Ensemble Kalman filtering with residual nudging

TL;DR

This paper introduces residual nudging to the ensemble Kalman filter, which adjusts estimates based on residual norms to improve accuracy and stability, especially in small ensemble scenarios.

Contribution

It proposes a novel residual nudging technique for EnKF that monitors and adjusts residual norms, enhancing filter performance and stability.

Findings

Residual nudging improves EnKF accuracy.

It enhances stability against filter divergence.

Effective in small ensemble scenarios.

Abstract

Covariance inflation and localization are two important techniques that are used to improve the performance of the ensemble Kalman filter (EnKF) by (in effect) adjusting the sample covariances of the estimates in the state space. In this work an additional auxiliary technique, called residual nudging, is proposed to monitor and, if necessary, adjust the residual norms of state estimates in the observation space. In an EnKF with residual nudging, if the residual norm of an analysis is larger than a pre-specified value, then the analysis is replaced by a new one whose residual norm is no larger than a pre-specified value. Otherwise the analysis is considered as a reasonable estimate and no change is made. A rule for choosing the pre-specified value is suggested. Based on this rule, the corresponding new state estimates are explicitly derived in case of linear observations. Numerical experiments in the 40-dimensional Lorenz 96 model show that introducing residual nudging to an EnKF may improve its accuracy and/or enhance its stability against filter divergence, especially in the small ensemble scenario.