The ecological problems of the planet are a topical object of research, as the anthropogenic impact on the environment grows every year and the number of emergencies increases. One of the serious problems is air pollution. To monitor environmental problems in the world and environmental forecasting of processes in the atmosphere use mathematical models with spatially distributed parameters, which require appropriate input data - the initial state and boundary conditions. The topical issue is the use of real input data and their correct interpretation in modeling the relevant processes. In recent years, with the launch of the European Space Agency's Copernicus program and the active development of remote and Earth observation systems, new sources of objective data have emerged that can be assimilated into environmental processes and increase the accuracy of forecasting air pollution. The application of such models for large areas requires significant computing resources and parallelization of calculations.
With the development of new technologies, new data sources are emerging. In particular, the satellite air quality data Sentinel-5p, which appeared in free access only in 2018 thanks to the program of the European Space Agency Copernicus, are useful in the tasks of modeling the transport of air pollutants. Satellite data consistently provide information on the state of air quality, in contrast to ground stations, as ground stations are located mostly in large settlements. E. Gerasopoulos, Giuseppe Zibordi are working on the problem of creating methods of satellite ecological monitoring of the atmosphere, and in Ukraine G. Milinevsky, N. Kussul, A. Shelestov and others. With the exponential increase in satellite data, there is a need to develop optimized mathematical models and improve methods for sharing satellite and model data. At the same time there are questions of increase of accuracy and increase of speed of modeling algorithms.
The schemes of McCormack, Brailovskaya, Lax-Wendroff, Alain-Chen, Dufort-Franklin and a number of others. This is due to the fact that the numerical methods used on multiprocessor systems must meet all the conditions of correctness and accuracy: to approximate the problem, be stable, reflect the conservation laws on the grid set, satisfy the required accuracy and be efficient in performance on each processor, etc. In addition, they must be effective in parallelization.
The aim of the dissertation research is to improve the mathematical apparat of modeling transfer processes by developing a two-step symmetric algorithm and the use of satellite data, which will increase the speed and accuracy of modeling by using multiprocessor calculations and geospatial data.
In the dissertation for the first time the following new scientific results are received:
- for the first time a two-step numerical algorithm for finding the solution of the problem of numerical modeling of a beam of Gaussian radiation in the conditions of thermal self-heating of the medium was developed. The conditions of existence and unity of the solution of the difference system, its order of approximation are established;
- for the first time, a two-step numerical algorithm for finding solutions of initial-boundary value problems for transfer systems (systems of parabolic equations of the second order without mixed derivatives) was developed, focused on the use of multiprocessor complexes. The conditions of existence and unity of the solution of the difference system, its order of approximation are established;
- for the first time a model and information technology of assimilation of satellite data into a model of air pollutant transfer were built. The developed algorithm is effective for use in cases when it is necessary to assess air quality not only in cities, but globally in the world or at the level of a particular country;
- the significance of using the DS algorithm to the problem of air pollution propagation by estimating the accuracy of modeling the concentration of pollutants in the air is proved;
- for the first time the task of monitoring air quality in the city using the DS algorithm and determining indicators of sustainable development goals to analyze the degree of land degradation;
- for the first time, the relationship between the ecological processes of land degradation (in particular, the burning of stubble in agricultural fields) and changes in air quality has been modeled.
The dissertation research was performed within the scientific topic "Mathematical modeling and optimization of dynamic systems for defense, ecology and medicine" (№ State Registration 0119U100337).
