Ensemble Kalman filter versus particle filter for a physically-based coupled surface–subsurface model

The ensemble Kalman filter (EnKF) and sequential importance resampling (SIR) are two Monte Carlo-based sequential data assimilation (DA) methods developed to solve the filtering problem in nonlinear systems. Both methods present drawbacks when applied to physically-based nonlinear models: the EnKF update is affected by the inherent Gaussian approximation, while SIR may require a large number of Monte Carlo realizations to ensure consistent updates. In this work we implemented EnKF and SIR into a physically-based coupled surface-subsurface flow model and applied it to a synthetic test case that considers a uniform soil v-shaped catchment subject to rainfall and evaporation events. After a sensitivity analysis on the number of Monte Carlo realizations and the correlation time of the atmospheric forcing, the comparison between the two filters is done on the basis of different simulation scenarios varying observations (outlet streamflow and/or pressure head), assimilation frequency, and type of bias (atmospheric forcing or initial conditions). The results demonstrate that both EnKF and SIR are suitable DA methods for detailed physically-based hydrological modeling using the same, relatively small, ensemble size. We highlight that the Gaussian approximation in the EnKF updates leads to a state estimation that can be not consistent with the physics of the model, resulting in a slowdown of the numerical solver. SIR instead duplicates physically consistent realizations, but can display difficulties in updates when the realizations are far from the true state. We propose and test a modification of the SIR algorithm to overcome this issue and preserve assimilation efficiency.