  Ever since its inception, the Ensemble Kalman Filter has elicited many
heuristic methods that sought to correct it. One such method is
localization---the thought that `nearby' variables should be highly correlated
with `far away' variable not. Recognizing that correlation is a time-dependent
property, adaptive localization is a natural extension to these heuristics. We
propose a Bayesian approach to adaptive Schur-product localization for the
DEnKF, and extend it to support multiple radii of influence. We test both the
empirical validity of (multivariate) adaptive localization, and of our
approach. We test a simple toy problem (Lorenz'96), extending it to a
multivariate model, and a more realistic geophysical problem (1.5 Layer
Quasi-Geostrophic). We show that the multivariate approach has great promise on
the toy problem, and that the univariate approach leads to improved filter
performance for the realistic geophysical problem.
