THERMODYNAMICS OF CLOUDS* 
By FRITZ MOLLER 
Gutenberg University at Mainz 
OBSERVATIONAL BASIS 
The radiosonde epoch, in which—from an aerological 
point of view—we are now living, is not favorable to a 
thermodynamical examination of clouds. The great age 
for thermodynamies and aerology was about twenty or 
twenty-five years ago, when Shaw [87], Sttive [40], 
Robitzsch [31, 32], Rossby [83], and others after them 
[47] computed and used their thermodynamic diagrams 
to make a careful examination of each sounding of the 
free atmosphere. Today it is still customary to plot each 
ascent on such diagrams, but only in rare cases is there 
a thorough analysis of the stability, the available en- 
ergy, etc. There are several reasons for this: 
1. The observational data are incomparably more 
numerous. Where formerly one had five ascents a day, 
one now has one or two hundred. Therefore, each sound- 
ing cannot be studied with as much attention and care. 
The analysis is made for synoptic purposes in most 
cases and is therefore exclusively dynamic in character. 
Tn consequence of this: 
2. The information which is transmitted is arranged 
to permit a quick, dynamic-synoptic representation, in 
other words, the drawing of isobaric surfaces. In the 
German weather service, thermodynamic measures of 
energy have been calculated and transmitted for every 
ascent for about ten years. These measures have not 
been adopted internationally, but their use would fa- 
cilitate synoptic-thermodynamic investigations. 
3. We have reason to assume that the instruments 
now in use, the radiosondes as well as the instruments 
designed for use with aircraft, do not represent the 
temperature distribution properly. Twenty years ago, 
Lautner [19] used sensitive resistance thermometers and 
found, in flying through a subsidence inversion, a dis- 
continuous temperature increase upward, in other 
words, a really ideal inversion. It is very likely that 
most inversions have the same form, but that, because 
of the lag of the instruments, this can never be estab- 
lished. In the writer’s opinion, an examination of the 
tropopause by a trained meteorological observer, who 
would test it with thermoelements or resistance ther- 
mometers, would yield many surprises. 
4. The most important obstacle to the successful 
development of cloud physics is related to this problem 
of inadequate instrumentation: The radiosonde fur- 
nishes only an inflexible, unmodifiable cross section of 
the atmosphere; the observer in an airplane is much 
more efficacious for cloud investigations. He can supple- 
ment the vertical pressure, temperature, and humidity 
curves by what he sees: the form and character of the 
clouds, vertical stratification, horizontal extent, spatial 
density, changes in the course of time, etc. He can circle 
* Translated from the original German. 
or penetrate an interesting cloud, taking along various 
special instruments or even an entire laboratory; this 
cannot be done with radiosondes except with tremen- 
dous difficulty. For this reason, airplane ascents and 
weather reconnaissance flights with meteorologically 
well-trained observers furnish invaluable observational 
material. Furthermore, such flights are of indirect value, 
because, in the process of observing, striking new prob- 
lems always occur which are much harder to detect 
when one is merely working at one’s desk. Observation 
flights will always be necessary for special problems; 
soundings alone will never suffice. 
PREREQUISITES FOR THE IDEAL MOIST- 
ADIABATIC PROCESS 
The basic problem around which the thermodynamic 
investigation of clouds must be centered is the moist- 
adiabatic process. This holds true for stratus as well 
as for cumulus clouds. Besides this macrophysical prob- 
lem, there are microphysical processes whose effect is by 
no means restricted to invisibly small elements. This 
group of processes will be treated in a later section of 
this article. The classical theory of the moist-adiabatic 
process has recently been supplemented by various 
considerations which take into account the influence of 
the environment of the vertically moving particle. In 
this connection the slice method and the concept of 
lateral entrainment may be mentioned here. Further 
additions to the theory will be required in order to 
describe fully the basic process of the thermal reaction 
of a cloud. Nevertheless, the simpler method still fur- 
nishes some interesting viewpoints which are worthy 
of consideration. 
The prerequisites for the ideal moist-adiabatic process 
are (1) the heat of condensation is exchanged so rapidly 
between condensing water vapor or evaporating water 
and the air that no temperature differences will develop; 
(2) there is no transfer of heat between the parcel and 
the environment; and (3) there is no transfer of mass, 
either water or air, between the parcel and the environ- 
ment. 
Heat Exchange between the Cloud Elements and the 
Air. Findeisen [10] has carried out a numerical in- 
vestigation of the heat exchange between droplets and 
the air. He has come to the conclusion that under 
normal cloud conditions the temperature difference be- 
tween the air and the droplets is not much greater than 
0.2C. However, for clouds of low density, that is, those 
with a very small number of droplets or crystals per 
unit volume (as in the upper parts of altostratus or 
cirrus), the distances along which heat is transferred 
through diffusion or conduction are so large that tem- 
perature differences may reach several degrees. The 
vertical movement of the air can then proceed almost 
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