  An original graph clustering approach to 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 linearizedstate-observation measure is
general and does not rely on any prior information such as relevant spatial
scales, empirical cut-off radius or homogeneity assumptions. It automatically
segregates the state and observation variables in an optimal number of clusters
(otherwise named as subspaces or communities), more amenable to scalable data
assimilation.The application of this method does not require underlying
block-diagonal structures of prior covariance matrices. In order to deal with
inter-cluster connectivity, two alternative data adaptations are proposed. Once
the localization is completed, an adaptive covariance diagnosis and tuning is
performed within each cluster. Numerical tests show that this approach is less
costly and more flexible than a global covariance tuning, and most often
results in more accurate background and observations error covariances.
