Generalization of the dual variational data assimilation algorithm to a nonlinear layered quasi-geostrophic ocean model

Didier Auroux 1
1 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : In this paper, we present a generalization to nonlinear models of the fourdimensional variational dual method, the 4D-PSAS algorithm. The idea of 4D-PSAS (physical space analysis system) is to perform the minimization in the space of the observations, rather than in themodel space as in the primal 4DVAR scheme. Despite the formal equivalence between 4D-VAR and 4D-PSAS in a linear situation (both for model equations and observation operators), the dual method has several important advantages: in oceanographic cases, the observation space is smaller than the model space, which should improve theminimization process; for no additional cost, it provides an estimation of the model error; and finally, it does not have any singularities when the covariance errormatrices tend to zero. The idea of this paper is to extend this algorithm to a fully nonlinear situation, as has been done in previous years with other classical data assimilation schemes: the 4D-VARand theKalman filter. For this purpose, we consider a nonlinear multi-layer quasi-geostrophic ocean model, which mimics quite well the mid-latitude circulation.
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Didier Auroux. Generalization of the dual variational data assimilation algorithm to a nonlinear layered quasi-geostrophic ocean model. Inverse Problems, IOP Publishing, 2007, 23, pp.2485-2503. ⟨10.1088/0266-5611/23/6/013⟩. ⟨inria-00189641⟩

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