MODIFIED EFFECTIVE EARTH'S RADIUS 



61 



Table 3.1. 



Refradivity statistics as a function of altitude above sea level as derived 

 from individual radiosonde observations 



•Range = maximum A^ — minimum A^. 



It is interesting to note that the range of A^ values has a minimum at 

 8 to 9 km above sea level but is systematically greater above and below 

 that altitude. The average value of 104.8 at 9 km corresponds to a 

 similar value reported by Stickland [9] as typical of the United Kingdom. 

 Further the altitude of 8 km corresponds to the altitude reported by 

 Humphreys [10] where the atmospheric density is nearly constant regard- 

 less of season or geographical location. Since the first term in the expres- 

 sion for refractivity is proportional to air density, and the water-vapor 

 term is negligible at an altitude of 9 km, the refractivity also tends to be 

 constant at this altitude. It seems quite reasonable, then, to adopt a 

 constant value of A^ = 105 for 9 km, thus further facilitating the specifica- 

 tion of model atmospheres. Further, as also noted in chai)ter 1, when 

 the values of table 3.1 are plotted such as on figure 3.3, it is seen that the 

 data strongly suggest that N may be represented by an exiwnential 

 function of height of the form: 



N{h) = iVoexp {-bh}, 



in the altitude range of 1 to 9 km above .sea level. 



The following recommendation is made when dealing with problems 

 involving ground-to-ground communications systems or other types of 

 low-altitude radio propagation problems where the ray paths involved do 

 not exceed 1, or at most 2, km above the earth's surface: use the effective 

 earth's radius method to solve the associated refraction problems. The 

 u.ser should refer to the tables in chapter 9, where effective earth's radius 

 factors are tabulated along with other refractivity variables. Table 9.27 

 may be entered with N ^ and table 9.28 may be entered with AN{N s sub- 

 tracted from the N value at 1 km above the surface). In both these 

 tables linear interpolation will suffice for any practical problem. The 

 variables listed in these tables are for the exponential model of N{h) that 

 is covered in the following .subsection. 



