EXPONENTIAL MODEL 65 



Table 3.2. Constants for the CRPL Reference Atmosphere — 1958 



Note: Oe is the effective earth's radius and is equal to a'k, a' = a + hs, where hs is the altitude of the earth's 

 surface above sea level, a = 3960 miles and c = 1/8— /is In Ni/105. 



been estimated to be no more than a few percent, it could be important 

 in such high precision applications as radar tracking of earth satellites. 

 It should be remembered in subsequent applications that a unique feature 

 of these reference atmospheres is the dependence of N s on the altitude of 

 surface above sea level. This feature was built in so that the reference 

 atmospheres would be completely specified by the single parameter N s. 



3.8. The Exponential Model 



The next model of the atmosphere to be considered may be specified 

 by assuming a single exponential distribution of A^: 



where 



N ^ Ns exp {-Ce {h - hs)], 



Ce = In 



Ns 



N{1 km) 



In 



Ns 



Ns + AN 



(3.43) 

 (3.44) 



and these equations are used to determine A'^ at all heights. This model 

 of atmospheric refractivity is a close representation of the average re- 

 fractivity structure within the first 3 km. Further, the single exponential 

 model has the advantage of being an entire function, and therefore is easily 

 used in theoretical studies. This model of the atmosphere has been 

 adopted for use within the National Bureau of Standards with specific 

 values of the constants in (3.43) and (3.44). These constants are given in 

 table 3.3 and specify the CRPL Exponential Reference Atmosphere — 

 1958. 



Figure 3.5 compares the A'^ structure of the above two models plus the 

 4/3 earth model. It can be seen that the assumption agrees with the 

 reference atmosphere in the first kilometer, which is to be expected since 

 A'^g = 301 is the value required to yield the 4/3 gradient from figure 3.5. 

 Figure 3.5 illustrates the essential agreement of the reference atmosphere 



