Chapter 3. Tropospheric Refraction 



3.1. Introduction 



If a radio ray is propagated in free space, where there is no atmosphere, 

 the path followed by the ray is a straight line. However, a ray that is 

 propagated through the earth's atmosphere encounters variations in 

 atmospheric refractive index along its trajectory that cause the ray path 

 to become curved. The geometry of this situation is shown in figure 3.1, 

 which defines the variables of interest. The total angular refraction of 

 the ray path between two points is designated by the Greek letter r, and 

 is commonly called the "bending" of the ray. The atmospheric radio 

 refractive index, n, always has values slightly greater than unity near the 

 earth's surface (e.g., 1.0003), and approaches unity with increasing height. 

 Thus ray paths usually have a curvature that is concave downward, as 

 shown in figure 3.1. For this reason, downward bending is usually defined 

 as being positive. 



If it is assumed that the refractive index is a function only of height 

 above the surface of a smooth, spherical earth (i.e., it is assumed that the 

 refractive index structure is horizontally homogeneous), then the path of 

 a radio ray will obey Snell's law for polar coordinates: 



riir^ cos 6-2 = niVi cos 9i, (3.1) 



the geometry and variables used with this equation are shown in figures 

 3.1 and 3.19. With this assumption r may be obtained from the following 

 integral, 



Ti 2 = - / cot 5 — , (3.2) 



which can be derived as shown later in the chapter or as derived by Smart 



The elevation angle error, e, is an important quantity to the radar 

 engineer since it is a measure of the difference between the apparent 



Figures in V:)rackets indicate the literature references on p. 87. 



49 



