50 TECHNICAL SURVEY 
It will suffice to mention here that, for waves 
larger than about 3 cm, the attenuation produced 
by hail of the same water precipitation rate as a rain 
will be but a few per cent of the rain attenuation. 
At shorter waves, in the millimeter region, hail 
attenuation may become larger than that of rain. 
Similarly the attenuation of snow should be con- 
siderably less than rain; however, Canadian reports 
indicate approximately the same value for. the same 
water content. 
As mentioned above, the whole theory of attenua- 
tion is based on equation (14). The formulas giving 
the amplitudes a, and 6b, are too complicated to be 
reproduced here. Their numerical evaluation for 
spherical drops of given size and temperature is 
quite laborious except for small values of the para- 
meter tD/\. They involve Bessel and Hankel fune- 
tions of half-integer order of the parameter rD/). 
A series of experimental results are given in Table 
13. These results are to be regarded as maximum 
attenuation values. 
If these results are compared with those of Table 
10 and Figure 2 one sees that, in view of the uncer- 
tainty in the temperature of the raindrops and their 
size distribution, the agreement between theoretical 
Tase 13. Experimental values of the maximum 
attenuation per unit precipitation rate. 
d, cm (a/p) db perkm/mm perhr References 
0.62 0.37 269 
0.96 0:15 256 
1.089 0.2 262 
0.19 176 
1.25 {000.040 276 
0.63 281 
3.2 0.032-0.042 261 
and observed values is, on the whole, satisfactory. 
It will be seen that the results reported on K-band 
rain attenuation in Hawaii by the U.S. Navy Radio 
and Sound Laboratory workers™! are higher than 
those observed by other workers on the same wave- 
length. The orographic character of these Hawaiian 
rains which were made up of drops falling about 
300 m instead of ordinary rains falling 1,500 to 
2,000 m may be one of the reasons for this divergent 
result. : 
CLoups AND FoG 
Observations indicate that fair weather clouds and 
fog are composed of droplets whose diameters do not 
seem to exceed 0.02 cm. Under these conditions the 
attenuation formula takes on a remarkably simple 
form since it becomes independent of the drop size 
distribution. The attenuation formula in this limit 
of very small values of the parameter 7D/) is 
4.092 mc, 
+ db/km , (17) 
Aan = 
where m is the mass of liquid water per cubic meter, 
d is the wavelength of the radiation in centimeters, 
and 
6e1 
"Fo + ee oe 
C1 
where e¢, and ¢, are the real and imaginary parts of 
the dielectrie constant of water at the temperature 
in question and for radiation of wavelength \. Figure 
4 represents the attenuation in clouds and fog in the 
range 0.2 to 10 cm. This graph corresponds to a 
°</M IN DB/KM/G/GU M 
0.2 0.5 1.0 2 5 10 
A IN CM 
Ficurs 4. Attenuation factor in liquid clouds and fogs. 
T =18C. 
liquid water concentration of 1 g per cu m, which 
is undoubtedly rather high. Actually, the observa- 
tions indicate that the liquid water concentrations 
in clouds and fog rarely exceed 0.6 g per cu m. 
To this may be added the Table 14 for attenuation 
by ice clouds. In ice clouds m will rarely exceed 0.5 
and will often be less than 0.1 g per cu m. 
Taste 14. Attenuation in decibels per kilometer for ice 
crystal clouds. 
Shape of crystals T = —40C T=0C 
Spherules 0.00044 m/r 0.0035 m/r 
Needles 0.00062 m/r 0.0050 m/d 
Disks 0.00087 m/d 0.0070 m/r 
ScatTrerine (EcHo) 
If we denote by o() the back-scattering cross 
section per unit solid angle of a spherical water drop 
