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.
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