A Rapid and Accurate Ray Tracing Algorithm for a Horizontally Stratified Atmosphere

Abstract

It is shown that the effective earth's radius technique may be applied to ray tracing through a horizontally stratified atmosphere over a smooth, spherical earth, where the refractive index profile consists of relatively thin layers of nearly‐constant n‐gradient. With this method the refraction (bending) of the radio ray becomes a closed form function of the elevation angle, which is itself a closed form function of the refractive index profile. This allows ray tracings to be performed with less computing time and with a much higher degree of internal precision than formerly. This latter advantage facilitates computation of small dispersive effects at optical wave lengths. It is shown that the radial distance power‐law model of n(r), inherent in the effective earth's radius approach, is nearly identical, for relatively thin layers, with the simple constant gradient model which has been widely used in the past, thus assuring compatibility with previous results.