ra above the surface.line are important aspects of the simulation. (Thismerger of the front and dryline has been studied byKoch, 1984, in the case of a developing squall line.)The magnitude of the horizontal temperature gradientnear the surface provides a valuable indicator of theposition of both the cold front and the dryline. Figure11 shows contours of this gradient magnitude field forthe same height, time period, and domain extent asshown in Fig. 10 in order to facilitate comparison withthat figure. At 0000 and 0100 UTC, the north-south gradientline, indicating the position of the dryline, roughlymatches the location of the 33- isotherm in Fig. 10.The cold front approaching from the northwest, assuggested by the isotherms in Fig. 10 at 0000 UTC and0100 UTC, is still ill defined, as discussed earlier. However, at 0200 UTC, a secondary gradient maximumappears in Fig. 11 on the north end of the dryline. Thisfeature, as well as the local maximum to the southwest,indicates the development of a more coherent surfacefront, which is indicated at 0200 UTC and thereafterby a dashed line in the figure. During the period of frontal approach to the dryline,the gradient maximum in the dryline is seen to weakenand move southward, suggesting a deterioration of thedryline temperature gradient to the north. This processcontinues at 0300 UTC with the front intensifying asthe dryline gradient weakens. The striking feature ofnearly parallel gradient lines in Fig. 11 at 0300 UTCis consistent with the squeezing of the warm surfaceair between the cold front and the dryline as shown inFig. 10. The subsequent eastward motion of the frontat 0400 UTC and 0500 UTC causes the remainingdryline gradient to be pushed well to the south as thefrontal gradient intensifies to dominate the flow field.Reference to Fig. 10 shows the front actually extendingto the western boundary but with a progressivelyweaker gradient to match the weaker temperature gradient imposed by the inflow conditions. The evaluation of the frontogenetic/frontolytic processes associated with a cold front, as first studied byMiller (1948), is a valuable way to define the dynamicmechanisms associated with the intensification of afront. Koch (1984) has performed an analysis of theOCTOBER I987 BRUCE B. ROSS 23110000 GMT 0100GMT 0200 GMT0500 GMT FIG. 11. Plots of the magnitude of the horizontal potential temperature gradient (in unitsof 10-6 -C m-') at a height of 887 m from the simulation without latent heat. The contourinterval is 50 x 10-6 -C m-L The dashed line, shown from 0200 to 0500 UTC, is the analyzedposition of the surface cold front. The box symbols indicate the position of the sounding sitereferenced in Fig. 13.frontogenetic function, which is the substantial derivative of the horizontal gradient, in order to explain thedevelopment of a squall line that was observed to formalong a surface front. He concluded from this analysisthat a transverse frontal circulation, enhanced by contrasts in the surface sensible heating, produced the observed squall line development. In the present case, we will evaluate the relevantindividual frontogenetic terms that are responsible forthe weakening of the dryline and the intensification ofthe cold front. The procedure used here is similar tothat followed by Ofianski et al. (1985), who computedthe terms for 15 successive model time steps (representing a total of nearly 6 model minutes) and thenaveraged so as to filter high frequency noise. The complete form of the frontogenetic equation is given schematically as follows:~t IV~,01 = convergence + deformation + twisting + diffusion + latent heatingwhere 1 convergence-- 2IVHOI 1deformation --- 21VH01-- (Ox2 + O?)(Sx + ry)[(0~ - 0y2)(ux- ['y) + O ~O~( Uy + twisting~ iv--~0l(0xWx+0ywy) 1 diffusion -= I-~0~ [V~. VF] 1 latent heating ~- I-~0~ [V~0- VH]. Figure 12 shows the three dominant terms, convergence, deformation, and diffusion, for the same level(487 m above the model surface) as in Fig. 11 and fortimes before, during, and after the merging of the cold2312 MONTHLY WEATHER REVIEW VOLUME 1150100 GMT0300 GMT0500 GMTZ-205 J1-195 # II/; FIG. 12. Composite map of the important frontogenesis terms as calculated from the nonlatent heat simulation at a height of 487 m above the surface for times prior to, during, andfollowing the merging of the front and dryline. Frontogenetic regions have solid contours,while frontolytic areas have dotted contours. Labels are in units of 10-~- -C m-~ s-'; thecontour interval is 100 units. Contours of temperature gradient, as in Fig. 11, are reproducedas dashed lines for reference.front and dryline. Regarding the other two terms, thelatent heating term is zero in this case, while the twistingterm is quite small at this height, which is the first gridpoint above the surface. Frontogenesis is indicated inthe figure by solid contours and frontolysis by dottedcontours. The corresponding temperature gradientfields are reproduced as heavy dashed contours for thepurpose of reference. The initial fields at 0100 show the form of the termsfor