Non-linear data assimilation via trust region optimization

Abstract

In this paper, we propose an efficient and practical implementation of the ensemble Kalman filter based on trust region method for non-Gaussian data assimilation. The proposed method works as follows: the empirical moments of an ensemble of model realizations are employed to estimate the parameters of the background error distribution, then an iterative method is proposed to, among iterations, build quadratic surrogate models of the three-dimensional variational (3D-Var) cost function, these models are utilized to approximate solutions of the 3D-Var optimization problem, and the quality of solutions are assessed using the trust region framework. Furthermore, the global convergence of the proposed trust region implementation is theoretically proven. Experimental tests are carried out making use the Lorenz 96 model. Even more, two different observation operators are considered during the experiments: a linear observation operator, and a non-convex and discontinuous one. Different ensemble sizes as well as number of observations (and their time frequencies) are employed to enrich the numerical results. The Maximum Likelihood Ensemble Filter (MLEF) is utilized as a reference filter to estimate the performance of our proposed filter implementation. Ten experiments (repetitions) are performed for each configuration of parameters. The results reveal that, in average, the proposed filter outperforms the MLEF in terms of root mean square errors and even more, it converges to posterior modes of error distributions in cases wherein filter divergence can be possible in the MLEF context.