A Graph Clustering Approach to Localization for Adaptive Covariance Tuning in Data Assimilation Based on State-Observation Mapping

An original graph clustering approach for the efficient localization of error covariances is proposed within an ensemble-variational data assimilation framework. Here, the localization term is very generic and refers to the idea of breaking up a global assimilation into subproblems. This unsupervised localization technique based on a linearized state-observation measure is general and does not rely on any prior information such as relevant spatial scales, empirical cutoff radii or homogeneity assumptions. Localization is performed via graph theory, a branch of mathematics emerging as a powerful approach to capturing complex and highly interconnected Earth and environmental systems in computational geosciences. The novel approach automatically segregates the state and observation variables in an optimal number of clusters, and it is more amenable to scalable data assimilation. The application of this method does not require underlying block-diagonal structures of prior covariance matrices. To address intercluster connectivity, two alternative data adaptations are proposed. Once the localization is completed, a covariance diagnosis and tuning are performed within each cluster, whose contribution is sequentially integrated into the entire covariance matrix. Numerical twin experiment tests show the reduced cost and added flexibility of this approach compared to global covariance tuning, and more accurate results yielded for both observation- and background-error parameter tuning.