Hydraulic conductivities identification via Ensemble Kalman Filtering with transformed data considering the risk of systematic bias

In subsurface hydrology, Ensemble Kalman Filtering (EnKF) has been coupled with groundwater flow and transport models to solve the inverse problem. Several extensions of the EnKF have been proposed to improve its performance when dealing with non-multi-Gaussian random field models of the hydraulic conductivity. One such variant is the EnKF with transformed data (tEnKF), which uses Gaussian anamorphosis within a conditioning step. Although this transformation has been used in the past to identify hydraulic conductivities, previous studies have ignored the risk of introducing a systematic bias in the spatiotemporal evolution of the hydraulic head field during the forecast steps that the update steps may not correct over time. This paper proposes that in order to evaluate the performance of tEnKFs, applications in synthetically generated random porous media should take into account this risk by incorporating prior knowledge with a multi-Gaussian conductivity correlation structure, and by adopting a reference field with asymmetric correlation structure. As an example of this application, hydraulic conductivities using the tEnKF were identified by solving a one-dimensional, single phase flow problem in a continuous random porous medium. Common concepts in Geostatistics are used to explain the hypothesis underlying both EnKF and tEnKF and to establish a clear link between the tEnKF and the stochastic simulation of conditional random fields.