中尺度模式的動力框架-

中尺度模式的動力框架_第一頁，共三十一頁，編輯于2023年，星期六z垂直坐標(biāo)系p垂直坐標(biāo)系第二頁，共三十一頁，編輯于2023年，星期六z垂直坐標(biāo)系和p垂直坐標(biāo)系并不適合解預(yù)報(bào)方程組，因?yàn)樗鼈儠c山脈交錯(cuò)并因此在預(yù)報(bào)區(qū)域消失。為了解決預(yù)報(bào)面不連續(xù)的問題，Phillips于1957年提出了一種地形跟隨（terrain-following）坐標(biāo)叫作σ坐標(biāo)

第三頁，共三十一頁，編輯于2023年，星期六坐標(biāo)系第四頁，共三十一頁，編輯于2023年，星期六σ坐標(biāo)用于NGM，AVN/MRF，NOGAPS和UKMET，MM5，COAMPS,RAMS

最簡單的形式中，σ坐標(biāo)定義為σ=，這里P是模式中預(yù)報(bào)層的壓力，是地球表面氣壓

坐標(biāo)系

坐標(biāo)系

第五頁，共三十一頁，編輯于2023年，星期六第六頁，共三十一頁，編輯于2023年，星期六Eta(ηorStep)VerticalCoordinatethecodehasbeenupgradedtotheArakawa-stylehorizontaladvectionschemeofJanjic(1984),thenrewrittentousetheetaverticalcoordinate(Mesingeretal.1988),andsubsequently,atNCEP,suppliedwithanadvancedphysicspackage(Janjic1990,MesingerandLobocki1991).ItbecameofficiallyoperationalatNCEPon8June1993(Black1994).在曾慶存先生的支持和指導(dǎo)下，中國科學(xué)院大氣物理研究所于1986年開始發(fā)展一個(gè)能考慮陡峭地形的數(shù)值預(yù)報(bào)模式框架（宇如聰，1989）。

現(xiàn)在為AREM3.0第七頁，共三十一頁，編輯于2023年，星期六Eta(ηorStep)VerticalCoordinateη坐標(biāo)實(shí)際是σ坐標(biāo)的另一種形式，但它以平均海平面氣壓為底參照面而不是地面氣壓。

第八頁，共三十一頁，編輯于2023年，星期六Eta(ηorStep)VerticalCoordinateTheetaverticalcoordinate(Mesinger1984),resultinginquasi-horizontalcoordinatesurfaces,andthuspreventionofpressure-gradientforce（PGF）errorsduetosteeptopographythancanoccurwithterrain-followingcoordinates;

第九頁，共三十一頁，編輯于2023年，星期六Isentropic(Theta)VerticalCoordinate(θ垂直坐標(biāo))

因?yàn)樽杂纱髿庵辛鲃邮堑褥氐?，位溫（θ）可以作為一個(gè)重要的坐標(biāo)系。但是，邊界層主要為非絕熱過程，而且等熵面與地表面交叉。

第十頁，共三十一頁，編輯于2023年，星期六HybridVerticalCoordinates混合垂直坐標(biāo)

1979年，Uccellini等做出了重大推進(jìn)，這提出了：混合等熵–σ垂直坐標(biāo)系Thehybridcoordinatesytemisacombinationofbothathetacoordinatesystem(abovetheboundarylayer)andasgimacoordinatesystem(belowtheboundarylayer).第十一頁，共三十一頁，編輯于2023年，星期六SigmaCoordinate

Advantges

1)Thesigmacoordinatesystemconformstonaturalterrain.Thisallowsforgooddepictionofcontinousfields,suchastemperatureadvectionandwinds,inareaswhereterrainvarieswidelybutsmoothly.2)Itlendsitselftoincreasingverticalresolutionneartheground.Thisallowsthemodeltobetterdefineboundary-layerprocesses,suchasdiurnalheating,low-levelwinds,turbulence,low-levelmoisture,andstaticstability.3)Eliminatestheproblemofverticalcoordinatesystemsintersectingtheground,unlikeheightorisentropiccoordinates第十二頁，共三十一頁，編輯于2023年，星期六SigmaCoordinate

Limitations

1)Themodelwindforecastdependuponaccuratecalculationsofthepressuregradientforce(PGF).Thisiseaslycalculatedinpressurecoordinateswhentheheightisknown.Yet,whensigmasurfacesslope,thePGFmustbeexpandedtoincludetheeffectsoftheslope.Thisintroduceserrorsbecausethelapseratemustbeapproximatedatpointsthatlieinbetweenthepressuresurfaceswhereheightisobserved.2)Sigmamodelshaveadifficulttimedealingwithweathereventsonthelee-sideofmountainranges(i.e.cold-airdamming,lee-sidecyclogenesis).3)Becauseofthesmoothingrequiredinthemountainrangesalongcoastlines,landpointscanbeforcedtoextendbeyondthetruecoastline.第十三頁，共三十一頁，編輯于2023年，星期六ETACoordinateModel

