106 N CLIMATOLOGY 



The data of table 4.5 indicate, for example, that identically equipped 

 tropospheric communications systems could display as much as a 32-dB 

 difference in mean signal-strength level due to the climatic difference of 

 say, Denver, Colo., and the tropics. Further, one might expect the 

 monthly mean field strength of this hypothetical system to vary through- 

 out the year from less than 12 dB in the high plains near Denver to as 

 much as 20 dB in the African Sudan. 



Under this same assumption, figures 4.10 and 4.11 allow the communi- 

 cations engineer to estimate the expected maximum and minimum 

 monthly mean field strength expected throughout the year. 



The year-to-year variations of the monthly mean A''^ listed in table 4.4 

 indicate that the monthly mean of field strength for a particular month 

 may differ in successive years by as little as 1.0 dB for chmatic category 

 V in November or as much as 5.1 dB for category VI in May. 



Another application of these worldwide charts is to aid in estimating the 

 refraction of radio waves. The most convenient method of accounting 

 for the effects of atmospheric refraction is by means of the effective- 

 earth's-radius concept (see chapter 3) of Schelleng, Burrows, and Ferrell 

 [16]. The effective earth's radius, Ug, is determined from 



tte = I ;^V' (4-7) 



I' + Ilj 



where a is the true radius of the earth, n is the refractive index, and 

 dn/dh is the initial n gradient with respect to height. A great simplifica- 

 tion of propagation calculations is accomplished by assuming that dn/dh 

 is a constant, thus allowing radio rays to be drawn as straight rays over a 

 fictitious earth of radius a^ rather than curved rays over the true earth of 

 radius a. This simplification allows, for example, the distance to the 

 radio horizon, d, of a radio ray leaving an antenna of height, h, to be 

 calculated from d = ■\/2ae h. 



One notes, however, that the determination of a^ involves dn/dh as 

 well as n and that our A^o charts allow only an estimation of n. This dis- 

 parity may be resolved by utilizing the observation that N s is highly 

 correlated with the value of A^ at 1 km above the surface. The difference 

 between A^^ and N at 1 km is denoted AN. It has been noted [9] that the 

 correlation coefficient between ^nJAA^j and Ns is 0.926 for 888 sets of 

 data from 45 U.S. weather stations representing many diverse climates. 



The regression equation 



-AiV = 7.32 exp {0.005577 N s} (4.8) 



results when both variables are averaged over 6 to 8 years of record. 



