CALCULATION OF DISSOLVED POLLUTANTS MASS FLOW ACCORDING TO THE DATA OF THEIR CONCENTRATION SPATIAL DISTRIBUTION IN THE SITES OF SMALL PLAINT RIVERS

Abstract

The paper presents the general solution of the stationary advection-diffusion equa- tion in the integral form for establishing the relationship between the concentration and the total mass flow rate of the pollutant on the plot of the catchment area. The resulting equation was used to solve the inverse problem of estimating the pollutant mass flow rate based on the arbitrary test functions. The unknown dependence of the total mass flow rate on the coordi- nate was represented as a polynomial. The coefficients of polynomials were determined by the least squares method. It was found that the increase in the degree of the polynomial ensures convergence to the exact solution over the entire interval under study. Such a representation describes test functions with high accuracy. When considering randomized concentration dis- tributions, it was established that an increase in the degree of the polynomial leads, on the contrary, to a deviation from the exact solution. These problems were eliminated with the use of the Lasso regularization method, which provides stable solutions to the inverse problem with a minor deviation from the test functions.