Hillslope-storage Boussinesq model for subsurface flow and variable source areas along complex hillslopes: 2. Intercomparison with a three-dimensional Richards equation model

The Boussinesq equation for subsurface flow in an idealized sloping aquifer of unit width has recently been extended to hillslopes of arbitrary geometry by incorporating the hillslope width function w(x) into the governing equation, where x is the flow distance along the length of the hillslope [Troch et al., 2003]. Introduction of a source/sink term N allows simulation of storm-interstorm sequences in addition to drainage processes, while a function S_c(x) representing the maximum subsurface water storage can be used to account for surface saturation response in variable source areas activated by the saturation excess mechanism of runoff generation. The model can thus simulate subsurface flow and storage dynamics for nonidealized (more realistic) hillslope configurations. In this paper we assess the behavior of this relatively simple, one-dimensional model in a series of intercomparison tests with a fully three-dimensional Richards equation model. Special attention is given to the discretization and setup of the boundary and initial conditions for seven representative hillslopes of uniform, convergent, and divergent plan shape. Drainage and recharge experiments are conducted on these hillslopes for both gentle (5%) and steep (30%) bedrock slope angles. The treatment and influence of the drainable porosity parameter are also considered, and for the uniform (idealized) hillslope case the impact of the unsaturated zone is examined by running simulations for different capillary fringe heights. In general terms, the intercomparison results show that the hillslope-storage Boussinesq model is able to capture the broad shapes of the storage and outflow profiles for all of the hillslope configurations. In specific terms, agreement with the Richards equation results varies according to the scenario being simulated. The best matches in outflow hydrographs were obtained for the drainage experiments, suggesting a greater influence of the unsaturated zone under recharge conditions due to transmission of water throughout the hillslope. In the spatiotemporal water table response a better match was observed for convergent than divergent hillslopes, and the bedrock slope angle was not found to greatly influence the quality of the agreement between the two models. On the basis of the intercomparison experiments we make some suggestions for further development and testing of the hillslope-storage model.