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Original Research Papers

A hybrid approach to estimating error covariances in variational data assimilation

Authors:

Haiyan Cheng,

Computational Science Laboratory, Department of Computer Science, Virginia Polytechnic Institute and State University, 2202 Kraft Drive, Blacksburg, VA 24060, US
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Mohamed Jardak,

Computational Science Laboratory, Department of Computer Science, Virginia Polytechnic Institute and State University, 2202 Kraft Drive, Blacksburg, VA 24060, US
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Mihai Alexe,

Computational Science Laboratory, Department of Computer Science, Virginia Polytechnic Institute and State University, 2202 Kraft Drive, Blacksburg, VA 24060, US
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Adrian Sandu

Computational Science Laboratory, Department of Computer Science, Virginia Polytechnic Institute and State University, 2202 Kraft Drive, Blacksburg, VA 24060, US
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Abstract

Data assimilation (DA) involves the combination of observational data with the underlying dynamical principles governing the system under observation. In this work we combine the advantages of the two prominent DA systems: the 4D-Var and the ensemble methods. The hybrid method described in this paper consists of identifying the subspace spanned by the major 4D-Var error reduction directions. These directions are then removed from the background covariance through a Galerkin-type projection, and are replaced by estimates of the analysis error obtained through a low-rank Hessian inverse approximation. The updated error covariance in one window can be used as the background covariance for the next window thus better capturing the ‘error of the day’. The numerical results for a non-linear model demonstrate how the hybrid method leads to a good estimate of the true error covariance, and improves the 4D-Var analysis results.

How to Cite: Cheng, H., Jardak, M., Alexe, M. and Sandu, A., 2010. A hybrid approach to estimating error covariances in variational data assimilation. Tellus A: Dynamic Meteorology and Oceanography, 62(3), pp.288–297. DOI: http://doi.org/10.1111/j.1600-0870.2009.00442.x
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  Published on 01 Jan 2010
 Accepted on 2 Mar 2010            Submitted on 2 Apr 2009

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