26 : RADIATION 
multiple scattering this rule is closely obeyed. Conse- 
quently from 7 to 8 per cent of the incident solar energy 
would be scattered back by the pure, dry, cloudless 
atmosphere. 
2. Water Vapor. The scattermg by water vapor and 
questions concerning it were discussed earlier. If one 
accepts 1 — a, as the depletion by water vapor due to 
seattermg, then scattering for the total spectrum can 
be computed as a function of air mass, as was done by 
Fowle, and also by Kimball (Fig. 6). From this func- 
tional relation, the scattermg by water vapor over the 
whole earth can be computed. But for this, of course, 
data on the distribution of water vapor with latitude 
are necessary. From a rough estimate of w, obtained 
from the distribution of surface vapor pressure, and 
after weighting the areas of the earth involved, it is 
found that 10 per cent of the incoming solar energy is 
reflected by water vapor [80]. 
This, again, represents the energy scattered in all 
directions, but the portion which is scattered back to 
space is not so readily ascertained as it is for air mole- 
cules. Fowle believed that the scattering particles were 
ageregates of water-vapor molecules; Angstrém sug- 
gested that dust might be the scattering agent. In either 
case, it is recognized that if the size of the particles 
approaches the wave length, the forward scattering 
exceeds the backward scattering. At any rate, two ex- 
tremes can be postulated: (1) Hither half the scat- 
tered energy (5 per cent) is directed upward; or (2) 
none of the scattered energy is directed upward. 
3. Dust. Concerning dust our knowledge is most 
meagre. Not only is the transmission coefficient for 
dust im doubt, but the distribution of dust over the 
world is inadequately known. Klein [53] gives a com- 
pilation of some values which serve as a guide, but even 
these “measured” values may be inaccurate in view of 
the madequate understanding of dust depletion. From 
Klein’s data one may estimate a depletion of about 5 
per cent of the initial radiation on a world-wide basis. 
In view of the probable greater forward scattermg and 
some absorption, less than 2.5 per cent is scattered 
back. An estimate of 1 per cent might be about right. 
4. Total Atmospheric Reflection. A sammation of the 
reflection by atmospheric elements gives a reflection 
lying between 8 and 13 per cent, depending on how 
much is allowed for upward seattermg by water vapor 
and dust. There are not very many direct measure- 
ments which yield the reflection by the atmosphere. 
In the lower layers of the atmosphere, some airplane 
measurements [29] indicate that about 5 per cent of 
the energy incident at 10,000 ft is scattered upward by 
the air below 10,000 ft. These measurements were made 
with a solar zenith distance Z of 53° on a rather smoky 
day. At greater heights and zenith distances greater 
reflection presumably would have been measured. Teele 
[75] measured the visible energy scattered back at 
72,000 ft. He imterpreted his measurements as indi- 
cating that 6 per cent of the incident energy is reflected 
by the air when Z is 60°. 
These measurements and calculations are valid for 
the cloudless atmosphere only. For the average con- 
dition of 0.54 cloudiness, calculation indicates that the 
cloudless portions of the atmosphere reflect about 6 or 
9 per cent of the incident solar energy, depending on the 
assumptions made, when about 2.7 per cent is included 
for the reflection by the air above the clouds. 
Clouds. Most of the solar energy reflected to space is 
reflected by clouds. However, the albedo of clouds is so 
Taste VY. ALBEDO or VARIOUS CLoup TypEs 
Albedo 
Source Cloud type (per 
cent) 
Luckiesh [57] (vis- | Very dense clouds of extensive 78 
ible light) area and great depth 
Dense clouds, quite opaque 55-62 
Dense clouds, nearly opaque 44 
Thin clouds 36-40 
Fritz [32] (totalra-| Stratocumulus, overcast 56-81 
diation, exten- Altostratus, occasional breaks 17-36 
sive systems; Altostratus, overcast 39-59 
cloud types be- | Cirrostratus and altostratus 49-64 
low measured Cirrostratus, overcast 44-50 
clouds not speci- 
fied) 
Aldrich [7] Stratus, 600-1000 ft thick 78 
variable, even for one type of cloud, and our informa- 
tion about the spatial distribution of cloud types is so 
poor that it is impossible, from individual cloud-albedo 
measurements, to specify an average value over time 
and space for the total reflection by clouds. Hence, in 
order to estimate the average albedo of clouds, it is 
20 
CAST 
EN CLOUDS 
CLOUD THICKNESS (HUNDREDS OF FEET) 
(0) 20 40 60 80 100 
ALBEDO OF CLOUD (%) 
Fie. 8.—Observed albedo of stratus clouds. (After Nei- 
burger [66].) 
necessary to measure the albedo of the whole earth 
first and then to subtract the contributions by the 
atmosphere and by the ground. The remainder is the 
albedo of clouds. 
