ATMOSPHERIC. ABSORPTION AND SCATTERING 



165 



procedure u.sually followed by the experimeutal work- 

 ers, as we have already mentioned. It is evident that 

 these curves have little, if any, direct physical signifi- 

 cance. Similarly the curves of Figure 11 associated 

 with different rains merely indicate the trend of varia- 



175 r 



150 

 125 



Table 11. ExperimenUil values of (he attenuation 

 per unit precipitation rate. 



5 25 



2/ / ° 



/ V 



40 



45 



50 



5 10 15 20 25 30 35 



PnECrPlTA"''''^!! RATp IN MM PFR "P 



Figure 14. (1) Computed S-band attenuations based on 

 experimental drop size distributions in different rains. 

 (2) Theoretical upper limit of a/p, attenuation per unit 

 rate of precipitation, is 6.10-<db/km/mm/hr. /. = 18C. 



tion of a as a function of the wavelength, since no 

 single curve of this type can characterize a rain of 

 given total precipitation rate of p mm per hour. 



Table 9 shows that the attenuation is of no practical 

 importance for S band and longer waves even with the 

 heeaviest rains or cloudbursts. This result is summar- 

 ized in Table 10 (the theoretical upper limits of the at- 

 tenuations per unit precipitation rate) . 



Table 10. Theoretical upper limits of attenuation 

 per unit precipitation rate (i -^ 18 C). 



X, cm 



(a/?^)max db/km/mm/hr 



1.25 



3 



5 



8 

 10 

 15 

 20 

 30 



1.6 X 10-1 

 4.5 X 10-2 

 5.0 X 10-3 

 1.0 X 10-3 

 6.0 X 10-< 

 3.0 X 10-^ 

 1.4 X 10-1 

 6.4 X 10-5 



These values in Table 10 correspond to raindrop 

 temp)eratures of about 18 C. At lower temperatirres the 

 values of (a/l^) included in this table might be in- 

 creased about 25 to 30 per cent. 



The results of the different workers in the field are 

 summarized in Table 11. 



It will be seen that the above values of a//; compare 

 favorably with the theoretical values.^' The difficulties 



'The same seems to be true of S-band wavelengths where 

 rough attenuation measurements are available in "solid" 

 storm clouds.3i 



in the interpretation of the experimental data as men- 

 tioned already should be kept in mind when compar- 

 ing the experimental values witli the theoretical 

 predictions. 



As remarked by Eyde and Eyde,^^ the attenua- 

 tion by hailstones and snow should be appreciably 

 smaller than that due to raindrops, the dielectric con- 

 stant of ice being considerably smaller than that of 

 liquid water. 



A final remark may be made concerning the theore- 

 tical results given here. It has Ijeen assumed through- 

 out the preceding discussion that the raindrops are 

 spherical. This is likely to be the case with practically 

 all the drop groups existing in rains, with the excep- 

 tion of the biggest drops, which may undergo deforma- 

 tions. Presimiably the effects of small deformations 

 are not of great importance. 



10.1.7 rpjjg Scattering of Microwaves 

 by Spherical Raindrops 



The cross section for scattering of electromagnetic 

 waves by spherical particles is gi\'en for any direction 

 Ijy equation (31). ITsiug the approximate expressions 

 of the amplitudes as given by equations (38) and (43) 

 and the notation «!<=>, aj'^', /3i('), JS/^) represent- 

 ing the real and imaginary coefficients of p^ in a\ 

 of p^ in V^, etc., as indicated above, we get the fol- 

 lowing expression for the total scattering cross sec- 

 tion : 



'V 



^ + 6[/3i('^>/3: 



(3) fl, (.5) 



+ ft '« ft <«] P- + 6 [ft (3) ^, («) + ^1 W -^^ (6)] p3 



+ l3[|ai(»M+|ft(«|2] 



+ 5|ft(='h}p^ + 6[ft(«ft(« 



Here, for instance, 



|ft"'l = [ft">]= + [ft"']Mai(«M 

 = («!<«)- + (Si<«)^ etc. 



■ cm-. 



(59) 



