A Maximum Likelihood Ensemble Filter via a Modified Cholesky Decomposition for Non-Gaussian Data Assimilation

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.

A Four Dimensional Variational Data Assimilation Framework for Wind Energy Potential Estimation

In this paper, we propose a Four-Dimensional Variational (4D-Var) data assimilation framework for wind energy potential estimation. The framework is defined as follows: we choose a numerical model which can provide forecasts of wind speeds then, an ensemble of model realizations is employed to build control spaces at observation steps via a modified Cholesky decomposition. These control spaces are utilized to estimate initial analysis increments and to avoid the intrinsic use of adjoint models in the 4D-Var context. The initial analysis increments are mapped back onto the model domain from which we obtain an estimate of the initial analysis ensemble. This ensemble is propagated in time to approximate the optimal analysis trajectory. Wind components are post-processed to get wind speeds and to estimate wind energy capacities. A matrix-free analysis step is derived from avoiding the direct inversion of covariance matrices during assimilation cycles. Numerical simulations are employed to illustrate how our proposed framework can be employed in operational scenarios. A catalogue of twelve Wind Turbine Generators (WTGs) is utilized during the experiments. The results reveal that our proposed framework can properly estimate wind energy potential capacities for all wind turbines within reasonable accuracies (in terms of Root-Mean-Square-Error) and even more, these estimations are better than those of traditional 4D-Var ensemble-based methods. Moreover, large variability (variance of standard deviations) of errors are evidenced in forecasts of wind turbines with the largest rate-capacity while homogeneous variability can be seen in wind turbines with the lowest rate-capacity.