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

arXiv: https://arxiv.org/abs/1809.08984 · HTML: https://mlsanity.com/paper/1809.08984/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Sep 2018.

## Built on by (most cited first, 2 of 2)

- [Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Physics-Informed Autoencoders](https://mlsanity.com/paper/2102.13025/) (2021)
- [The Ensemble Epanechnikov Mixture Filter](https://mlsanity.com/paper/2408.11164/) (2024)

## Abstract (arXiv)

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.