Mathematical simulation of infiltrating watersheds

Abstract

The partial differential equation for vertical, one-phase, unsaturated flow of water in soil s is used as a mathematical model governing infiltration.A nonlinear Crank-Nicolson implicit finite-difference scheme i s used to obtain solutions to this equation for realistic initial and upper boundary conditions.The kinematic wave approximation to the equations of unsteady overland flow on cascaded p lanes is used for the mathem~tical model of surface runoff .The difference equations of infiltration and overland flow are combined into a model for a simple watershed, employing compu tational logic so that boundary conditions match at the soil surface.The mathematical model is tested by comparison with data from a laboratory soil flume and with data f rom a small experimental waters hed .