University of Nice Sophia Antipolis

Didier Auroux

Description

Niveau: Secondaire
Didier Auroux University of Nice Sophia Antipolis Work in collaboration with : J. Blum (U. Nice) + work of E. Cosme (U. Grenoble) Back and Forth Nudging or SEEK (BFN, BF-SEEK) INSU-CNRS LEFE-ASSIM BFN/BFN2, Villefranche-sur-Mer, France. September 29, 2009

• lefe


• dx dt


• assim


• bfn


• optimal determination


• backward model


• stauffer-seaman


• xobs ?h


• nudging coeffcients


• forward nudging

Sujets

• Antipolis
• Auroux

Informations

• Publié par: profil-shien-2012
• Nombre de lectures: 52
• Langue: English

Extrait

DidierAuroux UniversityofNiceSophiaAntipolis [e-mail] Workincollaborationwith:J.Blum(U.Nice)+workofE.Cosme(U.Grenoble) INSU-CNRSLEFE-ASSIMBFN/BFN2, Villefranche-sur-Mer,France. BackandForthNudgingorSEEK (BFN,BF-SEEK) September29,2009

td = Forwardnudging F ( X )+ K ( X bos − Xd      X (0)= 0 where K isthenudging(orgain)matrix. X, H ( X )) , 0 <t<T, Inthelinearcase(where F isamatrix),theforwardnudgingiscalled Luenbergerorasymptoticobserver. –Meteorology:Hoke-Anthes(1976) –Oceanography(QGmodel):Verron-Holland(1989) –Atmosphere(meso-scale):Stauffer-Seaman(1990) –Optimaldeterminationofthenudgingcoeffcients: Zou-Navon-LeDimet(1992),Stauffer-Bao(1993), Vidard-LeDimet-Piacentini(2003) LEFE/ASSIM2009,Villefranche-sur-Mer,September29200931/1

Forwardnudging:linearcase Luenbergerobserver,orasymptoticobserver (Luenberger,1966)    d d X t = FX + K ( X obs − HX ) ,   dX ˆ = FX ˆ ,X obs = HX ˆ . td d d t ( X − X ˆ )=( F − KH )( X − X ˆ ) If F − KH isaHurwitzmatrix,i.e.itsspectrumisstrictlyincludedinthe half-plane{ λ ∈ C ; Re ( λ ) < 0},then X → X ˆ when t →+∞. LEFE/ASSIM2009,Villefranche-sur-Mer,September29200931/2

Backwardnudging Howtorecovertheinitialstatefromthefinalsolution? Backwardmodel:    dX ˜ = F ( X ˜ ) ,T>t> 0 , td   X ˜ ( T )= X ˜ T . Ifweapplynudgingtothisbackwardmodel: td = F ( ˜ X )−    dX ˜   X ˜ ( T )= X ˜ T . K ( X bos − LEFE/ASSIM2009,Villefranche-sur-Mer,September292009 H ˜ X ) ,T>t> 0 , /331