Skip to Main content Skip to Navigation
Theses

Régularisation de problèmes inverses à l'aide de l'équation de diffusion, avec application à l'assimilation variationnelle de données océaniques

Abstract : Correlation models are required in data assimilation to characterize the error structures of variables defined on a numerical grid. The diffusion equation provides a flexible and efficient framework for representing correlation functions for problems of large dimension such as those encountered in variational atmospheric or ocean data assimilation. In this thesis, an implicit formulation of the diffusion equation is first analyzed in detail for the one-dimensional (1D) case. It is shown that integrating a constant-coefficient implicit diffusion equation over M time steps is equivalent to convolving the initial condition with an M-th order autoregressive (AR) function. The correlation length scale of the AR function and the normalization factor required for generating a unit amplitude are given in terms of the diffusion coefficient and M. Extensions of the diffusion model to allow for correlation functions that are not affected by solid boundaries, and that account for varying length scales are described. An approximation of the normalization factors is then proposed. Products of 1D implicit diffusion operators are then used for constructing two- and three-dimensional correlation models for global configurations of a variational assimilation system for the NEMO ocean model. Their efficiency are compared to the existing explicit diffusion model, and examples of correlation structures are shown, where the length scales are either parametrized or estimated using an ensemble method. Finally, the efficiency of different normalization techniques are compared.
Document type :
Theses
Complete list of metadatas

https://tel.archives-ouvertes.fr/tel-00525590
Contributor : Isabelle Mirouze <>
Submitted on : Tuesday, October 12, 2010 - 11:28:42 AM
Last modification on : Thursday, March 5, 2020 - 5:57:09 PM
Long-term archiving on: : Friday, December 2, 2016 - 8:41:52 AM

Identifiers

  • HAL Id : tel-00525590, version 1

Citation

Isabelle Mirouze. Régularisation de problèmes inverses à l'aide de l'équation de diffusion, avec application à l'assimilation variationnelle de données océaniques. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2010. Français. ⟨tel-00525590⟩

Share

Metrics

Record views

476

Files downloads

596