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| Titel |
Posterior covariance versus analysis error covariance in variational data assimilation |
| VerfasserIn |
Victor Shutyaev, Igor Gejadze, François-Xavier Le Dimet |
| Konferenz |
EGU General Assembly 2013
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 15 (2013) |
| Datensatznummer |
250073049
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| Zusammenfassung |
| 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) [1]. The data contain errors (observation and background errors), hence there is an error in the analysis. For mildly nonlinear dynamics, the analysis error covariance can be approximated by the inverse Hessian of the cost functional in the auxiliary data assimilation problem [2], whereas for stronger nonlinearity - by the 'effective' inverse Hessian [3, 4]. However, it has been noticed that the analysis error covariance is not the posterior covariance from the Bayesian perspective. While these two are equivalent in the linear case, the difference may become significant in practical terms with the nonlinearity level rising. For the proper Bayesian posterior covariance a new approximation via the Hessian of the original cost functional is derived and its 'effective' counterpart is introduced. An approach for computing the mentioned estimates in the matrix-free environment using Lanczos method with preconditioning is suggested. Numerical examples which validate the developed theory are presented for the model governed by the Burgers equation with a nonlinear viscous term.
The authors acknowledge the funding through the Natural Environment Research Council (NERC grant NE/J018201/1), the Russian Foundation for Basic Research (project 12-01-00322), the Ministry of Education and Science of Russia, the MOISE project (CNRS, INRIA, UJF, INPG) and Région Rhône-Alpes.
References:
1. Le Dimet F.X., Talagrand O. Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus, 1986, v.38A, pp.97-110.
2. Gejadze I., Le Dimet F.-X., Shutyaev V. On analysis error covariances in variational data assimilation. SIAM J. Sci. Computing, 2008, v.30, no.4, pp.184-1874.
3. Gejadze I.Yu., Copeland G.J.M., Le Dimet F.-X., Shutyaev V. Computation of the analysis error covariance in variational data assimilation problems with nonlinear dynamics. J. Comp. Phys., 2011, v.230, pp.7923-7943.
4. Shutyaev V., Gejadze I., Copeland G.J.M., Le Dimet F.-X. Optimal solution error covariance in highly nonlinear problems of variational data assimilation. Nonlin. Processes Geophys., 2012, v.19, pp.177-184. |
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