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DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 289 
The rain echo cross section is then 
Sy = 2nd? (1 — cos 6) [sad Voile 
Here the summation extends over all the different drop 
groups forming the rain and o;(7) is the differential 
cross section for back scattering in the direction « with 
the direction of propagation of the initial beam. It 
should be rernembered that g;(7) is the cross section per 
unit solid angle. Hence, the received peak power, 
_ PiGiGs (3 \? ‘| Es | 
Ao = @| Add Nios(n) 
for small @ (6 in radians). The quantity [SNjo;(7) Ad] 
is tabulated in Table 16 for Ad =1 km and the 
different rains of Table 7. It is thus clear that the 
knowledge of the set characteristics permits at once the 
computation of the received power echoed by a rain 
falling at a certain distance r from the set provided 
the assumption is made, that the echoing rain layer is 
1 km thick. This is clearly arbitrary but is likely to 
give the right order of magnitude. 
There has been discussed in a rather unorthodox 
way” the effect of the absorption on the back scatter- 
ing of radiation taking into account also the finite 
pulse length of the radiation source. 
These results seem to be consistent with the meager 
quantitative information available in this field. This 
fact would tend to classify the atmospheric radar 
echoes as back scattering phenomena due to water 
drops of precipitation size. It may further be re-em- 
phasized that theory provides an adequate explanation 
for scattering and absorption of electromagnetic waves 
passing through different clouds or precipitation 
forms. The limitations imposed on the theoretical re- 
sults are due essentially to irregularities inherent in 
the meteorological elements. 
Summary 
The present report gives a detailed review of the 
theoretical and experimental status of microwave at- 
mospheric absorption. This absorption is due to the 
gases of the atmosphere, oxygen, and water vapor, on 
the one hand, and to the swarms of floating or falling 
water drops, clouds, fog, rain, and snow, on the other. 
The status of the gaseous absorption of the atmos- 
phere is reviewed briefly in Section 10.1.1. Figure 1 
gives the oxygen and water vapor attenuation curves: 
in the 0.2 to 10-cm wavelength range. The water vapor 
attenuation is given for a vapor content of 7.5 g/m* 
of air, or 6.2 g per kilogram of air. In the equatorial 
belt, 15° S to 15° N, at sea level, the attenuation due 
to the atmospheric gases is approximately constant. It 
is about 0.18 and 0.008 db per kilometer for 1.25- and 
3-em waves respectively. In the tropical region the 
seasonal variation of these attenuations is quite large. 
Figure 2 helps to give a clear picture of the atmos- 
pherie absorption due to oxygen and water vapor 
simultaneously with the absorption in rains of differ- 
ent types. It is seen that in the wavelength range 1 to 
5 em the rain attenuation is more important than the 
gaseous atmospheric attenuation. The latter predomi- 
nates at waves shorter than 1 em and longer than 
about 5 cm, losing entirely its practical importance 
at these longer waves. 
The theory of absorption and scattering of electro- 
magnetic waves by dielectric spheres (sce text on 
pp-271-274.) is briefly presented following theRayleigh 
method as developed by Stratton. 
The contribution of a swarm of spherical water 
drops of the same size, floating or falling in the atmos- 
phere, to the average field strength attenuation factor 
is given by 
a= 3N Q, neper per unit length, 
where WV is the average concentration of the drops, and 
Q: their total cross section. This total cross section is 
the ratio of the power removed from the incident beam 
by one drop, through scattering and internal absorp- 
tion to the power density of the incident beam. Similar 
definitions hold for the scattering cross section, absorp- 
tion cross section and differential cross section for 
back scattering or radar cross section. The total cross 
section Q; has the following form: 
2 n=o 
Q= -(—Re) D @n+1) (ant,), 
a n=1 
where A denotes the wavelengths in free space of the 
incident radiation and a, and b,, (n = 1,2,3,---) form 
an infinite set of scattering amplitudes or coefficients 
associated with magnetic and electric poles of increas- 
ing order induced in the water drop by the field 
strengths of the radiation. Thus a, is associated with 
a magnetic dipole, 6, with an electric dipole, b, with 
an electric quadrupole, etc. 
Pages 275-276 are devoted to study of the ampli- 
tudes a, and 6b,. These are complicated functions of 
the wavelength A, diameter D, or radius a of the drops, 
as well as the complex refractive index WN or dielectric 
constant «, of water. Approximate expressions of the 
amplitudes can be derived by expanding them in series 
of ascending powers of the parameter p = ~D/) for 
p <1. Retaining only terms up to p®, we found the 
following expressions of the first amplitudes, 
J 
mgs cg tibt 
b= —-2 
3 N242° 
2j N2—1 1¢ OAR S2 | Ape il ‘) 
5N24+2° 3 n242° )? 
pide Ne 
15 2N24+3°? 
2 = 
where WN is the complex refractive index of water with 
respect to free space and N? = ec, = (e,—je) is its 
complex dielectric constant. The numerical computa- 