Advantges

1)EtamodelsdonotneedtoperformtheverticalinterpolationsthatarenecessarytocalculatethePGFinsigmamodels(MesingerandJanji1985).ThisreducestheerrorinPGFcalculationandimprovestheforecastofwindandtemperatureandmoisturechangesinareasofsteeplyslopingterrain.2)Althoughthenumericalformulationnearthesurfaceismorecomplex,thelow-levelconvergenceinareasofsteepterrainarefarmorerepresentativeofrealatmosphericconditionsthaninthesimplerformulationsinsigmamodels(Black1994).3)Comparedwithsigmamodels,etamodelscanoftenimproveforecastsofcoldairoutbreaks,dammingevents,andleesidecyclogenesis第十四頁，共三十一頁，編輯于2023年，星期六ETACoordinateModel

Limitations

1)Thestepnatureoftheetacoordinatemakesitdifficulttoretaindetailedverticalstructureintheboundarylayerovertheentiremodeldomain,particularlyoverelevatedterrain.2)Etamodelsdonotaccuratelydepictgraduallyslopingterrain.Sinceallterrainisrepresentedindiscretesteps,gradualslopesthatextendoverlargedistancescanbeconcentratedwithinasfewasonestep.Thisunrealisticcompressionoftheslopeintoasmallareacanbecompensated,inpart,byincreasingtheverticaland/orhorizontalresolution.3)Etamodelshavedifficultypredictingextremedownslopewindevents.第十五頁，共三十一頁，編輯于2023年，星期六ThetaCoordinateModelSystem

Advantges

1)Potentialvorticityisbetterconserved,andprecipitationspin-upinshort-rangeforecastsisreduced.

2)3-Dadvectionbecomesessentially2-Dinthetacoordinates.

3)Thethetacoordinateallowsformoreverticalresolutioninthevicinityofbaroclinicregionslikefrontsandnearthetropopause4)Verticalmotionthroughisentropicsurfacesiscausedalmostexclusivelybydiabaticheating.

5)Isentropiccoordinatemodelsconserveimportantdynamicalquantitiessuchaspotentialvorticity.第十六頁，共三十一頁，編輯于2023年，星期六ThetaCoordinateModelSystem

Limitations

1)AMAJORlimitationofthethetacoordinatesystemoccursintheboundarylayer,wheretheflowcanbestronglynon-adiabatic.2)Isentropicsurfacesintersectthegroundsotheycannotbelocatedatalltimesduringtheday.That'swhysigmacoordinatesareusedintheboundarylayer.3)Isentropiccoordinatesmaynotexhibitmonotonicbehaviorwithheightintheboundarylayer.4)Verticalresolutioninnearbyadiabaticlayeriscoarse..第十七頁，共三十一頁，編輯于2023年，星期六HybridCoordinateModelsAdvantges

1)Thissystemretainstheadvantagesofisentropicmodelsinthefreeatmosphere,includingbetterprecipitationstartingtimesforisentropicupglidethaninsigma-coordinatemodels.

2)Thissystemeliminatestheproblemofisentropicsurfacesintersectingtheground.3)Thissystemrepresentssurfaceheatinganddynamicalmixingintheboundarylayerwell.

4)Thesystemallowsgoodsurfacephysicsinteractions,includingsurfaceevaporationandtreatmentofsnowcover.第十八頁，共三十一頁，編輯于2023年，星期六HybridCoordinateModels

Limitations1)Hybridisentopic-sigmamodelsnolongerpreserveadiabaticflowintheboundarylayeraseasilyaspureisentropicmodels.2)ThedepthofthesigmalayersdoesnotmatchthetruedepthofthePBL,soprocessesnearthePBL/freeatmosphereinterfacemaynotbedepictedwiththebestcoordinate.

3)Itcanbedifficulttoblendcoordinatetypesattheirinterfaces.第十九頁，共三十一頁，編輯于2023年，星期六SigmaandEtaCoordinates

1)

Thesigmaandetacoordinatesarebetterforusesnearthegroundsincetheyareterrain-followingcoordinatescomparedtothethetacoordinate,whichisnot.

2)

Thesigmaandetacoordinateshavemathematicaladvantagesofcastingthegoverningequationsoftheatmosphereintoarelativelysimpleform.

3)

Boththesigmaandetacoordinatesalsoguaranteeacertainverticalresolutionevenwhenthestratificationisweak.

4)

Alloftheadiabaticcomponentoftheverticalmotionontheisentropicsurfacesiscapturedinflowalongthe2-Dsurfaces.

5)

Bothofthesecoordinatesystemstendtobebetterforlongrangeforecastingforlargeareas.第二十頁，共三十一頁，編輯于2023年，星期六CriticalEvaluationofCoordinateTypes第二十一頁，共三十一頁，編輯于2023年，星期六第二十二頁，共三十一頁，編輯于2023年，星期六四、一些中尺度模式的介紹

第二十三頁，共三十一頁，編輯于2023年，星期六中科院大氣物理所的云模式第二十四頁，共三十一頁，編輯于2023年，星期六thefully-compressiblefluidsystemthissetofequationscontainssoundwaves,whichpropagateatmuchlargerspeedsthanthegravitywavesandrequireaverysmalltimesteptoinsurethenumericalstability.

Inpractice,itisalmostimpossibletoadoptsuchasmalltimestep,evenattheresearchmodeofnumericalsimulations.Inordertoimprovenumericalefficiencyoftheaboveatmosphericfluidsystem,KlempandWilhelmson(1978)proposedatime-splitting（時(shí)間分裂）scheme,whichwasoriginallyproposedbyMarchuk(1974).第二十五頁，共三十一頁，編輯于2023年，星期六KlempandWilhelmson(1978)propose