An iterative normal-score ensemble smoother for dealing with non-Gaussianity in data assimilation

Abstract

The ensemble Kalman filter (EnKF) has been widely applied to assimilate dynamic data such as hydraulic head in geologic models for improved predictions over the past decade. It has various advantages such as the capability of handling multiple sources of uncertainty and ease of coupling with forward simulators involving complex physics; however, it is not reliable for updating models that are characterized by curvilinear structures such as in fluvial deposits where high-permeability conduits play a dominant role for solute transport. Several methods have been proposed to handle non-Gaussian aspects in the EnKF. For instance, the EnKF has been coupled with the normal-score transform (NS-EnKF) for data assimilation in non-multi-Gaussian distributed conductivity fields, and this approach has been applied in a number of studies. As an alternative to the EnKF, the iterative ensemble smoother (ES) has been proposed for data assimilation, where all the data at all time steps are integrated into geologic models together, instead of the sequential data integration of the EnKF. The ES therefore has much less computational cost than the EnKF. This work coupled the normal-score transform and ensemble smoother (NS-ES) for data assimilation in non-multi-Gaussian distributed conductivity fields. The algorithm is compared to the NS-EnKF and evaluated in a synthetic bimodal aquifer. The results show that (1) the NS-ES is able to reproduce the curvilinear structures of the reference field, and the performance of updated models using the NS-ES is improved in terms of flow and transport predictions; and (2) the NS-ES can obtain results comparable to the NS-EnKF for characterization of non-multi-Gaussian conductivities, and has the advantage of less computational cost.