Improved Initial Ensemble Generation Coupled with Ensemble Square Root Filters and Boosting to Estimate Uncertainty

The accuracy of ensemble Kalman filter (EnKF) methods depends on the sample size compared to the dimension of the parameters space. In real applications often sampling error may result in spurious correlations which produce a bias in the mean and a strong underestimation of the uncertainty. The Ensemble Square Root Filters (ESRF) represents an advantage in uncertainty estimation respect to the traditional EnKF. Covariance inflation and localization are a common solution to these problems. In this work we propose a method that reduces the bias of ensemble techniques by means of a convenient generation of the initial ensemble. This regeneration is based on a Stationary Orthogonal-Base Representation (SOBR), obtained via a singular value decomposition of a stationary covariance matrix estimated from the ensemble. This technique is tested on a 2D slightly compressible single phase model and compared with ESRF. The comparison is based on a reference solution obtained with a very large ensemble (one million). The example gives evidence that the SOBR reduces the effect of sampling error in the mean but covariance inflation is essential to avoid the ensemble collapse.