Mathematical Modeling of Hazardous Natural Phenomena in a Shallow Basin

This paper is devoted to the construction and analysis of coupled mathematical models of hydrophysics and biological kinetics used for predicting hazardous natural phenomena occurring in shallow basins. The propagation and transformation of aquatic organisms is affected by such physical factors as three-dimensional spatial motion of water taking into account the advective transfer and microturbulent diffusion, spatially inhomogeneous distribution of temperature, salinity, and oxygen. Biogenic pollutants cause algae growth, including toxic and harmful ones; this growth can cause hazardous phenomena in the basin, including eutrophication and suffocation phenomena. A three-dimensional mathematical model of hydrodynamics is constructed and used for calculating the water flow velocity field. To investigate hazardous phenomena in a shallow basin related to suffocation phenomena in it, a three-dimensional spatially inhomogeneous ichthyological model of commercial fish dynamics is developed. Models of observations parameterized on the basis of stoichiometric relations, Monod, Michaelis–Menten, and Mitscherlich–Baule laws that describe the consumption and accumulation of nutrients by phytoplankton and commercial detritophagous fish and the growth of aquatic organisms depending on the spatial distribution of salinity, temperature, and oxygen regimen are considered. To calibrate and verify the models, constantly updated ecological databases obtained, in particular, in field research of the Sea of Azov and Taganrog Bay are used. To improve the accuracy of predictive simulation, the field data is filtered using the Kalman algorithm. As a result of processing the hydrological data, salinity and temperature isolines in the surface layer are obtained; for this purpose, a recognition algorithm is used. Using interpolation and superposition of domain boundaries, more detailed depth, salinity, and temperature maps for the Sea of Azov are obtained. Numerical methods for solving the formulated problems that are based on finite difference schemes taking into account the degree of filling of the computation domain control cells are developed. These methods are implemented on high-performance computers, and they decrease the numerical solution error and reduce the computation time by several fold. Based on the numerical implementation of the developed models, hazardous natural phenomena in shallow basins (related to the propagation of harmful pollutants), eutrophication, and alga