the dryline structure. Convergence is the dominantpositive term and occurs on the north end of the drylinewhere the convergence shown in Fig. 10 is maximum.The negative diffusion somewhat counteracts this convergence and balances the positive deformation to thesouth. Deformation is negative on the extreme northwest end of the dryline. This apparently has the' effectOCTOBER 1987 BRUCE B. ROSS 2313of weakening the gradient there and contributes to theclockwise rotation of the dryline evident in Fig. 11. The most significant aspect of the front-drylinemerger period of 0300 UTC is the dominance of diffusion effects. This is evident in the very large negativediffusio, n term lying between the front and dryline gradients in the figure. This frontolytic term produces therapid decay of the dryline adjacent to the front. Thisresult from the model simulation suggests that turbulent mixing played a dominant role in the breakdownof the dryline in this case as the cold front merged withit. At the same time, even though the convergence itselfis shown in Fig. 10 to reach a maximum value at thistime, the convergence term in Fig. 12 is considerablyweaker than at 0100 UTC. This is explainable by thefact that the temperature gradient across the convergence line is now much weaker as the air masses merge. By 0500 UTC, the terms associated with the coldfront exhibit a more typical form characteristic of anisolated cold front (although the lengthwise extent ofthe apparent front is quite short). Both convergenceand deformation are strongly frontogenetic, while diffusion is frontolytic in character, except for small positive regions adjacent to the frontal line. The diffusiveregion at the front-dryline intersection has movedsouth as the extension of the front, with too small agradient to be contoured in Fig. 11, moves to the south. Finally, in view of the importance of the surface coldfront to the evolution of the dryline and the development of the squall line, it is worthwhile to evaluate themovement and intensity of the simulated front bycomparing it with observati'0ns. A comparison of thefrontal position and characteristics at 0300 UTC weremade using Figs. 4 and 5 for the non-latent heat simulation and the analysis of observations; this showedthe analyzed and simulated positions to be similar, although the scales of the analyzed front are inevitablyquite broad. A potentially more severe evaluation of the frontalstructure involves a comparison of "soundings" obtained from the model solution with actual observedsoundings. An attempt to compare model results withsurface observations was inconclusive, primarily because of poor surface station coverage in key areas overTexas. This comparison has 'the advantage that individual observed soundings do not involve the strongsmoothing that is inherent in objective analyses; onthe other hand, the raw soundings are contaminatedwith small-scale noise that would normally be eliminated by an analysis procedure. The sounding site chosen for this comparison is located at Childress, Texas,indicated in Fig. 11 by solid boxes at 0000 and 0300UTC proximal to the southwest corner of Oklahoma.This site was chosen for two reasons. First, the datafrom the three soundings for the period are fairly complete and do not show any direct effects of local convection. Also, the site is well away from the modelborders and is situated where it can provide an indication of the frontal movement during the period. Figure 13 shows a comparison of winds and potentialtemperature taken from the SESAME observations andthe model output, both of which have been verticallyinterpolated to 25-mb pressure levels. For the sake ofsimplicity, the model soundings are vertical and instantaneous for the times shown, with no attempt madeto simulate balloon rise rate or drift. The comparison shows a number of similarities aswell as some revealing differences. The winds abov~700 mb are quite similar in both direction and speed,in agreement with Figs. 4 and 5, although there is sometendency for the observed winds to be somewhat larger.The major difference occurs in the wind direction below800 mb, particularly for the earliest time (2312 UTCin the observations, 0000 UTC in the simulation).Similarities are also evident but less striking betweenthe observed and model temperature fields in the middie and upper troposphere. The major difference intemperature also appears to occur in the lower levelsaround the first sounding time. Some of these discrepancies, such as that related to the strong cooling in theobservations near the surface, are attributable to thesimplicity of the model's treatment of surface conditions and its coarse resolution of the boundary layer.However, the primary cause appears to be due to adelay in the passage of the surface front through thissite as compared to the observations. In fact, whenwind "soundings" were taken hourly in the modelrather than on the 3-h interval shown in the figure, the0100 sounding was found to exhibit a low-level winddirection very similar to that shown in the