A Tabu Search implementation for adaptive localization in ensemble-based methods

Abstract

In this paper, we propose an efficient and practical implementation of the ensemble Kalman filter based on adaptive localization via Tabu search. The proposed method works as follows: during assimilation steps, observed components from the model state are split into two groups: the training set and the validation set, after which analysis states are obtained by using the training data, while posterior errors are estimated by means of the validation set. These steps are repeated for a fixed number of iterations and based on a Tabu search implementation, for each model component an optimal radius of influence is estimated. Experimental tests are performed by using the Lorenz 96 model which mimics the chaotic behaviour of the atmosphere. We assess the accuracy of the proposed method by contrasting its numerical results with those obtained by reference filters from the specialized literature such as the local ensemble transform Kalman filter and the ensemble Kalman filter based on modified Cholesky decomposition. Besides, numerical simulations are enriched by using different ensemble sizes, radii of influences (where appropriate), and inflation factors. The results reveal that, for all configurations, the proposed adaptive localization-based filter can improve the accuracy as well as the convergence of ensemble-based methods in the context of sequential data assimilation methods.