The Relation between Cloud Droplet Spectra 
and the Spectrum of Cloud Nuclei 
P. Squires AND 8. Twomny 
Division of Radiophysics, Commonwealth Scientific and Industrial Research Organization, 
Sydney, NS.W., Australia 
Abstract—Observations of cloud droplet spectra in various kinds of clouds have 
shown that the microstructure of clouds very largely determines the efficiency of the 
coalescence process in forming rain. They have also suggested that the observed differ- 
ences in microstructure must be primarily explained by differences in the spectra of 
cloud nuclei in different air masses. This hypothesis has now been confirmed by simul- 
taneous observations of the spectra of cloud nuclei and cloud droplets. 
Introduction—In a classical paper, Houghton 
[1950] discussed the significance of the various 
processes leading to the formation of precipita- 
tion. He showed that sublimation onto ice crys- 
tals could quickly give rise to the formation of 
particles equal in mass to a droplet of several 
hundred microns diameter, and that, given a 
cloud droplet spectrum which was broad enough, 
raindrops could form by coalescence. The caleu- 
lations were based on the collection efficiencies 
computed by Langmuir [1948] and it appeared 
that only those clouds which had very broad 
spectra and very large median droplet diameters 
could form rain by coalescence in a sufficiently 
short period of time. Telford [1955] has drawn 
attention to the fact that only a very small frae- 
tion of the ‘most fortunate’ droplets in a cloud 
grow to raindrops, and that consequently it is 
necessary to consider the statistical fluctuations 
in the growth time of individual drops, arising 
from the random and discrete nature of droplet 
growth by collision. In one example, he showed 
that one large (collector) cloud drop in a hun- 
dred thousand would experience its first ten col- 
lisions in five minutes, whereas the average large 
cloud drop would require 33 minutes to grow to 
this extent. This kind of consideration makes the 
production of rain by coalescence somewhat 
easier, but it still seems to be possible only in 
clouds with quite broad spectra and large aver- 
age and maximum drop sizes. 
Howell [1949] carried out computations of the 
growth of cloud droplets starting from assumed 
distributions of cloud nuclei and reached the con- 
clusion that, as a result of the quadratic law of 
growth, condensation tended to produce rather 
uniform droplet spectra. 
A study of the condensation phase of droplet 
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growth [Squires, 1952], aimed specifically at find- 
ing those conditions which could bring about the 
formation of large droplets, led to the recogni- 
tion of a kind of threshold effect: The size of 
the cloud nucleus has relatively little influence 
on the growth of a cloud droplet once it has 
grown through the critical activation region. Its 
influence is largely restricted to determining 
whether, with a given maximum supersatura- 
tion in the cloud-forming region, the droplet 
shall grow unstably or remain in the stable ‘haze’ 
stage. This simplification of the role of the nu- 
cleus made it possible to discuss the conditions 
leading to the formation of only a restricted 
number of cloud droplets, apparently a neces- 
sary and certainly a sufficient condition for the 
production of relatively large droplets. If the 
number of droplets formed is to be restricted, 
the nucleus spectrum must be such that only a 
small number of nuclei become activated; since 
a nascent cloud in which this has happened has 
only a relatively small absorptive power for 
water vapor, the supersaturation tends to rise 
to relatively high values; if, therefore, the few 
nuclei already activated are to continue to mo- 
nopolize the supply of water, all the remaining 
nucle: must be appreciably smaller than they. 
Slow upward movement in the cloud-forming 
region obviously tends to keep the supersatura- 
tion low and so to help the processes tending to 
produce few and large droplets. However, a 
semi-quantitative analysis indicated that the var- 
lations in the spectra of cloud nuclei from one 
air mass to another were probably the dominant 
factor in determining the size of droplets pro- 
duced by condensation; on the basis of the fact 
that Aitken counts are higher over the conti- 
nents than over the oceans, this view appeared 
