Numerical Comparison of Iterative Ensemble Kalman Filters for Unsaturated Flow Inverse Modeling

This study evaluated three algorithms of the iterative ensemble Kalman filter (EnKF). They are Confirming EnKF, Restart EnKF, and modified Restart EnKF developed to resolve the inconsistency problem (i.e., updated model parameters and state variables do not follow the Richards equation) in vadose zone data assimilation due to model nonlinearity. While Confirming and Restart EnKF were adapted from literature, modified Restart EnKF was developed in this study to reduce computational costs by calculating only the mean simulation, not all the ensemble realizations, from time t = 0. A total of 11 cases were designed to investigate the performance of EnKF, Confirming EnKF, Restart EnKF, and modified Restart EnKF with different types and spatial configurations of observations (pressure head and water content) and different values of observation error variance, initial guess of ensemble mean and variance, ensemble size, and damping factor. The numerical study showed that Confirming EnKF produced considerable inconsistency for the nonlinear unsaturated flow problem, which differs from the apparent consensus opinion that Confirming EnKF can resolve the inconsistency problem. In contrast, Restart EnKF and its modification can resolve the inconsistency problem. Restart EnKF and its modification outperformed EnKF and Confirming EnKF in the various cases considered in this study. It ws also found that combining different types of observations can achieve better assimilation results, which is useful for monitoring network design.