In this paper, a distributed numerical model is proposed on the basis of (1) a hydrologic model for the water exchange laws; (2) a surface runoff model based on a hybrid two-dimensional (2D) diffusive/kinematic wave approximation able to calculate flow over all kinds of wet/dry ground surface slopes; (3) a groundwater flow model based on the 2D Darcy law for both saturated and partly saturated zones; (4) a 2D hillslope erosion model for the sediment transport; and (5) a explicit finite-volume discretization with specific schemes according to the characteristics of the flow equations, upwind for the hyperbolic equations and centered for the parabolic equations. The resulting model offers a variable time step, ensuring numerical stability with the time step size sensitive to the grid cell size in the diffusive wave case and an entropy correction of the upwind fluxes to ensure conservative solutions near local maxima in the slopes controlling the water movement. The validation and practical applicati...