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

TL;DR

This paper introduces a Bayesian method for adaptive localization in ensemble data assimilation, allowing for multiple influence radii, and demonstrates its effectiveness on toy and realistic geophysical models.

Contribution

It presents a novel Bayesian framework for multivariate adaptive localization in the DEnKF, extending to multiple radii of influence, with validation on toy and real-world models.

Findings

Multivariate adaptive localization shows promise on Lorenz'96.

Univariate approach improves performance on geophysical model.

Bayesian method effectively supports multiple influence radii.

Abstract

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.