Semi-empirical method for calculating diffuse runoff of conservative pollutants in small rivers: 1. Method for reconstructing the total mass flow rate

Relevance. The quality of river water is the most important factor in ensuring environmental safety and rational use of natural resources. Diffusion runoff of river pollutants is the most dangerous because it is uncontrolled and unregulated. The impossibility of directly assessing the consumption of pollutants in diffuse pollution processes requires fundamental research and the development of adequate mathematical models based on methods for solving inverse problems. The presented work proposes a method for calculating the total mass flow rate of conservative pollutants entering a watercourse from a catchment area. Methods. Based on the integral representation of the stationary one-dimensional equation of pollutant transport, a method for calculating the spatial distribution of the total mass flow rate of conservative pollutants in a catchment area is proposed. To determine the unknown distribution parameters, the global nonlinear optimization method and the Monte Carlo method were used. Results. The use of the nonlinear global optimization method allowed us to determine both the value of the total mass flow rate of the pollutant in the study area and the value of the Peclet number included in the advection-diffusion equation. Using the Monte Carlo method, the stability of the obtained results with respect to random deviations in concentration values is demonstrated when a thousand possible deviations are realized in a given interval.