Water Quality Forecasting Under the Influence of Runoff Based on a Mathematical Model

Abstract

Runoff is one of the main sources of diffuse pollution of surface water. Suspended solids are the most typical contaminants of runoff. Suspended solids have a great influence on water quality and ecological status of water bodies. The content of suspended solids in water bodies is determined not only by their receipt from external sources, but also by the ability to transport sediments by flow. There is a permanent exchange of suspended solids between water bodies and bottom deposits. This fact stimulates specific requirements for modeling the transfer of suspended solids. For the most cases, models which describe the transfer of suspensions in a turbulent flow are based on the three-dimensional equation of turbulent diffusion or its two-dimensional simplification, which allows to take into account the spatial distribution of substances or it’s distribution to the width of stream. The use of such models requires a significant amount of initial data to determine the parameters of the models and is associated with a significant amount of calculations. At the same time, one-dimensional interpretation of processes is common and practically sufficient for shallow watercourses. It is more important to take into account the dynamics of the exchange of suspended solids between water mass and bottom deposits. The article is devoted to the development of a mathematical model for estimating the influence of non - point sources of pollution on the content of suspended solids in narrow watercourses. The model is based on the principle of mass balance of substances entering the flow section and takes into account the processes of sedimentation and resedimentation of suspended solids. A mathematical model in the form of a differential equation for the case of normal and overloaded flow is developed. Analytical solutions of equations for both cases are obtained. The influence of hydraulic size of the suspension on the content of suspended solids in watercourses and its distribution along the flow length is analyzed. The developed model was used for estimation of the impact of runoff from the urban area of Kharkiv city (Ukraine) on the river Lopan. The model demonstrated satisfactory compliance with field data.