48 TECHNICAL SURVEY 
dielectric properties was completely worked out 
before systematic experimental work was done on 
these phenomena.*** 277279 The electromagnetic 
theory predicts that the total scattering cross section 
of a sphere of given electrical properties is 
55 be 2 GoD (lan |2 + |b, |2) em? , (13) 
where \ is the wavelength in centimeters of the 
incident radiation in air and a, and b, are the so- 
called scattering amplitudes associated with the 
magnetic and electric 2n-poles induced in the sphere 
by the incident electromagnetic field. Similarly the 
absorption cross section of a sphere defined as the 
ratio of the total power removed from the incident 
beam both by “internal absorption” (heating) and 
by scattering is 
A= x (— Re) yen + 1) (Qn + b,) em2. (14) 
Here Re means “‘Real part of ... .”” The complex 
scattering amplitudes depend on thé dielectric con- 
stants of the sphere, its diameter, and the wavelength 
of the incident radiation. The observations which 
are available seem to indicate that a collection of 
spherical particles with random distribution scatter 
microwaves incoherently, although under certain 
circumstances, existing for very short time intervals, 
they may scatter coherently.*!9 On the assumption 
of incoherent scattering, given a collection of 
spherical particles of diameters D,, De, ---, D,,---, 
D,, whose number per unit volume or cc is m1, 2, ---, 
M,*** , Nn, the scattering cross section of such a 
collection per unit volume or the absorption coeffi- 
cient due to scattering is 
a, = 4.343 x 10° Y) n, S,db/km, (15) 
i=1 
where S, is the scattering cross section of one drop 
of diameter D, centimeters, and the summation 
extends over all possible drops present in the col- 
lection. Similarly, the “absorption coefficient” or 
“attenuation” associated with the absorption cross 
section A, (sphere of diameter D,) defined by 
equation (14) is 
n 
aa = 4.343 X 10° Yn, Ay db/km. (16) 
i=l 
Rain AND Hain ABSORPTION 
In order to compute the theoretical absorption 
coefficient of a rain or thunderhead (heavy storm 
cloud) one has to know the raindrop size distribution, 
since the computation of the cross sections for one 
spherical drop is straightforward provided its dielec- 
tric properties are known. The greatest uncertainties 
in the theoretical predictions of scattering or absorp- 
tion by rain are due to the relatively limited knowl- 
edge of drop size distributions in rains of different 
rates of fall. There is no evidence that a rain with a 
known rate of fall has a unique drop size distribution 
though the latest studies on this problem seem to 
indicate that a certain most probable drop size 
distribution can be attached to a rain of given rate 
of fall.44° Results of this study are included in Table 
9. On the basis of these results the absorption cross 
TaBLeE 9. Drop size distribution. 
Percentage of total volume 
0.25 1.25 25 12.5 25 50 100 150 
0.05 280 109 73 26 41.7 412 10 1.0 
(0.10 50.1 37.1 27.8 115 76 54 46 4.1 
0.15 18.2 31.3 32.8 245 184 125 88 7.6 
0.20 3.0 13.5 19.0 25.4 23.9 19.9 13.9 11.7 
0.25 0.7 #49 79 17.3 19.9 20.9 17.1 13.9 
0.30 15 3.3 101 128 15.6 184 17.7 
0.35 06 11 43 82 109 150 16.1 
0.40 0.2 06 23 35 67 90 11.9 
0.45 0.2 #12 21 33 58 7.7 
0.50 06 11 #18 30 3.46 
0.55 OF, Os) iil tle | Ba 
0.60 03 #05 410 1.2 
0.65 0.2 0.7 1.0 
0.70 0.3 
section of raindrops of different size has been com- 
puted for use in Table 10. This table gives the decibel 
attenuation per kilometer in rains of different rates 
of fall and for radiation of wavelengths between 
0.3 and 10 cm. In Table 11, similar to Table 10, 
another set of results is contained for rains of 
measured drop size- distributions. This table is 
extended to include radiations of wavelengths up to 
100 cm. It seems equally interesting to give a graphi- 
cal representation of those results. Figure 2 corres- 
ponds to Table 10 and Figure 3 to Table 11. All 
these data refer to raindrops at 18 C. 
Since the scattering coefficients a, and b, depend 
on the temperature, because of its effect on the 
DB/KM 
a2 03 05 o7 1 bs Oo 7 20 
XIN CM 
2 
Ficure 2. Graphical presentation of data-given in Table 
10. 