first observedsounding (with a release time of 2312 UTC). Hencethere appears to be a delay of nearly 2 h in the effectivefrontal passage at Childress in the model compared toobservations. This delay may not be a simple shift inthe movement of the front but rather may reflect aslower development of the front at this position dueto inflow boundary influences. In any event, this delaywould appear to explain the slow formation of thesquall line compared to observations, as was found insubsection 4a from the comparison of model cloudpatterns with satellite imagery.d. Latent heating effects With the inclusion of latent heating in the modelsolution, a considerable increase in the vertical motioncan be expected in the potentially unstable regionswhen air parcels are lifted to their level of free convection. The vertical displacement of over 1000 m produced by the convergence zone, as indicated in thecross sections of Fig. 9, should be sufficient to achievefree convection if the air parcels advected from thesouthwest ahead of the zone contain sufficient moisture. This will be the case for the 0400 UTC case inthe non-latent heat case; however, at 0100 UTC, vertical diffusion above the moist layer seems to be re2314 MONTHLY WEATHER REVIEW VOLUME II53004005006OO70O8OO9OO OBS MODEL0514 0225 2312 OOOO 0300OBS MODEL0000 0514 0225 2321 0600 0300 OOOO FIG. 13. Comparison of horizontal winds and potential temperature between observed soundings andmodel-derived "soundings" at Childress, Texas (see Fig. 11 for location) for the three sounding times ofinterest. See text for details. The horizontal wind barbs use the standard meteorological convention; a northward wind direction is indicated by a vertically pointing wind flag. The contour interval for potential temperature is 2-C.quired in order to produce saturation and free convection because of the dryness of the aix~ in low levtlsupwind of the convergence zone. The trajectory analysis presented in section 5 will further clarify this point. Figure 14 shows'the horizontal convergence field at487 m above the surface from the solution with latentheating at l-h intervals for the period from 0000 to0500 UTC 11 April. This figure should be comparedwith the convergence contours in Fig. 10. Such a comparison shows the southwestern, upwind portion ofeach convergence zone in Fig. 10 to be virtually identical with that in Fig. 14. In fact, the maximum con~vergence for the latent heat case within each large liftingzone prior to 0400 is quite close to the correspondingpeak in the non-latent heat case. However, Fig. 14shows the northern end of the convergence zone to bedistorted when latent heat release is included in themodel. As parcels move from the southwest into thezone, their lifting .initially has little effect on the convergence, until saturation is achieved and a net positivebuoyancy is then produced by diabatic effects. Thereafter, however, vertical motion is intensified as theconvective instability is released. In the present model, latent heat release is includedexplicitly in the model's energy equation. Therefore,when a condition of free convection develops withinthe model, a small-scale "cell" develops in the presquallline case with intense vertical motion above and corresponding larger convergence near the surface. Figure14 shows the creation of several of these cells on thenortheast end of the larger-scale lifting zone. As eachcell intensifies and penetrates into the middle troposphere, it begins to move to the northeast, driven bythe stronger winds higher in the atmosphere. Thismechanism explains the behavior of the convergencefields in the figure prior to 0300 UTC with cells beingshed from the downwind side of the larger-scale zoneas they form and intensify. The subsequent displacement of these cells during the next hour is indicatedby the arrows shown in each frame. Note that the intensity of each cell's surface convergence tends to bemaximum' in the vicinity of the larger-scale convergence zone and then decreases as it moves downstream.If these cells are the meso-beta model's equivalent ofisolated supercells, one cannot expect them to be sufficiently well resolved'by the 20-km resolution modelto have the necessary updraft-downdraft structure required for their maintenance over a period of severalhours. However, while their initial development isshown from trajectory analyses (stction 5) to have beenproduced by air parcels from the southeast, they aresubsequently fed by the very moist air east of the drylineonce their surface convergence intensity increases. Asa result, they become separate convective entities, withsome similarities to isolated supercells, once they moveaway from the original meso-beta scale lifting zone. At 0300 UTC and later, the behavior of the mesoscale convergence changes. Unlike the convergence atearlier times, the lifting zone at 0300 UTC is quitesimilar to that of the non-latent heat case along itsentire length. It thus appears that parcel lifting has nothad time to produce significant latent heat effects inthis region