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1 Jp1.14 a Preferred Scale for Warm Core Instability in A JP1.14 APREFERREDSCALEFORWARMCOREINSTABILITYIN ANON-CONVECTIVEMOISTBASICSTATE BrianH.Kahn JetPropulsionLaboratory,CaliforniaInstituteofTechnology,Pasadena,CA DouglasM.Sinton * DepartmentofMeteorology,SanJoséStateUniversity,SanJosé,CA ABSTRACT 1.INTRODUCTION The existence, scale, and growth rates of sub- Tropical cyclones, mesoscale convective systems synoptic scale warm core circulations are investigated (MCS), and polar lows require moisture supplied by withasimpleparameterizationforlatentheatreleasein warmcore,sub-synoptic-scalecirculationsthatdevelop a non-convective basic state using a linear two-layer in generally saturated, near neutral conditions over a shallow water model. For a range of baroclinic flows range of weak to moderate vertical shears (Xu and frommoderatetohighRichardsonnumber,conditionally Emanuel 1989; Emanuel 1989; Houze 2004). stable lapse rates approaching saturated adiabats Accountingforthescaleofsuchwarmcorecirculations consistentlyyieldthemostunstablemodeswithawarm- has proven to be elusive. In a recent paper on the corestructureandaRossbynumber ~O (1)withhigher relationship between extra-tropical precursors and Rossby numbers stabilized. This compares to the ensuing tropical depressions, Davis and Bosart (2006) corresponding most unstable modes for the dry cases state: whichhavecold-corestructuresandRossbynumbers~ O(10 -1) or in the quasi-geostrophic range. The “Notheoryexiststhataccuratelydescribesthe maximumgrowthratesof0.45oftheCoriolisparameter scale contraction from the precursor are an order of magnitude greater than those for the disturbance (1000 – 3000 km) to the corresponding most unstable dry modes. Since the developingdepression(100–300km).” Rossby number of the most unstable mode for nearly saturated conditions is virtually independent of This provides the primary motivation for this study: to Richardsonnumber,thepreferredscaleofthesewarm determine if there is a preferred scale for warm core coremodesvariesdirectlywiththemeanverticalshear instability similar to the scale of the warm core foragivenstaticstability. circulations that supply moisture to tropical cyclones. Thisscalerelationsuggeststhattherequirement Whenembarkingonalinearinstabilitystudy,itis to maintain nearly saturated conditions on horizontal important to consider how such studies apply to real scales sufficient for development can be met more atmospheric phenomena (e.g. Descamps et al. 2007) easily on the preferred sub-synoptic horizontal scales given their inappropriateness for all but the most associated with weak vertical shear. Conversely, the primitive simulations where there is no interaction lackofinstabilityforhigherRossbynumbersimpliesthat between the perturbation and the basic state. stronger vertical shears stabilize smaller, sub-synoptic Furthermore, Descamps et al. (2007) conclude that regions which are destabilized for weaker vertical linear scales only broadly agree with those of real shears. This has implications for the scale and phenomena. Any consideration of convection existenceofwarmcorecirculationsinthetropics such interacting with larger scales is clearly not appropriate asthoseassumed apriori inWISHE. for a linear study and correspondingly, the current investigationislimitedtoanon-convectivebasic state. Nevertheless,ifitcanbeshownthatapreferredscale for warm core instability exists, its sensitivity to basic stateparameterssuchasbaroclinityandsaturationmay shed some light on the aforementioned scale gap ______________________________________________________ describedbyDavisandBosart(2006). A review of previous efforts to find a preferred * Corresponding author address: Douglas M. Sinton, scale for warm core instability reveals the problems Dept. of Meteorology, San José State University, One associated with the disparity between the convective WashingtonSquare,SanJosé,CA95192-0104:e-mail: scaleandlargerscales.Earlierinvestigationsinto the [email protected] scale of warm core phenomena focused on the 1 interactionofcumulusscaleconvectionwiththelarger accounting for the spectrum of observed sub-synoptic scale circulation that is required to converge the scalewarmcorestructures. moisture that sustains theconvection. These types of Atwolayershallowwatermodelonan f-planeis investigations are commonly described as conditional one of the simplest models that is capable of both instability of the second kind (CISK). Because the producingthebaroclinicfirstinternalmodediscussedin cumulus scale is a preferred scale for convective Frank and Roundy (2006) while also resolving instability arising from the conversion of CAPE and ageostrophic flows precluded by quasi-geostrophic downwardavailablepotentialenergy(DAPE),CISKhas limitations. Its