CUMULUS CONVECTION AND ENTRAINMENT 
shape since they indicate that the cloud mass continues 
to increase with height. These graphs should be in- 
terpreted as representing, at any elevation, the fraction 
of the cloud air which has originated at a lower eleva- 
tion. For example, im the case y, = 9 X 10°C cm 
and H = 0.50 in Fig. 5, the air at 2 km above the 
cloud base contains one part of air which originated at 
the base and five parts of air which have come from the 
environment. However, this may not necessarily mean 
that the mass of the cloud at 2 km is six times as great 
as the mass at the base. In fact, it is probable that not 
all of the air which reaches a particular level continues 
to ascend. 
Data on Convective Showers 
In view of the eddy diffusion to which a cloud is 
subject, it seems probable that the ideal conditions for 
the persistence of a cumulus cloud are a high liquid- 
water content and large horizontal extent. For the 
development of the vertical accelerations to force the 
cloud upward it seems desirable that there be a steep 
lapse rate of temperature. The analysis, as summarized 
in Table I, indicates that it is not possible to satisfy 
all three conditions; for example, a condition which 
gives rise to a high liquid-water content does not appear 
to favor the development of vertical accelerations. 
Therefore, it should not be expected that a steep lapse 
rate of temperature in the environment is necessarily 
the most favorable condition for cumulus growth. Con- 
sequently, attempts have been made to obtain some 
empirical data on cumulus clouds which would give an 
insight into the mixing process. 
Austin [1] studied the occurrence of convective 
showers in the vicinity of three radiosonde stations in 
the eastern United States. It was found that the relative 
humidity of the environment was as important.a con- 
sideration for the development of showers as the vertical 
stability of the air. Chalker [7] confirmed this con- 
clusion and showed that showers occur most frequently 
in regions where the lapse rate is about 6C km, that 
is, only slightly steeper than the moist-adiabatic lapse 
rate. These studies were restricted to the. occurrence 
or nonoccurrence of shower-type clouds. It would be 
desirable to have extensive empirical information on 
eumulus humilis and cumulus congestus clouds in order 
to determine more precisely the effect of the humidity 
of the environment on the cloud growth. However, at 
present, such information is not readily obtainable. 
Prediction of Cumulus Development 
Since the unstable state may be created in various 
ways, as pointed out in the introduction, the problem 
of forecasting cumulus development can conveniently 
be divided into two sections. 
1. Convectively Unstable Air. Petterssen [11] has pro- 
vided an analysis of cumulus development in con- 
vectively unstable air. In brief, if a layer of air is 
characterized by a decrease of the wet-bulb potential 
temperature with height and if this layer becomes 
saturated, an unstable state will exist. Asa consequence 
of the instability, cumulus cells develop in the saturated 
699 
layer. The prediction of this phenomenon requires first, 
a determination of the convective state of the air 
before it is subjected to some rising motion which pro- 
duces the saturation; and second, an estimate of whether 
rising motion will occur. The convective state is de- 
termined from the distribution of the wet-bulb potential 
temperature. If a deep layer of the air is convectively 
unstable the forecaster must estimate the likelihood 
of the air being lifted to saturation. Risimg motion may 
be expected in the vicinity of fronts, along mountain 
ranges, and in general regions of horizontal convergence 
near the earth’s surface. The best example of the latter 
process is the horizontal convergence in the vicinity of 
isallobaric minima. 
The principal defect of the forecast procedure is the 
vague qualitative approach. More information is needed 
on the manner in which a deep layer of air overturns 
and on the distribution of rising velocities. Radar ob- 
servations [10] of precipitation areas have shown that 
the vertical extent of rain cells, and presumably that 
of convection cells, varies directly with the degree of 
convective instability. Hence it should be expected that 
highly convectively unstable air will give rise to tall 
cumulus cells of thunderstorm dimensions. 
2. Surface Heating. Surface heating may arise from 
the transport of cool air over a warmer surface or from 
direct radiational heating. A method for the prediction 
of cumulus development may be applied to either type 
of heating. 
The parcel-method analysis of the equilibrium state 
leads to a forecast method which involves the so-called 
positive and negative areas, as illustrated in Fig. 7. 
HEIGHT 
TEMPERATURE ——> 
Fia. 7—The positive and negative area analysis for eum- 
ulus convection. The dashed line is a moist adiabatic and the 
dotted line is a dry adiabatic. 
ABP D is the path on an adiabatic chart followed by an 
air parcel which is lifted through an atmosphere 
ALPMD. The forecast method states that cumulus 
clouds will develop to shower dimensions provided that 
