ATMOSPHERIC ABSORPTION AND SCATTERING 



167 



tualitios, licru ouly 

 absorption. Hence, 



two, nainelj', scattering and true 

 - Qs 



10 20 so 40 50 60 70 80 90 100 

 X IN CM 



Figure 16. Scattering cross section, Qs, of spherical 

 water drops as a function of the wavelength. The 

 abscissa gives the wavelength, X, of the incident radia- 

 tion in centimeters. The ordinate scale gives logic Qs, 

 the cross section Qs being expressed in square centi- 

 meters. The numbers of the curves indicate the drop 

 diameter, D, in centimeters. 



scattered in any direction and the absolute probabil- 

 ities cOjj^^ for being absorl^ed by the drops, the absorbed 

 energy being then transformed into heat in the drops 

 (true absorption). Indeed, this probability i^^ of the 

 wax'es being scattered in any direction is equal to the 

 ratio of the scattering cross section Qs to the cross sec- 

 tion Qi which is associated with all the possible even- 



Qt 



(62) 



and, consequently, the probability of true absorption is 



t^abs = 1 — lis. (63) 



In Table 13 are given the probabilities Z)s in t^^^ 

 drop diameter range 0.05 to 0.55 cm and wavelength 

 range 3 to 100 cm. A glance at this table shows that 

 with the exception of the shortest wavelengths and 

 largest drops the probability of the weaves being truly 

 absorbed is always much larger than that of their being 

 scattered. The smaller the drops the greater the chance 

 of absorption, since, according to the cross-section 

 formulas, for small drops Qs is proportional to Z>"/A* 

 (Hayleigh's law) whereas Qt — ' Q;,hs is proportional 

 to D^/X and in our case the drop diameter D is always 

 smaller than the wavelength A of the radiation. 



*"^' Back Scattering (Echoes) 



Whereas the attenuation of microwaves is of inter- 

 est to both communication and radar, back scattering 

 is of importance to radar only. The importance of the* 

 echo phenomena is twofold. On the one hand, it is 

 of operational interest to distinguish between atmos- 

 pheric echoes of the waves and their reflection from 

 other targets in the atmosphere. On the other hand, 

 the observation of these phenomena has led to the rec- 

 ognition of its meteorological value in helping to map 

 tlie storm topography of the atmosphere (storm detec- 

 tion) around the position of the observer and at 

 ranges limited only by the characteristics of the radar 

 set used."'^^'^^ 



The echo intensities may be computed from for- 

 mula (35) for the differential cross section of drops 

 <t(tt) for back scattering (scattering angle tt). 



Table 13. Probability of scattering to,, by spherical water drops of D cm diameter. 



