A data-driven method for improving the correlation estimation in serial ensemble Kalman filters

TL;DR

This paper introduces a data-driven linear transformation approach to enhance correlation estimates in serial ensemble Kalman filters, significantly improving filter accuracy especially with small ensembles.

Contribution

It presents a novel offline training method to learn a linear map that corrects correlation estimates in ensemble Kalman filters without tuning.

Findings

Improved filter estimates in Lorenz-96 model simulations.

Effective especially with small ensemble sizes.

No tuning required due to offline training.

Abstract

A data-driven method for improving the correlation estimation in serial ensemble Kalman filters is introduced. The method finds a linear map that transforms, at each assimilation cycle, the poorly estimated sample correlation into an improved correlation. This map is obtained from an offline training procedure without any tuning as the solution of a linear regression problem that uses appropriate sample correlation statistics obtained from historical data assimilation products. In an idealized OSSE with the Lorenz-96 model and for a range of cases of linear and nonlinear observation models, the proposed scheme improves the filter estimates, especially when the ensemble size is small relative to the dimension of the state space.