172 



DIELECTRIC CONSTANT. ABSORPTION AND SCATTERING 



data on the real part of the dielectric constant of water 

 are relatively abundant in the microwave region and 

 around 18 C, data on the imaginary part or the con- 

 ductivity are very scarce. The Debye theory has, there- 

 fore, been used to compute the dielectric constant of 

 water in the mi<-r()wa\e region, and the theoretical 

 results seem to be supported by the new experimental 

 data (see Table 1). Eoceut data in the K band on 

 the temperature variation of the dielectric constant of 

 water are given in Table 2. The graphical representa- 

 tion of both real and imaginary parts of the dielectric 

 constant in the wavelength range 1 to 11 cm appears 

 on Figure 4. The numerical values of a-^, b^. and &, are 

 discussed briefly at the end of this section. 



The attenuation factor (see Section 10.1.1:) is here 

 computed to the appro.ximation of taking into account 

 the amplitudes a^. h„ and b.,. Clearly, inasmuch as 

 these amplitudes are expressed in the form of series 

 in ascending powers of the parameter p = ttD/X. the 

 attenuation factor takes on a similar form. One gets 



•) neper per unit length, 



a = {ci+Cop- + C3p'+ 



20 X 



where m is the mass of liquid water in the form of 

 drops per unit volume of the atmosphere, A is the 

 wavelength of the radiation in free space, and c^, c^, 

 c^, etc. are dimensionless coefRcients depending on the 

 wavelength implicitly through the dielectric constant 

 of the substance of the sphere. For values of p small 

 compared with unity, i.e., for waves long compared 

 with the diameter of the drops, for which the terms 

 in p-, p^ 



. . can be neglected, the attenuation fac- 



tor reduces to one term, 



"^<<' = 20 T 



= JL^H tl neper per unit length. 



10 X {er+2r-+ir 



This shows that for small drops or longer waves the 

 attenuation factor becomes independent of the drop 

 size and depends only on the amount of liquid water 

 per unit volume present in the atmosphere. Tal)lo 3 

 contains (in the 1- to 100-cm wavelength range) the 

 values of the coefficients Cj, Co, Cg. It also gives the 

 critical drop diameters below which, for a given X, 

 the one term attenuation formula holds within 10 

 per cent accuracy. A few values of Dc are the fol- 

 lowing : 



X,cm 1 1.26 3 5 10 15 



Dc.cm 6.56X10-= 7.13X10- 1.21X10-1 1.S7X10-1 3.63X10"' 5.34X10-1 



Taljle -i gi\es the total cross sectiuii of spherical 

 water drops in the diameter range 0.0-5 to 0.55 cm 

 and wavelength range 1.25 to 100 cm. Table 5 gives 

 attenuation values in decibels per kilometer. Figures 

 5 and 6 represent in graphical form the variation of 

 the absorption cross section and attenuation factor 

 ( 1 ) at constant drop diameter, as a function of the 

 wavi'leiigth, and (2) at constant wavelength, as a 

 function of the drop diameter, respectively. 



The.se results are directly applicable to any pre- 

 cipitation forms of which drop size distribution and 

 average drop concentration have been determined. 



Meteorological data necessary to the computation 

 of the attenuation factor of different ijrecipitatiou 

 forms have been collected in Section 10.1.5. Data on 

 drop concentrations and drop size distributions are 

 extremely scarce. 



In liquid water clouds of different altitudes and in 

 fogs, observations indicate that the drop diameters do 

 not exceed 0.03 cm. In low and medium altitude good 

 weather clouds the liquid water concentration varies 

 between 0.15 and 0.50 g per cubic meter, and a con- 

 centration of 1 g/m^ is very likely an extreme upper 

 limit. In fogs, with the possible exception of heavy 

 sea fogs, the liquid water concentration seems to be 

 considerably smaller. 



The data on drop size distribution in rains used in 

 this work are given in Table 6, and, in a different 

 form, directly applicable to the computation of the 

 attenuation factor, in Table 7. These data indicate 

 tliat the precipitation rate does not determine the drop 

 size distribution of a rain, inasmuch as a rain of given 

 precipitation rate can be built up with different drop 

 size distributions. It does not seem, therefore, that 

 the precipitation rate can play the role of a true phys- 

 ical variable in the attenuation law of rains. 



Attention is also called to observed irregularities 

 in the precipitation rate over relatively small dis- 

 tances (alwut 1 km), which makes it difficult to in- 

 terpret the experimental data on radio wave attenua- 

 tions even in terms of this a^jparent variable of total 

 precipitation rate. These and other meteorological 

 irregularities seem to eliminate the possibility of a 

 quantitative theory of attenuation or back scattering 

 (if radio waves by rain or other precipitation forms. 

 Clearly, the experimental study of these as yet chaotic 

 meteorological features might disclose certain trends 

 which could be advantageously incorporated in the 

 theory of attenuation of a stormy atmosphere. 



Figure 7 gives the empirical relationship between 

 the terminal velocity of raindrops and their diameter. 



