SCATTERING: AND ABSORPTION OF MICROWAVES 51 
and if there is a distribution m, m2, ++ - , 7%, °°") Nn 
drops per cubic meter, the cloud or rain cross section 
for scattering is 
St) = p> no (AV (19) 
where AV is the scattering volume of the cloud, on 
the assumption of incoherent scattering on account 
of the random character of the drop distribution. 
The summation includes all the drop groups. The 
rain front is usually wider than the irradiated area 
so that the radar beam intersects it. Under these 
conditions, taking AV approximately as a spherical 
shell of thickness Ad, at a distance d from the radar 
set, and denoting by 26 the half-power beam width 
of the radar beam, one gets 
AV = 2nd? (1 — cos @) Ad. (20) 
The rain echo cross section is then 
S(m) = 2nd? (1 — cos (aa Me nit ()) (21) 
Remembering that o,(z) or S(z) is precisely the cross 
section per unit solid angle in the direction of the 
radar set, one gets instead of equation (6) for the 
ratio of received to transmitted power 
= ca a &) 6 (ae) Te @) (22) 
for small angles 6 which must be given in radians. 
TasBLE 15. Fraction of incident power scattered back- 
ward by a layer of 1 km of rain in different types of rain. 
: (Decibels) 
Drop size 
distri- P; Wavelength in centimeters 
bution*mm/hr 3 5 8 10 15 20 30 50 
A 2.46 —45 —54 —61 —65 —72 —77 —84 —93 
D 6.0 —38 —46 —54 —58 —65 —69 —76 —85 
E 15.2 —32 —37 —45 —48 —55 —61 —68 —77 
H 343 —29 —35 —42 —46 —53 —58 —65 —74 
I 43.1 —27 —33 —40 —44 —51 —56 —63 —71 
*See Table 11 for drop size distributions. 
The quantity (Ad2,n,0,(z)] or its ‘value in decibels for 
known drop size distributions has been tabulated in 
Table 15. With this table and the known characteris- 
tics of a radar set the ratio P;/P2 can be computed 
at once. In the table Ad is taken as 1 km. Since the 
maximum thickness Ad cannot exceed the pulse 
length, the values found in the table can be adapted 
immediately to any pulse length J by adding to it 
(10 logis 2), 2 being expressed in kilometers. Using 
equation (22) for particular radar sets it is found 
that the theoretically computed echo powers from 
rains agree well with the observed values, if the 
uncertainties of the meteorological knowledge of the 
echoing elements, which are mostly rains and’ storm 
clouds, is kept in mind. As expected, the echoing 
power of snow is very much less than that of rain. 
The systematic observations on S band by the 
Canadian group**” and on X band by Bent*24 
clearly indicate that precipitation either in the form 
of rain or snow is necessary to produce an echo on 
the scope of the radar set. 
ABSORPTION BY THE ATMOSPHERIC GASES 
It was predicted that oxygen and water vapor will 
absorb electromagnetic waves in the microwave 
range.”>*275 In particular, oxygen was predicted as 
having a resonance band around 5 mm and one line 
at 2.5mm, while the water vapor absorption is caused 
mainly by a single rotational line of relatively small 
strength around 1 cm. Experiments have confirmed 
both these absorption effects.277273 In Figure 5, the 
individual oxygen and water vapor attenuation 
curves have been plotted in the 0.2- to 10-cm wave- 
length range. Any change in the water vapor content 
from the one adopted for this graph (7.5 g per cum 
or 6.5 g per kg of air) or the total pressure can be 
taken into account in computing the combined 
100.0 
ABSORPTION IN DB PER KM 
60 90 I50 
FREQUENGY IN 10° MC-——> 
Eryn ancline cnn aaornl acral yeaa elseslsndnrecl: 
10 §43 215 108 050403 02 
—————) IN CM 
Ficure 5. (1) Absorption due to water vapor in an atmos- 
phere at 76-cm pressure containing 1 per cent water 
molecules, or 7.5 g per cu m. The water resonance liné is 
assumed to be at 24,000 me, and its half width at half 
maximum (line breadth) is 3,000 me. (2) Absorption 
due to oxygen in an atmosphere at 76-cm pressure whose 
resonance band at 60.103 mc is supposed to have a line 
breadth of 600 me. 