simplicity and versatility make it a yet to provide a satisfactory explanation for the valuabletoolforfindinginstabilitiesthatmight underlie observed,sub-synopticscaleastheonlypreferredscale someofthecirculations,suchasthoseassumed apriori for instability with a finite growth rate (Charney and in WISHE, that serve as catalysts for the recent Eliassen 1964; Mak 1981; Fraedrich and McBride advances in warm core numerical simulations. In this 1995). spirit, the motivation for the current investigation is to: GiventhatthelatentheatinginCISKredistributes (1) determine if there is an instability underlying the moist entropy without generating it (Xu and Emanuel originofwarmcorecirculationsthatactasprecursorsto 1989;Arakawa2004),someofthemorerecentstudies tropicalcyclones;(2)assessthesensitivityofthegrowth of warm core, sub synoptic-scale phenomena have rateandspatialscaletobasicstateparameters;and(3) taken afinite amplitudeapproach that shifts the focus determine whether the structure of such circulations fromconvectiveheatingasasourceofinstabilitytothe might serve to converge water vapor as assumed a issueofhowtherequiredmoiststaticenergyissupplied priori inWISHE,Montgomeryetal.(2006),andinother while assuming a priori the existence of a suitably works.Theexistenceofsuchaninstabilitymayshed scaledcirculationtoconvergeit(Emanuel1986;Holton somelightonfactorsaffectingtheorigin,development, 2004).Wind induced surface heat exchange (WISHE) and scale of circulations, which heretofore have been has emerged as an efficient process for injecting the initiallyprescribedtofunctionasprecursorsfortropical required amounts of moist static energy to sustain cyclogenesis as in a recent zero vertical shear convection in tropical cyclones and polar lows (Craig simulationbyNolanetal.(2007). andGray1996).Inarecentsimulation(Montgomeryet Accordingly,thecurrentinvestigationusesthetwo- al. 2006), a pre-existing midlevel cyclonic mesoscale layer shallow water model from Orlanski (1968; convectivevortex(MCV)wasneededinordertoprovide henceforthIFW)andSintonandHeise(1993)modified asuitableenvironmentfororganizingconvectionleading byasimpleparameterizationforlatentheating.Section totropicalcyclogenesis. 2 describes the model configuration and physics, the A recent study of the role of tropical waves in latent heat parameterization, and model energetics. tropical cyclogenesis (Frank and Roundy, 2006) found Section 3 examines the model solutions: a moist but thatadominantbaroclinicfirstinternalmodestructureis non-convectivemodewithawarmcorestructureanda commontotropicalwavesnearthegenesisoftropical convergentcirculation,withenhancedgrowthratesona cyclones. Previous investigations into the effect of preferredscaledeterminedbythemagnitudesofvertical latentheatreleaseonbaroclinicinstabilityusingquasi- shearandsaturation.Finally,Section4summarizesthe geostrophic models (Tokioka 1973; Mak 1982, 1983; characteristics of the non-convective moist mode and Bannon1986;WangandBarcilon1986;Thorncroftand thenexaminestheimplicationsofthemode’sexistence Hoskins 1990) have shown moderate decreases in anditsscaledependenceonverticalshearstrengthand preferredscaleandcorrespondingincreasesingrowth saturation. rate(seeFig.1inMak1982)comparedtothedrycase alongwithmodestincreasesinupshearphasetiltwith 2.METHODOLOGY height(seeFig.4inMak1982).Thereare,however, two limitations to the quasi-geostrophic approach to warm core, sub-synoptic-scale phenomena. First, the 2.1Latentheatingparameterization assumptionofneargeostrophymaynotapplyforsub- synoptic scales especially when the Rossby number The fluid interface in the two-layer shallow water (Ro) exceeds O(10 -1) (Moorthi and Arakawa 1985; model that separates two fluid layers with different Thorpe and Emanuel 1985) and the growth rate densities (see Fig. 1) is analogous to an isentropic approaches the Coriolis parameter, f (Fraedrich and surfaceinastablystratifiedatmosphere(e.g.Andrews McBride 1995). Second, warm core systems are et al. 1987). Latent heating due to vertical motion equivalentlybarotropicbecausethethicknessandmass occursasamassexchangeacrossisentropicsurfaces. fields align as vertically-stacked structures. The To emulate this in the shallow water system, the resultinglackofthicknessadvectionbythegeostrophic continuityequationinSintonandHeise(1993)foreach wind prevents any conversion of zonal available layerismodifiedbyadditionofthescalar q, potentialenergy( PM)toeddyavailablepotentialenergy (PE)bythegeostrophicwindthusprecludinganyquasi- geostrophicbaroclinicinstabilityforwarmcoresystems. It is thus unsurprising that previous studies that used quasi-geostrophic formulations modified by latent heating parameterizations have been unsuccessful in 2 FIG. 2 Behavior of the fluid interface in the two-layer model. The
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