Comparison of Methods for Assessing the Assimilation Capacity of the Kazakhstani Sector of the Ili River

A mixed inverse problem for determining the biochemical oxygen demand of water ( L 0 ) and the rate of biochemical oxygen consumption ( k 0 ), which are important indicators of water quality, has been formulated and numerically solved based on real experimental data. The inverse problem is reduced to the optimization problem consisting in minimization of the deviation of the calculated values from the experimental data, which is solved numerically using the Nelder–Mead method (zero order) and the gradient method (first order). A number of examples of processing both model experimental data and field experimental data provided by hydrological stations monitoring pollutants in the Kazakhstani part of the Ili River basin are presented. A mathematical model that adequately describes the processes in the river system has been constructed.