A Posterior Ensemble Kalman Filter Based On A Modified Cholesky Decomposition

Abstract

In this paper, we propose a posterior ensemble Kalman filter (EnKF) based on a modified Cholesky decomposition. The main idea behind our approach is to estimate the moments of the analysis distribution based on an ensemble of model realizations. The method proceeds as follows: initially, an estimate of the precision background error covariance matrix is computed via a modified Cholesky decomposition and then, based on rank-one updates, the Cholesky factors of the inverse background error covariance matrix are updated in order to obtain an estimate of the inverse analysis covariance matrix. The special structure of the Cholesky factors can be exploited in order to obtain a matrix-free implementation of the EnKF. Once the analysis covariance matrix is estimated, the posterior mode of the distribution can be approximated and samples about it are taken in order to build the posterior ensemble. Experimental tests are performed making use of the Lorenz 96 model in order to assess the accuracy of the proposed implementation. The results reveal that, the accuracy of the proposed implementation is similar to that of the well-known local ensemble transform Kalman filter and even more, the use of our estimator reduces the impact of sampling errors during the assimilation of observations.