DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 279 
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Ficure 6. Absorption cross section, Q;, and attenuation 
constant, a, of spherical water drops as a function of the 
drop diameter. The abscissa gives the drop diameter, 
D, in centimeters. The right-hand ortimate scale gives 
logis (a/N), where «/N, the attenuation constant in a 
rain with 1 drop per cu em, is expressed in decibels per 
kilometer. The numbers on the curves give the wave- 
length, , of the incident radiation in centimeters, The 
left-hand ordinate scale gives logio Q,, with Q; being 
expressed in square centimeters. 
kept constant, and Q;(D), and 2(D),/N, 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 Ryde 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 
rains to be used in this work. 
Typical Data on Clouds, Fogs, 
and Rains 
To compute the attenuation due to the different 
forms of condensation demands a knowledge of the 
water drop size distributions and their volume concen- 
tration. Indeed, if such a form of condensation con- 
tains N;, droplets per cubic centimeter having a diam- 
eter of 4 cm, with & varying from, say, 0 to s, then the 
attenuation factor due to this form will be the sum 
of the attenuation factors associated with each of the 
different drop groups with diameter of 1, 2,---,---, 
++-,7,---,8 cm. In other words, 
Sota = >, ox = 0.4343 X10° >, NeQux 
k=0 k=0 
db perkilometer, (54) 
according to equation (31), where WN; is the number 
per cubic centimeter of the drops &, and Q;,, is the 
total absorption 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 Q;, provided the dielec- 
tric constant of water is given at the temperature of 
the drops. The concentration of NV; 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. 
Recently, observations were made available on drop 
size distributions in clouds of different types.*.° The 
main results of interest to the attenuation problem are 
that in clouds of different altitudes the diameter of 
the drops does not seem to exceed 0.02 cm. The liquid 
water content of the clouds examined by Mazur® varied 
between about 0.15 and 0.50 g/m*. The results of 
Diem§ are, on the whole, similar. 
Some data on ice clouds are included in Best’s 
memoranda.** 
Data on fogs are extremely meager. The diameter of 
fog droplets appears to be of the same order of mag- 
nitude as those of liquid water clouds.”*?> Humphreys, 
in his table of precipitation values, gives 0.006 g/m 
as the liquid water content in fog. 
The data on rains used in this report are those from 
reference 11. For additional data recently collected 
see reference 26. 
The most important set of data which is directly 
usable in this work is contained in Table 6. In the 
last row of this table p is the precipitation rate or rate 
of rainfall, expressed in millimeters per hour, and 
results directly from the total volume of water fall- 
ing per square meter per second, since p = 36 X 
10+V, where V is expressed in cubic millimeters per 
square meter per second. 
Rains 1 and 2 refer, according to Best,! to a rain 
looking very ordinary, falling over a large area. Type 
3 is a rain with breaks and sunshine. Type 4 corre- 
sponds to the beginning of a short rainfall like a 
thundershower. Type 5 refers to a sudden rain from 
a small cloud, associated with a calm, sultry atmos- 
phere. Type 6 was a violent rain like a cloudburst with 
some hail. Types 7, 8, an 9 are for the heaviest period 
and the period of stopping of a continuous fall which 
at times took the form of a cloudburst. The preceding 
characteristics of the rains in Table 6 are quotations 
from the paper of Best. 
‘These data on drop size distributions are the only 
data available to the writer. Clearly the rate of rain- 
fall cannot be correlated from these data to any drop 
size distribution. A priori, it seems unlikely that a 
strict correlation between drop size distribution and 
tate of rainfall should exist. To a rain of given drop 
size distribution corresponds necessarily a determined 
tate of rainfall, but the reverse is not true, since a 
given rate of rainfall might be obtained with a large 
variety of drop size distribution.1° In other words, 
the drop size distribution is the only physical charac- 
