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Reduced-space inverse Hessian for analysis error covariances in variational data assimilation

Victor P. Shutyaev 1 François-Xavier Le Dimet 2 Igor Yu. Gejadze 3
2 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function (analysis). The equation for the analysis error is derived through the errors of the input data (background and observation errors). This equation is considered in a reduced control space to show that the analysis error covariance operator can be approximated by the inverse Hessian of an auxiliary data assimilation problem based on the tangent linear model constraints. The reduced-space Hessian is constructed in the explicit form, which allows an efficient computation of the analysis error covariance operator.
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Submitted on : Monday, February 11, 2013 - 5:11:28 PM
Last modification on : Tuesday, October 19, 2021 - 11:12:58 PM

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Victor P. Shutyaev, François-Xavier Le Dimet, Igor Yu. Gejadze. Reduced-space inverse Hessian for analysis error covariances in variational data assimilation. Russian Journal of Numerical Analysis and Mathematical Modelling, De Gruyter, 2010, 25 (2), pp.169-185. ⟨10.1515/rjnamm.2010.011⟩. ⟨hal-00787295⟩

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