THERMODYNAMICS OF CLOUDS 
subsidence causing the dry air and the divergence of 
the horizontal flow. The statistics of Petterssen and his 
collaborators, mentioned above, also confirm this. It is, 
therefore, surprising to note that, according to the most 
recent investigations, this hindrance to convection is 
explained by a lateral entrainment of dry air masses in 
the ascending cloud. This theory is already well de- 
veloped [2] and is treated in a separate article in this 
Compendium.” However, neither the ordinary observa- 
tions of a cumulus cloud nor the processes visible in 
time-lapse motion pictures lead to the conclusion that a 
cumulus cloud is fed in any other way than by the en- 
trance of air masses through its base. Indeed the cauli- 
flower-like forms of cumulus have been considered as 
proof that no mixing with the surrounding air takes 
place. At best, only the barrier layers that are pierced 
by cumulonimbus clouds and surround the cloud towers 
like collars as, for example, a wreath of stratocumulus 
cumulogenitus, can be considered as locations of sub- 
stantial feeding of the cloud by lateral entramment. 
This takes place only at discrete heights, and not con- 
tinuously at all heights. 
Theoretical computations based on observational ma- 
terial show the lateral supply of mass and the liquid 
water content as a function of height. The second 
quantity, which can be measured from an airplane, 
should serve as a criterion for testing this theory [89]. 
However, another point must also be considered: The 
theory has taken into account only the parcel method of 
the moist-adiabatic and has supplemented it by the 
consideration of the lateral entrainment. This leads to 
a temperature lapse rate within the cloud which is 
greater than the moist-adiabatic and which approaches 
the dry-adiabatic. We come to the result already pre- 
sented above by the slice method of convection. Per- 
haps a combination of the two methods would lead to 
different ideas about lateral entrainment in cumulus 
clouds. However, a simultaneous test of the two theories 
would require a very extensive observational program. 
Cellular Convection. Perhaps an entirely different 
method of studying the instability conditions of cumu- 
lus humilis may be necessary. The time-lapse motion 
pictures by Miigge [24] mentioned above indicate that a 
cumulus humilis is not a single swelling structure. The 
individual parts of a cumulus are in constant motion. 
In the vertical wind shear the cloud mass, which appears 
calm to the eye, is, in fact, rolling; condensing cloud 
masses ascend continuously in the rear, pass the summit 
of the cumulus, and then dissolve while descending in 
front. The cumulus is not to be considered as the top 
cover of a chimney of ascending warm air, but rather as 
the upper portion of a rolling ball or cylinder. If this 
picture is correct, then the laws of cellular convection 
[20] must control the formation of such convective 
structures [388]. In this case, the existence of convection 
currents or cells depends not only on the lapse rate’s 
exceeding a certain value, but also on the vertical thick- 
ness of the layer in which the convection takes place. 
2. Consult ‘(Cumulus Convection and Entrainment’’ by 
J.M. Austin, pp. 694-701. 
203 
Furthermore, it depends on the viscosity and heat con- 
ductivity of the air (thus on the austausch coefficient) 
and, finally, on the horizontal dimensions of the vari- 
ous convection cells. The theoretical concepts of cellu- 
lar convection, which have been successfully applied to 
the explanation of stratocumulus-and altocumulus 
structure [21, 44], must then also be valid for cumulus 
humilis [45]. A complicated picture would result: The 
laws of cellular convection apply to the distribution of 
clouds, the parcel method is applicable to the con- 
densation level, and the slice method applies to the 
vertical extent of the clouds. In fact, clouds of vertical 
development are formed in layers characterized by uni- 
form convection, because Petterssen and his collabora- 
tors [29] found that in a region of cumulus the vertical 
wind shear and shift are particularly small while di- 
rectly above the summit of a cumulus cloud the wind 
shear is four times larger than at lower levels. This fact 
seems to justify the use of the cellular method. How- 
ever, as 1s quite often the case in meteorology, it is 
problematic whether the small wind shear is the cause 
of cumulus formation, or whether, inversely, the exist- 
ence of strong convective mixing is responsible for the 
absence of a large variation of wind with height. 
Radiational Influences on Certain Cloud Forms. The 
influence of long-wave radiation upon cloud surfaces 
has already been mentioned above. This influence is 
most important for stratocumulus and altocumulus. As 
a consequence of the heat supplied at the cloud base 
and the heat lost at the top, parcels of air in the lower 
portion of the cloud are heated, evaporate their liquid 
water, and rise, while particles near the top cool and 
descend. Thus the heating and cooling establishes an 
internally driven convection cell [22], which, according 
to Bénard, operates in conjunction with the cellular 
convection to break up the cloud layers into individual 
globules. This internal convection transports heat from 
the bottom to the top of the cloud; for this reason, 
Raethjen has called stratocumulus clouds “the ther- 
modynamic singularity in the vertical flux of radia- 
tion” [80]. 
In the tropies, the effect of radiation on high cloud 
layers (when there are no low or middle clouds below) 
becomes so great that above approximately 14 km 
clouds can no longer exist. Even a broken cloud cover 
would receive so much energy from the warm surface 
of the earth that it would be subject to evaporation and 
dissolution in a short time [23]. The fact that the upper 
limit of cirrus clouds in the tropics is found 3-4 km 
below the tropopause can probably be explained by 
this process alone. 
The effect of radiation on thunderclouds has not been 
so clearly determined. The summit of a high-towered 
cumulonimbus loses much heat by radiation. In day- 
time this cooling is probably cancelled in part by radia- 
tion from the sun, but toward evening or during the 
night the emission from the cloud tops prevails. It is 
possible that because of this emission a kind of cold 
convection from above will be initiated in the remnants 
of thunderclouds, which might lead to a revival of 
earlier thunderstorm activity in the late evening or 
