# A Shallow Water Model for Water Flow on Vegetated Hillslope

## TL;DR

This paper develops a PDE-based shallow water model incorporating vegetation effects to simulate water flow on vegetated hillslopes, validated through numerical tests against analytical and real-world data.

## Contribution

It introduces a novel PDE model that accounts for vegetation porosity in water flow simulation on hillslopes, using finite volume discretization.

## Key findings

- Model accurately predicts water flow dynamics in vegetated terrains.
- Numerical results align well with laboratory and real basin data.
- The model captures key physical properties of water-vegetation interactions.

## Abstract

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.