Ensemble Kalman filtering for hydraulic conductivity characterization: Parallelization and non-Gaussianity

Abstract

The ensemble Kalman filter (EnKF) is nowadays recognized as an excellent inverse method for hydraulic conductivity characterization using transient piezometric head data. and it is proved that the EnKF is computationally efficient and capable of handling large fields compared to other inverse methods. However, it is needed a large ensemble size (Chen and Zhang, 2006) to get a high quality estimation, which means a lots of computation time. Parallel computing is an efficient alterative method to reduce the commutation time. Besides, although the EnKF is good accounting for the non linearities of the state equation, it fails when dealing with non-Gaussian distribution fields. Recently, many methods are developed trying to adapt the EnKF to non-Gaussian distributions(detailed in the History and present state chapter). Zhou et al. (2011, 2012) have proposed a Normal-Score Ensemble Kalman Filter (NS-EnKF) to character the non-Gaussian distributed conductivity fields, and already showed that transient piezometric head was enough for hydraulic conductivity characterization if a training image for the hydraulic conductivity was available. Then in this work, we will show that, when without such a training image but with enough transient piezometric head information, the performance of the updated ensemble of realizations in the characterization of the non-Gaussian reference field. In the end, we will introduce a new method for parameterizing geostatistical models coupling with the NS-EnKF in the characterization of a Heterogenous non-Gaussian hydraulic conductivity field. So, this doctor thesis is mainly including three parts, and the name of the parts as below. 1, Parallelized Ensemble Kalman Filter for Hydraulic Conductivity Characterization. 2, The Power of Transient Piezometric Head Data in Inverse Modeling: An Application of the Localized Normal-score EnKF with Covariance Inflation in a Heterogenous Bimodal Hydraulic Conductivity Field. 3, Parameterizing geostatistical models coupling with the NS-EnKF for Heterogenous Bimodal Hydraulic Conductivity characterization.