at this time. However, by 0400 UTC, diabatic effects have caused a major change. On the onehand, Fig. 10 showed the nondiabatic convergencemaximum to be decreasing after 0300 UTC, once theOCTOBER 1987 BRUCE B. ROSS 2315 oooo GMT.... (3 780100 GMT 0200 GMT70300 GMT 0400 GMT 0500 GMT102 FIG. 14. Comparison of divergence (in units of 10-5 s-~) at 887 m height from simulation withlatent heat included. Line segment, CD, at 0400 UTC is at same position as in Fig. 8. Arrowsextending to the northeast indicate the cells' movement during the next hour.surface front has merged with the dryline. On the otherhand, F!g. 14 shows a near doubling of the convergencemaximum between 0300 and 0400 UTC with latentheat included. At the same time, the band remainsrelatively intact over a distance of 400 km. Them is agradual increase in convergence along the band fromzero in the southwest extreme to a maximum of 150x 10-5 s-~ beyond the middle of the line. The downwind end of the band apparently produces a separatecell after 0400 UTC which breaks off and movesdownstream as seen in the 0500 frame. However, unlike the earlier convective system, cell formation alongmuch of the squall line tends to be suppressed eventhough latent heating within the line is quite intense. Figure 15 shows wind, potential temperature, andcloud fields in the vertical cross section indicated bythe line segment CD in the 0400 frame of Fig. 14. Thisline segment is identical to that used for the nonlatentheat case of Fig. 8. Comparison of Fig. 15 with the0400 UTC frame of Fig. 9 shows that, upstream of thecloud zone, the potential temperature and wind fieldsare virtually unchanged by the inclusion of latent heating, as one might expect. However, within the cloud,diabatic warming due to latent heating produces a potential temperature increase of over 9-C. (While thisanomaly may be possible for the updraft core of a supercell, it is unrealistically large in the present caseconsidering its horizontal extent in the model.) At thesame time, the vertical velocity increases to a maximumof 4.3 m s-1 near the rear of the cloud where the temperature increase is largest. This intense lifting also creates adiabatic cooling in the lower levels of the stormwhere the temperature decreases to nearly 2- belowthat of the nonlatent heat case. The deep penetrationof the cloud causes the winds near 10 km to deflecttoward the east as shown by the larger negative maximum of the wind component directed out of the planein the upper part of the cloud. The map of total precipitation from the 18-h simulation with latent heat included (Fig. 16) provides asummary of'the way in which convection developedwithin the model. Initially, convection occurred overthe northern extreme of the Texas Panhandle with theresulting storm moving off to the north-northeast as a0400 GMT1005Li.I0 I , I C 100 200 300 400 500 D DISTANCE (km) f 2 ms -1 -,.-- ~ ms -1 FIG. 15. As in Fig. 9 but taken from run with latent heat included. Cross section corresponds to line segment, CD, shown in Figs. 8 and 14. PRECIPITATIONOBSERVED MODELED'12 GMT 10 APR-12 GMT 11 APR 12 GMT 10 APR U. Ut.45 .2006 GMT 11 APR T ,6 .07 .48 T ,~ !!~i.2s-2.s ':::~:~2.s-s.o ..... ~s.o-7.s 'l > 7.s ~O. 16. Compa~son between obeyed 24-h precipitation (ie~ frame) and 18-h model precipitation (~t frame).Amoun~ ~ ~ven in cm of ~nwater. (An~yfis of ob~ pr~pimfion is county ofH~w ~dpimfion'For~ngGroup, Nafion~ Meteorolo~c~ Center.) 2316OCTOBER 1987 BRUCE B. ROSS 2317narrow track of rainfall. Then as the convergence zonemoved toward the southeast, new storm cells formedwhich also moved downwind in a similar direction.Finally the axis of the convergence zone rotated to alignwith the direction of the previous storm tracks as thefront overtook the dryline, and the squall line developed. Because of the increased efficiency for rain production of this system, compared to that of the isolatedconvective cells, the squall line generated the maximumprecipitation of the simulation. Also, the interactionof convection with the eastern boundary produced localized rainfall maxima, which were apparently farenough away to have had no effect on the region wherethe squall line developed. An analysis of observed precipitation for the 24-hperiod from 1200 UTC 10 April to 1200 UTC 11 Aprilis also shown in the figure for comparison with themodel results. Warm season precipitation is recognizedas one of the most difficult quantities for a numericalmodel to predict (see, e.g., Fawcett, 1977). In fact, because of the small scale, and intermittent nature ofconvectively generated precipitation, the analysis ofsuch rainfall is itself subject to considerable uncertainty(Kreitzberg, 1979; Ross, 1986). Even with these difficulties, it is useful to compare observed and predictedrainfall for the present model, since such a comparisonprovides another way in which to verify the startinglocation and track of the simulated convective systems.This comparison indicates similar starting location anddirection of the early rainfall tracks between observations and