166 A^ CLIMATOLOGY 



with height is 



WW) = RA) - 1] 10« = 313 exp {-V6.95) (4.42) 



where h is the height above the earth's surface in kilometers and 313 is the 

 long-term average value of (n — 1) 10^ at the earth's surface for the United 

 States. In practice it is convenient to utilize this average N{h) function 

 to refer the observed N{h) data to the common level oi h = by means of 



A{h, 313) = N{h) + 313 [1 - exp {-h/Q.95}]. (4.43) 



Chapter 1 shows that A{h,31S) is analogous in concept to potential tem- 

 perature but utilizes the normal A'^ gradient rather than the adiabatic 

 gradient of the potential refractive modulus of Lukes [46] and Katz [20]. 

 The notation A{h, 313) is used to indicate that A is determined from the 

 refractive index at the height h and the 313 exponential atmosphere. It 

 has been found to be advantageous to use several atmospheres of exponen- 

 tial form in applications involving different climatic regions [47]. The 

 particular form of (4.43) emphasizes departures of A^ structure from 

 normal as shown by recent studies of synoptic variations of N(h) about 

 frontal systems [21] and, in addition, permits direct calculation of radio 

 ray bending for any observed refractive index structure. When A{h 313) 

 is introduced into (4.41) for ray bending, one obtains (see chapter 3, 

 sec. 3.10). 



r,, = - L ' IQ "^^^^ dAih, 313) + Tih, 313) (4.44) 



JA^ n 



which indicates that the bending can be regarded as the resultant of the 

 bending in the normal atmosphere, t(/i, 313), and a perturbation compo- 

 nent representing departures of refractive index structure from that of the 

 313 exponential atmosphere. The value of r(/i, 313) can be obtained from 

 refraction tables [9], and the perturbation term can be evaluated by 

 graphical methods to yield an overall accuracy of a few percent in esti- 

 mating ri,2 [47]. 



Some A(h, 313) profiles were prepared from typical temperature, pres- 

 sure, and humidity distributions within a range of air masses as published 

 in the literature [48, 49, 50] and climatic summaries of upper air data [31]. 

 Two of these profiles, one for maritime tropical air and the other repre- 

 senting continental tropical air, are plotted on figures 4.57 and 4.58 to 

 represent the extremes of A{h, 313) profiles. These profiles clearly show 

 that the two air masses have quite different refractive index structures. 

 The difference is most pronounced near the ground. At heights of 20 

 km, however, A{h,313) rapidly approaches the asymptotic value of 313, 



