An Efficient Implementation of the Ensemble Kalman Filter Based on an Iterative Sherman-Morrison Formula
This work provides a faster implementation of the EnKF for practitioners in geosciences and data assimilation, though it is an incremental improvement over existing methods.
The authors present an efficient implementation of the Ensemble Kalman Filter using an iterative Sherman-Morrison formula, achieving computational speed comparable to or better than existing methods while maintaining similar accuracy, as demonstrated on Lorenz 96 and quasi-geostrophic models.
We present a practical implementation of the ensemble Kalman (EnKF) filter based on an iterative Sherman-Morrison formula. The new direct method exploits the special structure of the ensemble-estimated error covariance matrices in order to efficiently solve the linear systems involved in the analysis step of the EnKF. The computational complexity of the proposed implementation is equivalent to that of the best EnKF implementations available in the literature when the number of observations is much larger than the number of ensemble members. Even when this conditions is not fulfilled, the proposed method is expected to perform well since it does not employ matrix decompositions. Computational experiments using the Lorenz 96 and the oceanic quasi-geostrophic models are performed in order to compare the proposed algorithm with EnKF implementations that use matrix decompositions. In terms of accuracy, the results of all implementations are similar. The proposed method is considerably faster than other EnKF variants, even when the number of observations is large relative to the number of ensemble members.