An optimal control model for the surface runoff contamination of a large river basin

In this paper surface water contamination in a large river basin is analyzed. We develop an optimal control model that incorporates variations in pollution loads, benefits and environmental damage costs across several subbasins into a basin-wide decision framework. The river basin is assumed to consist of multiple subbasins, where each of these is composed of a water canal emptying into one major river flow. Thus, the chemical and sediment loading, which represents the control variable, is treated as a point inflow source of contaminant. The flow of contaminants in the main river is modelled by an advection–diffusion partial differential equation. The management problem is to determine the optimal pollutant loads at these different influx points such that the discounted economic return from the pollutant-generating activities less the environmental costs of the contaminant is maximized. Existence of a unique optimal solution for a finite time problem is proved. In addition, the management implications of this area-wide optimal control strategy are discussed.