THERMODYNAMICS OF CLOUDS 
THE MOIST-ADIABATIC PROCESSES 
Ascending Motions. Despite the influence of the 
processes just mentioned, the classical theory of the 
moist-adiabatic still represents the basic process upon 
which all refinements must be made. The fundamental 
concept has been checked by Schnaidt [86] and Bleeker 
[6] in careful theoretical mvestigations. Schnaidt no 
longer distinguishes between the obsolete rain, snow, 
and hail stages. He defines, according to Dinkelacker’s 
suggestion [9], (1) the cloud-adiabatic, in which all 
condensed water is retained in the ascending mass and 
is carried along, (2) the general pseudo-adiabatic, m 
which part of the water drops out, and part is carried 
along, and (8) the special pseudo-adiabatic, m which 
all the water drops out. All three stages can take place 
with condensation or sublimation. The first and third 
processes do not occur in nature. The normal process 1s 
the second one which, however, cannot be theoretically 
evaluated, since no numerical estimate can be made of 
the amount of precipitation elements which drop out or 
are carried along. The temperature curve for the three 
eases is different. For the same pressure decrease, the 
temperature decrease is smaller for the cloud-adiabatic 
than for the pseudo-adiabatic. The case which can be 
handled most easily from a numerical standpoint does 
not permit a physical interpretation: In the pertment 
equation, the specific heat of the mixture of air, water, 
and water vapor contains a term cM (where c is the 
specific heat of the water, and IM is the entire content of 
water plus water vapor); this term is set equal to zero. 
The resulting equation can be integrated as a whole 
and is the basis for the diagrams of Rossby and Shaw; 
however, the trend of the curve yields a still more rapid 
temperature decrease with decreasing pressure than do 
the cloud- and pseudo-adiabatics. Dinkelacker has 
called this the “main-adiabatic.” Distinguishing these 
eases and their computation should not be considered 
mathematical sophistry; the selection of the proper 
adiabatic as the basis for a graphical determination of 
instability criteria or for the precise computation of 
the lateral entramment can become very important. 
Descending Motions. It must be noted that the 
moist-adiabatic is also being followed by air parcels 
that conta liquid water and have a vertical, descend- 
ing motion [26]. One example of this process is the 
descending motion which the falling precipitation es- 
tablishes below a thundercloud. As the air descends 
moist-adiabatically to the ground, it loses part of its 
charge of water droplets by evaporation; the tempera- 
ture difference between this air and the dry-adiabati- 
cally stratified air surrounding the thunderstorm be- 
comes increasingly negative toward the ground. The 
instability thus released is, to a large extent, responsible 
for the kinetic energy of the squall that is, so to speak, 
squeezed out from the region of falling precipitation. 
Suckstorff [41, 42] has studied these processes very 
thoroughly. 
Waener [43], in a careful study, has recently drawn 
attention to a second phenomenon, the formation of 
mammatus clouds. If the top of a thundercloud takes 
the form of an anvil, then this part of the cloud air is in 
201 
thermal equilibrium with the dry air underneath it; 
it is therefore neither heavier nor lighter than the latter. 
Through a renewed swelling of neighboring cumulus 
tops, the anvil is quite often forced to descend, particu- 
larly in the rear of the thunderstorm. The layers of dry 
air below the anvil, and the cloud’s air, are descending 
simultaneously, the former dry-adiabatically, the latter 
moist-adiabatically. Therefore, a temperature discon- 
tinuity develops, with cold air above warm air, in other 
words, a region of instability with an almost horizontal 
boundary surface. The mammatus pouches form either 
through horizontal differences of temperature or water 
content or through dynamic perturbations of the bound- 
ary surface. As they penetrate deeper into the dry air 
underneath, they become increasingly colder than their 
environment. Under certai conditions they can even 
detach themselves from the upper anvil clouds. Similar 
extended layers of altostratus mammatus are frequently 
observed on the north side of low-pressure areas (in 
central Europe, for instance, to the west of Vb-lows 
which are moving from south to north), where the 
warm air masses have ascended above the lower air 
and where divergence in the horizontal flow may cause 
a subsidence of the entire stratified mass of air. 
EXTENSION OF THE THEORY OF CONVECTIVE 
CLOUDS 
In the last decade, two fundamental lines of investiga- 
tion have been followed with the purpose of widening 
the theory of the dynamics of convective clouds. On the 
one hand, we have the theories of Bjerknes [5] and 
Petterssen [28] dealing with the descent and dynamic 
heating of the air masses surrounding cumulus clouds; 
on the other hand, we have investigations into the en- 
trainment of the surrounding air in the rismg movement 
of cumulus, an approach developed particularly by 
Austin [2]. Both ideas may be based on the observation 
that an indication of marked “moist-instability” from 
the sounding is not always accompanied by a strong for- 
mation of convective clouds. On the contrary, even with 
large temperature lapse rates convection is often missing 
or only very feebly developed. Both theories, therefore, 
lead to a higher instability lapse rate than does the 
parcel method. 
The Slice Method. The simple theory of moist- 
adiabatic change does not take into account the fact 
that an ascending air parcel is surrounded by air which 
must descend in order to preserve continuity of mass. 
This becomes quite clear when we consider that the 
exact theory does not describe the temperature change 
with respect to height, but with respect to pressure; 
in other words, it may also hold true for air in the 
chamber of an air pump. Actually, the descending air 
masses in the environment of a convective cloud are 
warmed so that the temperature excess, which the as- 
cending air will take on because of the released heat of 
condensation, becomes smaller. This decrease in tem- 
perature difference is insignificant because the tem- 
perature excess is so large when the ascending cloud 
columns are small, and a slow descent takes place over 
the large spaces between the columns. However, the 
