288 
RADIO WAVE PROPAGATION EXPERIMENTS 
TaBLE 15. Absorption coefficient due to back scattering (echo) 2e- km7! in rains of known drop size distribution and 
rate of fall. 
A, cm Distri- 
mom/br 3 5 8 10 15 20 30 50 75 100 bution 
2.46 2.9410-5 4.2110-6 7.011077 2.8610-7 5.741078 1.8210°8 3.6010-9 4.6610-19 9.201071! 2.91 10-1 A 
4.0 5.0610-5 7.311076 1.171076 4.811077 9.631078 3.0310-§ 5.9910-9 7.7610-1° 1.5310-19 4.851071! Cc 
6.0 1.4410-4 2.3210-5 3.9010-6 1.6110-6 3.2510-7 1.171077 2.3110-8 2.9910-9 5.9110-10 1.87 10-10 D 
15.2 6.1210-4 1.7310-4 3.3010-5 1.4110-5 2.9410-§ 7.621077 1.501077 1.9410-8 3.831079 1.211079 E 
18.7 6.6710-4 1.271074 2.2210-5 9.2510-§ 1.9010-§ 6.5110-7 1.2810-7 1.6610-§ 3.2810-9 1.041079 F 
22.6 5.691074 1.0110-4 1.74107 7.24 10-§ 1.4710-§ 4.9110-7 9.7010-8 1.2610-§ 2.4910-9 7.8810-10 G 
34.3 1.2810-3 3.0210-4 5.5810-5 2.3610-5 4.9010-§ 1.63107 3.221077 4.1710-8 8.241079 2.6110-9 H 
43.1 1.83 10-3 4.8910-4 9.1610-5 3.9010-5 8.1410-§ 2.6610-§ 5.261077 6.8210-8 1.3510-8 4.261079 I 
0 10 20 30 40 50 60 70 80 90 100 
2 IN GM 
Ficure 17. Absorption coefficient, 2 ax, due to back 
scattering (echo) as a function of the wavelength in 
different rains. The abscissa gives the wavelength, 2, 
in centimeters. The ordinate scale gives logio(2ax), the 
absorption coefficient 2ax being expressed in km7!. 
The letters on the curves refer to the drop size distribu- 
tions listed in Table 7. 
tion in different rains of given drop size distribution 
and precipitation rate. As already emphasized in con- 
nection with the study of the attenuation, these curves 
are characteristic, probably, of those rains, but they 
are not unique, since a given rain of known precipita- 
tion rate might very likely be built up from a variety 
of drop size distributions. 
Since the absorption coefficient (2«,) for back scat- 
tering represents also the fraction of the incident power 
back scattered per unit thickness of the scattering 
medium, Tables 14 and 15 allow the computation and 
estimation of the echo power to be expected in radar 
observations under given conditions. The difficulties 
which seemed to exist earlier are cleared up by assum- 
ing that in those clouds which give rise to echoes pre- 
cipitation actually occurs, even though no rain reaches 
the ground.** This is substantiated to some extent by 
recent work*> which succeeded in verifying Rayleigh’s 
law by observing cloud echoes simultaneously with 
both S- and X-band radar’ sets. Further- proof was 
added by the Canadian group,* whose exhaustive 
study in the S band clearly showed the role of rain- 
drops in cloud echo phenomena. In fact, these workers 
stated that there was no record of an echo without rain. 
It is interesting to extract from Table 15 the frac- 
tion of the incident power back-scattered from differ- 
ent rains of 1-km depth expressed in decibels. As just 
mentioned, the power back-scattered by a thickness 
Az is 
AP, = 
—2a, P; Az, (71) 
and the fraction of the incident power P; scattered 
backward by a layer Ax = 1 km is then 10 log,, AP,/ 
P, db or (10 log,, 2a,) db (2a,) is given in Table 15. 
The results are included in Table 16. 
With Table 16 and the known sensitivity of a radar 
set, the maximum free space distance from the set at 
which these rains are observable can be computed at 
TaBLE 16. Power scattered backward by a layer of 
1 km of rain in different rains (decibels). 
Distri- p, A,cm* 
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 
once. The peak power received by a radar set from 
Volume 3, Chapters 2 and 9, is 
Sx aa) 
Pra Pua a (5a 
where P, is the transmitted power (peak power), 
G, and G, are respectively the transmitter and 
receiver antenna gains relative to a doublet, 
d is the distance of the set from the echoing 
Tain drops, and 
S, is the back scattering cross section. 
The beam usually intersects the rain boundary and 
therefore it can be assumed that S, is made up of the 
combination of all the drops included in the echoing 
volume. This volume may be taken as a spherical shell 
of thickness Ad whose base is a spherical segment of 
area 
2nd?(1 — cos 6), 
26 being approximately the half-power beam width of 
the set. 
