Ensemble Kalman Filter assimilation of transient groundwater flow data: stochastic moment solution versus traditional Monte Carlo approach

The ensemble Kalman filter (EnKF) allows assimilating newly available data in transient groundwater and other earth system models through real-time Bayesian updating of system states (e.g., hydraulic heads) and parameters (e.g., hydraulic conductivities). Assimilating data in groundwater transient stochastic flow equations via the traditional EnKF entails computationally intensive Monte Carlo (MC) simulations. Previously we proposed a way to circumvent the need for MC through (1) an approximate direct solution of nonlocal (integrodifferential) equations that govern the space-time evolution of conditional ensemble means (statistical expectations) and covariances of hydraulic heads and fluxes and (2) the embedding of these moments in EnKF. Here we compare the accuracies and computational efficiencies of our newly proposed EnKF approach based on stochastic moment equations and the traditional Monte Carlo approach.