EFFICIENT IMPLEMENTATION OF ENSEMBLE BASED METHODS IN SEQUENTIAL DATA ASSIMILATION: ACCOUNTING FOR LOCALIZATION
In ensemble-based methods, the (empirical) moments of an ensemble of model realizations work as estimates of those of the background error distribution. Since model resolutions range in the order of millions while ensemble sizes are constrained by the hundreds, sampling errors can impact the quality of innovation matrices and consequently, spurious correlations can degenerate the quality of posterior ensembles. In this talk, we discuss ensemble Kalman filter (EnKF) implementations based on a modified Cholesky decomposition. In these methods, a well-conditioned estimator of the precision background-error-covariance matrix can be obtained in terms of Cholesky factors. Besides, by exploiting the conditional independence of model components with regard to a pre-defined localization radius, sparse Cholesky factors can be obtained. This allows for efficient and matrix-free implementations of the EnKF. Experimental tests are performed in order to assess the accuracy of the proposed implementations. Two numerical models are employed during the tests: an Atmospheric General Circulation Model (AT-GCM) and the Lorenz 96 model. The results reveal that, the use of the proposed implementations can improve the quality of analysis ensembles and even more, the impact of spurious correlations can be mitigated by using the proposed implementations.
Keywords: ensemble Kalman filter, modified Cholesky decomposition, precision covariance matrix.
Dr. Elias David Nino-Ruiz Department of Computer Science, Universidad del Norte, BAQ 080001, Colombia.