Thermal wind balance

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1、ThermalwindbalanceLargescaleflowalmostgeostrophicNCEPReanalysis–1July20002cyclostrophicHurricanesalsoalmostcyclostrophic3ComparisonofbalancedflowssmallscaleorrapidflowRossbynumberlargescaleflow4FleagleandBusinger,AnintroductiontoAtmosphericPhysics,pg.164Hydrostaticand

2、geostrophic•Amatchmadein…err…aGFDlab?Thermalwind•Fromhydrostatic(hypsometric)equation,weknowchangesinhighrelatedtomeantemperature•Considerthedifferenceingeostrophicflowattwolevels:1VV21g2g1fnpRTln121p21VVVTg2g121fnRTpVln1Tfnp2•Therm

3、alwind(V)definedasa(vector)differenceingeostrophicwindwithTheight(i.e.,geostrophicwithshear)•Robustresultasfromhydrostaticandgeostrophicassumptions6ExampleQ:NHmid-latitudetemperaturegradientisabout1K/1000km.Thezonalmeanzonalwindspeedisabout5m/s.Whatisthezonalwindspeed

4、atthetropopause?RTpuuln1A:Tgfyp2RTpu(1000)u(250)ln1000ggfyp250So,u(250)=5+35.8~41m/sg7ThermalwindbalanceForzonalmean,wecanwriteugRTzfHyAsbefore,vertical(geostrophic)windshearrelatedtohorizontaltemperaturegradient.Sincegeostrophicandhydrostaticas

5、sumptionsarerobust,thisisalsoarobustassociation,oneofthemostimportantequationsforlargescale8meteorologyThermalwindvectorRpInvectorform,Vln1kTTfp2Thusparalleltoisotherms(analogoustogeostrophicwindforpressurecontours).Recallformofgeostrophicwind,1Vkg

6、Forthermalwind,coldontheleftinNHandontherightinSHfPossibletodetermine(3d)geostrophicwindfieldknowingthe3dtemperaturefieldandsurfacegeostrophicflow(veryusefulifyoucanmeasuretemperaturebyballoonorsatellite9sounding)Implicationsdiagnosis•Geostrophictemperatureadvectionle

7、adstochangesinwindspeedwithheightColdadvectioncausesbacking(sameasplanetaryrotation)WarmadvectioncausesveeringwithheightYouobservelowcloudsmovingwest,andhighcloudsmovingsouth.Whatpredictiondoyoumake?10Implicationsforcyclones•Coldcorelowsintensifyupward(e.g.,extratropi

8、calcyclones)•Warmcorelowsweakenupward,andcaninfactreverse(e.g.hurricanes)•Alsoforhighs…11BarotropicandbaroclinicatmospheresC