282 RADIO WAVE PROPAGATION EXPERIMENTS 
o</M IN DB/KM/G/CUM 
A IN CM 
Figure 9. Attenuation factor in liquid clouds and fogs. 
t=18 C. 
where V; is the volume of a raindrop of & em diam- 
eter, v; is its terminal velocity in meters per second 
and N;, is their number per cubic centimeter. The 
attenuation of a rain of total precipitation rate p is, 
then, according to equation (54), 
_s _ 0.4343 5 iQue 
yp = S on(pe) = 3.6. » Wan 
k=0 k=0 
db per kilometer, (57) 
after substituting N, from equation (56) into (54). 
For a given wavelength A, the ratio Q:4/Vivz is a 
constant characteristic of drops whose diameter is k 
em. This ratio will be denoted by g,. The attenuation 
formula then becomes, finally, 
ap= 0.126 >, Dede, (58) 
k=0 
which shows that the attenuation in rains of a total 
precipitation rate of p mm per hr depends linearly on 
the individual precipitation rates p, of all the drop 
groups & which build up this rain. The attenuation 
does not depend directly on the total precipitation 
rate p. The points representing the experimental ob- 
servations in the coordinate plane (a,p) should cover 
a certain region of this plane, but no single curve 
a(p,) exists, since there is no direct relationship be- 
tween ~ and p. A curve drawn in this plane is sig- 
nificant only in so far as it permits one to predict a 
possible attenuation value in any rain of given pre- 
cipitation rate or vice versa. 
It is, however, possible to draw in the (a,p) co- 
ordinate plane a straight line which, at a given wave- 
length, will represent the theoretical upper limit for 
the attenuation. Indeed, using Table 6 for the attenua- 
tion in fictitious rains with a distribution of one drop 
per cubic centimeter, and Table 9, giving the precipi- 
tation associated with the same fictitious rains, one 
may compute the ratio %,/p; for any such rain formed 
by a single group of drops of diameter & cm and the 
precipitation rate p; of the same rain. This ratio for 
a given wavelength A of the radiation varies with k, 
the diameter of the drops, and in the diameter range 
0 to 0.55 em this ratio takes on an optimum value for 
a certain diameter D. This, then, is the slope of the 
straight line in the (a,p) plane which determines the 
theoretical upper limit ¢max of the attenuation in any 
rain of total rainfall p. 
Taste 8. Precipitation rates p/N in fictitious rains 
with a concentration of one drop per cubic centimeter. 
Drop diameter D, cm p/N mm/hr 
0.05 4.99 x 10? 
0.10 7.34 X 108 
0.15 3.34 x 104 
0.20 9.6 x 104 
0.25 2.14 x 105 
0.30 4.08 x 105 
0.35 6.76 x 105 
0.40 1.05 x 106 
0.45 1.54 x 106 
0.50 2.17 x 108 
0.55 2.92 x 106 
The different steps taken in computing the total 
attenuation equation (58) in a rain of total rate of 
fall of p mm per hour appear in Figure 10 where the 
drop size distribution and the partial attenuations 
due to the different drop groups of a 22.6-mm per 
Tasie 9. Attenuation in rains of known drop size distribution and rate of fall (db/km). 
A, cm 
mm/hr 1.25 3 5 8 10 
20 30 50 75 100 _—rbution 
2.46 1.93107! 4.92107? 4.241073 1.23 10-8 7.3410~4 2.8010-4 1.52104 6.49 10-5 2.33 10-5 1.03 10-5 5.85 10-6 
4.0 3.1810! 8.63 10-2 7.1110-8 2.0410-8 1.19 10-8 4.69 10-4 2.53 10-4 1.08 10-4 3.88 10-5 1.7210-5 9.75 10-6 
6.0 6.15 107-1 1.921071 1.25 10-3 3.02 10-8 1.67 10-8 5.84104 3.0210-4 1.2510-4 4.3410-5 1.9310-5 1.09 10-5 
6.13 107! 5.91 10-2 1.17 10-2 5.681078 1.691078 7.851074 2.95 10-4 9.23 10-5 4.1510-5 2.35 10-5 
8.01 107! 5.13 10-2 1.101072 6.46 10-8 1.85 10-8 9.09 10-4 3.6010-4 1.2010-4 5.36 10-5 3.03 10-5 
7.28 10-1 5.291072 1.211072 6.9610-8 2.27 10-8 1.171078 4.81 10-4 1.6610-4 7.41 10-5 4.19 10-5 
1.12101 2.32 10-2 1.17 10-2 3.641078 1.75 10-8 6.8310~ 2.2410-4 9.9510-5 5.63 10-5 
1.65107! 3.33 10-2 1.62107? 4.96 10-8 2.29 10-8 8.71 10-4 2.78 10-4 1.23 10-4 6.98 10-5 
15.2 2.12 
18.7 2.37 
22.6 2.40 
34.3 4.51 1.28 
43.1 6.17 1.64 
STO oO> 
