Ensemble Kalman Filter vs Particle Filter in a Physically Based Coupled Model of Surface-Subsurface Flow (Invited)

Data assimilation (DA) has recently received growing interest by the hydrological modeling community due to its capability to merge observations into model prediction. Among the many DA methods available, the Ensemble Kalman Filter (EnKF) and the Particle Filter (PF) are suitable alternatives for applications to detailed physically-based hydrological models. For each assimilation period, both methods use a Monte Carlo approach to approximate the state probability distribution (in terms of mean and covariance matrix) by a finite number of independent model trajectories, also called particles or realizations. The two approaches differ in the way the filtering distribution is evaluated. EnKF implements the classical Kalman filter, optimal only for linear dynamics and Gaussian error statistics. Particle filters, instead, use directly the recursive formula of the sequential Bayesian framework and approximate the posterior probability distributions by means of appropriate weights associated to each realization. We use the Sequential Importance Resampling (SIR) technique, which retains only the most probable particles, in practice the trajectories closest in a statistical sense to the observations, and duplicates them when needed. In contrast to EnKF, particle filters make no assumptions on the form of the prior distribution of the model state, and convergence to the true state is ensured for large enough ensemble size. In this study EnKF and PF have been implemented in a physically based catchment simulator that couples a three-dimensional finite element Richards equation solver with a finite difference diffusion wave approximation based on a digital elevation data for surface water dynamics. We report on the retrieval performance of the two schemes using a three-dimensional tilted v-catchment synthetic test case in which multi-source observations are assimilated (pressure head, soil moisture, and streamflow data). The comparison between the results of the two approaches allows to discuss some of the strengths and weaknesses, both physical and numerical, of EnKF and PF and to learn the implications related to the choice of the statistics used to build the ensemble of realizations.