On optimal solution error covariances in variational data assimilation problems

Igor Yu. Gejadze 1 François-Xavier Le Dimet 2 Victor P. Shutyaev 3
1 University of Strathclyde
2 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
3 INM-RAS - Institute of Numerical Mathematics [Moscou]
Abstract : The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find unknown parameters such as distributed model coefficients or boundary conditions. The equation for the optimal solution error is derived through the errors of the input data (background and observation errors), and the optimal solution error covariance operator through the input data error covariance operators, respectively. The quasi-Newton BFGS algorithm is adapted to construct the covariance matrix of the optimal solution error using the inverse Hessian of an auxiliary data assimilation problem based on the tangent linear model constraints. Preconditioning is applied to reduce the number of iterations required by the BFGS algorithm to build a quasi-Newton approximation of the inverse Hessian. Numerical examples are presented for the one-dimensional convection-diffusion model.
keyword : Variational data assimilation Parameter estimation Optimal solution error covariances Hessian preconditioning
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Journal articles
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https://hal.inria.fr/hal-00787292
Contributor : Eric Blayo <>
Submitted on : Monday, February 11, 2013 - 5:07:21 PM
Last modification on : Wednesday, April 11, 2018 - 1:58:44 AM

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Igor Yu. Gejadze, François-Xavier Le Dimet, Victor P. Shutyaev. On optimal solution error covariances in variational data assimilation problems. Journal of Computational Physics, Elsevier, 2010, 229 (6), pp.2159-2178. ⟨10.1016/j.jcp.2009.11.028⟩. ⟨hal-00787292⟩

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