  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 nondimensional 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.
