Combined assimilation of soil moisture and streamflow data by an ensemble kalman filter in a coupled model of surface–subsurface flow

Hydrologic models can largely benefit from the use of data assimilation algorithms, which allow to update the modeled system state incorporating in the solution of the model itself information coming from experimental measurements of various quantities, as soon as the data become available. In this context, data assimilation seems to be well fit for coupled surface--subsurface models, which, considering the watershed as the ensemble of surface and subsurface domains, allow a more accurate description of the hydrological processes at the catchment scale, where soil moisture largely influences the partitioning of rain between runoff and infiltration and thus controls the flow at the outlet. The need for a better determination of the variables of interest (streamflow at the outlet section, water table, soil water content, etc.) has led to a many efforts focused on the development of coupled numerical models, together with field and laboratory observations. Nevertheless, uncertainty in the schematic description of physical processes and inaccuracies on source data collection induce errors in the model predictions. The ensemble Kalman filter (EnKF) represents an extension to nonlinear problems of the classic Kalman filter by means of a Monte Carlo approach. A sequential assimilation procedure based on EnKF is developed and integrated in a process-based numerical model, which couples a three-dimensional finite element Richards equation solver for variably saturated porous media and a finite difference diffusion wave approximation based on a digital elevation data for surface water dynamics. A detailed analysis of the data assimilation algorithm behavior within the coupled model has been carried out on a synthetic 1D test case in order to verify the correct implementation and derive a series of fundamental parameters, such as the minimum ensemble size that can ensure a sufficient accuracy in the statistical estimates. The assimilation frequency, as well as the effects induced by assimilation on the surface and/or subsurface system state, was tested on a 3D synthetic test case represented by a 1.62 km2 tilted v-catchment, for which observations of pressure head and streamflow data are assimilated in order to retrieve the true watershed state in 2 scenarios: i) starting from a drier initial condition and ii) intentionally imposing a biased atmospheric forcing. In general, streamflow prediction is improved by assimilation of both pressure head and streamflow individually and by coupled assimilation. However, assimilation of streamflow data only does not improve the subsurface system state, leading to a deficit in soil moisture compared to both the true and the open loop simulations. Combined assimilation is therefore more adequate for the description of the entire surface—subsurface system state. The sensitivity analysis to the assimilation frequency yields contradictory results: as expected, a higher assimilation frequency improves the true state retrieval in the drier initial condition scenario, while for the biased atmospheric forcing scenario an analogous improvement is not manifest.