990 RADIO WAVE PROPAGATION EXPERIMENTS 
tion of these amplitudes requires knowledge of the 
dielectric constant of water in the desired wave- 
length and temperature range. Whereas experimental 
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 microwave region, and the theoretical 
results seem to be supported by the new experimental 
data (see Table 1). Recent data in the Keband 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,, 6, and b, are 
discussed briefly at the end of this section. 
The attenuation factor (see pp. 277-279) is here 
computed to the approximation of taking into account 
the amplitudes a,, b,, and 6,. Clearly, inasmuch as 
these amplitudes are expressed in the form of series 
in ascending powers of the parameter p = 7D/d, the 
attenuation factor takes on a similar form. One gets 
a= = = (e1-+- cop? + csp? * °°) neper per unit length, 
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 ¢,, ¢3, 
C3, etc. are dimensionless coefficients 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, 
_ 3m my 
Txt 
20 Xr 
Bey x ea MNES 
10 X (¢-+2)?-be? 
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. Table 3 
contains (in the 1- to 100-em wavelength range) the 
values of the coefficients c,, C2, cs. It also gives the 
critical drop diameters below which, for a given A, 
the one term attenuation formula holds within 10 
per cent accuracy. A few values of D, are the fol- 
lowing: 
neper per unit length. 
A,em 1 1.26 3 5 10 15 
De, cm 6.56 X10- 7.13 X10—* 1.21 X10-1 1.87 X10-1 3.63 X10-! 5.34 X10-1 
Table 4 gives the total cross section of spherical 
water drops in the diameter range 0.05 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 
wavelength, and (2) at constant wavelength, as a 
function of the drop diameter, respectively. 
These 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 precipitation 
forms have been given on pages 2:79 -280. 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 0.02 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 
that 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 (about 1 km), which makes it difficult to in- 
terpret the experimental data on radio wave attenua- 
tions even in terms of this apparent variable of total 
precipitation rate. These and other meteorological 
irregularities seem to eliminate the possibility of a 
quantitative theory of attenuation or back scattering 
of 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. 
The measurements cover practically the whole range 
of drops which reach the ground in rains, or from 0.05 
to 0.55 cm. The terminal velocity of these drops varies 
between 2 and 9 m per second approximately. Figure 
8 represents another empirical relationship between 
the liquid water concentration of the rainy atmos- 
phere and the rate of rainfall. A rough linear approxi- 
mation to the apparent empirical curve leads to a 
water content 0.038 g/m* for each millimeter per 
hour precipitation rate. But, strictly speaking, there 
