ASYMPTOTIC METHOD FOR DIFFUSE RUNOFF ESTIMATION OF CONSERVATIVE POLLUTANTS FOR SMALL PLAIN RIVERS

Abstract

The paper considers a method for estimating the total mass flow rate of conservative pollutants using an asymptotic representation of the advection-diffusion equation solution under the assumption of the smallness of the Peclet number reciprocal value. Based on the method of matched asymptotic of the corresponding singularly perturbed problem, an algebraic relationship between the concentration of the pollutant, its total mass flow rate and the Peclet number was obtained. The exact calculation of the direct problem was based on the analytical representation of the initial test source functions for the advection-diffusion equation. The calculation of the inverse problem was carried out based on the global optimization method when determining the absolute minimum of the corresponding quality functional. A satisfactory agreement between the results of solving the inverse and direct problems has been established, while the deviation of the calculated parameters from their exact values ​​does not exceed several percent. To take into account possible random deviations of pollutant concentration values ​​from the exact solution, the Monte-Carlo method was used. It has been established that in this case, the calculation also yields stable results, and the deviations of the sought parameters from their exact values ​​do not exceed ten percent. The proposed method yields correct results in terms of estimating the values ​​of the parameters under consideration.