ATMOSPHERIC ABSORPTION AND SCATTERING 



159 



in diameter from 0.05 to 0.55 cm. For wavelengths 

 X > 5 cm, the three-term series expansion (48) was 

 used. It is expected that at these sliorter waves, where 

 the critical diameters are smaller than the drop diam- 

 eters mentioned, the cross sections and attenuation 

 factors given in the taltles will be hut fair approxima- 

 tions of the exact values of these quantities. 



The range of values of p covered by these tables ex- 

 tends from about p = 0.0016 to p = 1.4. Tn Figures 

 5 and () two fanulies of curves are drawn giving 

 Q, (A);j and ot{X)„/N, the diameter of the drops being 

 kept constant, and Qt{J^>)>, nrid a(/))^/iV, the wave- 

 length of the radiation being kept constant. Since our 

 computations cover the range from X = 5 cm, we have 

 extended our curves on Figure 5 so as to cover the K 

 and X bands, using the values of the cross sections and 

 attenuations given in these bands by Eyde and Ryde. 

 Their data are represented again in the upper curves 

 of Figure 6. 



We are now prepared to apply these results to 

 meteorological phenomena and shall, for this purpose, 

 give a summary of typical data on clouds, fogs, and 

 I'ains to be used in this work. 



10.1.5 Typical Data on Clouds, Fogs, 

 and Rains 



To compute the attenuation due to the different 

 forms of condensation demands a knowledge of the 



10 20 30 40 50 60 70 80 90 100 



N IN CM 



FiCiURE 5. Absoriition cross section, Q,, and attenua- 

 tion constant, a, of spherical water drops as a function 

 of the wavelength. The abscissa gives the wavelength, 

 X, in centimeters. The right-hand ordinate scale gives 

 logio (a/N), where a/N, the attenuation constant in a 

 rain with 1 drop per cu cm, is expressed in decibels per 

 kilometer. The numbers on the curves give the diameter, 

 D, of the drops in centimeters. The left-hand ordinate 

 scale gives logu Qt with Qt being expressed in square 

 centimeters. 



0.05 0.10 0.15 



0.20 0.25 0.30 0.35 0.40 0.45 ttSO 0.55 

 D IN CM 



Figure 6. Absorption cross section, Q,, and attenuation 

 constant, a, of spherical water drojis as a function of the 

 drop diameter. The abscissa gives the drop diameter, 

 Z>, in centimeters. The right-hand ordinate scale gives 

 logio (a/N), where a/N, the attenuation constant in a 

 rain with 1 drop per cu cm, is expressed in decibels per 

 kilometer. The numbers on the curves give the wave- 

 length, X, of the incident radiation in centimeters. The 

 left-hand ordinate scale gives logio Qi, witli Qi being 

 expressed in square centimeters. 



water drop size distributions and their volume concen- 

 tration. Indeed, if such a form of condensation con- 

 tains N,c droplets per cubic centimeter having a diam- 

 eter of k cm, with k varying from, say, to s, then the 

 attenuation factor due to this form will l>e the sum 

 of the attenuation factors associated with each of the 

 different drop groups with diameter of 1, 'i, ■ ■ ■ , ■ ■ ■ , 

 ■ ■ ■ , n, ■ ■ ■ , s cm. In other words. 



ffltotal 



= 2 «* = 0.4343 X 10'= X NkQ' 



t,k 



db per kilometer, (54) 



according to equation (31), where N^ is the nimiber 

 per cubic centimeter of the drops k, and Qt,ic is the 

 total aljsorption cross section in square centimeters 

 of one spherical water drop of diameter k cm. 



It was shown above that theory allows a precise com- 

 putation of the cross sections Qt, provided the dielec- 

 tric constant of water is given at the temperature of 

 the drops. The concentration of N,c is a purely meteor- 

 ological datum and must be obtained experimentally. 

 As far as as the writer is aware, data on drop concentra- 

 tions and drop size distributions are extremely scarce, 

 and it appears that no systematic researches have as yet 

 been undertaken for the purpose of obtaining such data. 



