Rays and modes in a nonuniform troposphere

Abstract

A version of the hybrid (ray mode) representation of wave fields has been suggested which is convenient with refractive index profiles corresponding to simultaneously existing surface and elevated ducts. The field at the reception point is represented as a sum of normal modes peculiar to an isolated surface duct and an assembly of rays reflected from the elevated layer.However, refractive ducts often reveal characteristic spatial zones where the geometrical optics is not valid. One of these is the near transhorizon region where the receiver is shadowed from the source by the terrestrial sphere, hence unattainable for direct rays, while it still cannot be reached by rays reflected from the elevated inversion as these return to earth at much greater distances. Ray optics cannot be applied near caustic surfaces either.A number of writers [e.g., Juz•, 1975; lshihara et al., 1978; lshihara and Felsen, 1979; Kukushkin and Sinitsin, 1979, 1980; Migliora et al., 1980] have recently developed hybrid, ray modal techniques permitting one to describe wave fields in structures where none of the classical methods per se can provide a concise description of diffraction phenomena. This paper suggests a version of the hybrid representation which might be convenient for tropospheric M profiles like those of Figure 1, with hi >) hs and h, ho < hs. Part of the results were presented at the URSI 1980 Commission F Symposium [Kukushkin and Sinitsin, 1980]. CONTOUR INTEGRAL First, we assume • to depend solely on height, which allows use of the familiar contour integral representing the attenuation function (against the free space level) of a vertically polarized (i.e., 'electrical') 573 574 KUKUSHKIN AND SINITSIN: RAYS AND MODES IN TROPOSPHERE

Analytic Parabolic Equation Solutions.

“…The saddle point condition In (31) Is the equation for a ray path reflected ntimes at y= 0, the term r n in (32) incorporates the associated reflection doefficient at y=O, the exponential term In (32) describes the phase accumulation along that path, (-i)n accounts for n ray encounters with a…”