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In this thesis, we propose a class of methods to represent spatial observation error correlations numerically in variational data assimilation. Based on the existing link between solutions of the time-implicit diffusion equation and Matérn correlation functions, we design correlation operators and inverse correlation operators that are appropriate for large datasets. Discretizing the diffusion equation with the finite element method allows us to account for data that do not necessarily lie on a structured mesh, as is the case with satellite observations assimilated in meteorology. Experiments are carried out using data from the infrared imager Seviri, the images of which are known for containing strong horizontal correlations. We show that the quality of our correlation model may depend locally on the spatial distribution of the observations. Nevertheless, by introducing an auxiliary mesh to perform the finite element computations, we can control this dependency to a large extent. Improving the accuracy of the method this way comes at the expense of making the inverse correlation operator more complicated. Finally, strategies for efficiently modelling the inverse of the correlation operator are proposed.

Jury :

Anthony Weaver           (Cerfacs)                                      Advisor
Michel Yann                  (Météo-France)                            Co Advisor
Marcin Chrust               (ECMWF, UK)                              Examiner
Selime Gürol                (Cerfacs)                                      Examiner
Serge Gratton              (INPT-IRIT)                                   Examiner
Marc Bocquet              (Ecole des Ponts Paris Tech)       Rapporteur
Emmanuel Cosme       (Université Grenoble Alpes)        Rapporteur
Arthur Vidard               (INRIA)                                         Rapporteur
Xavier Vasseur            (ISAE-Supaero)                           Invited member