Hierarchical Ensemble Kalman Filter

This paper presents the hierarchical ensemble Kalman filter (HEnKF) as a robust extension of the ensemble Kalman filter (EnKF). The HEnKF is developed to he robust against features like estimation uncertainty and rank deficiency related to covariance estimation in EnKF. The HEnKF imposes a hierarchical model on the state variables and uses prior distributions from the Gauss conjugate family of distributions to obtain more-robust estimates. An empirical study demonstrates that the HEnKF provides more-reliable results than the traditional EnKF approach. Better predictions and more-realistic prediction intervals are provided. The latter is caused by model-parameter uncertainty being an integral part of the HEnKF approach, while this effect is ignored in traditional EnKF. The two versions of the ensemble Kalman filter are also compared on a synthetic-reservoir study. The HEnKF appears as significantly better.