Balance-aware covariance localisation for atmospheric and oceanic ensemble Kalman filters
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Covariance localisation is used in many implementations of the ensemble Kalman filter (EnKF) but has been shown by Lorenc and by Kepert to significantly degrade the main balances in the atmosphere and ocean. Kepert recently introduced an improved form of localisation that reduced or eliminated this problem. This paper presents an extension to that approach, in which the background state is decomposed into balanced and unbalanced parts as part of the localisation. This new balance-aware localisation is shown to be a slight improvement on the earlier work of Kepert and a substantial improvement on the standard Schur-product localisation. Balance-aware localisation also enables the use of some sets of alternative analysis variables that do not work well with conventional localisation in the EnKF. It is shown using identical-twin experiments with a global spectral shallow-water model and no separate initialisation step that analysis to geopotential, streamfunction and velocity potential is slightly more accurate than is analysis to geopotential and the wind components. Analysis to unbalanced (instead of total) geopotential, streamfunction and velocity potential leads to slightly less accurate but significantly better balanced analyses than the other choices of analysis variables. If nonlinear normal modes initialisation is incorporated in the analysis cycling, then the conventional localisation becomes the most accurate method. However, initialisation may be undesirable or unavailable, and the comparison of system performance without localisation is useful since it helps improve understanding of the balance issues in EnKF-based assimilation systems.
KeywordsEnsemble Kalman filter Covariance localisation Balance
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