simulation. In particular, note the similarorientation of the rainfall lines in southwestern Kansas.The precipitation associated with the modeled squallline is larger than was observed at the location shown.However, it is similar in magnitude to the observedrainfall maximum occurring 100 km to the west, suggesting that this disparity may reflect the delay in thesimulated squall line's development as it moved eastward. The simulation clearly misses the major precipitationamounts occurring downstream over central Oklahomaand into Missouri. Much of this rain seems to havebeen associated with the first convective system whichdeveloped prior to the squall line. This deficiency maybe due in part to the artificially elevated terrain usedin the present model which will tend to reduce thesoutherly flow of moisture on the eastern side of thedomain. A further cause of the reduced rainfall to thenortheast is the tendency, as mentioned earlier, for isolated cells to decay in the model as they move downstream of the large-scale convergence zone. This premature decay seems to be due to the inability of themeso-beta model to portray the meso-gamma scalestructure properly, including the gust front caused byevaporative cooling, that is thought to maintain theselong-lived supercell systems which produced most ofthe precipitation in the first convective outbreak. Thesquall line, however, is more meso-beta-scale in itsstructure and thus is better represented by the model.5. Discussion of results The position of the 0000 UTC convergence on thedownwind side of the warm air mass, where the drylinebulges to the northeast, is consistent with the preferredregion for severe storm development for.a class ofspringtime severe weather cases in the OldahomaTexas region as analyzed by Moiler (1979, 1980).Moiler (1980) presented an analysis of surface observations from 10 April which showed this case to bequite typical of situations in which severe storms devclop northeast of the dryline bulge. In particular, someof the major features common to such cases are anorth-south orientation of the thermal ridge to thewest, a moist tongue of air east of it, and strong windsin the middle troposphere directed toward the northeast. The latter winds arc at an angle to the axes of thethermal ridge and the moist tongue and therefore blowacross the dryline interface separating them. The intensity of the dryline convergence will be determined primarily by the strength of the wind componcnt near the surface directed normal to the line.Danielsen (1974) has suggested that this low-level flowintensifies when stronger winds in the middle troposphere are entrained into the well-mixed boundarylayer over the heated terrain to the west. McCarthyand Koch (1982) have concluded that this downwardtransport mechanism was partly responsible for a similar observed convergence zone that occurred,along thedryline prior to the convective outbreak in a case whichthey analyzed. They also observed a region of blowingdust immediately upwind of the convergence zone inthis case; Daniclsen suggested that such blowing dustwas evidence of the intensification of these boundarylayer winds. Similar indicators were evident in the 10April case as well, including a swath of blowing dustin the visible satellite imagery at 2300 UTC (Fig. 2a)immediately west of the reference line and surface observations of blowing dust and gusty winds in this sameregion. Analysis of the simulation also shows strong lowlevel winds ahead of the dryline. However, because ofthe model resolution of the boundary layer, the simplified physics used to represent it and the short distanceover which boundary-layer mixing can act upstreamof the dryline, it is unlikely that such mixing can causea major change in the low-level wind profile betweenthe time when air enters the domain and reaches theconvergence zone. Rather it is more probable that theseboundary-layer effects, if they occurred, acted largelyoutside of the model domain to form the vertical windstructure which was prescribed on the inflow boundaries.4 The effect of the model's treatment of the 4 The technique of constructing bogus fields below the terrain, aswas described in section 2a, may also contribute to the more intensewinds in the lower layer by its effect on the wind profile prescribedat inflow boundaries. However, this should only be significant atlocations along the western boundary where terrain heights exceed1000 m above sea level (see Fig. 3). Such points are located north ofthe inflow region affecting the convergence zone.2318 MONTHLY WEATHER REVIEW VOLUME 115boundary layer on the formation of the convergencezone has been tested by performing sensitivity tests inwhich the magnitude of the drag coefficient Co wasincreased by factors of 2 and 5 over its control valueof 0.25 x 10-3. Comparison of low-level convergence,wind and temperature structure (not shown) indicatesvirtually no change in the convergence zone when Cois doubled. Increasing the coefficient to five times thecontrol produces some changes in the structure of