A Hierarchical Bayes Ensemble Kalman Filter

TL;DR

This paper introduces a Hierarchical Bayes Ensemble Kalman Filter (HBEF) that models covariance uncertainties as random matrices, improving data assimilation accuracy over traditional methods in various regimes.

Contribution

The paper presents a novel hierarchical Bayesian approach to ensemble filtering that incorporates covariance uncertainty and allows for more flexible assimilation of observations.

Findings

HBEF outperforms EnKF and HEnKF in multiple filtering regimes.

The filter effectively updates covariance matrices using a hierarchical Bayes scheme.

Numerical experiments demonstrate improved accuracy in state estimation.

Abstract

A new ensemble filter that allows for the uncertainty in the prior distribution is proposed and tested. The filter relies on the conditional Gaussian distribution of the state given the model-error and predictability-error covariance matrices. The latter are treated as random matrices and updated in a hierarchical Bayes scheme along with the state. The (hyper)prior distribution of the covariance matrices is assumed to be inverse Wishart. The new Hierarchical Bayes Ensemble Filter (HBEF) assimilates ensemble members as generalized observations and allows ordinary observations to influence the covariances. The actual probability distribution of the ensemble members is allowed to be different from the true one. An approximation that leads to a practicable analysis algorithm is proposed. The new filter is studied in numerical experiments with a doubly stochastic one-variable model of "truth". The model permits the assessment of the variance of the truth and the true filtering error variance at each time instance. The HBEF is shown to outperform the EnKF and the HEnKF by Myrseth and Omre (2010) in a wide range of filtering regimes in terms of performance of its primary and secondary filter.