On the development and analysis of coupled surface-subsurface models of catchments. Part 2. A three-dimensional benchmark model and its properties

The objective of this three-part work is to formulate and rigorously analyse a number of reduced mathematical models that are nevertheless capable of describing the hydrology at the scale of a river basin (i.e. catchment). Coupled surface and subsurface flows are considered. In this second part, we construct a benchmark catchment scenario and investigate the effects of parameters within their typical ranges. Previous research on coupled surface–subsurface models have focused on numerical simulations of site-specific catchments. Here, our focus is broad, emphasising the study of general solutions to the mathematical models, and their dependencies on dimensionless parameters. This study provides a foundation based on the examination of a geometrically simple three-dimensional benchmark scenario. We develop a non-dimensional coupled surface–subsurface model and extract the key dimensionless parameters. Asymptotic methods demonstrate under what conditions the model can be reduced to a two-dimensional form, where the principal groundwater and overland flows occur in the hillslope direction. Numerical solutions provide guidance on the validity of such reductions, and demonstrate the parametric dependencies corresponding to a strong rainfall event.