Methods of predicting the atmospheric bending of radio rays

Abstract

Threc Illcthod~ for prcdi cting t he bcnd ing of r adio mys ",hcn the rcfracti,'c index I~,;ofi l c a bove t hc s Ul'facc laye r is unknown havc bec n d C\'cl~pe d !'('cently by, the auLl:o r:,:, ~ hl'o;l' m ethods a re : a s t atistical tec hniqu e for rcfraetlOn at hi g h llll tIal l' le \'atlOn a ng les, l st."l1ctt!on of bend in g from an cxp o ncntial mod el of at mosphe ric l'ef rad lvc Index, a nd a 1Il0dlfi ?atlon of the expont'nt ial Illodel t o accoun t for the h.eavI ly \\,l' lghtl'cl dlccts of ll ilomalolis In It Ial re[racti,'c in dl'x grad ie nts at s mall initial eiC'\'at ion angll's , 1';ac l1 model IS dl' l?eudent UP O!I t he ,'alue of the rcfractiH' index at g rou udle,'el 01', III L1w CH'iC of S Ul)(' rrc fracL l ~n , t he add l-Lional kn o\\'ledge of L1,e refract i,'e index ,grad il' n L next to the ea rlil 's s urface" I-,nch method works best in a parti cu lar ra ngl' of JII lk ll r1entilOn 1tnglr's 01' Ille teorolog lcal cond lL10!lS, The hcig llt a nd a ngu lar mngl's of a ppli catio n of t':w h lllct hod an' che cked by co mpa l'l so ll Wl t,h valllcs obtain ed frolll 77 di verse rl'fractl vc Inde x profill' s rl' prl'sc nt a t'." c of \\ Ide clilnaLlC "l1ria lio n, H is found Lhat 1I11' ll ~C of Lite b('st of Lhe t hree Ill ClilOcl s \\:111 always l:csul L In a prl'cl iction of the tolal aL mos phl'ric bl'nding wilhin 10 p Cl'cc nt for ' ,l lI tm l l'll'ntt lo n angles from zer o to 10 lIli ll iraci ia ns an d to \\'i th in •1 p e rc e ul fol' Itl llIal l'lcnLt lo n a ll g l e~ g reater t han J 7 m ill iradian s ( ...... I dl'g) ,

Proceedings of the Second Tropospheric Refraction Effects Technical Review Meeting. Volume I. Agenda. Opening Remarks and Introduction, Papers by the Air Force Cambridge Research Laboratory the Mitre Corporation the National Bureau of Standards, Presented at the Mitre Corporation Bedford, Massachusetts on November 13 and 14, 1963

“…to the problem of determining the degradation in the precision of frequencies and of time intervals after propagation over a line-ofsight path is discussed in a recent paper by Norton, Barrows, Janes and Thompson [1962]. Barrows [1963] In Equations (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) and (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14), c is the velocity of light. Note that, as v 1 approaches v 2 , fc 12 increases without limit, the correlation between…”

Techniques for computing refraction of radio waves in the troposphere

“…Condition (1) will be violated if there is a discontinuity in the refractive index (which will not occur in nature), or if the gradient of refractive index, dn/dr, is very large, in which case condition (2) will also be violated. Condition (1) should be satisfied if (dn/dh)perkm <0 N kc where refractivity, N, is defined as N = (n-1) x 10 and f is the carrier K.C frequency in kilocycles [Bean and Thayer, 1959]. Condition (2) is a basic requirement resulting from Fermat's principle for geometrical…”

A world atlas of atmospheric radio refractivity [by] B. R. Bean [and others]

“…There has been a need in radio engineering for a method whereby the radio refractivity, A'^, at some height, z, or the gradient of A'^with respect to height, dN/dz, could be accurately estimated for any world location during any season of the year. Previous studies have attempted to solve this problem by determination of the value of surface refractivity, N^, and the use of an exponential decay with height [Bean et al, 1960a] S or by presenting seasonal means and distributions of N at fixed pressure levels in the atmosphere for various radiosonde stations [U. S. Navy, 1955-59;Michaelis and Gossard, 1958]. However, these results did not provide any means whereby N {z) could be obtained at any arbitrary location, i.e., places for which meteorological measurements were not available.…”