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The hillslope hydrological processes are very important in watershedhydrology research. In this paper we focus on the water flow over the soilsurface with vegetation in a hydrographic basin. We introduce a PDE model basedon general principles of fluid mechanics where the unknowns are water depth andwater velocity. The influence of the plant cover to the water dynamics is givenby porosity (a quantity related to the density of the vegetation), which is afunction defined over the hydrological basin. Using finite volume method forapproximating the spatial derivatives, we build an ODE system which constitutesthe base of the discrete model we will work with. We discuss and investigateseveral physical relevant properties of this model. Finally, we use numericalresults to validate the model.

A Shallow Water Model for Hydrodynamic Processes on Vegetated Hillslope. Water Flow Modulus