Open AccessSampling Errors in Ensemble Kalman Filtering. Part I: Theory
Author(s) -
William Sacher,
Peter Bartello
Publication year - 2008
Publication title -
monthly weather review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.862
H-Index - 179
eISSN - 1520-0493
pISSN - 0027-0644
DOI - 10.1175/2007mwr2323.1
Subject(s) - ensemble kalman filter , kalman filter , covariance , covariance matrix , fast kalman filter , covariance intersection , computer science , context (archaeology) , mathematics , invariant extended kalman filter , extended kalman filter , statistics , algorithm , paleontology , biology
This paper discusses the quality of the analysis given by the ensemble Kalman filter in a perfect model context when ensemble sizes are limited. The overall goal is to improve the theoretical understanding of the problem of systematic errors in the analysis variance due to the limited size of the ensemble, as well as the potential of the so-called double-ensemble Kalman filter, covariance inflation, and randomly perturbed analysis techniques to produce a stable analysis—that is to say, one not subject to filter divergence. This is achieved by expressing the error of the ensemble mean and the analysis error covariance matrix in terms of the sampling noise in the background error covariance matrix (owing to the finite ensemble estimation) and by comparing these errors for all methods. Theoretical predictions are confirmed with a simple scalar test case. In light of the analytical results obtained, the expression of the optimal covariance inflation factor is proposed in terms of the limited ensemble size and the Kalman gain.