ATMOSPHERIC ABSORPTION AND SCATTERING 



157 



Eadiatiou Laboratory in the K band'' gave the results 

 shown in Table 2. 



As might have been expected, the dielectric absorp- 

 tion e; increases with decreasing temperature. 



With the above values of e,- and €i the computation 

 of the amplitudes a^ and &» is straightforward. The 

 amplitudes a„ and &„ have the form 



Z (a«+ia«)p', 



(45) 



/=2n+3 



bn= E Wl?+M?)p'. (46) 



/=2h+1 



Thus we lot tZi*"* denote the real part of the coeffi- 

 cient of p° in «i and a^'"' its imaginary part. Similarly, 

 Pi'-^K /?j('^ are the real and imaginary parts of the co- 

 efficient of p^ in 6i, etc. 



As equation (43) shows a,i<-'5' andosi'''' are directly 

 proportional to ( — e,) and (e,- — 1) respectively. As 

 the wavelength increases, «!*''' changes approximately 

 from — 0.9 to — 0.03 after passing through a shallow 

 minimum on account of the variation of ej. In the 

 same interval ai'°' increases from about 0.5 to 1.8. 



/?iW turns out to be practically negligible, in coiu- 

 parison with /JjO, which is almost constant in this 

 wavelength range. /S^^^^') and yS/^' behave similarly. 

 With Z?/'') and p^^''''> the roles are inverted. 



Finally ^2'°' and /8o'°* both vary in the range under 

 consideration. 



As a rule, those coefficients of the powers of p ( = 

 ttD/X) (D = diameter of the sphere) which do not 

 contain terms in t,- and powers of cr separately in the 

 numerator, but only the products £r «;, and powers 

 of £,-, are considerably smaller than those which do 

 contain e,- and its powers separately. 



10.1. t 'pi-jg Attenuation of Radio Waves 

 by Spherical Raindrops •> 



The knowledge of the coefficients a„ and b„, allows 

 ffiially the computation of the absorption cross section 

 for any spherical water drops of given diameter D at 

 those temperatures where the amplitudes can be 

 comjDuted. 



The absorption coefficient becomes, with the cross 

 section found above, [equations (33) and (43)], 



■■The attenuation values given in this report refer always 

 to one-way transmission and are additive to the free space 

 attenuation. 



a = 0.4343 X W^{- Re) E (2« + D (a„ + 5„) 



db per kilometer. (47) 



In our approximation for the amplitudes, we may 

 write 



a = 0.4343 X 10« ^^ (ci + f,p2 + cgp3 + . . .) 



db per kilometer (48) 



where N is the number of spherical drops, each of 

 volume V per cubic centimeter, A is the wavelength in 

 centimeters of the incident radiation. The parameter 

 p is, as above, ttD/X, D being the diameter in centi- 

 meters of a drop, and the coefficients p,, c,, Cg, • ■ • are 

 the following functions of the wa\'elength, the tem- 

 perature of the drops being taken as a constant (t'-' 

 ISC), 



Ci = 



(er + 2y- + e.2 



03=-^ 



c = -^ I ^ ^' 



' 15 3 {2,r+zy+w 



6 e,[(6.+2)(76,-10) + 76,^] 

 5 [(e,-H2)^-Fe,-2]2 



4(e.-l)2(e.+2)2+t,2[2(6,-l)(6,+2)-9]-f6i^ 



Tt is possible to give the attenuation formula another 

 simple form by noticing that NV is the total volume 

 of water per cubic centimeter in tlie form of drops or 

 10" NV is the total volume of water per cubic meter. 

 Since the density of water is 1 g per cubic centimeter, 

 numerically, the quantity 10" NV is the mass m of 

 liquid water per cubic meter, in air. The transformed 

 attenuation formula becomes finally 



a = 4.092 — (ci-f-cop2-f cap'H ) db per kilometer. 



' (50) 



It is seen that when p = ttD/X « 1 so that all the 

 terms in the expansion in equation (.50) are small in 

 comparison with c^. the attenuation factor reduces to 



4.092 mcx 24.55 



VUi 



>;p«i = 



db per kilometer. 



(51) 



Hence, when the diameter of the water drops is very 

 small in comparison with the wavelength of the inci- 

 dent radiation, the attenuation does not depend on the 



