Ensemble Kalman filtering with residual nudging: an extension to state estimation problems with nonlinear observation operators

TL;DR

This paper extends residual nudging to nonlinear observation operators in ensemble Kalman filtering, creating an iterative framework that improves stability and accuracy in nonlinear data assimilation problems, demonstrated on the Lorenz 96 model.

Contribution

The authors develop an iterative residual nudging method for EnKF with nonlinear observation operators, enhancing stability and estimation accuracy.

Findings

Iterative filter remains stable where standard EnKF diverges.

Proposed method achieves better estimation accuracy in nonlinear settings.

Numerical tests on Lorenz 96 model validate the approach.

Abstract

The ensemble Kalman filter (EnKF) is an efficient algorithm for many data assimilation problems. In certain circumstances, however, divergence of the EnKF might be spotted. In previous studies, the authors proposed an observation-space-based strategy, called residual nudging, to improve the stability of the EnKF when dealing with linear observation operators. The main idea behind residual nudging is to monitor and, if necessary, adjust the distances (misfits) between the real observations and the simulated ones of the state estimates, in the hope that by doing so one may be able to obtain better estimation accuracy. In the present study, residual nudging is extended and modified in order to handle nonlinear observation operators. Such extension and modification result in an iterative filtering framework that, under suitable conditions, is able to achieve the objective of residual nudging for data assimilation problems with nonlinear observation operators. The 40 dimensional Lorenz 96 model is used to illustrate the performance of the iterative filter. Numerical results show that, while a normal EnKF may diverge with nonlinear observation operators, the proposed iterative filter remains stable and leads to reasonable estimation accuracy under various experimental settings.