A curvilinear coordinate-based split-step parabolic equation method for propagation predictions over terrain

Propagation of radiowaves over irregular terrain and in an inhomogeneous atmosphere is solved by the parabolic equation method using the split-step Fourier algorithm on a terrain-conformal mesh. A piecewise continuous coordinate system is generated by the specification of: (1) the terrain profile shape at discrete points and (2) an upper height. The resulting mesh is conformal to the terrain at the lower boundary and gradually flattens off at the maximum height. In addition to preserving the number of points on any vertical line between the terrain and the maximum height from one range step to another, the coordinate transformation used in the paper produces a correction term in the refractive index whose gradient diminishes with height. As a result, the sampling requirements over steep terrain are relaxed when compared to the Beilis-Tappert transformation. Formulation and results are given both for the horizontal and vertical polarizations.