DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 281 
VELOCITY IN M PER SEC 
0.05 GIO QI5 O20 0.25 O50 0.35 Of0 045 050 0.55 
DROP DIAMETER INCM 
Figure 7. Terminal velocity of raindrops (experi- 
mental). 
cluded in Table 6, may be regarded as characteristic 
for rains of the indicated precipitation rate, but they 
are not necessarily typical for those rains. Also given 
is the liquid water content of the atmosphere as- 
sociated with the rains of Table 6 and its graphical 
representation in Figure 8. The curve drawn on this 
graph should not, however, be considered as represent- 
ing any functional relationship between the liquid 
water concentration of the rainy atmosphere and the 
rate of rainfall. It can indeed easily be proved that 
the liquid water concentration associated with a rain 
depends only on the fractional precipitation rates of 
the different drop groups. It does not depend directly 
on the total rate of rainfall. Any rain of given total 
precipitation rate can be built up by a number of drop 
size distributions which determine different liquid 
water concentrations in the atmosphere. This means 
that it is theoretically incorrect to draw a graph entitled 
“Liquid Water Concentration versus Rate of Rainfall”, 
as is frequently done. A curve so drawn can however be 
of considerable practical value when rough concentra- 
tions corresponding to given rates of rainfall are 
desired. 
It can be seen that the resulting liquid water dis- 
tributions are in fair agreement with those reported 
by Humphreys in his table of precipitation values”® 
MASS OF LIQUID WATER ING PER CU M 
PRECIPITATION RATE IN MM PER HR 
Ficure 8. Computed liquid water distribution (em3/ 
m§ or g/m’) based on experimental drop size distribu- 
tions in different rains. The slope of the straight line 
approximation is 0.038 g/m*/mm/hr. 
already mentioned. It may be added here that aloft 
and in certain parts of rain clouds, where considerable 
updraft exists, the drop concentrations may be ex- 
pected to be larger than those derived from Table 6. 
These data will now be used in the computation of 
attenuation and back scattering by the different pre- 
cipitation forms, assuming always ideal conditions 
and leaving aside the above-mentioned irregularities 
in space. For reasons stated above, theoretical results 
are significant only with regard to orders of magnitude. 
Attenuation by Idealized 
Precipitation Forms 
The data included in the preceding section show, 
first of all, that in clouds and fogs the attenuation 
can be given rigorously. Indeed, Table 3 indicates 
that the critical diameter even for waves of 1-cm 
wavelength is over 0.06 cm. Since we have seen that 
in clouds and fogs the drop diameters never exceed 
0.02 cm, it appears that formula (51) is applicable, 
and the attenuation of all waves of wavelength A > 
1 cm is independent of the size of the drops. Further- 
more, taking m =1 g per cubic meter in formula 
(51) one probably obtains an upper limit for the 
attenuation of these waves.’ In Figure 9 the atten- 
uation is plotted down to A = 0.2 cm. The dielectric 
constant of water has been computed in this range by 
using the Debye formula for wavelengths A > 1 cm. 
Clearly the attenuation in fogs and clouds even in 
the region A ~ 1 em is not of great importance ex- 
cept for long ranges and radar observations. The 
attenuation becomes negligible for waves with A > 
10 cm. 
Table 3 also shows that the attenuation becomes 
practically independent of the drop size distribution 
for wavelengths equal to or larger than about 20 cm. 
In the 5- to 20-cm range the three-term formula 
(48) or (50) in connection with (54) will represent 
fairly well the attenuation in different rains, with 
increased accuracy at longer wavelengths. Below A 
= 5 em this formula is inapplicable, but there Ryde 
and Ryde’s'* exact attenuation values are available. 
The attenuation formula in a rain, as given by equa- 
tion (54), can be transformed easily to another form. 
If p; denotes the partial precipitation rate of the drops 
of & cm diameter in a given rain of total precipitation 
tate p, then clearly, 
p= > Pe (55) 
k=0 
s being the diameter of the largest drops in this rain. 
Now 
pe = 3.6 X 108 Vv. N. mm per hour, (56) 
iAttention may be called to the absence of data on the 
liquid water distributions in heavy sea fogs. 
