284 RADIO WAVE PROPAGATION EXPERIMENTS 
points indicated on these figures, and the smooth curve 
passing through these points serves to illustrate the 
procedure usually followed by the experimental work- 
ers, as we have already mentioned. It is evident that 
these curves have little, if any, direct physical signifi- 
cance. Similarly the curves of Figure 11 associated 
with different rains merely indicate the trend of varia- 
tion of @ as a function of the wavelength, since no 
single curve of this type can characterize a rain of 
given total precipitation rate of p mm per hour. 
Table 9 shows that the attenuation is of no practical 
importance for S band and longer waves even with the 
heaviest rains or cloudbursts. This result is summar- 
ized in Table 10 (the theoretical upper limits of the at- 
tenuations per unit precipitation rate). 
Taste 10. Theoretical upper limits of attenuation 
per unit precipitation rate (t ~ 18C). 
A, cm (a/p) max db/km/mm/hr 
1.25 1.6 x 1071 
3 4.5 x 10 
5 5.0 x 1078 
8 1.0 x 10° 
10 6.0 x 10-4 
15 3.0 x 10-4 
20 1.4 x 10-4 
30 6.4 x 1075 
These values in Table 10 correspond to raindrop 
temperatures of about 18 C. At lower temperatures the 
values of (a/p) included in this table might be in- 
creased about 25 to 30 per cent. 
The results of the different workers in the field are 
summarized in Table 11. 
It will be seen that the above values of «/p compare 
favorably with the theoretical values.1 The difficulties 
TaBLe 11. Experimental values of the attenuation 
per unit precipitation rate. 
A, em (a/p) db/km/mm/hr Authority 
0.62 0.37 Mueller’ 
0.96 0.15 Adam et al28 
1.089 0.2 Robertson27 
1.25 0.19 Southworth ef al?9 
‘ 0.09—0.40 Rado!? 
3.2 0.032—0.042 King and Robertson* 
in the interpretation of the experimental data as men- 
tioned already should be kept in mind when compar- 
ing the experimental values with the theoretical 
predictions. 
As remarked by Ryde and Ryde,” the attenua- 
tion by hailstones and snow should be appreciably 
smaller than that due to raindrops, the dielectric con- 
stant of ice being considerably smaller than that of 
liquid water. 
A final remark may be made concerning the theore- 
tical results given here. It has been assumed through- 
out the preceding discussion that the raindrops are 
iThe same seems to be true of S-band wavelengths where 
Tough attenuation measurements are available in “‘solid’’ 
storm clouds.*! 
spherical. This is likely to be the case with practically 
all the drop groups existing in rains, with the excep- 
tion of the biggest drops, which may undergo deforma- 
tions. Presumably the effects of small deformations 
are not of great importance. 
The Scattering of Microwaves 
by Spherical Raindrops 
The cross section for scattering of electromagnetic 
waves by spherical particles is given for any direction 
by equation (34). Using the approximate expressions 
of the amplitudes as given by equations (38). and (43) 
and the notation «,°), a‘), 8,@), B,@) represent- 
ing the real and imaginary coefficients of p° in a’, 
of p* in 6, etc., as indicated above, we get the fol- 
lowing expression for the total scattering cross sec- 
tion : 
r2 
Q.= M 913/612 +6188 
TC . 
+ B® Bi ©] p? + 6 [Gr © 6 + B® B®] p? 
+43[| on] 2+ | Bi [2] 
+ 5/62 |*}o'+ 6 [6 B® 
+ ROR 1+ 3180 [20+ +b om 
(59) 
Here, for instance, 
[a | = (8: 2 + (BO H5| x | 
= (ai)? + i), ete. 
For values of p< 1 and when the terms in p? and 
higher powers can be neglected in the braces, the 
total cross section for scattering reduces, v-‘ng the ex- 
plicit expressions of B,) and B,“?, to 
1287°a® 
Qs, << = "ayer 
(e,-—1)?(¢, +2)? +e7[2(e,-—1) (e- +2) +9) + et om? 
[(e- + 2)? + €?]? ; 
(60) 
When the dielectric absorption vanishes, i.e., «—0, 
this reduces further to 
1287°a§ /n? — 1 
Qs, p<, ¢; 0 = —s 4 
2 
: | 
an sao) gare 
which is the well-known Rayleigh scattering cross 
section, since e, = 27 in this case. 
In Table 12 are given the scattering cross sections 
computed within the range of p, 0.00157 to 0.576, or 
in the drop diameter range 0.05 to 0.55 cm and wave- 
length range 3 to 100 em. Needless to say, the actual 
cross sections for scattering at the larger p values are 
always larger than the Rayleigh cross sections [equa- 
tion (60) ]. For p < 0.10 the scattering cross sections 
‘are, within a few per cent, given by the first Rayleigh 
term (60) of equation (59). However, in the present 
case of absorbing spherical drops, the parametric 
