A maximum likelihood ensemble filter via a modified cholesky decomposition for non-gaussian data assimilation
Elias David Nino-Ruiz (Universidad del Norte)
Alfonso Mancilla-Herrera (Universidad del Norte)
Santiago Lopez Restrepo (TU Delft - Mathematical Physics, Universidad EAFIT)
Olga Quintero-Montoya (Universidad EAFIT)
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Abstract
This paper proposes an efficient and practical implementation of the Maximum Likelihood Ensemble Filter via a Modified Cholesky decomposition (MLEF-MC). The method works as follows: via an ensemble of model realizations, a well-conditioned and full-rank square-root approximation of the background error covariance matrix is obtained. This square-root approximation serves as a control space onto which analysis increments can be computed. These are calculated via Line-Search (LS) optimization. We theoretically prove the convergence of the MLEF-MC. Experimental simulations were performed using an Atmospheric General Circulation Model (AT-GCM) and a highly nonlinear observation operator. The results reveal that the proposed method can obtain posterior error estimates within reasonable accuracies in terms of ℓ − 2 error norms. Furthermore, our analysis estimates are similar to those of the MLEF with large ensemble sizes and full observational networks.
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