Ensemble Kalman filtering with shrinkage regression techniques

The classical ensemble Kalman filter (EnKF) is known to underestimate the prediction uncertainty. This can potentially lead to low forecast precision and an ensemble collapsing into a single realisation. In this paper, we present alternative EnKF updating schemes based on shrinkage methods known from multivariate linear regression. These methods reduce the effects caused by collinear ensemble members and have the same computational properties as the fastest EnKF algorithms previously suggested. In addition, the importance of model selection and validation for prediction purposes is investigated, and a model selection scheme based on cross-validation is introduced. The classical EnKF scheme is compared with the suggested procedures on two-toy examples and one synthetic reservoir case study. Significant improvements are seen, both in terms of forecast precision and prediction uncertainty estimates.