Forecasting the Coastal Systems State using Mathematical Modelling Based on Satellite Images
Authors: Panasenko N. D. 
Published: January 2024

Introduction. Coastal systems of Southern Russia are constantly exposed to biotic, abiotic and anthropogenic factors. In this regard, there is a need to develop non-stationary spatially inhomogeneous interconnected mathematical models that make it possible to reproduce various scenarios for the dynamics of biological and geochemical processes in coastal systems. There is also the problem of the practical use of mathematical modelling, namely its equipping with real input data (boundary, initial conditions, information about source functions). An operational source of ﬁeld information can be data received from artiﬁcial Earth satellites. Therefore, the problem arises of identifying phytoplankton populations in images of reservoirs, which, as a rule, have a spotty structure, with low image contrast relative to the background, as well as determining the boundaries of their location.

Materials and Methods. This work is based on the correct application of modern mathematical analysis methods, mathematical physics and functional analysis, the theory of diﬀerence schemes, as well as methods for solving grid equations. Biogeochemical processes are described based on convection-diﬀusion-reaction equations. Linearization of the constructed model is carried out on a time grid with step τ. A method for recognizing the boundaries of spotted structures is being developed based on Earth remote sensing data. A combination of methods is considered as image processing algorithms: local binary patterns (LBP) and a two-layer neural network.

Results. The developed software-algorithmic tools for space image recognition are presented, based on a combination of methods — local binary patterns (LBP) and neural network technologies, focused on the subsequent input of the obtained initial conditions for the problem of phytoplankton dynamics into a mathematical model. Regarding the necessary mathematical model, a continuous linearized model has been proposed and studied, and on its basis a linearized discrete model of biogeochemical cycles in coastal systems, for which practically acceptable time step values have been established for numerical (predictive) modelling of problems of the dynamics of planktonic populations and biogeochemical cycles, including in the event of death phenomena, which makes it possible to reduce the time of operational forecasting. At the same time, for the constructed discrete model, properties that are practically signiﬁcant for discrete models are guaranteed to be satisﬁed: stability, monotonicity and convergence of the diﬀerence scheme, which is important for reliable forecasts of adverse and dangerous phenomena.

In the process of work, referring to satellite images, which make it possible to obtain the state of coastal systems with high accuracy, initial conditions are entered into the mathematical (computer) model. The model analyzes satellite image data and determines levels of “pollution”, the formation of extinction zones and other factors that may threaten nature.

Discussion and Conclusion. Discussion and conclusions. Using this model, it is possible to predict possible changes in coastal ecosystems and develop strategies to protect them. The results obtained make it possible to signiﬁcantly reduce the time of forecast calculations (by 20−30 %) and increase the likelihood of early detection of unfavorable and dangerous phenomena, such as intense “blooming” of the aquatic environment and the formation of extinction zones in coastal systems.