Semi-empirical method for calculating diffuse runoff of conservative pollutants in small rivers: Communication 2. Influence of the number of measurements on the results of the inverse problem calculation

Relevance. When analyzing the inverse problems of reconstruction the spatial distribution of the diffuse pollutant runoff flow characteristics in areas of small rivers, the question related to the required number of calculation points inevitably arises. To conduct a correct mathematical analysis, the number of calculation points used must be quite significant (usually hundreds). A real natural experiment is usually limited to a small number of points (dozens). It can be stated that to date, the question of the influence of the number of calculation points on the stability of the inverse problems solution has been little studied. Meanwhile, it is very relevant when comparing data from mathematical calculations and natural measurements. In the presented work, an analysis of the influence of the number of a dissolved pollutant concentration measurements on the value of its total mass flow rate in the process of diffuse runoff in areas of small rivers was carried out. Methods. The calculation was carried out based on the Monte Carlo method with randomization of the dissolved pollutant concentration values. Results. In the process of implementing a numerical experiment for a given set of test functions, it was established that the stable values of the sought parameters (total mass flow rate and Peclet number) depend on the number of calculation points that determine the spatial distribution of the pollutant concentration in the study area. It was found that stable values of the sought parameters are determined by a number of points that is five to ten times greater than the number of unknown coefficients of the approximating polynomial. The dependence of the values of the sought parameters on the number of calculation points for the results of field measurements is analyzed.