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Assimilation de données et analyse de sensibilité. Une application à la circulation océanique

Abstract : This thesis deals with " a posteriori" study of variational data assimilation. It concerns feasibility approach in order to settle tools for diagnostic (qualitative and quantitative) analysis of variational assimilation process, namely about: the influence of data noise on the assimilation process together with its propagation over the retrieved fields (this leads to sensitivity analysis); and the influence of spatial and temporal sampling of the data on the assimilation process. The traditional use of adjoint equations in sensitivity analysis is reviewed in the context of variational data assimilation. By a simple example, we show that sensitivity analysis should be carried out in a different way. We propose a method enabling to derive the sensitivity correctly. This method is based on the use of second order adjoint equations obtained by the adjoint of the optimality system. The sensitivity is deduced from the second order adjoint variables by inverting the Hessian matrix of the cost function through the minimization of a quadratic functional. Application is made on a quasi-geostrophic general circulation ocean model, and we study the existence and uniqueness of the solution of the second order adjoint equations of the model used, in order to justify the use of the Hessian and the applicability of our method. We also study the influence of data sampling on the assimilation process through the Hessian matrix whose eigenvalues vary with the data sampling at the optimum. Finally, we study the predictability of the optimality system.
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Hans Emmanuel Ngodock. Assimilation de données et analyse de sensibilité. Une application à la circulation océanique. Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 1996. Français. ⟨tel-00005006⟩

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