A Structurally Localized Ensemble Kalman Filtering Approach

TL;DR

This paper introduces a new ensemble Kalman filtering method that is inherently localized by approximating the analysis pdf with independent marginals, eliminating the need for manual localization tuning.

Contribution

The proposed approach localizes the analysis pdf through variational Bayesian optimization, avoiding ad-hoc localization techniques and simplifying the filtering process.

Findings

Performance comparable to traditional localized EnKF and ETKF

Reduces manual tuning of localization parameters

Maintains accuracy with similar computational cost

Abstract

State-of-the-art ensemble Kalman filtering (EnKF) algorithms require incorporating localization techniques to cope with the rank deficiency and the inherited spurious correlations in their error covariance matrices. Localization techniques are mostly ad-hoc, based on some distances between the state and observation variables, 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 explicitly applying localization on ensembles, the idea is to first 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 the variational Bayesian optimization. These marginals are then sampled following stochastic EnKF and deterministic ensemble transform Kalman filtering (ETKF) procedures, using ensembles larger than the partitions' size. The resulting filters involve the same forecast steps as their standard EnKF and ETKF counterparts but different analysis steps, iteratively adjusting the EnKF and ETKF updates of each partition 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 new filters' performances are comparable to those of the EnKF and ETKF with already tuned localization, both in terms of computational burden and estimation accuracy.