Parametric spatial covariance models in the ensemble Kalman filter

Abstract

Several applications rely on data assimilation methods for complex spatio-temporal problems. The focus of this paper is on ensemble-based methods, where some approaches require estimation of covariances between state variables and observations in the assimilation step. Spurious correlations present a challenge in such cases as they can degrade the quality of the ensemble representation of probability distributions. In particular, prediction variability is often underestimated. We propose to replace the sample covariance estimate by a parametric approach using maximum likelihood estimation for a small number of parameters in a spatial covariance model. Parametric covariance and precision estimation are employed in the context of the ensemble Kalman filter, and applied to a Gauss-linear autoregressive model and a geological process model. We learn that parametric approaches reduce the underestimation in prediction variability. Furthermore rich, non-stationary models do not seem to add much over simpler models with fewer parameters.