THERMODYNAMICS OF CLOUDS 
lower parts of the clouds than in the higher parts. For 
the numerical computation of these processes on falling 
snow crystals it would be valuable to consider the in- 
vestigations of Wall [46] and the indices of crystal 
erowth introduced by him. The greater heat release in 
the lower cloud portions increases the vertical tempera- 
ture gradient and augments the instability in all clouds 
which already contain falling particles of precipitation. 
Now, the slice method shows that when air ascends or 
descends moist-adiabatically within the cloud, the re- 
leased instabilities and vertical motions are considerably 
larger than would be expected according to the parcel 
method. Therefore, these comparatively minor amounts 
of released heat have a certain importance for the ther- 
modynamics and mechanics of the cumulonimbus as 
well as for the upgliding nimbostratus. A numerical 
calculation of all these processes would be very de- 
sirable. 
Droplet Accretion and Graupel Formation. A quanti- 
tative evaluation of the thermal effects of accretion of 
small cloud droplets on fallmg ice crystals and hail 
grains has not been made. Only the accretion on falling 
rain droplets has been computed in the theory of 
“chain reaction” processes in convective clouds by 
Langmuir [18]. We will not go mto any further details 
here. However, the thermal consequences will be 
stressed again. It is evident that the heat of condensa- 
tion does not play a role in this accretion. In the forma- 
tion of precipitation, accretion on falling droplets is 
more important than condensation, but it is of no sig- 
nificance m the thermal processes. This is similarly true 
of the accretion of supercooled droplets on ice crystals 
(formation of graupel). In this process only the heat of 
fusion is released, whereas the amount of heat released 
in the sublimation of water vapor on ice crystals is 842 
times greater per unit mass. The accreted masses, how- 
ever, are considerably larger in the process of graupel 
formation than in sublimation or the formation of rime; 
therefore the quantities of heat involved may be com- 
parable. Here, too, the effects of the growth and the 
mereasing fall velocity of the droplets, etc., are such that 
larger amounts of the heat of fusion are released in the 
lower portions of the cloud, thus causing an additional 
instability [15]. 
This becomes particularly important for the inter- 
mittent formation of a thundercloud. It has already 
been emphasized that a cumulonimbus does not form 
all at once, but that only one cloud tower at a time 
builds upward, spreads to an anvil (éncus), glaciates, 
and stops growing; immediately following and quite 
close to the old tower, a new one rises. At first this con- 
tains only supercooled droplets, but soon it mushrooms 
into the existing anvil consisting of ice crystals, thus 
providing the best possible natural seeding of the as- 
cending cloud. Consequently, conditions are favorable 
for the precipitation of large drops, graupel, and hail; 
for whenever one cloud tower or cell has fulfilled its 
task of producing precipitation, the next one swells up, 
ready to catch the falling ice particles and carry them 
upward again. Thus the processes of graupel formation 
and the release of heat of fusion causes additional in- 
205 
stability in each subsequent tower which enables it to 
ascend higher than the preceding one. Also noteworthy 
is the interaction between the upper glaciated part of a 
nimbostratus cloud, which effects the seeding, and the 
lower part, which contains a large supply of liquid 
water [25]. A separation of the two cloud parts from 
each other may, under certain conditions, occur at 
mountain barriers when the lower current (and thus the 
cloud) is held back, while the upper current passes over 
the top of the mountain (Bergeron [3]). This can also 
happen with warm fronts, where the rain areas will be 
either very narrow or very wide, depending on the vari- 
ation of wind with height. 
Melting Processes. Somewhat more complicated 
processes exist in or directly below the freezing level. 
If the cloud reaches below this level, melting of the 
fallmg ice particles will not immediately occur, but 
rather, intensified condensation and sublimation will 
take place. Thus, the instability will spread below the 
freezing level. Only at some lower level will the melting of 
the falling ice affect the thermal processes. This melting 
will consume so much heat that the air is considerably 
cooled and its temperature kept constant at OC. In this 
layer an isothermal lapse rate and thus marked stability 
will develop. This isothermaley has nothing to do with 
the hail stage of the old classification of the moist- 
adiabatic processes (rain, hail, and snow stages), for 
here we do not deal with temperature changes of an 
individual quantity of moist air moving either upward 
or downward vertically, but with air that can remain 
at rest while precipitation falls through it. A strong in- 
stability will develop below this stable layer if the lapse 
rate was previously adiabatic or less. Findeisen [13] has 
called attention to this instability and has shown that 
it frequently causes the formation of scud clouds below 
the rain cloud proper. At this level, there are squalls 
and strong vertical turbulence, which permit formation 
only of fractocumulus clouds, but not of a closed cloud 
layer [15]. 
PROBLEMS FOR FUTURE RESEARCH 
The discussion in this article has been presented with 
the principal idea that, fundamentally, we are con- 
cerned with disturbances or modifications of the simple 
moist-adiabatie process. It should be the aim of further 
scientific investigations to combine all the separate 
stones of our mosaic into a coherent picture of the heat 
balance of the clouds, in particular, (1) the heat bal- 
ance of clouds in general, (2) the heat balance of the 
individual types of clouds, and (3) the role of the indi- 
vidual cloud types in the heat balance of the entire 
atmosphere. 
REFERENCES 
1. Ausrecut, F., “Theoretische Untersuchungen tiber den 
Strahlungsumsatz in Wolken.’ Meteor. Z., 50:478-486 
(1933). 
2. Austin, J. M., and Freisupr, A., “A Thermodynamic 
Analysis of Cumulus Convection.” J. Meteor., 5:240-243 
(1948). 
3. Bercrron, T., “The Problem of Artificial Control of Rain- 
fall on the Globe. II—The Coastal Orographic Maxima 
