Adaptive covariance inflation in the ensemble Kalman filter by Gaussian scale mixtures

TL;DR

This paper introduces a hybrid adaptive inflation method for the ensemble Kalman filter that combines Gaussian scale mixtures with the EnKF-N, improving accuracy in complex, nonlinear, and imperfectly modeled systems.

Contribution

It develops a novel hybrid adaptive inflation technique by integrating Gaussian scale mixtures with the EnKF-N, enhancing filter performance in realistic scenarios.

Findings

Hybrid method improves accuracy over existing adaptive inflation techniques.

Systematic accuracy gains demonstrated on Lorenz models.

Adaptive inflation effectively addresses sampling and model errors.

Abstract

This paper studies multiplicative inflation: the complementary scaling of the state covariance in the ensemble Kalman filter (EnKF). Firstly, error sources in the EnKF are catalogued and discussed in relation to inflation; nonlinearity is given particular attention as a source of sampling error. In response, the "finite-size" refinement known as the EnKF-N is re-derived via a Gaussian scale mixture, again demonstrating how it yields adaptive inflation. Existing methods for adaptive inflation estimation are reviewed, and several insights are gained from a comparative analysis. One such adaptive inflation method is selected to complement the EnKF-N to make a hybrid that is suitable for contexts where model error is present and imperfectly parameterized. Benchmarks are obtained from experiments with the two-scale Lorenz model and its slow-scale truncation. The proposed hybrid EnKF-N method of adaptive inflation is found to yield systematic accuracy improvements in comparison with the existing methods, albeit to a moderate degree.