Controlling Overestimation of Error Covariance in Ensemble Kalman Filters with Sparse Observations: A Variance-Limiting Kalman Filter

Georg A. Gottwald School of Mathematics and Statistics, University of Sydney, Sydney, Australia

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Lewis Mitchell School of Mathematics and Statistics, University of Sydney, Sydney, Australia

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Sebastian Reich Universität Potsdam, Institut für Mathematik, Potsdam, Germany

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Abstract

The problem of an ensemble Kalman filter when only partial observations are available is considered. In particular, the situation is investigated where the observational space consists of variables that are directly observable with known observational error, and of variables of which only their climatic variance and mean are given. To limit the variance of the latter poorly resolved variables a variance-limiting Kalman filter (VLKF) is derived in a variational setting. The VLKF for a simple linear toy model is analyzed and its range of optimal performance is determined. The VLKF is explored in an ensemble transform setting for the Lorenz-96 system, and it is shown that incorporating the information of the variance of some unobservable variables can improve the skill and also increase the stability of the data assimilation procedure.

Corresponding author address: Georg A. Gottwald, School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia. E-mail: georg.gottwald@sydney.edu.au

Abstract

The problem of an ensemble Kalman filter when only partial observations are available is considered. In particular, the situation is investigated where the observational space consists of variables that are directly observable with known observational error, and of variables of which only their climatic variance and mean are given. To limit the variance of the latter poorly resolved variables a variance-limiting Kalman filter (VLKF) is derived in a variational setting. The VLKF for a simple linear toy model is analyzed and its range of optimal performance is determined. The VLKF is explored in an ensemble transform setting for the Lorenz-96 system, and it is shown that incorporating the information of the variance of some unobservable variables can improve the skill and also increase the stability of the data assimilation procedure.

Corresponding author address: Georg A. Gottwald, School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia. E-mail: georg.gottwald@sydney.edu.au
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