Mathematical simulation of interdependent surface and subsurface hydrologic processes

It has become popular with some hydrologists to consider runoff produced by rainfall intensities in excess of soil infiltration capacity (‘Horton’ excess) and runoff produced by rain falling on saturated soil zones (saturation excess) to be alternative or competitive models for describing surface runoff. On the contrary, we contend with Freeze (1972) that these two mechanisms, along with subsurface stormflow, are three parts of a continuum of hydrologic response that are controlled by the relative properties of the soil and the rainfall. We introduce a model which trades some of the generality of the Freeze (1972) hillslope model for increased efficiency, by selecting efficient approximations for key elements in hillslope hydrodynamics: infiltration and movement in the unsaturated flow zone. The hillslope is considered to consist of two soil layers with the lower soil capable of restricting vertical flow at the interface to create a perched aquifer and subsurface stormflow. The slope of the interface is arbitrary. A kinematic method for routing unsaturated vertical flow is described and is linked consistently with a modern analytically derived infiltration model, which operates when rainfall exceeds surface saturated hydraulic conductivity K s . The model is used to demonstrate several of the relationships between rainfall flux, soil hydraulic properties, hillslope geometry, and runoff characteristics. The model is also applied to simulate experimental data from a hillslope in Western Australia. Subsurface stormflow recessions are demonstrated to be affected by the ratio K s / q l , anisotropy, and spatial distribution of saturated hydraulic conductivity K s , where q l is the rate of loss from the perched aquifer. Vertical growth of the saturated zone depth is demonstrated to have a potentially greater effect on runoff than horizontal movement in cases where anisotropy and/or slope is not severe.