Propagation of Short Radio Waves in a Normally Stratified Troposphere

Experiments of the past decade give stronger fields well beyond the horizon than are calculated by the 4/3 airless earth approximation. Post-war work on the theory of the WKB approximation for wave propagation in slowly varying inhomogeneous media, and the peculiar results for eigenvalues of the bilinear refractive index proffle offer valuable clues in the search for an oversight in conventional propagation theory. If the absolute value as well as the gradient of the refractive index at the earth´s surface be specified, with a refractive index profile which tapers to vacuum at some arbitrarily large height, then allowed modes of the wave equation permit the field to be calculated within, just beyond, and well beyond the horizon, in agreement with many vhf and microwave experiments. Modes thus calculated are supported by ordinary coherent molecular scattering in normal air dielectric layer. At times, superrefraction and macroscopic turbulence are additional mechanisms for propagation deep into the shadow of the earth bulge.