Application of Methods of Observational Data Assimilation to Model the Spread of Pollutants in a Reservoir and Manage Sustainable Development

Introduction. Mathematical models and methods are widely used to study natural phenomena, replacing more expensive field experiments. However, one of the main challenges in modeling processes in complex systems is the lack of available input data and difficulty in selecting model parameters. The use of observational data assimilation methods is one of the ways to provide mathematical models with input data and parameter values. The aim of this study was to predict the development of complex natural systems under conditions of pollution using mathematical modeling techniques. To achieve this, several tasks were completed: a method for assimilating observational data was selected, a mathematical model for biological kinetics was updated, it was integrated with a hydrodynamic model, and a software package was developed. The significance of the work lies in the to the implementation of a model of the dynamics of phytoplankton populations (eutrophication) of the Azov Sea in the presence of pollutants, based on the use of variational methods for assimilating data obtained during expeditionary research. Materials and Methods. The spread of pollutants was modeled using a three-dimensional mathematical model based on a system of convection — diffusion — reaction equations. The vector of movement of the aquatic environment was the input data for the model. The components of the current velocity vector in the coastal system were calculated using a mathematical model of hydrodynamics, based on three equations of motion and the equation of continuity. The software package developed based on these models received full-scale data collected during expeditionary research as input, and allowed us to refine the model of pollution in the aquatic environment and biota using variational methods for data assimilation. Results. A short-term forecast for the spread of pollutants at the outlet of the Taganrog Bay was developed. The conducted computational experiment reflected the dynamics of pollutant spread from sources of contamination over a period of 3 to 12 days. Discussion and Conclusion. The variational methods of assimilating observational data discussed in this study allow for the refinement and supplementation of mathematical models of phytoplankton population dynamics and pollutant spread. The software based on these mathematical models enables the creation of short- and medium-term forecasts for the spread of harmful substances, assessment of their impact on the growth of major phytoplankton species in the Azov Sea, and determination of strategies for sustainable development management.