64 TROPOSPHERIC REFRACTION 



the AA^^ obtained from (3.40) are in rather good agreement with the values 

 calculated from actual A'' profiles, even those observed in southern 

 California. 



Equation 3.40 offers a convenient method of specifying various models 

 of the refractivity structure of the atmosphere, since it allows an estima- 

 tion of the value of A^ at 1 km in addition to the two values already 

 known; i.e., A''^ and A'' = at /i = oo. 



It may be further assumed that A'^ decreases exponentially from hs + 1 

 to a constant value of 105 at 9 km above sea level. In this altitude 

 range N is defined by: 



A^ = A^i exp \-c{h - h, - l)\,hs + I < h < 9 km, (3.41) 



where 



^ S - h, 105 ' 



and A^^i is the value of A'' at 1 km above the surface. 



Above the altitude of 9 km, where less than 10 percent of the total 

 bending occurs, a single exponential decrease of A'^ may be assumed. The 

 coefficients in the exponential expression: 



A^ = 105 exp { -0.1424 (h - 9)},h> 9 km, (3.42) 



were determined by a least squares analysis of The Rocket Panel data 

 [12]. This expression is also in agreement with the ARDC Model Atmos- 

 phere 1956 [13] and Dubin's [14] conclusion that a standard density- 

 distribution may be used to determine the refractivity distribution at 

 altitudes in excess of 20,000 ft. 



The three-part model of the atmosphere expressed by (3.39)-(3.42) has 

 the advantage of the effective earth's radius approach, particularly for 

 such applications as point-to-point radio relaying over distances up to, 

 say, 100 mi, where the radio energy is generally confined to the first 

 kilometer, plus being in reasonably good agreement with the average A^ 

 structure of the atmosphere. The reader is cautioned, however, that 

 application of this model to mode-theory calculations would be mislead- 

 ing, since the resultant diffraction region fields would be enhanced by the 

 addition of strong reflections from the r?-gradient discontinuities at /is + 1 

 and at 9 km. The specific combinations of A^s, hs, and AA^, that define 

 the CRPL Reference Atmosphere — 1958 are given in table 3.2. 



The station elevations corresponding to given combinations of N s and 

 AA'^ were chosen to correspond with an average decay of A^ with station 

 elevation. Although the error in neglecting this height dependence has 



