88 



SCATTERING AND ABSORPTION OF MICROWAVES 



Table 13. Experimental values of the maximum 

 attenuation per unit precipitation rate. 



10 



X, cm 



0.62 

 0.96 

 1.089 



1.25 



3.2 



(a/p) db per km/mm per hr References 



0.37 



0.15 



0.2 

 C0.19 

 < 0.09-0.40 

 1 0.63 



0.032-0.042 



269 

 256 

 262 

 176 

 276 

 281 

 261 



and observed values is, on the whole, satisfactory. 

 It will be seen that the results reported on K-band 

 rain attenuation in Hawaii by the U. S. Navy Radio 

 and Sound Laboratory workers 281 are higher than 

 those observed by other workers on the same wave- 

 length. The orographic character of these Hawaiian 

 rains which were made up of drops falling about 

 300 m instead of ordinary rains falling 1,500 to 

 2,000 m may be one of the reasons for this divergent 

 result. 



Clouds and Fog 



Observations indicate that fair weather clouds and 

 fog are composed of droplets whose diameters do not 

 seem to exceed 0.02 cm. Under these conditions the 

 attenuation formula takes on a remarkably simple 

 form since it becomes independent of the drop size 

 distribution. The attenuation formula in this limit 

 of very small values of the parameter ttD/\ is 



dab = 



4.092 raci 



db/km , 



(17; 



where m is the mass of liquid water per cubic meter, 

 X is the wavelength of the radiation in centimeters, 

 and 



Cl = 



(i 



ti 



(e r + 2) 2 + e,» 



(18) 



where e r and e t are the real and imaginary parts of 

 the dielectric constant of water at the temperature 

 in question and for radiation of wavelength X. Figure 

 4 represents the attenuation in clouds and fog in the 

 range 0.2 to 10 cm. This graph corresponds to a 



0.5 





* 0.2 



- 0.1 



f 



0.05 



0.0 2 



0.01 



0.004 



0.2 



0.5 



1.0 2 



A IN CM 



10 



Figure 4. Attenuation factor in liquid clouds and fogs. 

 T = 18 C. 



liquid water concentration of 1 g per cu m, which 

 is undoubtedly rather high. Actually, the observa- 

 tions indicate that the liquid water concentrations 

 in clouds and fog rarely exceed 0.6 g per cu m. 

 To this may be added the Table 14 for attenuation 

 by ice clouds. In ice clouds m will rarely exceed 0.5 

 and will often be less than 0.1 g per cu m. 



Scattering (Echo) 



If we denote by cr(x) the back-scattering cross 

 section per unit solid angle of a spherical water drop 

 and if there is a distribution n h ni, ■ • • , n k , • • • , n„ 

 drops per cubic meter, the cloud or rain cross section 

 for scattering is 



S(x) = J] »^WAF 



(19) 



where AV is the scattering volume of the cloud, on 

 the assumption of incoherent scattering on account 

 of the random character of the drop distribution. 

 The summation includes all the drop groups. The 



