A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman Filtering

Operational Ensemble Kalman Filtering (EnKF) methods rely on model-specific heuristics such as localization, which are typically implemented based on the spacial locality of the model variables. We instead propose methods that more closely depend on the dynamics of the model, by looking at locally averaged-in-time behavior. Such behavior is typically described in terms of a climatological covariance of the dynamical system. We will be utilizing this covariance as the target matrix in covariance shrinkage methods, from which we will be drawing a synthetic ensemble in order to enrich both the ensemble transformation and the subspace of the ensemble.