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 as-similation step. Spurious correlations present a challenge in such cases as they can degrade the quality of the ensemble represen-tation of probability distributions. In particular, prediction vari-ability 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.

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