thelifting zone but only a slight weakening of its magnitude. This insensitivity of the convergence to changesin Co provides further evidence of the dominance ofthe inflow boundary conditions in determining thestructure of the lifting zone. The effect of low-level convergence and latent heatrelease on cloud formation can be shown more clearlyby means of a trajectory analysis of the developingconvective system. This analysis has been done for caseswith and without latent heat fo3 two representativetimes: 0100 UTC, prior to squall line formation, and0400 UTC, when the squall line was well developed.A predictor-corrector iterative method was used to obtain trajectories from model history data which weresaved at time intervals of 7.5 min (20 time steps). Trajectories were integrated backwards in. time, startingfrom points located within the cloud system. In orderto compare differences due to diabatic effects betweenthe shallower cloud without latent heat and the deepcloud with latent heat, all trajectories were integratedbackwards from a height of 22100 m above the surface. Figure 17 shows a comparison of three-dimensionalclouds and tiajectories for the two cases at 0100 UTC,which was nearly 2 h prior to the first appearance ofclouds within the simulated squall line. The cloudsshown represent regions in which cloudwater exceeds0.10 gm kg-~. The domain extends up to 6.5 km inthe vertical and covers the southwestern two-thirds ofthe horizontal area shown in Fig. 8. In Fig. 17, thenorthern boundary is identified by a vertical plane. Thedashed contours indicate the approximate positions ofthe dry line as denoted by the 9 gm kg-~ line of watervapor mixing ratio at 887 m height (projected downto the surface). Each parcel trajectory terminates at thesame height (2400 m) with the vertical lines denotingparcel positions at 15-minute time intervals. The cloud systems, both with and without latent heatincluded, are each located in the same position justeast of the dryline. However, the more intense upwardmotion occurring in the latent heat case produces dramatic differences in the structure of the system. Theclouds to the south (toward the right side of the figure)extend deeper into the atmosphere when diabatic effectsare included. Also, in contrast to the continuous cloudfield shown in the left frame, the cloud with latent heatforms a cellular structure consistent with that producedin the low-level convergence pattern of Fig. 14. Thesecells tend to merge at middle levels in the northernend of the system. Finally, one should recognize thatplotting the 0.10 gm kg-~ cloudwater surface alone canbe somewhat misleading, since this ~ends to overemphasize regions of small cloudwater such as that shownby the weak cloud above 5 km evident in the foreground of each frame in Fig. 17. (The increase incloudwater content when latent heat is included isclearly shown by a comparison at 0400 UTC betweenFigs. 9 and 15 of the area of light stippling, the regionwhere cloudwater amounts exceed 2 gm kg-~.) The trajectory paths of parcels entering both cloudsare most instructive in indicating how each system isformed and maintained. In the case without latent heat,parcels flow smoothly into the lower levels of the cloudfrom the warm drier air to the west. By comparingheights of these paths moving back in time, one canconclude that parcel A was still being lifted by the con0100 GMTNO LATENT HEAT LATENT HEAT INCLUDED FIG. 17. Comparison of three-dimensional cloud fields and parcel trajectories at 0100 UTC between caseswithout and with latent heat. Dashed contours indicate horizontal position of 9 g kg-~ contour at 887 m.Stippled region on surface indicates that cloudwater is located above it within the field shown. Tick marksin vertical are separated by I kin. Tick marks in horizontal are in 100:km increments. The arrows on thesurface indicate the direction of north.OCTOBER 1987 BRUCE B. ROSS 2319vergence zone at 0100 UTC, parcel B experienced thislifting I h earlier, and parcel C was lifted prior to the1.75-h time period shown. In view of the initial dryness of the air advected fromwest of the dryline, vertical diffusion of moisture upward through the dryline interface must have playeda dominant role in moistening this dry air to producesaturation in the case without latent heat release. Infact, such mixing due to turbulence immediately abovethe dryline is quite realistic; however, the deepening ofthe cloud is excessive, due in part to this diffusion. When latent heat release was included, the trajectoryanalysis indicates that resolved vertical advection wasthe primary mechanism for supplying this moisture tothe cloud system. As the right frame of Fig. 17 shows,parcel B', the only parcel to terminate within the cloudupdraft, was lifted directly from the moist layer below.Parcels A' and C', both of which terminated in the clearair between cloud cells, originated in the drier air tothe west and had similar paths to their non-latent heatcounterparts (although their direction is more eastward). Hence, the buoyancy produced