数值预报模式动力框架发展的若干问题综述

12113110002921000293UniversityofMarylandMarylandUSAterrain-followingstep-mountainη1006-9895200501-0120-11P435AReviewofSomeNumericalAspectsoftheDynamicFrameworkofNWPModelJILi-Ren12CHENJia-Bin1ZHANGDao-Min1andWANGHou-Jun31InstituteofAtmosphericPhysicsChineseAcademyofSciencesBeijing1000292StateKeyLaboratoryofNumericalModelingforAtmosphericSciencesandGeophysicalFluidDynamicsInstituteofAtmosphericPhysicsChineseAcademyofSciencesBeijing1000293UniversityofMarylandMarylandUSAAbstractAnoverviewofsomenumericalaspectsofthedynamicframeworkforNWPmodelispresented.Onmodelingorographythemeritsproblemsandremediesofterrain-followingcoordinateandstepmountainηcoordinatearediscussed.Thedevelopmentofconservativeschemesfromtransientschemestofullincludingtemporaldiscretizationconservationforimplicitexplicitandsemi-implicitschemesisreviewedandthatforsemi-Lagrangianschemesisalsodiscussed.Somerecentprogressofacceleratingtheiterationfornon-linearimplicitproblemisintroduced.Finallythepresentstatusandoutlookforthewidelyusedglobalspectralmodelisaddressedandabriefintroductiontospectral-elementmethodisgiven.Keywordsmodelorographictreatmentconservativescheme[e-mail]129120051ChineseJournalofAtmosphericSciencesVol.29No.1═════════════════════════════════════════════════════════════════Jan.2005ECMWFGFDL1231972452ZZ=ZtZ=Z*xyw=0Z=Ztw=w*=V*ΔZ*Z=Z*{1p1ω=0p=ptω=∂p*∂t+V*Δp*p=p*{2ω=dp/dtp*=p*xyZ*t12Z*2.11957Phillips6σp/p*·σ=0σ=1σZ7θ8terrain-followingT-FT-F9～11pσx∂φ/∂xp∂φ/∂xσ+RT∂lnp*/∂xσp*1/f∂φ/∂xp10ms-110-31/f∂φ/∂xσ≈102ms-1RT∂lnp*/∂xσσ1Corby12∂φ∂x+RT∂lnp*∂x=-φxx+R-Txlnp*xx.3Tp=Alnp+BABφp=φ0+12RAlnp02-lnp2+RBlnp0-lnp44332p13pp∂φ/∂x∂φ/∂y3φTφxypt=-φp+φ'xyptTxypt=-Tp+T'xypt1211No.1JILi-Renetal.ReviewofSomeNumericalAspectsoftheDynamicFrameworkofNWPModel①-φ-Tφ'T'∂φ∂x+RT∂lnp*∂x=∂-φ∂x+R-T∂lnp*∂()x+∂φ'∂x+RT'∂lnp*∂()x5-φ-T∂-φ/∂x+R-T∂lnp*/∂x≡05∂φ∂x+RT∂lnp*∂x=∂φ'∂x+RT'∂lnp*∂x.61415C0C20=RR-T/cp-∂-T/∂lnpC0-φ-T161718Simmons1912C0C0p20C0p21C0C0pφ22DDDAΔ2Tp=AΔ2Tσ-A∂T∂lnσΔ2lnp*+7σ7θdθdt=u∂θ∂x+w∂θ∂z.8xy^zdθdt=u∂θ∂()x^z+^w∂θ∂^z9-1dθdt=u∂θ∂()xz+u∂z∂()x^z∂θ∂[]z+w∂θ∂z-u∂z∂()x^z∂θ∂[]z9-2^zzT-F^w=d^z/dt9-29-19-1dθ/dt89-1^w^w≈w-uZ*x9-1Klemp23metrichx=H/1+x2/a21x^zdk/dtk^zu24H=400ma=1000mr=1.25×103mr=|1+h'3/2/h|Ou=10ms-1u2/r=10-1ms-2u^wσ=p/p*p*xyt①σ^z1Fig.1Schematicdiagramofabell-shapedorography221ChineseJournalofAtmosphericSciences29Vol.29^zσ2.2ησMesinger25step-mountainηη=p-ptps-ptηsηs=prfZs-ptprf0-pt⎧⎨⎩⎪⎪⎪⎪10strf①1982ση①198210ηs=1ηση10p=prfps=prfZsηpΔφpprfΔpφ=Δηφ+RT/pΔηpηΔηφΔpφη·