Determination of the Concentration of Contaminants at the Outlet of the Underwater Source Based on the Variation Algorithm

Abstract

A variation algorithm for determining the concentration of the contaminating admixture at the outlet of the underwater source $C_{p}$ is proposed. It is based on a minimization of the quadratic functional, which is determined by the residual values of the measured and calculated values of the pollution concentration and the solution of the corresponding problem in variations. The algorithm for determining the $C_{p}$ tested in the framework of numerical three-dimensional hydrothermodynamic model of the spread of sewage in the coastal zone of the Crimean Peninsula, adjacent to the city of Sevastopol. Numerical experiments were carried out to restore the $C_{p}$ for different number of measurements and different levels of random noise in the measurements. A measurement scheme was used in which a moving sensor consistently measured the vertical profile of pollution concentration at fifteen stations. It is shown that without taking into account the random noise in the initial data, the $C_{p}$ parameter is restored accurately for any number and combination of stations. When random noise is taken into account, parameter $C_{p}$ recovery occurs when the most informative stations are used. The proposed algorithm can be useful in the interpretation and planning of natural experiments on the study of wastewater distribution in coastal waters.