A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman Filtering

TL;DR

This paper introduces a stochastic covariance shrinkage method for Ensemble Kalman Filters that leverages climatological covariance to reduce sampling errors, improving filter performance especially with limited ensemble sizes.

Contribution

It proposes a novel stochastic covariance shrinkage approach using climatological covariance as a target, enhancing EnKF accuracy beyond traditional localization techniques.

Findings

Method significantly outperforms LETKF in certain setups.

Enables localization of the covariance shrinkage approach.

Reduces sampling errors with synthetic ensemble members.

Abstract

The Ensemble Kalman Filters (EnKF) employ a Monte-Carlo approach to represent covariance information, and are affected by sampling errors in operational settings where the number of model realizations is much smaller than the model state dimension. To alleviate the effects of these errors EnKF relies on model-specific heuristics such as covariance localization, which takes advantage of the spatial locality of correlations among the model variables. This work proposes an approach to alleviate sampling errors that utilizes a locally averaged-in-time dynamics of the model, described in terms of a climatological covariance of the dynamical system. We use this covariance as the target matrix in covariance shrinkage methods, and develop a stochastic covariance shrinkage approach where synthetic ensemble members are drawn to enrich both the ensemble subspace and the ensemble transformation. We additionally provide for a way in which this methodology can be localized similar to the state-of-the-art LETKF method, and that for a certain model setup, our methodology significantly outperforms it.