A structurally localized ensemble Kalman filtering approach

Abstract State‐of‐the‐art ensemble Kalman filtering (EnKF) algorithms require incorporation of localization techniques to cope with rank deficiency and inherited spurious correlations in their error covariance matrices. Localization techniques are mostly ad hoc, based on some distances between the state and observation variables and requiring demanding manual tuning. This work introduces a new ensemble filtering approach, which is inherently localized, avoiding the need for any auxiliary localization technique. Instead of applying localization to ensembles explicitly, the idea is first to localize the continuous analysis probability density function (pdf) before ensemble sampling. The localization of the analysis pdf is performed through an approximation by a product of independent marginal pdfs corresponding to small partitions of the state vector, using variational Bayesian optimization. These marginals are then sampled following stochastic EnKF and deterministic ensemble transform Kalman filtering (ETKF) procedures, using ensembles larger than the partition size. The resulting filters involve the same forecast steps as their standard EnKF and ETKF counterparts, but different analysis steps, adjusting the EnKF and ETKF updates of each partition iteratively based on the ensemble means of the other partitions. Numerical experiments are conducted with the Lorenz‐96 model under different scenarios to demonstrate the potential of the proposed filters. The performance of the new filters is comparable with that of the EnKF and ETKF with already tuned localization, in terms of both computational burden and estimation accuracy.