202 
temperature excess becomes considerably smaller with 
an increase in the downward displacement of air or an 
increase in the quotient M’/M where the ascending 
and descending masses of air are M’ and M, respec- 
tively. These ideas of Bjerknes and Petterssen have 
already been adopted in a number of textbooks, there- 
fore a detailed derivation is unnecessary here. It ought 
to be borne in mind, however, that the smaller the 
quotient M’/M, the more valid are the instability 
criteria of the parcel method according to Shaw, Nor- 
mand, or Stiive. Furthermore, in this case the ‘“‘moist— 
instability” is much greater with the same lapse rates, 
and a much smaller lapse rate in the surrounding air can 
still be considered as an unstable stratification. As the 
ratio M'/M becomes larger, it becomes increasingly im- 
perative to take into account Petterssen’s slice method, 
since the energy associated with the instability, which 
is decisive for the possible vertical velocities, becomes 
so much smaller, and a greater lapse rate corresponds to 
neutral equilibrium. 
Petterssen and collaborators [29] have been able to 
demonstrate the usefulness of the slice method by an 
excellent statistical investigation; according to this new 
method the maximum possible height of convective 
clouds is much smaller than it is according to the parcel 
method. In fact, the heights attained by the tops of 
cumulus clouds have been found to be in good agree- 
ment with the heights predicted by the slice method. 
The parcel method yields no clues concerning the 
amount of cloudiness, whereas the slice method pro- 
vides some information which corresponds to the actual 
cloudiness, although the correspondence displays con- 
siderable scattering. Nevertheless, it should not be 
overlooked that in other respects the parcel method 
yields useful information. For instance, it answers ques- 
tions such as how high the condensation level is, and 
whether or not cumulus clouds are to be expected at all. 
However, the degree of instability is less important 
here than is the stability of the stratification which has 
to be overcome initially. 
Here, too, there seems to be a minor defect in the 
slice method. In establishing the criteria, it is assumed 
that the mass of air ascending per unit time equals the 
descending mass of air. This means that on the average 
no vertical component of motion will result over a 
sufficiently large horizontal area. It has already been 
proved, through the valuable investigations of Calwa- 
gen [7], that the most favorable condition for the oc- 
currence of local summer showers is the existence of an 
old front, believed dissipated, which sometimes will be 
steered back into the region under observation. Such 
old fronts are simply minor convergence zones in the 
horizontal air flow; their presence requires the simul- 
taneous existence of weak vertical motion over the given 
region according to the continuity of mass. Petterssen 
[29] implicitly comes to the same conclusion when he 
shows that 50 per cent of the cases of weak convection 
are coupled with cyclonic curvature or wind shear, 
whereas this holds true in 85-95 per cent of the cases of 
stronger convection. This, however, means conver- 
gence, although it may be only weakly developed. Then, 
CLOUD PHYSICS 
however, the consideration of a resultant upward com- 
ponent (in other words, the prevalence of ascending 
masses M’ over the descending masses /) leads, in 
turn, to an increase in the instability lapse rate, so that 
the parcel method yields a more accurate measure than 
does the slice method. 
A further point should be taken into account when 
considering an isolated convective cloud. In the deriva- 
tion of the slice method, the assumption must be made 
that a cloud tower has already penetrated the whole 
layer, and that the ascent and descent of the air masses 
take place uniformly throughout the entire layer. How- 
ever, a growing cumulus cloud pierces vertically into 
the layer, so that the downward displacement and heat- 
ing of the air around the intruding head are relatively 
slight, while around the lower portions of the cloud 
these processes are intensified. The parcel method is 
therefore more applicable to the conditions at the cloud 
top than to the conditions in the cloud column beneath. 
Perhaps this effect is the explanation of the detachment 
frequently observed in rapidly developing castellatus 
towers which ascend without a supply of air from below 
—much in the manner of free balloons. 
The slice method makes the following particularly 
valuable contribution: When the ascending and de- 
scending particles are subject to the same changes of 
state, it predicts a released energy of instability that 
is significantly larger than would be indicated by the 
parcel method. This is the case in the dry convection 
below the condensation level, the violence of which can 
thus be explained. It is likewise true for the rapidly 
ascending masses in the interior of a cumulonimbus 
which give rise to vertical squalls. The theory of the 
formation of waterspouts and tornadoes (for which 
Koschmieder [17] considered the unstable spouting up 
of cloud particles within the cumulonimbus to be neces- 
sary) thus finds a welcome support. The difference be- 
tween the two types of instability can be seen directly 
from cloud observations. In time-lapse motion pictures, 
taken by Miigge [24], one can recognize that the growth 
of cumulonimbus does not occur in the form of a sym- 
metrical and uniform ascent. A cloud tower shoots up 
quickly and calms down; immediately a second one 
shoots up by its side, partly piercing the old one which, 
in turn, descends and may evaporate in its thinner por- 
tions. The vertical motion of the new tower ceases only 
when it has reached the height of the top of the old 
tower and finally comes to rest, whereupon another 
tower builds up. This rapid ascent and quick succession 
of the individual protuberances (which has also been 
demonstrated in the Thunderstorm Project) is caused 
by moist-adiabatic ascent within an environment that 
descends moist-adiabatically. The slow lifting of the 
top levels of the entire multiple cloud structure mani- 
fests the restricted energy of moist-adiabatic ascents in 
a dry environment. 
The Lateral Entrainment of Air. A second and older 
assumption by Calwagen [7] would indicate that cumu- 
lus convection becomes more difficult when the air to be 
penetrated is particularly dry. The synoptic investiga- 
tor who is familiar with this explains it as the result of 
