42 RADIATION 
colder vapor masses are ‘‘nearer”’ than the warmer ones 
in terms of radiation, because the vapor density is 
lower above that altitude than below it. Therefore, 
more heat is emitted upward than is received from 
below. Thus, the cooling in the free atmosphere exists 
by virtue of the fact that T is not proportional to w. 
This behavior of radiation, which is similar to heat 
conduction, is also clearly revealed by a break in the 
curve of vertical temperature distribution. There is an 
abrupt transition (schematically) from 07/dz = —y 
to 07 /dz = O at the tropopause. Hence the vapor 
particle at this pomt receives radiant heat from the 
mass below, but cannot emit anything to the masses at 
equal temperature above. Therefore, in the absence of 
other influences, it should become warmer. 
However, at higher altitudes the cooling does not 
depend only on a process similar to heat conduction, 
but in this case true emission occurs, that is, heat is 
radiated to space. Therefore, the amount of cooling is 
only partially due to the vertical temperature gradient 
and for the remainder to the mass of water vapor 
above and its screening effect on any heat radiation 
to space. The smaller this mass is, the greater the cool- 
ing. It was formerly assumed that the stratosphere had 
a high vapor content, or that the specific humidity re- 
mained constant with altitude.* This assumption leads 
to vapor contents that are too large and to contra- 
dictions between the magnitude of outgoing radiation 
and the actual temperature distribution. Today it is 
known from measurements by Regener [41] and by 
Dobson and others [13] that the relative humidity 
decreases sharply Just above the tropopause. A more 
recent publication by Barrett and collaborators [5] also 
confirms these results. They found a decrease in hu- 
midity from about 10 per cent at the tropopause to 
about one per cent at 30-km altitude, but with a thin 
saturated layer interposed. Therefore, these altitudes 
are already close to the upper boundary of the ‘‘water- 
vapor sphere” and the radiation of the intensive ab- 
sorption bands proceeds to space almost completely 
unscreened. Hence, the maximum of cooling lies at 
altitudes between 8 and 10 km. A calculation based on 
Elsasser’s chart would shift this emitting layer to a 
somewhat lower level. 
Probably, as a third factor, the radiation by haze at 
the tropopause must be considered. The troposphere is 
always filled with haze, whereas the stratosphere, con- 
tiguous to this hazy stratum, contains very dry and 
extremely clear air (as has been confirmed by numerous 
observations from aircraft). To be sure, the nature of 
this haze is not definitely known; but, whether minute 
droplets or solid particles constitute this haze, both are 
capable of emitting thermal radiation, even in the range 
from 9 to 12 p, where the efficient “window” for out- 
going radiation exists. Thus the haze boundary at the 
tropopause causes an additional cooling which may 
reach several degrees per day. Similar effects appear 
also at haze boundaries within the troposphere [31]. 
3. In the troposphere the decrease of the specific humidity 
with altitude indicates that vapor is lost and liquefied through 
cloud formation in the ascending currents of water vapor. 
Cloud Radiation 
The great effect of clouds on atmospheric radiation 
is also based on the fact that they radiate like black 
bodies in the wave-length range of heat radiation. 
Therefore, the upper cloud surfaces emit a very great 
quantity of heat in the range from 9 to 12 p at every 
altitude of the atmosphere where they may occur; in 
these intervals there is almost no downcoming radiation 
from above. This produces an intensive heat loss, con- 
centrated in a very thin layer. Naturally, this heat loss 
can become effective only if it is not counteracted by 
another process—as, conceivably, by an approximately 
equal absorption of radiant solar heat. However, 50 to 
70 per cent of the solar radiation is reflected (Fritz 
[19]), and of the remainder only a very small portion is 
absorbed, whereas the greater portion traverses the 
clouds as a diffuse radiative flux and reaches the earth 
as scattered sky radiation (daylight). There is almost 
no absorption of solar radiation in the clouds and thus, 
the heat emission from cloud surfaces is not compen- 
sated by the solar radiation, but acts unimpeded as a 
heat sink in the atmosphere. Indeed, the higher such a 
cloud surface lies, the lower is the black-body radiation 
corresponding to its temperature. However, the at- 
mospheric radiation which impinges on the cloud sur- 
face from above is diminished even more, for it de- 
creases not only with temperature but also with the 
vapor content of the air situated above. Thus, the 
effective emission of the cloud increases with altitude. 
A different process takes place at the lower boun- 
dary of the cloud. This surface receives from the under- 
lying atmosphere, which is generally warmer, and from 
the ground, which is likewise warmer, a quantity of 
radiation that is greater than the black-body radiation 
emitted by the cloud in a downward direction. For this 
reason, the under surface of the cloud is heated by 
radiation from below. In this case there is also no com- 
pensation by other processes. The heating imereases 
with increased altitude of the cloud, because of the 
increasing temperature difference between cloud and 
ground. 
For a very thin cloud layer whose vertical extent 
must not exceed 100 m, both processes, the heat loss 
above and the heat gain below, can be considered to- 
gether. Usually, the former is dominant, especially with 
low clouds such as stratus, and with middle clouds such 
as altostratus. If we assume that the heat budget of a 
thin cloud at an altitude of 5 km is distributed by tur- 
bulence and similar processes over a layer of air 1 km 
thick, we find a cooling of this mass of about 5C per 
day. A high cloud in the upper troposphere does not 
cool the air, because the radiation from below is rela- 
tively greater. In a tropical atmosphere, however, the 
conditions are quite different. The temperature differ- 
ence between ground and cloud increase continuously 
up to about 18 km because of the normal decrease of 
temperature with height in the troposphere. Even if 
the assumption of a closed cloud cover is discarded and 
a scattered cloud cover of only 140 is assumed, the heat 
balance of the cloud becomes positive at about 14 km. 
This means that even a thin cirrus cloud at this altitude 