by latent heatrelease created a positive feedback in this case to increase greatly the supply of low-level moisture to thecloud system. Figure 18 shows the three-dimensional fields for 0400UTC when the squall line was developing. In order toemphasize the vertical structure of the trajectory paths,the depth of the fields shown has been reduced to 4.5km. Up to this height, the cloud structures with andwithout latent heat are very similar. (Note that comparison between Figs. 9 and 15 at this time showedlatent heat to produce a much deeper cloud which isnot reflected in the present figure.) The only differenceswhich are evident are: 1) the absence of a shallow cloudconnecting the squall line to the north system; and 2) -the narrowing of the squall line width in the latent heatcase, due to more intense convergence. In contrast to the earlier time, the effect of latentheat release on parcel trajectories is much less dramaticat 0400 UTC. Parcels A and A' are seen to have virtuallyidentical paths into the nose of the system, implyingnegligible influence of diabatic effects on this flow region. The primary change in the paths of the parcelsentering the squall line on its flanks is the tendency fortrajectories to form sharper angles to the line's axiswhen latent heat is included. This feature reflects themore intense convergence due to diabatic effects. Comparison of the trajectory paths for the latentheat case between 0100 and 0400 UTC provides anindication of the differences between the two systems.One can identify similarities in the source regions ofparcels B' and C' in each case, although the terminationpoints inside each storm system are different. The primary difference lies in the origin of the parcels designated by A'. At 0100 UTC, this parcel, like C', originated in the dry air to the west; however, at 0400 UTC,because of the rotation of the convergence zone causedby the arrival of the surface front, parcel A' entered thesystem from the moist air mass that was now locatedto the southwest. Because of this, there was now a plentiful supply of moisture into the system at 0400 UTC,not only from the eastern flank of the system, as occurred in the 0100 UTC case, but also from upwindof the nose of the squall line as well. An important feature of Fig. 18, compared to Fig.17, is the fact that inclusion of latent heat did notcause the cloud system to break up into cells. In fact,at 0500 UTC, a cell did form on the downwind (northeast) end of the system and moved downstream (seeFig. 14). However, the fact that cell formation in thesimulation was suppressed over most of the squall lineis an aspect of the simulation that deserves furtherstudy. There may be some counterpart to this in radarobservations that sometimes show a so-called "solidline" of convection on radar reflectivity displays (Burgess and Curran, 1985). In fact, the 11 April squall lineexhibited this solid line structure on operational radarduring its early stages of development. Such convectionis actually multicellUlar in character but with the scalesof these cells apparently too small to be resolved bythe radar; as a result, the broader squall line structureis the only detectable feature. Likewise, in the presentmodel with its 20-km grid size, these small-scale cellsNO LATENT HEAT0400GMT LATENT HEAT INCLUDEDFIG. 18. As in Fig. 17 except at 0400 UTC.2320 MONTHLY 'WEATHER REVIEW VOLUME 115 are absent, because they cannot be resolved by the model. One might then speculate that when a meso beta simulation, such as the present one, produces cel lular convection, this might be a region in the real sys tem where convection might produce larger-scale cells. 6. Summary and conclusions The effects of mesoscale forcing and diabatic heatingon the development of a squall line have been investigated by means of a simplified numerical simulationof an observed situfition. The meso-beta model usedin this study employed data, analyzed from upper airand surface measurements taken at 3 h intervals fromthe first observing day of the SESAME Experiment, toprovide external forcing at the nearby lateral (and surface) boundaries to force the developing mesoscale system. The resulting simulation showed a complex interaction of these different air masses: a moist tongueof southerly air to the east; very warm, dry air blowingfrom the southwest off the Mexican plateau; and coolair behind a cold front moving into the region fromthe northwest. Although the simulations were initiatedat 1200 UTC 10 April, the Primary period of interestfor this study was from 2300 UTC 10 April, prior tothe squall line formation, to 0600 UTC, when the system was mature. During the early period prior to 0200 UTC, the coldfront was located northwest of the region of interest sothat the major external forcing of the mesoscale systemin the simulation involved the confluence of.the moistair to the east and the warm, dry air to the west. Thedryline, which formed the interface between these airmasses, was the site of strong low-level convergencein the model as warm air from the southwest