Ocean Dynamics

, Volume 53, Issue 4, pp 343–367 | Cite as

The Ensemble Kalman Filter: theoretical formulation and practical implementation

  • Geir EvensenEmail author


The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.


Data assimilation Ensemble Kalman Filter 


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I would like to express my thanks and gratitude to co-workers at the Nansen Center and elsewhere for providing valuable inputs and stimulating discussions during the work with this paper. In particular I would like to thank L. Bertino, K. A. Lister, Y. Morel, L. J. Natvik, D. Obaton, and H. Sagen, who have helped implementing and testing the new algorithms, checked derivations and contributed to making this paper readable and hopefully useful for the community developing ensemble methods for data assimilation. I am also grateful for comments by two anonymous reviewers, which helped me to improve the consistency of the paper. This work was supported by the EC FP–5 projects TOPAZ (EVK3-CT2000-00032) and ENACT (EVK2-CT-2001-00117), and has received support from The Research Council of Norway (Programme for Supercomputing) through a grant of computing time.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Nansen Environmental and Remote Sensing CenterBergen Norway Edvard GriegsveiSolheimsvikenNorway

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