Covariance localization in the ensemble transform Kalman filter based on an augmented ensemble

Abstract

With the increased density of available observation data, data assimilation has become an increasingly important tool in marine research. However, the success of the ensemble Kalman filter is highly dependent on the size of the ensemble. A small ensemble used in data assimilation could cause filter divergence, undersampling and spurious correlations. The primary method to alleviate these problems is localization. It can eliminate some spurious correlations and increase the rank of the forecast error covariance matrix. The ensemble transform Kalman filter has been widely used in various studies as a deterministic filter. Unfortunately, the covariance localization cannot be directly applied to ensemble transform Kalman filter. The new covariance localization needs to be presented to adapt the ensemble transform Kalman filter. Based on the method of expanded ensemble and eigenvalue decomposition, this study describes a variation of covariance localization that takes advantage of an unbiased covariance matrix from the expanded ensemble. Experiments described herein show that the new method outperforms the localization methods proposed by others when used in the ensemble transform Kalman filter. The new method yields an analysis estimate that is closer to the true state under different experimental conditions.