Parametric Covariance Estimation in Ensemble-based Data Assimilation

Ensemble-based data assimilation methods like the ensemble Kalman filter must estimate covariances between state variables and observed variables to update ensemble members. In high-dimensional, geostatistical estimation settings where the system state consists of spatial random fields, spurious entries in estimated covariance matrices can degrade the predictive performance of posterior ensembles. We propose to avoid spurious correlations by specifying a parametric form for the state covariance, and fitting this model to the forecast ensemble. The idea is demonstrated on a partially synthetic North Sea test case involving forward stratigraphic modeling.