Development of a Computational Algorithm for Electromagnetic Wave Propagation in the Tropospheric Environment Based on the Fractal Method

Abstract: Accurate modeling of electromagnetic wave propagation in the troposphere is crucial for enhancing the reliability and efficiency of communication systems. This study proposes a mathematical model based on the fractal method, specifically the Weierstrass-Mandelbrot function, to represent the fluctuations of dielectric permittivity in the troposphere. Using the fractal approach, the atmospheric medium was modeled as a multi-scale surface with inherent spatial variability. Based on the proposed model, the trajectory of electromagnetic wave propagation was calculated and simulated under various test conditions. Increasing antenna height and signal frequency significantly affects the variability of the wave path in a fractal medium. The scientific significance of this algorithm lies in its ability to model wave propagation with high precision in unstable and uncertain media. The findings can be effectively applied in meteorological monitoring, above-ground communication systems, and military signal transmission networks. This research contributes to developing more robust and adaptable algorithms for modeling electromagnetic wave behavior in real atmospheric environments, especially in the presence of turbulence and structural irregularities inherent to the troposphere.

Keywords: Weierstrass-Mandelbrot, fractal function, Electromagnetic Wave Propagation, Tropospheric Environment.