Mathematical modeling of rainwater runoff over catchment surface and mass transfer of contaminant incoming to water stream from soil

Abstract

The subject of an article is the mathematical modeling of the rainwater runoff along the surface catchment taking account the transport of pollution which permeates into the water flow from a porous media of soil at the certain areas of this surface. The developed mathematical model consists of two types of equations: the equations for calculating of the water layer thickness over the slope surface given the precipitation and evaporation, and equation of the mass transfer of impurity coming into the surface water during its filtration in zone of incomplete saturation of soil. The model also takes into account a reverse process – adsorption of impurity in soil with its low concentration or in the uncontaminated soil. Water content in the zone of incomplete saturation is determined within the approximate approach based on the model of capillary impregnation. The principal features of nonlinear differential equations are theoretically studied. In particular, it is shown that the equation for water content in this zone can become a differential equation with lagging argument.

Keywords: Mathematical Modeling, Runoff, Transport of Contaminant, Catchment, Sorption, Desorption, Incomplete Saturation