Analytical solutions to hillslope subsurface storm flow and saturation overland flow

We present the analytical solutions to a hillslope-based formulation of subsurface storm flow and saturation overland flow. Here a hillslope is defined as the area between two streamlines originating from two ends of a channel link or from the channel head and ending at the ridgelines. The three-dimensional soil mantle of a hillslope is reduced to a one-dimensional profile along which the soil moisture and discharge are modeled. Continuity and a kinematic form of Darcy's law lead to quasi-linear wave equations solvable with the method of characteristics. Examples are given to illustrate the ability and limitations of the solutions in capturing the essential runoff behavior of different slope types.