Inverse algorithm for Streeter–Phelps equation in water pollution control problem

Abstract

In this study, for the first time in the literature, we consider the inverse problem that arises in the problem of controlling water pollution in streams. The problem here is to determine the source’s load of pollution based on the results of measuring water quality in places remote from the waste source. Based on the results of measuring the concentration of dissolved oxygen (DO), which characterizes the level of pollution of surface water in a stream, will determine the level of the pollutant load of the waste discharger. Using classical Streeter–Phelps model, showing the relationship between the source power and the water quality of river channels, the inverse algorithm is constructed to determine the load capacity of the waste source. The resulting algorithm in this study is for general case and refers to several sources of waste. The article also presents the numerical results of applying the algorithm obtained for specific examples. The results of this study contribute to the scientific and substantiated issue of environmental decision making.