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Ever since its inception, the Ensemble Kalman Filter has elicited manyheuristic methods that sought to correct it. One such method islocalization---the thought that `nearby' variables should be highly correlatedwith `far away' variable not. Recognizing that correlation is a time-dependentproperty, adaptive localization is a natural extension to these heuristics. Wepropose a Bayesian approach to adaptive Schur-product localization for theDEnKF, and extend it to support multiple radii of influence. We test both theempirical validity of (multivariate) adaptive localization, and of ourapproach. We test a simple toy problem (Lorenz'96), extending it to amultivariate model, and a more realistic geophysical problem (1.5 LayerQuasi-Geostrophic). We show that the multivariate approach has great promise onthe toy problem, and that the univariate approach leads to improved filterperformance for the realistic geophysical problem.

A Bayesian Approach to Multivariate Adaptive Localization in Ensemble-Based Data Assimilation with Time-Dependent Extensions