132 A^ CLIMATOLOGY 



4.4. The Climatology of Ground-Based Radio Ducts 



4.4.1. Introduction 



The occurrence of atmospheric ducts places limitations upon ray tracing 

 of VHF-UHF radio waves. Ducting is defined as occurring when a radio 

 ray originating at the earth's surface is sufficiently refracted so that it 

 either is bent back towards the earth's surface or travels in a path parallel 

 to the earth's surface. Although the rigorous treatment of ducting in- 

 volves consideration of the full wave eciuation solution [31] rather than a 

 simple ray treatment, the present study will be based upon a geometrical 

 optics definition of the limiting case in which ray tracing techniques may 

 be used. This simple criterion is then applied to several years of radio- 

 sonde observations from stations typical of arctic, temperate, and tropical 

 climates to derive estimates of the variation of the occurrence of radio 

 ducts with climatic conditions. 



4.4.2. Meteorological Conditions Associated With Radio 

 Refractive Index Profiles 



The path followed by a radio ray in the atmosphere is dependent upon 

 the gradient of the refractive index along that path. Of the vertical and 

 horizontal gradient components that compose the path gradient, the 

 horizontal gradient is normally negligibly small. Thus, the atmosphere 

 is considered horizontally homogeneous and only the vertical gradient of 

 the refractive index is utilized. The numerical value of the vertical 

 gradient of the index of refraction depends on the vertical distribution 

 of atmospheric temperature, humidity, and pressure. 



Normally, temperature and humidity decrease with height in the atmos- 

 phere, since turbulence prevents any great changes in structure. How- 

 ever, there are periods of time in which the air becomes fairly calm, 

 whereupon temperature inversions and humidity lapses can be built up 

 and maintained. Temperature inversions have a twofold importance in 

 that (a) they can be widespread in area and persist over a relatively long 

 period of time, and (b) they exercise a stabilizing influence on air motion 

 such that turbulence is suppressed and strong humidity gradients may 

 develop. Layers in which there is intense superrefraction to the point of 

 duct formation may be formed as a result of these gradients and trapping 

 of radio waves may follow. The inversions may start at ground level or 

 at some greater height. The thickness of the layer can show great 

 variability. Three processes that form temperature inversions are: 



Advection: Advection is the horizontal flow of air having different heat 

 properties. Such a process is of importance in microwave propagation 

 since it may lead to a different rate of exchange of heat and moisture be- 

 tween the air and the underlying ground or ocean surface, thus affecting 