movedover this cooler southerly air. This convergence zone,which was forced by these larger-scale processes andthus was not dependent upon moist processes for itsexistence, was responsible for initiating the resultingconvection in the simulation. ' As the cold front moved southeastward into the domain, it merged with the dryline, leading to a diffusive'breakdown of the dryline's structure at its intersectionwith the front. As a result, -the north-south orientedconvergence line associated with the dryline was replaced by the frontal convergence, which had a southwest-northeast orientation. A major effect of this wasto rotate the convergence line from an orientation atan angle to the influx of air from the southwest to onein alignment with this airstream. With this new alignment, the upgliding mechanism which was previouslyresponsible for the dryline lifting was replaced by aconvergence structure more typical of a surface coldfront with cool, dry air behind the front convergingwith the moist air ahead of it. The warm Mexican airstream from the southwest no longer acted to drive theconvergence; in fact, this southwesterly flow now originated in the moist air east of the dryline and providedan influx into the nose of the convergence line of moistair with nearly neutral stratification. This new configuration determined the structure of the developingsquall line and seemed to be responsible for the uniqueplume-like character of the resulting system. The effect of latent heat on the earlier line systemwas to enhance the moisture supply to the convectivesystem forming at the western edge of the moist air'mass. Without latent heat, the dry air flowing abovethis air mass was moistened primarily by subgrid-scalevertical diffusion. However, when latent heat was included, the intensified low-level convergence causedby this latent heat release produced direct, resolvedlifting of moisture into the system. The convectionwhich developed downstream of the large-scale convergence zone (i.e., the zone which formed independent0f latent heating) produced separate, isolated cellswhich then moved downstream in a manner suggestiveof the supercell-type convection that occurred duringthis period. 'The inclusion of latent heat produced less dramaticeffects on the squall line but still caused an overall intensification of convection. Its primary effect was toincrease and maintain the low-level convergence zone,with a resulting narrowing of the width of the zone anda considerable deepening of cloud penetration throughthe upper troposphere and into the stratosphere. Also,whereas the convergence zone in the simulation without latent heat achieved a maximum intensity at 0300UTC and decayed thereafter, the convergence in thelatent heat case continued to increase after this time,reaching a peak value of nearly twice that of the nonlatent heat case. A significant feature of the simulation was the failureof the squall line system to break up into convectivecells when latent heat was included, as had occurredin the earlier convective system. A primary determinantof this was the alignment of the convergence zone relative to the low-level inflow of moist air. In the earliercase, when the convergence line was more perpendicular to the inflow, air parcels encountered a brief, intense period of lifting that produced cellular structure.In the later squall line Case, low-level flow was in alignment with the convergence line; as a rqsult, the airparcels were more gradually lifted over a longer distance. This produced a more reversible process thatwas less favorable to cell formation in the model. Finally, in both convective systems, cells tended todevelop downstream of the externally imposed convergence zones. It is not possible, in the present study,to determine whether this behavior has a physical basisor is a result of the coarse model resolution, with itscorrespondingly slower time scales for convective development. Acknowledgments. The author is very much indebtedto Dr. Isidoro Orlanski for his help and support duringthe course of this research and for his comments regarding the manuscript. I also appreciate the help ofDrs. Frank Lipps and Richard Anthes and, particularly,an anonymous reviewer in clarifying and improvingOCTOBER 1987 BRUCE B. ROSS 2321the manuscript. In addition, I would like to thank Professor Dayton Vincent and Mr. Thomas Carney forkindly providing me with the gridded SESAME dataset.The Heavy Precipitation Forecasting Group of the National Meteorological Center provided the precipitationanalysis shown in Fig. 16. I also appreciate the graphicssupport provided by Larry Polinsky and John Baumand the figure preparation provided by John Connor,Phil Tunison, and other members of the GFDL Drafting Group. REFERENCES Alberty, R. L., D. W. Burgess, C. E. Hane and J. F. Warner, 1979: SESAME 1979 Operations Summary. NOAA/ERL, Boulder, 253 pp. Anthes, R. A., 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. --, , D. P. Baumhefner, R. M. Errico and T. W. 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