On model error in variational data assimilation

Victor Shutyaev 1 Arthur Vidard 2 François-Xavier Le Dimet 2 Igor Gejadze 3
1 INM-RAS - Institute of Numerical Mathematics [Moscou]
2 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Inria Grenoble - Rhône-Alpes
3 IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture
Abstract : The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition. The optimal solution (analysis) error arises due to the errors in the input data (background and observation errors). Under the Gaussian assumption the optimal solution error covariance can be constructed using the Hessian of the auxiliary data assimilation problem. The aim of this paper is to study the evolution of model errors via data assimilation. The optimal solution error covariances are derived in the case of imperfect model and for the weak constraint formulation, when the model euations determine the cost functional.
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Victor Shutyaev, Arthur Vidard, François-Xavier Le Dimet, Igor Gejadze. On model error in variational data assimilation. Russian Journal of Numerical Analysis and Mathematical Modelling, De Gruyter, 2016, 31 (2), pp.105-113. ⟨10.1515/rnam-2016-0011⟩. ⟨hal-01309018⟩

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