Tropospheric bending of radio waves

Abstract

A simple and accurate method is presented for computing the refractive bending of radio waves in the lower 100,000 ft of the atmosphere. A given refractive‐index profile is approximated by a series of straight lines (layers of constant gradient) and the incremental bending computed for each layer. The method is applied to the ‘standard’ atmosphere, and total bending is plotted against the surface refractive index for various vertical angles of arrival from 0 to 1 radian.

Techniques for computing refraction of radio waves in the troposphere

“…An exponentially decreasing refractive index in the troposphere has been recognized for some time [Bauer, Mason, and Wilson, 1958;Anderson, 1958] . Recently Bean and Thayer [ 1959] introduced an exponential model for N(h) based on an analysis of observed profiles from many climatic areas (mostly in the U.S. ).…”

On the calculation of the departures of radio wave bending from normal

“…The height variation of 0, al though dep end ent upon the refractive index distribution tlll'ough Snell 's law, is at least four times more sensitive to purely geometric changes than to r efractive index ch anges [2] . This th en suggests that we m ay simplify our problem by assuming that 0 may always b e determined by its val ue in th e N(h ) = N s exp ( -ch) atmosphere for the h eigh t under consideration .…”

“…The purpose of this paper is to consider departures of n structure from normal, as specified by (2), th e effect of these departures upon ray refraction, and to present a n ew m ethod for calculating 7 based upon th ese departures which will differ from other approximate methods already in th e literature [1,2,5,12,18,19,20].…”

Correlation between hourly median scattered signals and simple refractivity parameters

“…The r elationship is not linear ; its exact form is h ard to assess, ~imil ar attem pts to fit P to values of t::, .N computed usmg N -valu es from 3,000 to 10,000 ft over th e midpoint yielded much poorer results, The r eason for this is not completely clear . R ay tracing by Anderson's [1958] graphical methods indicated that the I base of th e common volume varied from arolmd 7,500 It in ~om e tropic~l air masses to as bigh as 12,000 f t 111 polar all' masses, However the important bendin g occurs in th e frrst few hu'ndred feet above ground at th e ends of t h e p ath , Most of the r efractivity versu s heigh t profiles given in Volume II of Latour's report can be approximated by straight lines up to a h eight of 5 000 to 10000 ft.…”