LONG-WAVE RADIATION 43 
receives more heat than it emits. Thus it cannot exist 
as a cloud and must evaporate. This is probably the 
reason for the phenomenon observed in the tropics, 
namely, that the highest cirrus clouds are not found 
near the stratosphere, but at an altitude of about 14 km. 
Also the diurnal variation in the cirrus clouds (¢.e., dis- 
solution toward noon, re-formation toward evening), 
which has been occasionally observed in the subtrop- 
ical deserts, can probably be ascribed to the fact that 
the ground temperature is very high at noon [36]. 
A further consequence of the interaction between 
absorption of radiation from below and emission upward 
is the fact that a cloud layer must develop its own in- 
ternal convection system. The absorption of heat in the 
lower portions will lead to an evaporation of the drop- 
lets, while the emission from the upper portions will lead 
to increased condensation and a descent of the heavier 
cloud. Thereby, the stratified cloud is resolved into 
individual convection cells, stratus is turned into strato- 
cumulus and altostratus into altocumulus. This process 
may take place fairly rapidly. A stratified cloud 14 km 
thick, at an altitude of about 5 km, is converted and 
“destabilized” from the isothermal state to one with 
a temperature gradient of 0.5C per 100 m in approxi- 
mately twenty minutes, whereas a similar cloud at a 
height of 2 km requires three quarters of an hour to 
complete the same change [82]. Keeping this in mind, 
it seems scarcely credible that an ordinary cloud layer 
can exist unchanged in the atmosphere for any length of 
time without being dissolved. If, in spite of the fore- 
gomg discussion, thin, closed, and stable altostratus 
cloud layers are observed, it becomes clear from the 
radiation calculations to what degree they must be sus- 
tained by a process which constantly re-forms them 
by new condensation. This process may be vertical 
austausch or upgliding, and its effectiveness must be 
considerable even in a cloud that appears to be stable 
and unchanging. 
Synoptic Situations and Radiation of the Free Atmos- 
phere 
It is easy to survey schematically the radiation proc- 
esses of an individual cloud. However, conditions be- 
come more complicated if it is desired to calculate 
approximately the effect of the clouds under different 
weather conditions or in different climatic regimes. 
Nevertheless, such calculations are necessary, since they 
offer the first possibilities for surveys. An attempt in 
this direction [36] is reproduced in Fig. 4. In this figure 
the average cloud conditions of a low-pressure area in 
middle latitudes are assumed, that is, 10 per cent of the 
area is clear, 20 per cent has clouds resting on the 
ground, 50 per cent has clouds with the lower level 
between 0 and 2 km, and 20 per cent has clouds with 
the lower level between 2 and 8 km. Correspondingly, 
in 40 per cent of the total low-pressure area, the upper 
cloud boundary is assumed to lie between 0 and 3 km, 
in 20 per cent between 3 and 8 km, and in 30 per cent 
between 8 and 10 km. In the average cooling curve 
shown in Vig. 4, the heat loss of the most important 
cloud levels at 2 and 9 km is distinctly noticeable, the 
lower by a cooling of almost 2C per day, the upper by 
more than 5C per day, for at this level the heat loss by 
the radiating upper cloud surface becomes more effec- 
tive because of the reduced density of the air. The hori- 
zontal distribution in the low-pressure system cannot 
be distinguished, because the various factors are aver- 
aged over the entire area. However, the cooling rate 
must be about three times as great im the advance 
portion of the cyclone where the upgliding cloud screen 
lies as a closed, though loose and diffuse, cover at 8 km 
altitude. It is obvious that such a cooling of 15C per 
day will noticeably influence the weather development 
and the cloud dynamics. Further vestigations of this 
kind should yield valuable insight into the thermo- 
dynamics of weather. 
HEIGHT (KM) 
6 5 4 3 2 (0) 
COOLING (°C PER DAY) 
Fic. 4—Cooling of the atmosphere by water-vapor radia- 
tion in degrees per day. The dashed line applies to a cloudless 
atmosphere and the solid line to an average distribution of 
clouds in a low-pressure area. 
In 1935 the author tried to give a balance of all heat- 
ing and cooling processes in the free atmosphere and 
their vertical distribution [29], in which not only the 
outgoing radiation but also the incoming solar radiation 
and the liberation of the latent heat of condensation 
were considered. The calculations for long-wave radia- 
tion will be revised here. 
A normal temperature and humidity distribution for 
middle latitudes was assumed as a basis for the calcu- 
lations. The cooling of the cloudless atmosphere, as now 
computed, differs from the earlier calculation. At that 
time, the cooling of the entire troposphere was found 
to be constant at 1C per day. In the new calculation 
(Fig. 5, curve A) it increases with altitude to 2°4C 
per day (at 9 km). The cause of this difference lies in 
