Asymptotic solutions of the wave equation for a two-dimensional ionospheric model

The propagation of HF radio waves through a stratified ionosphere perturbed by dielectric irregularities varying both horizontally and vertically is studied in this paper. A method for obtaining two-dimensional approximate solutions, complementary to the WKB approximation, is discussed and illustrated. Previous results of a one-dimensional model, showing enhanced scintillation due to irregularities localized near the turning point of the wave, are confirmed. By matching the ionosphere with an uniform atmosphere the reflection coefficient for an incoming s-polarized plane wave is calculated. The case of wave reflection by a rippled specular surface is finally derived in the limit of the ionospheric gradient length approaching zero.