Chapter 5 
DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 
ABSORPTION AND SCATTERING OF 
MICROWAVES BY THE ATMOSPHERE* 
| ies PRESENT REPORT deals with the absorption of 
microwaves in the 0.2- to 100-cm wavelength range, 
by the atmospheric gases and by floating or falling 
water drops like clouds, fog, and rain of maximum 
drop diameter 0.55 cm. 
The theory of absorption and scattering of waves 
by spherical particles is briefly reviewed. The results 
are applied to water drops. 
For small drops, the attenuation, which depends 
only upon the amount of liquid water per unit volume 
and is independent of the drop size, is 0.28, 0.049, and 
0.0045 db per kilometer for each gram of liquid water 
per cubic meter of air for the K, X, and S bands, re- 
spectively. Since the concentration of liquid water in 
clouds does not seem to exceed 1 g per cubic meter of 
air, the above values represent upper limits. These 
values refer to water droplets at temperatures around 
18 C. The attenuation increases with decreasing tem- 
perature of the water drops. 
While the attenuation does not depend upon the 
total rate of rainfall, it is -possible to calculate the 
maximum values to be expected for any precipitation 
rate. These are 0.16, 0.45, 0.005, 0.001, and 0.0006 db 
per kilometer for each millimeter precipitation per 
hour at 1.25, 3, 5, 8, and 10 cm, respectively. These 
theoretical maximum values of attenuation compare 
fairly well with the values observed and are for water 
drops at 18 C. 
Tn the wavelength range mentioned it is shown that, 
with the exception of the biggest drops and shortest 
waves, the wave energy converted into heat inside the 
drops is much larger than the scattered energy. 
The radar absorption coefficient, defined as the frac- 
tion of the incident power scattered backward per unit 
layer thickness of the echoing medium, has been com- 
puted for different rains. This allows the estimation of 
the power received in radar observations of storm clouds 
and rains. The theoretical predictions seem to be con- 
sistent here also with the results of the few recent radar 
studies which tend to show that echoes are due mainly 
to water drops of the dimensions occurring in rains. 
In the introduction a résumé is given of the status 
of microwave absorption by atmospheric oxygen and 
water vapor. With the exception of the resonance re- 
gion of oxygen (resonance wavelength: around 0.5 em), 
“By L. Goldstein, Columbia University Wave Propagation 
Group. 
269 
this absorption turns out to be of only very limited 
practical importance for waves longer than about 3 to 
5 cm. 
Introduction 
The present report is intended to review the status 
of microwave propagation through rain, clouds, and 
fog. In order, however, to convey a precise idea of the 
total atmospheric absorption, we shall include here 
some of the most important numerical results recently 
obtained ‘on the absorption of microwaves by atmos- 
pheric gases, like oxygen and water vapor.** 
First of all, in medium- and low-altitude fair- 
weather clouds and fogs, with the possible exception of 
heavy sea fogs, the attenuation is of negligible impor- 
tance for longer waves. It may become important at 
shorter waves. For instance, in the K band the atten- 
uation? is 0.28 db per kilometer for each gram of liquid 
water per cubic meter of air. The X- and S-band 
waves are attenuated, respectively, 0.049 and 0.0045 
db/km/g/m. Since in these clouds and ordinary fogs 
the liquid water concentration does not seem to exceed 
1 g/m, these values are very likely upper limits. Actu- 
ally, by halving these numbers one would be nearer the 
true values, inasmuch as liquid water contents reported 
in clouds®® varies between 0.15 and 0.50 g/m®. An in- 
teresting and simplifying feature of cloud and fog 
absorption is the fact that the smallness of their 
water drops, as compared with the wavelength, makes 
the attenuation independent of the drop sizes. The 
cloud and fog attenuation depends linearly on the 
liquid water concentration of the atmosphere, and in 
the microwave region it decreases monotonically with 
increasing wavelength. 
In rains or rain clouds the attenuation does not 
depend directly on the total rate of rainfall, a variable 
so familiar to meteorologists. It is, nevertheless, pos- 
sible to give upper limits to the attenuation per unit 
precipitation rate. These are as follows: 0.16, 0.45, 
0.005, 0.001, and 0.0006 db per kilometer for each mil- 
limeter per hour rate of rainfall, at 1.25-, 3-, 5-, 8-, and 
10-cm wavelengths, respectively. The drops forming 
these rains were supposed to be at temperatures near 
18 C. By imereasing the preceding values by about 30 
per cent one would very likely take care of raindrops at 
lower temperatures, since the absorption increases 
with decreasing temperature of the drops. 
In the computation of attenuation for rains it was 
bThe attenuation values given in this report are always for 
one-way transmission. 
