A localization technique for ensemble Kalman filters

TL;DR

This paper introduces a novel continuous ODE-based localization method for ensemble Kalman filters, improving covariance accuracy and reducing spurious correlations in high-dimensional data assimilation.

Contribution

It presents a new ODE formulation for ensemble Kalman filter updates that incorporates localization within the ensemble transform framework.

Findings

The ODE approach accurately reproduces the Kalman filter update.

Localization reduces spurious long-range correlations.

Method applicable to nonlinear observation operators and continuous data streams.

Abstract

Ensemble Kalman filter techniques are widely used to assimilate observations into dynamical models. The phase space dimension is typically much larger than the number of ensemble members which leads to inaccurate results in the computed covariance matrices. These inaccuracies can lead, among other things, to spurious long range correlations which can be eliminated by Schur-product-based localization techniques. In this paper, we propose a new technique for implementing such localization techniques within the class of ensemble transform/square root Kalman filters. Our approach relies on a continuous embedding of the Kalman filter update for the ensemble members, i.e., we state an ordinary differential equation (ODE) whose solutions, over a unit time interval, are equivalent to the Kalman filter update. The ODE formulation forms a gradient system with the observations as a cost functional. Besides localization, the new ODE ensemble formulation should also find useful applications in the context of nonlinear observation operators and observations arriving continuously in time.