ABSORPTION \m> s<:\ti i;kin». in clouds, fog. kvin. iivii,. \ni> snow 



85 



Table 6. Radar cross section of submarine (SS-171), 

 broadside aspect: a = 0.01, B = 83 m, // = 7.(i m. 



8 = 



-Y 



■2-k —J 



2n + 1) (k | 2 + |6„! 2 ) cm 2 ', (13) 



typical of the ship for aspects other than direct 

 broadside. 



In Table 8, the same ship is analyzed at direct 

 broadside. No theoretical calculation of a has been 

 attempted because of a lack of sufficient data from 

 other ships of this type. The column XV is near 



Table 8. Radar cross section of aircraft carrier (CV-36), 

 direct, broadside aspect. 



enough to a constant to indicate the existence of 

 specular reflection. Since the hull at broadside can 

 be considered as a flat surface, specular reflection is 

 to be expected under normal incidence with a radar 

 cross section proportional to 1/X 2 as indicated by 

 equation (9). 



In view of the complicated reflecting properties of 

 targets of operational interest,- it may be said that 

 the experimental results can be considered as being 

 in fair agreement with theoretical predictions. 



104 ABSORPTION AND SCATTERING 



BY CLOUDS, FOG, RAIN, HAIL, AND SNOW 



The theory of the scattering and absorption of 

 microwaves by a collection of spherical particles of 

 known concentration, size, distribution, and given 

 dielectric properties was completely worked out 

 before systematic experimental work was done on 

 these phenomena. 258 ' 277 ' 279 The electromagnetic 

 theory predicts that the total scattering cross section 

 of a sphere of given electrical properties is 



where X is the wavelength in centimeters of the 

 incident radiation in air and a„ and 6„ are the so- 

 called scattering amplitudes associated with the 

 magnetic and electric 2/i-poles induced in the sphere 

 by the incident electromagnetic field. Similarly the 

 absorption cross section of a sphere defined as the 

 ratio of the total power removed from the incident 

 beam both by "internal absorption" (heating) and 

 by scattering is 



A = A- (-Re) 2 (2n + D (a. + b n ) ci 



(14) 



Here Re means "Real part of . . . ." The complex 

 scattering amplitudes depend on the dielectric con- 

 stants of the sphere, its diameter, and the wavelength 

 of the incident radiation. The observations which 

 are available seem to indicate that a collection of 

 spherical particles with random distribution scatter 

 microwaves incoherently, although under certain 

 circumstances, existing for very short time intervals, 

 they may scatter coherently. 419 On the assumption 

 of incoherent scattering, given a collection of 

 spherical particles of diameters D\, D 2 , • • - , D k , • • • , 

 D n , whose number per unit volume or cc is ?ii, n%, ■ ■ ■ , 

 n k> " ' ' > n m the scattering cross section of such a 

 collection per unit volume or the absorption coeffi- 

 cient due to scattering is 



n 



a s = 4.343 X 10 6 ^ n t S t db/km , (15) 



where S t is the scattering cross section of one drop 

 of diameter D t centimeters, and the summation 

 extends over all possible drops present in the col- 

 lection. Similarly, the "absorption coefficient" or 

 "attenuation" associated with the absorption cross 

 section A t (sphere of diameter D t ) defined by 

 equation (14) is 



n 



a a = 4.343 X 10 5 Y\ n i A * db/km . (16) 



Rain and Hail Absorption 



In order to compute the theoretical absorption 

 coefficient of a rain or thunderhead (heavy storm 

 cloud) one has to know the raindrop size distribution, 

 since the computation of the cross sections for one 

 spherical drop is straightforward provided its dielec- 

 tric properties are known. The greatest uncertainties 