η=0Z=Zsη=ηsη=ηs·ηs=0σηΔφZpηEgger26Genoa27V=028ηNMCNCEP291986ηREMREM29REMAREM30η24σηLaprise31σSchär32T-FT-FZ33.1Δx24Δx/33211No.1JILi-Renetal.ReviewofSomeNumericalAspectsoftheDynamicFrameworkofNWPModel4ΔxPhillips33Orszag3435～37WalshArakawa38～40Lilly4142433.2JFNK44∂u∂t+u∂u∂x=011un+1-unΔt+Aαu*un+1+un2=012Aαu*um=1-αu*mum+1-um-12Δx+α2u*m+1um+1-u*m-1um-12Δx13u*mα=2/3121313u345JFNFJacobian-FreeNewton-Krylov46NewtonFx=014FxNewton14Jxkδkk=-Fxkk=0115Jijxk=∂Fi∂xkjxk+1=xk+δxk1615KrylovGMRESmKrylovδxkm=a0r0+a1Jr0+a2J2r0++amJmr017r0=Jδxk0-Fxk18δxk0Jacobian17KrylovJacobianJacobianJacobianJv≈Fx+#v+Fx#19471917JacobianKrylov15Jxkp-1pδxk=-Fxk20ppreconditionerJ'=Jp-121421ChineseJournalofAtmosphericSciences29Vol.29δx'=pδx.22Krylovδxk0=p-1Fxk231715δx=p-1δx'.24pJFNK3.34849∂F∂t=-~AF25Fn+1i-FniΔt+AFni+εnΔtBFni=026An~AAFF=0Bnεn26εnAnFRossby-Haurwitz50143.4505125un+1-unΔt+An-AnL+AnLun+1+ΔtεnBnun=027AnLA3.3εn=2c11+1-4Δt2c1cﾍ2282725c1c2c3AnAnLBnFnBnun=-ΣJj=1Δtj-11j+1∂j+1un∂tj+1+ε0AnLj∂jun∂t[]j29ε001Δt4r1εn3+Δt2r2εn2+r3εn+r4=0302725r1r2r3AnAnLBnFnpsu2+v2/2pspﾍsu2+pﾍsv2/2pﾍsu=U3.5σpslnps5253ps10500hPa3.6Robort54554～65211No.1JILi-Renetal.ReviewofSomeNumericalAspectsoftheDynamicFrameworkofNWPModelMachenhauer5657∂u∂t+u∂u∂x+g∂h∂x=0∂h∂t+u∂h∂x+h∂u∂x=0{31∂u∂x=1δxddtδxδx31ddtEδx+δx∂∂x12gh2()u=032ddthδx=033E33hn+1jΔx=-h-jδx-j34j-jΔxδx-jΔx333434δx-jhn-1PPMPCM58～61δx-jΣjhn+1jΔx=Σ-j-h-jδx-j=Σjhn-1jΔx3532En+1jΔx=-E-jδx-j-gΔth2uj+12-αj-h2uj-12-αj-136αΔx36ΣjEn+1jΔx=Σ-j-E-jδx-j=ΣjEn-1jΔx3734hn+1jun+1j36un+1j=±2Gj/hn+1j-ghn+1ﾍj38Gj3634uh-jδx-j38343658～606263342070FFTSpectraltransform642080ECMWFGFDL1621ChineseJournalofAtmosphericSciences29Vol.2923HelmholtzΔ21Zpη2Gibbs3pseudo-spectral44Temperton65T1000FFTFLT2080Canuto66Navier-Stokes67SpectralElementMethodsDeville68Gauss-Lobatto-LegendreGLLN+1GLL!N+1=ξ0ξ1ξN1-ξ2L'Nξ=01-ξ2L'Nξ=0ξ∈^Ωξ-1≤ξ≤1L'NξNGLLξk∈!N+1uξNINuξ=ΣNk=0uξkπkξ.Nπkξ=-1NN+11-ξ2L'Nξξ-ξkLNξk0≤k≤Nξ∈^Ω.INuξj=uξj=ΣNk=0uξkπkξj0≤j≤Nξj∈&N+1GLLcollocationGLL∫+1-1fxdx=ΣNk=0’kfξk∀fx∈P2N-1P2N-12N-1GLL’k=2NN+11LNξk20≤k≤Nξk∈&N+1.Galerkin6869(7071717211No.1JILi-Renetal.ReviewofSomeNumericalAspectsoftheDynamicFrameworkofNWPModel1..19522233～47YehTu-Cheng.ImpactoftheTibetanPlateauontheseasonalvariationofthegeneralcirculationoftheatmosphere.ActaMeteorologicaSinicainChinese19522233～472..195728108～121YehTu-ChengLoSzu-WeiChuPao-Chen.ThewindstructureandheatbalanceinthelowertroposphereoverTibetanPlateauanditssurrounding.ActaMeteorologicaSinicainChinese195728108～1213..196434409～423YehTu-ChengLiMai-