22 RADIATION 
This amount of absorption is much higher than the 
maximum of 6 per cent which Hewson’s theoretical 
computations indicate [45]. If it is assumed that the 
measurements are correct, the discrepancy can be at- 
tributed to several factors. Clouds are complex aniso- 
tropic physical entities, and the theory must make 
numerous assumptions to handle even isotropic clouds 
of Liquid water drops. In particular, the theory does not 
include absorption by water vapor in clouds. A cloud 
whose liquid-water content is 0.5 g m~ could easily 
contain 5 g m~ of water vapor, and 10 g m™ or more 
are quite possible. Hence with the radiation undergoing 
numerous reflections by the liquid water drops, the 
path length of a ray through the water vapor could 
easily be 10 to 20 times that of its path through liquid 
water. Furthermore, the fractional absorption of water 
vapor is by no means negligible by comparison with 
that of liquid water [6]. The absorption by the water 
vapor might therefore be comparable with that by 
liquid drops. Such an effect would brmg computations 
such as Hewson’s more in line with the measurements. 
Another factor is absorption by the ice and snow par- 
ticles which exist in cirrus and altostratus clouds. The 
mechanism of such absorption is unknown and has not 
been included in theoretical discussions. In view of these 
and other theoretical complexities, measurements for 
many types of clouds are required to establish firmly 
the magnitude of absorption by clouds. Apparently, 
relatively diffuse thick clouds (such as altostratus) will 
reflect a smaller amount of energy than less diffuse 
thick clouds, such as stratus or stratocumulus clouds 
of the same or even smaller vertical thickness [18, 32]. 
Mecke [59] has pointed out that, for infinitely thick 
clouds, high reflection will be associated with low ab- 
sorption and vice versa. These ideas are in qualitative 
agreement with the relatively low absorption in thick 
stratus with its high albedo [66] and with the relatively 
high absorption in thick altostratus of extensive cloud 
systems with its low albedo. 
The Earth’s Surface. The energy which reaches the 
surface of the earth is either absorbed or reflected. The 
albedo of the earth’s surface will be discussed later; it 
is the order of magnitude of the absorbed energy which 
should be emphasized here. In middle latitudes, at 
least, during cloudless conditions about 80 per cent of 
the energy Qz incident in a day at the outer atmosphere 
reaches the ground. Except for snow-covered areas, an 
albedo of 10 per cent may be assumed for purposes of 
rough evaluation. Hence under these conditions, about 
72 per cent of Qz is absorbed by the earth’s surface. 
This is very much larger than the absorption of 2 per 
cent by ozone, or of about 8 per cent by water vapor, 
or even of the 20 (?) per cent by extensive cloud sys- 
tems. Of course, in overcast areas, the energy which is 
absorbed by the ground is smaller than 70 per cent and 
may be equal to or less than the energy absorbed in the 
cloud. But with average cloudiness, the ground ab- 
sorption approaches about 50 per cent of the extra- 
terrestrial radiation. 
Therefore, although absorption by ozone may cause 
large temperature changes at 40 km because of the low 
atmospheric density at that height, by far the largest 
amount of energy which potentially becomes available 
for atmospheric processes is absorbed by the earth’s 
surface itself. 
Miscellaneous Absorptions. Several gases absorb 
minor amounts of solar energy. Oxygen, in addition to 
the important absorptions in the ionosphere and ozono- 
sphere, has some minor absorptions in the near infrared 
(Fig. 4). Nitrogen compounds and COQ, absorb small 
amounts. Carbon dioxide is, of course, of great im- 
portance in long-wave terrestrial radiation, but plays a 
minor role in solar radiation absorption [50]. The pres- 
ence of methane has recently been announced by several 
authors [54]. Its role in the heat balance of the atmo- 
sphere has not yet been considered. 
Scattering. In the absence of clouds, energy is de- 
pleted from the direct solar beam through absorption 
and scattering by air molecules, water vapor, and dust. 
Where absorption is negligibly small the scattering coef- 
ficient may be expressed as i 
Sh ==" (San aim SWAN (Sans (10) 
where Say, Swa, and sa are the scattering coefficients of 
pure dry air, water vapor, and dust, respectively. 
Spectral Molecular Scattering. When the isotropic par- 
ticles which cause scattering of energy are very small . 
by comparison with the wave length of the light (< 
0.1 d), the theory developed by Rayleigh [34] shows that 
the scattering coefficient depends on \~ or, if the mass 
of air in the vertical at sea level is taken as unity, 
1 32m (mm = 1) HAT 
aN, ; (11) 
Sa) 
where m is the index of refraction of air for light of 
wave length \, N. is the number of molecules per cubic 
centimeter of air, and H is the height of the homogen- 
eous atmosphere. 
If scattering by air molecules alone is considered, the 
monochromatic energy which reaches sea level as the 
original parallel beam is given by 
Ty, = Ip, exp(— Say sec Z). (12) 
Values of s,, and of the transmission an = 1/1 for 
the Rayleigh scattering law are given by List [56]. 
For air molecules which are not spherical it might be 
necessary to multiply those values of sa by 1.04 [76]. 
Total Molecular Scattering. We are often interested 
not in the spectral transmissions but in the total trans- 
mission J/J). If equation (12) is integrated, we see that 
I/ty = O/t) [ byan 
(13) 
= a/t) | To, exp(— Sax m) dd. 
The data for Ip are available from Smithsonian Insti- 
tution measurements (Fig. 1), and several authors have 
computed J/IJ) from equation (13). Figure 6 shows such 
a computation by Kimball [52]. Curve (1), for w = 0, 
