Modélisation mathématique et assimilation de données lagrangiennes pour l'océanographie

Abstract : In this work we consider modelling and Data Assimilation problems in oceanography through both theoretical and numerical analysis. In the first part we study linear Primitive Equations of the ocean and we establish new regularity results, thanks to an explicit calculation of the pressure term. In the second part we study variational assimilation of Lagrangian data into an ocean model. Data Assimilation covers all methods which allow to blend optimally all sources of information about a physical system (observations and model equations) in order to obtain forecasts of its evolution. We use a variational method to assimilate Lagrangian data, namely positions of drifting floats. We first establish new a priori estimations, in order to study the associated optimal control problem. We then describe the implementation of the variational method into a realistic Primitive Equations ocean circulation model. Finally we perform many numerical experiments, particularly sensitivity studies, which show that Lagrangian Data Assimilation is technically feasible and relevant from the oceanographic point of view.
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Mathématiques [math]. Université Nice Sophia Antipolis, 2005. Français
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Maëlle Nodet. Modélisation mathématique et assimilation de données lagrangiennes pour l'océanographie. Mathématiques [math]. Université Nice Sophia Antipolis, 2005. Français. 〈tel-00011159〉

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