C. I. ANDERSON 
Geophysics Research Directorate, Air Force Cambridge Research Center, Bedford, Massachusetts 
Abstract—The dynamics of the evolution of Cumulus congestus and Cumulonimbus 
clouds may be described in terms of V. Bjerknes’ second circulation theorem wherein 
a frequency factor, »*, pertaining to the bouyancy restoring force per unit length, is 
defined as a function of the temperature lapse rate and the scale of the disturbance. It 
is shown that either exponential or sinusoidal development of large local storms in the 
Southwest is described, together with the associated vertical velocity field and precipita- 
tion release. 
Although no direct evidence is available that supports an exponential or runaway 
growth for local thunderstorms, it is suggested that such may be the case for intense 
local storms of the cloudburst variety. Several examples of this are shown where an ex- 
ponential solution is possible. The paper concludes with speculations on the creation 
of self-sustaining local storms by altering the scale of the disturbance through the use 
Energetics and the Creation of a Self-Sustaining Local Storm 
of solar energy converting chemicals. 
On observing the development of Cumulus 
clouds, one often wonders if it is possible for a 
small Cumulus to grow to thunderstorm size by 
continuously enlarging itself. Experience shows 
how ordinary fair weather Cumuli disappear after 
fifteen minutes or so, and the maximum size at- 
tained during their lifetimes is quite small com- 
pared with a Cumulonimbus cloud. Except in 
regions of strong orography, one has little oppor- 
tunity to watch the birth and death of a thunder- 
storm. The observer usually notes that the 
thunderstorm drifts into his field of view rather 
than develops before his eyes. However, in the 
Southwest of the United States, light prevailing 
winds and pronounced orography combine to af- 
ford the study of the life cycles of all ranges of 
Cumulus types, from the very small to the gi- 
which may have resulted when the flow fields of 
several isolated Cumuli merged to form a large 
and active convective area. 
Viewing Cumulus growth as a cellular circula- 
tion, one can introduce the idea of the horizontal 
scale of the convection cell as having a bearing 
on its lifetime and vigor. This is accomplished by 
using a modification of V. Bjerknes’ Second Cir- 
culation Theorem developed by Hdéiland [1939] 
and Eliassen and Kleinschmidt [1957]. For a cell- 
ular circulating system, the circulation of the ac- 
celeration is equal to the circulation of the verti- 
cal restoring force 
au at Ow 
hes dz 
PNoi at 
gantic Cumulonimbus. It was in this region that were 
data on the growth of Cumulus clouds were ob- gence Beles (2) 
tained for this study. Tages 
The data consist of stereo pairs of cloud photo- ' 
graphs, 9 X 9 inches, which were analyzed stereo- Y = environment lapse rate 
scopically for the rate of vertical growth of vari- va = dry adiabatic lapse rate 
ous clouds. These photographs were made at 
Tucson, Arizona, by the Institute of Atmospheric 
Physics, University of Arizona, in 1956; and at 
Flagstaff, Arizona, by personnel of the Cloud 
Physies Branch, Geophysics Research Directo- 
rate, in 1958. 
From the limited number of clouds thus far 
studied, it appears that thunderstorm-size clouds 
do not develop by the continuous growth of small 
Cumuli. The earliest precursor of a thunderstorm 
is itself a vigorously growing Cumulus congestus 
6 
= 
The other symbols have the usual meteorologi- 
cal meanings. As used in (1), v is the static 
stability or vertical restoring force per unit 
length. For a closed streamline, the motion will 
be either a stable standing oscillation or an un- 
stable cellular circulation. At a point where the 
closed streamline of the cell is tangent to the 
vertical axis of the cloud, we may determine the 
nature of the vertical velocity variation with time 
because the frequency of the circulation accelera- 
