Modeling water flow and chemical and sediment transport in watershed systems

This paper presents a numerical model simulating water flow and chemical and sediment transport in watershed systems that may include a 2-D overland regime, a 1-D river/stream network, and 3-D subsurface media. The diffusion wave approach is used in modeling flow in surface systems, while the subsurface flow is described by the Richards equation. In the surface chemical system, both dissolved and particulate chemicals are taken into account. While in the subsurface systems, we include dissolved chemicals, adsorbing sites, and adsorbed chemicals. Chemical kinetics based the collision theory is used to describe interactions among chemicals. The interaction between surface and subsurface is accounted for through infiltration/seepage. We employed the backward method of characteristics to solve diffusion wave flow equations. The Picard method was applied to deal with the non-linearity of the flow equations. Richards' equation is discretized with the Galerkin finite element method. The predictor-corrector numerical scheme was employed to solve transport equations. The Newton-Raphson method was used to solve the set of ordinary differential equations describing chemical kinetics among all chemical species in the corrector step. An example is given for demonstration.