Resampling the Ensemble Kalman Filter

Ensemble Kalman filters (EnKF) based on a small ensemble tend to provide collapse of the ensemble over time. It is shown that this collapse is caused by positive coupling of the ensemble members due to use of one common estimate of the Kalman gain for the up-date of all ensemble members at each time step. This coupling can be avoided by resampling the Kalman gain from its sampling distri-bution in the conditioning step. In the analytically tractable Gauss-linear model finite sample distributions for all covariance matrix es-timates involved in the Kalman gain estimate are known and hence exact Kalman gain resampling can be done. For the general non-linear case we introduce the resampling ensemble Kalman filter (ResEnKF) algorithm. The resampling strategy in the algorithm is based on bootstrapping of the ensemble and Monte Carlo sim-ulation of the likelihood model. An empirical study demonstrates that ResEnKF provides more reliable prediction intervals than tra-ditional EnKF, on the cost of somewhat less accuracy in the point predictions. In a synthetic reservoir study, it is shown the the hi-erarchical ensemble Kalman filter (HEnKF) provides more reliable predictions and prediction intervals than both ResEnKF and tradi-tional EnKF. HEnKF requires additional modeling, however