322 REFRACTION AND REFRACTIVE INDEX MODELS 



Territory, Canada, for February) and for humid tropical areas (Canlon 

 Island, South Pacific, February) from 5-yr means of A'^ versus height 

 and are listed in table 8.2. 



The extreme meteorological differences of these two locations are quite 

 evident. The Ha = 9.4 km and 7/^, = 2.0 km at Canton Island indicate 

 a warm atmosphere with a strong humidity gradient, while the value 

 of H d = 6.3 km at Isachsen indicates very stratified air with high surface 

 density and a strong density decrease with height. The value of //„, = 

 6.5 km at Isachsen reflects a very low humidity gradient; in fact, at no 

 point in the troposphere does W exceed 3 A^ units for this location and 

 season. 



Table 8.2. Hd and Yi^ifor arctic and tropical locations 



The value of //„, = 2.6 km reported for the characteristic altitude of 

 water vapor for the middle belt of the U.S.S.R. [7] also appears to be in 

 agreement with the conclusions of the present study. 



8.2. Effect of Atmospheric Horizontal 

 Inhomogeneity Upon Ray Tracing 



8.2.1. Introduction and Background 



It is common in ray tracing studies to assume that the refractive index 

 of the atmosphere is spherically stratified with respect to the surface of 

 the earth. Thus, the effect of refractive index changes in the horizontal 

 direction is normally not considered, although Wong [13] has considered 

 the effect of mathematically smooth horizontal changes in airborne propa- 

 gation problems. 



Neglecting the effect of horizontal gradients seems quite reasonable in 

 the tropospheric because of the relatively slow horizontal change of 

 refractive index in contrast to the rapid decrease with height. In fact, 

 examination of climatic data indicates that one must compare sea-level 

 stations located 500 km from each other on the earth's surface in order to 

 observe a difference in refractive index values which would be comparable 

 to that obtained by taking any one of these locations and comparing its 

 surface value with the refractive index 1 km above the location. Although 

 the assumption of small horizontal changes of the refractive index appears 



