Analysis Scheme in the Ensemble Kalman Filter

TitleAnalysis Scheme in the Ensemble Kalman Filter
Publication TypeJournal Article
Year of Publication1998
AuthorsBurgers, G, van Leeuwen, PJ, Evensen, G
JournalMonthly Weather Review
Number of Pages1719-1724
Date Published06/1988
PublisherAmerican Meteorological Society

This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter. It is shown that the observations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the observations and generate an ensemble of observations that then is used in updating the ensemble of model states. Traditionally, this has not been done in previous applications of the ensemble Kalman filter and, as will be shown, this has resulted in an updated ensemble with a variance that is too low.
This simple modification of the analysis scheme results in a completely consistent approach if the covariance of the ensemble of model states is interpreted as the prediction error covariance, and there are no further requirements on the ensemble Kalman filter method, except for the use of an ensemble of sufficient size. Thus, there is a unique correspondence between the error statistics from the ensemble Kalman filter and the standard Kalman filter approach.

Refereed DesignationUnknown
Author Address


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