264 TRANSHORIZON PARAMETERS 



height (n"), above the crossover height (n'), and Qe- As hsted in table 

 6.6, n represents the value of (6.27) for the height increment zero to 3 km. 

 Before proceeding, the method of calculating ge will be described. The 

 concept of the equivalent gradient is closely related to that of the effective 

 earth's radius. The curvature of the effective earth is given by: 



1 1 , 1 dn 



— = - -\- - -,T cos d 



re a n ah 



where r^ is the effective earth's radius; a is the radius of the earth; and 

 (1/n) idn/dh) cos d is the curvature of the radio ray. 

 The value of r^ is determined from the geometrical relationship 



h ^-'^ 



where c?,, the ground distance to the crossover height, h^, has already been 

 determined by the ray-tracing procedures discussed in chapter 3. Thus 

 one obtains 



dn \ _ 2hc 1 

 dhj ~ d;' 



for 6 = and setting (cos d)/n c^ 1. In order to obtain the equivalent 

 gradient as a positive quantity in the more convenient refractivity units, 

 the following expression is used: 



(i _ 2^Y 



0- = Ka - t^r- 



It is evident from table 6.6 that the results obtained with IT are com- 

 parable with those using 11', due supposedly to the crossover height being 

 on the order of 100 m for these paths. The value 11" appears to contribute 

 little to the final value of 11 and is poorly correlated with the radio data. 

 An interesting exception to this observation is the subrefractive case 

 where 11" yields a larger correlation coefficient than either n or U'. The 

 overall conclusion that one reaches from the data of table 6.6 is that the 

 most promising of the parameters considered is U, closely followed by 

 AA^ and N s- In fact, the difference between the results obtained with 

 n and AN gives one pause to consider if the added complexity of deter- 

 mining n is worth the relatively small gain in correlation with the radio 

 data. The results obtained with Qe and go (the N gradient of the initial 

 layer as reported by the radiosonde) are disappointingly small and are of 

 no practical significance when compared with those of H, AN, and even 

 A.,. 



