Three-Dimensional Modeling of Wave Propagation over Different Types of Terrains and Environments Using the Parabolic Equation Solved by Higher Order Approximation of the Finite Difference Method

Mohammad Ahmad, Dayalan Kasilingam


Designing communications and radar systems depends on accurate modeling of ground waves in three-dimensional environment. Propagation of ground waves in the VHF and UHF bands affected by the characteristics of the terrain and the troposphere. Although some three-dimensional modeling of ground waves was found in the literature based on solving the parabolic equation, they were limited to a specific terrain and/or environment. Also, a lot of important factors such as the refractive index of the troposphere were ignored. In this paper, a computational model was developed for predicting the electromagnetic wave propagation over different types of terrains and environments under three-dimensional conditions. The model is based on solving the parabolic equation using higher order approximation of the finite difference method. The model allows specifications of an antenna and the electrical characteristics of the ground. Moreover, the model treats flat and non-flat terrains, mixed path with different electrical characteristics, and forest environment. Furthermore, the model enables calculations to be performed under standard and non-standard refractive conditions of the troposphere that varies in height, width, and range. The results were compared with two-dimensional parabolic equation solved by Fourier split-step and showed excellent agreement.


Wave propagation, Three dimensional, Parabolic equation, Finite difference method

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Indonesian Journal of Electrical Engineering and Informatics (IJEEI)
ISSN 2089-3272

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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