Recovery of the Concentration of Suspended Matter in the Upper Layer of the Sea of Azov Based on a Variational Algorithm for Assimilation of Measurement Data

The purpose of this work is to test the variation algorithm and create a program code for assimilation of the measured concentration of suspended matter. The paper considers an example of variational assimilation of data on the concentration of suspended matter in the upper layer of the Azov Sea. The most up-to-date information is received from satellites, but it often contains omissions due to various reasons, including the scattering effect of clouds. Therefore, taking into account satellite information, a model solution was developed from which measurement data with omissions were selected. This information simulated presence of clouds. The numerical implementation of the passive impurity transport model used the results of calculations based on the dynamic model of the Sea of Azov, gradient methods for minimizing the forecast quality function, and the solution of an adjoint problem for constructing its gradient in the parameter space. When implementing the variation procedure, integration is performed of the main and adjoint tasks as well as the task in variations. The last is necessary for determining the iterative parameter when performing a gradient descent. Integration problems are solved using TVD approximations. As a result of numerical experiments, the reliable operation of the procedure under the specified conditions is shown, which allows to restore the initial field with good accuracy. The implemented variational algorithm for assimilation of measurement data can be applied to identify the input parameters of numerical modeling based on information distributed over time and space to solve various environmental problems.