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| Titel |
Optimal solution error covariance in highly nonlinear problems of variational data assimilation |
| VerfasserIn |
V. Shutyaev, I. Gejadze, G. J. M. Copeland, F.-X. Dimet |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 19, no. 2 ; Nr. 19, no. 2 (2012-03-16), S.177-184 |
| Datensatznummer |
250014186
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| Publikation (Nr.) |
 copernicus.org/npg-19-177-2012.pdf |
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| Zusammenfassung |
| The problem of variational data assimilation (DA) for a nonlinear evolution model is formulated as
an optimal control problem to find the initial condition, boundary conditions and/or model
parameters. The input data contain observation and background errors, hence there is an error in
the optimal solution. For mildly nonlinear dynamics, the covariance matrix of the optimal solution
error can be approximated by the inverse Hessian of the cost function. For problems with strongly
nonlinear dynamics, a new statistical method based on the computation of a sample of inverse
Hessians is suggested. This method relies on the efficient computation of the inverse Hessian by
means of iterative methods (Lanczos and quasi-Newton BFGS) with preconditioning. Numerical
examples are presented for the model governed by the Burgers equation with a nonlinear viscous
term. |
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