Assimilation variationnelle de données pour des modèles emboîtés

Ehouarn Simon 1
1 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : Nested models are commonly used in meteorology and oceanography. Such systems allow a local increase of the mesh resolution in areas where it seems to be necessary, by running the same model on a hierarchy of grids. In the cas of one-way interaction, coarse grid solution provides (by interpolation) boundary conditions for the high resolution grid. In the case of two-way interaction, a feedback from the fine grid to the coarse grid is added. However, the problem of variational data assimilation in such systems has not, or not very, been studied. These classes of methods, notably the 4D-Var algorithm, allow improvements of the solution of the model, up to here monogrid, by minimizing a cost function mesuring the gap of this model and the observations. The aim of this work is to formulate a variational assimilation algorithm locally multigrids. For the generic case of a local high resolution grid embedded within a coarser resolution one, we derive the adjoint system in the two cases of one-way and two-way interactions. It is shown that the adjoint formulation adds new interactions between the grids, in the opposite sense of the interactions existing in the direct formulation. Furthermore, we propose several variants of these algorithms that realize a weak coupling between the solutions of the two grids by adding design variables on the intergrids transfers. We show the application of a multigrid method, the Full Approximation Scheme, to the variational data assimilation. This approach allows to obtain a multigrid assimilation algorithm potentially efficient. These formulations are illustrated and discussed in the test case experiment of a 2D shallow water model. We observe a real improvement of the RMS error of the nested solution and an acceleration of the convergence of these algorithms.
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https://tel.archives-ouvertes.fr/tel-00194593
Contributor : Ehouarn Simon <>
Submitted on : Thursday, December 6, 2007 - 5:37:23 PM
Last modification on : Wednesday, April 11, 2018 - 1:58:06 AM
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Ehouarn Simon. Assimilation variationnelle de données pour des modèles emboîtés. Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 2007. Français. ⟨tel-00194593⟩

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