136 



A^ CLIMATOLOGY 



The gradient of the refractivity, AA'', with respect to height may then 

 be expressed : 



AN = AD -\- AW. 



(4.ii: 



Average values of AA^, AD, and AW are given in table 4.6 for two incre- 

 ments between the earth's surface and 1 km above sea level for Fairbanks, 

 Alaska; Washington, D.C.; and Swan Island, W.I. 



Table 4.6. Gradient of N, D, and W in N units per kilometer 



Several general observations may be made of the data of table 4.6: 

 The gradient of the dry term is relatively less variable than that of the 

 wet term when considered as a function of season or height; the increase 

 of AA^ from winter to summer at a particular location or from arctic to 

 tropical climate at a given time is most strongly reflected in AW rather 

 than in AD. The marked increase of gradient with height for Swan Island 

 reflects the drop of refractivity across the interface of the trade wind 

 inversion where dry subsiding air overlies the moist oceanic surface layer. 



A fundamental equation used in radio ray tracing is Snell's law, which, 

 for polar coordinates, is given in chapter 3 as 



nr cos 6 = rioVo cos do, 



(4.12) 



where n is the radio refractive index of the atmosphere, r is the radial 

 distance from the center of the earth to the point under consideration, and 

 6 is the elevation angle made by the ray at the point under consideration 

 with the tangent to the circle of radius r passing through that point. The 

 radius to any point, r, is equal to (a + h), where a is the radius of the 

 earth and h is the height of the point above sea level. The zero subscript 

 refers to the value of n, r, or d at the earth's surface. 



For the present study, geometrical optics techniques, similar to those 

 considered by Bremmer [32], are used to indicate when refraction is 



