Modeling overland flow and soil erosion on nonuniform hillslopes: a finite volume scheme.

This paper presents a finite volume scheme for coupling the St. Venant equations with the multi- particle size class Hairsine-Rose soil erosion model. A well-balanced MUSCL-Hancock scheme is proposed to minimize spurious waves in the solution arising from an imbalance between the flux gradient and the source terms in the momentum equation. Additional criteria for numerical stability when dealing with very shallow flows and wet-dry fronts are highlighted. Numerical tests show that the scheme performs well in terms of accuracy and robustness for both the water and sediment transport equations. The proposed scheme facilitates the application of the Hairsine-Rose model to complex scenarios of soil erosion with concurrent interacting erosion processes over a non-uniform topography.