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On optimal solution error covariances in variational data assimilation problems

Gejadze, I.Y. and Le Dimet, F.X. and Shutyaev, V. and (Funder), Scottish Founding Council via GRPE (2010) On optimal solution error covariances in variational data assimilation problems. Journal of Computational Physics, 229 (6). pp. 2159-2178. ISSN 0021-9991

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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.

Item type: Article
ID code: 16315
Keywords: variational data assimilation, parameter estimation, optimal solution error covariances, hessian, preconditioning, mathematics, Engineering (General). Civil engineering (General), Physics and Astronomy (miscellaneous), Computer Science Applications
Subjects: Technology > Engineering (General). Civil engineering (General)
Department: Faculty of Engineering > Civil and Environmental Engineering
Depositing user: Dr Igor Gejadze
Date Deposited: 09 Feb 2010 17:06
Last modified: 23 Jul 2015 21:21

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