A LINEAR CONCEPTUAL SUBSURFACE STORM FLOW MODEL

A zero-dimensional (lumped), linear conceptual model of the subsurface storm flow from hillslopes has been developed by integrating, over the length of the hillslope, the linearized one-dimensional (Dupuit-Forchheimer approximation) discharge relationship for saturated flow over an inclined plane. The derived two-term storage function accounts for gravity- and gradient-driven flow. Coupled with the storage balance equation for the plane, the model allows direct, analytical computation of the outflow hydrograph at the foot of the hill in response to an infiltration step input. The model is the conceptual counterpart of the linear advection-diffusion (LAD) flow equation derived from the extended Boussinesq equation through linearization. In contrast to the kinematic wave approximation, the outflows normalized by their equilibrium values are properly given as functions of the infiltration rate. The outflow hydrographs computed by the conceptual LAD model approximate nonlinear behavior closely over a wide range of conditions encountered in field applications.