TOTAL RADIO PATH ABSORPTION 283 



Zhevankin and Troitskii [31] have indicated that 7^^ and 7^,^ can be repre- 

 sented as exponential functions of height, Z, above the earth's surface, 



7d. = 7d.o exp [j^~), Iw. = Tu-.o exp \j[—)> (7-5) 



where 7<f„o and 7^;,o are the values of jdv and jwy, respectively, at the 

 earth's surface, and H dv and //„,;, are called the "scale heights" of 7^^ and 

 7^,„. This model is known as the "bi-exponential" model of absorption, 

 and ydy and 7,^,^ are often called the "dry" and "wet" terms of y^. The 

 scale height for the dry term in the frequency range 6 to 45 Gc/s can be 

 written as [32] 



Hd. (m km) ^ -—V (7.6) 



where To is the surface temperature in °K, a is the temperature lapse rate 

 with height in °K/km, and b, c, are constants determined from thermo- 

 dynamic considerations. Because of the hump in the Hy,^ curves as op- 

 posed to the flat H dp curve in figure 7.28, such a handy expression as (7.6) 

 for H „,^ is not possible in the 6 to 45 Gc/s frequency range (fig. 7.28 was 

 determined from actual radiosonde data at Verkhoyansk, U.S.S.R.). 



7.5. Total Radio Path Absorption 



The total path absorption is determined by calculating the various 

 absorption coefficients as functions of the heights along the ray path and 

 then numerically integrating the values along the entire path using stand- 

 ard ray tracing techniques outlined in chapter 3. The values of total path 

 integration over a 100-km path thus obtained are presented in figure 7.12 

 for Bismarck, N. Dak., and Washington, D.C. The difference between 

 the two climates is evident principally at the higher frequencies, where 

 the Washington absorptions are consistently above the Bismarck values. 

 This is apparently due to a combination of generally greater humidities 

 and greater refractive effects. These two effects are related. The in- 

 creased humidity at Washington enhances the water vapor absorption 

 and increases the refraction causing the radio ray to travel consistently 

 through lower levels of the atmosphere with consequent increase in total 

 path absorption. 



