SEIK - the unknown ensemble Kalman filter

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Nerger, L. , Janjic Pfander, T. , Hiller, W. and Schröter, J. (2009): SEIK - the unknown ensemble Kalman filter , 5th WMO Symposium on Data Assimilation, Melbourne, Australia, October 5 - 9 .
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The SEIK filter (Singular "Evolutive" Interpolated Kalman filter) hasbeen introduced in 1998 by D.T. Pham as a variant of the SEEK filter,which is a reduced-rank approximation of the Extended KalmanFilter. In recent years, it has been shown that the SEIK filter isan ensemble-based Kalman filter that uses a factorization rather thansquare-root of the state error covariance matrix. Unfortunately, theexistence of the SEIK filter as an ensemble-based Kalman filter withsimilar efficiency as the later introduced ensemble square-root Kalmanfilters, appears to be widely unknown and the SEIK filter is omittedin reviews about ensemble-based Kalman filters. To raise the attentionabout the SEIK filter as a very efficient ensemble-based Kalmanfilter, we review the filter algorithm and compare it with ensemblesquare-root Kalman filter algorithms. For a practical comparison theSEIK filter and the Ensemble Transformation Kalman filter (ETKF) areapplied in twin experiments assimilating sea level anomaly data intothe finite-element ocean model FEOM.

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