Comparison of data assimilation techniques for a coupled model of surface and subsurface flow

Data assimilation in the geophysical sciences refers to methodologies to optimally merge model predictions and observations. The ensemble Kalman filter (EnKF) is a statistical sequential data assimilation technique explicitly developed for nonlinear filtering problems. It is based on a Monte Carlo approach that approximates the conditional probability densities of the variables of interest by a finite number of randomly generated model trajectories. In Newtonian relaxation or nudging (NN), which can be viewed as a special case of the classic Kalman filter, model variables are driven toward observations by adding to the model equations a forcing term, or relaxation component, that is proportional to the difference between simulation and observation. The forcing term contains four-dimensional weighting functions that can, ideally, incorporate prior knowledge about the characteristic scales of spatial and temporal variability of the state variable(s) being assimilated. In this study, we examined the EnKF and NN algorithms as implemented for a complex hydrologic model that simulates catchment dynamics, coupling a three-dimensional finite element Richards' equation solver for variably saturated porous media and a finite difference diffusion wave approximation for surface water flow. We report on the retrieval performance of the two assimilation schemes for a small catchment in Belgium. The results of the comparison show that nudging, while more straightforward and less expensive computationally, is not as effective as the ensemble Kalman filter in retrieving the true system state. We discuss some of the strengths and weaknesses, both physical and numerical, of the NN and EnKF schemes.