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Optimal solution error quantification in variational data assimilation involving imperfect models

Victor Shutyaev 1 Igor Gejadze 2 Arthur Vidard 3 Francois-Xavier Le Dimet 3
3 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Inria Grenoble - Rhône-Alpes, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, UGA [2016-2019] - Université Grenoble Alpes [2016-2019], LJK - Laboratoire Jean Kuntzmann
Abstract : The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition. If the model is ‘perfect,’ the optimal solution (analysis) error rises because of the presence of the input data errors (background and observation errors). Then, this error is quantified by the covariance matrix, which can be approximated by the inverse Hessian of an auxiliary control problem. If the model is not perfect, the optimal solution error includes an additional component because of the presence of the model error. In this paper, we study the influence of the model error on the optimal solution error covariance, considering strong and weak constraint data assimilation approaches. For the latter, an additional equation describing the model error dynamics is involved. Numerical experiments for the 1D Burgers equation illustrate the presented theory.
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Victor Shutyaev, Igor Gejadze, Arthur Vidard, Francois-Xavier Le Dimet. Optimal solution error quantification in variational data assimilation involving imperfect models. International Journal for Numerical Methods in Fluids, Wiley, 2017, 83 (3), pp.276-290. ⟨10.1002/fld.4266⟩. ⟨hal-01411666⟩



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