Didier Auroux Institut de Mathematiques de Toulouse Projet MOISE

Didier Auroux

Description

Niveau: Secondaire
Didier Auroux Institut de Mathematiques de Toulouse Projet MOISE Universite Paul Sabatier Toulouse 3 INRIA Rhone-Alpes Quelques resultats numeriques sur l'algorithme BFN Projet LEFE Assimilation de donnees BFN, 15 Juin 2007 INRIA Sophia-Antipolis.

• nudging direct


• rhone-alpes auroux


• resultats numeriques sur burgers


• assimilation de donnees bfn


• stauffer-seaman


• reunion lefe


• forward nudging

Sujets

• Sabatier
• Auroux

Informations

• Publié par: profil-shien-2012
• Publié le: 01 juin 2007
• Nombre de lectures: 107

Extrait

Didier Auroux University of Nice Sophia Antipolis [e-mail]

Work in collaboration with : J. Blum (U. Nice) + work of E. Cosme (U. Grenoble)

INSU-CNRS LEFE-ASSIM BFN/BFN2, Villefranche-sur-Mer, France.

Back and Forth Nudging or SEEK

(BFN, BF-SEEK)

September 29, 2009

Forward nudging      X dX d ( t 0 = )=X F( 0 X  )+K(X obs −H(X))0 < t < T

whereKis the nudging (or gain) matrix.

In the linear case (whereFis a matrix), the forward nudging Luenbergeror asymptotic observer.

– Meteorology : Hoke-Anthes (1976)

– Oceanography (QG model) : Verron-Holland (1989)

– Atmosphere (meso-scale) : Stauffer-Seaman (1990)

– Optimal determination of the nudging coeffcients : Zou-Navon-Le Dimet (1992), Stauffer-Bao (1993), Vidard-Le Dimet-Piacentini (2003)

LEFE/ASSIM 2009, Villefranche-sur-Mer, September 29 2009

is

called

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oFwrradungdnig:ilen

Luenberger observer, or asymptotic observer (Luenberger, 1966)

ar

 Xd td =F X+K(X obs −H X)     dX =F XX obs =H X ˆ ˆˆ dt

d (X−X = ( ˆ ) F−KH)(X−X ˆ ) dt

acse

IfF−KHis a Hurwitz matrix, i.e. its spectrum is strictly included in the ˆ half-plane{λ∈C;Re(λ)<0}, thenX→Xwhent→+∞.

LEFE/ASSIM 2009, Villefranche-sur-Mer, September 29 2009

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Backward nudging

How to recover the initial state from the final solution ?

Backward model :

˜   d ˜    d X X(T t )= =F( X X T )>t>T  0 ˜ ˜

If we apply nudging to this backward model : ˜   dX =F(X ˜ )−K(X obs −H X) > t > T0 ˜    X d ( t T) =X T  ˜ ˜

LEFE/ASSIM 2009, Villefranche-sur-Mer, September 29 2009

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