DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 291 
cannot be an analytical connection between the liquid 
water concentration and the rate of rainfall. Inasmuch 
as the same rate of rainfall can be achieved by a num- 
ber of different drop size distributions, therefore, to 
a single value of the abscissa — the precipitation rate 
— there may be associated a series of ordinate values 
or liquid water concentrations. The curves of Figure 
8 are, therefore, of interest only because they are 
helpful in predicting very roughly liquid water con- 
centrations in different rains. 
The text on pp281-284 discusses computation of 
the attenuation in different precipitation forms, no 
account being taken of the inherent irregularities. 
Since the size of the drops in fogs and fair weather 
clouds are small compared with even the shortest wave- 
length (1.25 cm) considered in this report, the one 
term attenuation formula holds rigorously. Figure 9 
represents the attenuation curve in decibels per kilo- 
meter in clouds and fogs for a liquid water concentra- 
tion of 1 g/m’ which, as mentioned above, is an upper 
limit. 
A few attenuation values may be given as follows: 
d, cm 1.25 3 5 10 
a/m db/km/gm/m$ 0.28 0.049 0.018 0.0045 
Even for 1.25-cm waves the attenuation would be- 
come important only at long ranges for radar observa- 
tions. For waves of length A > 3 cm the attenuation 
in fair weather clouds and fogs is of no practical 
importance. 
Table 3, on the critical diameter of water drops, 
shows that the attenuation becomes practically in- 
dependent of the drop size distribution in rains for 
wavelengths longer than about 15 or 20 cm, inasmuch 
as raindrops whose diameter is larger than 0.55 cm 
or 0.6 cm do not reach low altitudes. In the 5- to 20- 
em wavelength range the three-term attenuation 
formula will represent fairly well the attenuation in 
different rains. At wavelengths smaller than 5 cm 
exact computations of the amplitudes a,, b, are nec- 
essary. 
It is shown that in any rain the attenuation de- 
pends linearly on the partial precipitation rates of 
the different drop groups making up this rain, but 
it does not depend directly on the total rate of rain- 
fall. 
Figure 10 purports to show the connection between 
the drop size distribution in a given rain and the 
partial or fractional attenuation values in the K and 
X bands of the different drop groups making up this 
rain. It is seen that the numerous small drops do not, 
for practical purposes, contribute to the attenuation, 
which is due mainly to the bigger drops. 
Table 9 contains attenuation values of different 
rains of known drop size distribution and rate of rain- 
fall. Figure 11 is a graphical representation of these 
results. It will be seen that at the shorter waves the 
attenuation may become important in heavy: rains. 
Figures 12, 13, and 14 are graphical representa- 
tions of certain results included in Table 9 at K-, 
X-, and 8-band wavelengths, respectively. The attenua- 
tion values corresponding to the points in these graphs 
have been- computed for the rains of Table 9, and we 
have drawn a cyrve through the computed points. 
Accordingly, the plot of attenuation as a function of 
total precipitation is a mass plot. That is, for any 
given total precipitation the attenuation will have 
different values, depending upon the distribution of 
the drop size for the rain in question. Figures 12, 
13, and 14 represent mass plots of the meager data 
available for K, X, and S bands, respectively, together 
with the limiting curve that would result if all the 
drops were of the size that gives maximum attenua- 
tion. Tables 10 and 11 contain, respectively, the theo- 
retically predicted upper limits of attenuation for 
water drops around 18°C and the experimental atten- 
uation per unit rate of precipitation. In view of the 
difficulties in the interpretation of the experimental 
data, it may be said that there is fair agreement be- 
tween the observed and predicted attenuation values 
in rains. 
The attenuation due to hailstones and snow should 
be considerably smaller than that caused by rain. The 
reason for this difference is due to the small dielectric 
absorption of ice as compared with the dielectric ab- 
sorption of liquid water. 
Pages 284-286. deal with the total scattering (in 
the whole solid angle) of microwaves by spherical 
water drops. The scattering cross-section formula is 
given in a series of ascending powers of p = D/A, 
the first term of the series being p°®. For small 
values of p, the cross. section reduces to the first term 
of this series, which, when the dielectric absorption 
is negligible, reduces to the Rayleigh scattering cross 
section. Table 12 includes the results of the numer- 
ical computations and Figures 15 and 16 are their 
graphical representation. 
The knowledge of the total cross section and scat- 
tering cross section allows the computation of the 
absolute probabilities, for the waves to be’ scattered 
in any direction or to be absorbed internally by spher- 
ical water drops. The scattering probabilities are 
given in Table 13. The probabilities for internal ab- 
sorption are complementary to these, i.e., they are 
equal to (1 —@,). It is thus seen that, with the 
exception of the shortest waves and the biggest rain- 
drops, the probability of the waves being absorbed in- 
ternally, the absorbed wave energy heating the drops, 
is much larger than the probability of their being 
scattered in any direction. 
On pp. 286-289 the differential scattering cross 
section in a chosen direction is first derived rapidly and 
then is given explicitly so as to show clearly the con- 
tributions of the induced electric dipole, electric quad- 
tupole, magnetic dipole, and their interference terms. 
