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A Matrix-Free Posterior Ensemble Kalman Filter Implementation Based on a Modified Cholesky Decomposition

Applied Math and Computational Science Laboratory, Department of Computer Science, Universidad del Norte, Barranquilla 080001, Colombia
Atmosphere 2017, 8(7), 125; https://doi.org/10.3390/atmos8070125
Received: 31 March 2017 / Revised: 10 July 2017 / Accepted: 12 July 2017 / Published: 18 July 2017
(This article belongs to the Special Issue Efficient Formulation and Implementation of Data Assimilation Methods)
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Abstract

In this paper, a matrix-free posterior ensemble Kalman filter implementation based on a modified Cholesky decomposition is proposed. The method works as follows: the precision matrix of the background error distribution is estimated based on a modified Cholesky decomposition. The resulting estimator can be expressed in terms of Cholesky factors which can be updated based on a series of rank-one matrices in order to approximate the precision matrix of the analysis distribution. By using this matrix, the posterior ensemble can be built by either sampling from the posterior distribution or using synthetic observations. Furthermore, the computational effort of the proposed method is linear with regard to the model dimension and the number of observed components from the model domain. Experimental tests are performed making use of the Lorenz-96 model. The results reveal that, the accuracy of the proposed implementation in terms of root-mean-square-error is similar, and in some cases better, to that of a well-known ensemble Kalman filter (EnKF) implementation: the local ensemble transform Kalman filter. In addition, the results are comparable to those obtained by the EnKF with large ensemble sizes. View Full-Text
Keywords: ensemble kalman filter; posterior ensemble; modified cholesky decomposition ensemble kalman filter; posterior ensemble; modified cholesky decomposition
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Nino-Ruiz, E.D. A Matrix-Free Posterior Ensemble Kalman Filter Implementation Based on a Modified Cholesky Decomposition. Atmosphere 2017, 8, 125.

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