数值天气预报Ch5 (3).ppt

Kalmanfilter(KF)isalinear,recursiveestimatorthatproducestheminimumvarianceestimateinaleastsquaresense.1794Gaussinventedleast-squaresmethodforastronomicalestimation1941KalmogorovandWienerindependentlydevelopedlinearminimummean-squareestimation(aprobablisticversionofleast-square)1955J.W.Follinsuggestedarecursiveapproach1960Kalmanpublisheddiscrete-timerecursivemean-squarefilteringKalmanfilter：ArecursiveBLUEHowdidKFcomeout?*Recursive?AformthatallowsstorageofonlymostrecentobservationsandstateofsystemAsimplescalarexampleofwhatwemean:Consideranestimatethatconsistsofkpreviousobservationsyi:Whenanewobservationyk+1arrives,

theestimatebecomes:Hence,itcanbeputintotherecursiveform:Therecursiverelationshipcanbealsoexpressed

inthefollowingform,whichisthebasicform

oftheKalmanfilter:KF:Derivation由无偏估计分析值假定为：KF:DerivationKalmangain***Monotonic单调的Theweightscanbedefinedindifferentways.Cressman(1959)definedtheweightsinSCMasRnSCM:权重函数rikSCM:影响半径影响半径，随迭代次数减小，分析场在多次迭代后收敛到较小尺度。(1980s,theSwedishoperationalsystem)ForupperairanalysisR1=1500km,R2=900kmForsurfacepressureanalysisR1=1500km,R2=1200km,R3=750km,R4=300km.Strength:-simpleandeconomical-providesreasonableanalyses.SCM:StrengthandweaknessWeakness:-Nodirectwaytospecifyoptimumweight-high-qualitybackgroundcouldbereplacedbypoorobs-NophysicalconstraintsandsmoothingeffectNudging

(HokeandAnthes1976,Kistler1974)Anotherempiricalandfairlywidelyusedmethod“Nudge”----topushgentlyPerformedinmodelspaceObsisinterpolatedtogridpointAddingtotheprognosticequationsatermthatnudgestowardstheobservationsExampleofnudginginaprimitivemodelrelaxationtimescale,ischosenbasedonempiricalconsiderationsandmaydependonthevariab