Modeling Tropospheric Radiowave Propagation Over Rough Sea Surfaces Using the Parabolic Equation Fourier Split-step Method

This thesis develops the theory for solving the parabolic equation (PE) using the Fourier Split-step method for the purpose of modeling tropospheric radiowave propagation over the sea surface. Beginning with Maxwell's equations, the standard parabolic equation (SPE) approximation is derived from a linearly polarized scalar wave equation in Cartesian coordinates. Then, an introduction to the Fourier Split-step method is presented as a solution to the PE equation. Next, we make necessary approximations to the PE formulation to appropriately represented propagation through the troposphere including a conformal transformation of the coordinate system and the inclusion of refractivity profiles to represent evaporation duct conditions. The PE derivation concludes with the incorporation of the effects of finite impedance boundary conditions and sea surface roughness, which has a Split-step solution using the mixed Fourier transform (MFT). Finally, numerical examples are given to compare the field predictions of two well known PE/Split-step propagation models: Tropospheric ElectroMagnetic Parabolic Equation Routine (TEMPER) and Advanced Propagation Model (APM).