Didier Auroux Jacques Blum

U-Auroux-D810\Didier Auroux, S-1-5-21-172797399-3483302530-1805387423-1005

Description

Didier Auroux, Jacques Blum Laboratoire MIP - Institut de Mathematiques de Toulouse Universite Paul Sabatier Toulouse 3 France The Back and Forth Nudging (BFN) algorithm Laboratoire J.A. Dieudonne, Universite de Nice 19 Octobre 2006

• dx˜ dt


• bfn algorithm


• backward model


• observation operator


• xobs ?


• ups-tlse


• universite de nice


• forward nudging

Sujets

• Sabatier
• Institut de Mathématiques de Toulouse
• Auroux
• Inverse problem
• Universidad de Niza Sophia Antipolis

Informations

• Publié par: pefav
• Publié le: 01 octobre 2006
• Nombre de lectures: 59

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