A data-driven localization method for ensemble based data assimilation

Abstract

In this paper, we propose a dynamic localization method for ensemble-based data assimilation via a modified Cholesky decomposition. The method exploits the information brought by ensemble members to estimate optimal radius lengths of model components. This estimation process is performed by using Bayes’ Theorem; our prior beliefs and likelihood functions are modeled via Gamma distributions: in priors, hyper-parameters are fixed based on our prior knowledge of error dynamics while to build likelihood functions, model parameters are fitted with empirical statistics from background ensembles at assimilation steps. Once the optimal radius lengths are estimated, a modified Cholesky decomposition is employed to estimate precision covariances of background error distributions. The assimilation process is then performed similarly to that of the EnKF based on a modified Cholesky decomposition (EnKF-MC). Experimental tests are performed by using the Lorenz-96 model. To compare our results, we employ an EnKF-MC implementation with different structures of background error correlations. In terms of ℓ2-norm of errors, the proposed filter implementation can outperform the EnKF-MC method for fixed radius lengths across all model components, and even more, different hyper-parameters can be tried in our filter formulation without degrading its convergence.