  The hillslope hydrological processes are very important in watershed
hydrology research. In this paper we focus on the water flow over the soil
surface with vegetation in a hydrographic basin. We introduce a PDE model based
on general principles of fluid mechanics where the unknowns are water depth and
water velocity. The influence of the plant cover to the water dynamics is given
by porosity (a quantity related to the density of the vegetation), which is a
function defined over the hydrological basin. Using finite volume method for
approximating the spatial derivatives, we build an ODE system which constitutes
the base of the discrete model we will work with. We discuss and investigate
several physical relevant properties of this model. Finally, we perform
different quantitative validation tests by comparing numerical results with
exact solutions or with laboratory measured data. We also consider some
qualitative validation tests by numerically simulating the flow on a
theoretical vegetated soil and on a real hydrographic basin.
