268 R. H. DOUGLAS 
The most striking feature of these growth- 
rate curves is the relative insensitivity of growth 
rate to particle density. For any given mass, 
variation of density by a faetor of 18 results 
in a variation of growth rate by a factor of only 
3 or less; for a given mass, a reduction in den- 
sity tends to increase the swept volume, but re- 
duces the effective collection efficiency by an al- 
most equivalent amount. The major control of 
growth rate is clearly the liquid water content. 
At the upper ends of the curves, the growth rate 
is proportional to the 5/6 power of the particle 
mass. 
Curves showing particle mass as a function of 
time are given in Figure 2. Initial particle mass 
was taken to be 10° pgm, but the individual 
curves can be used for any greater initial mass. 
Also included is one curve for growth by accre- 
tion only, of a particle of density 0.9 in 4 gm m™ 
Cumulus, which may be considered to represent 
droplet growth by coalescence; this curve begins 
at droplet radius 20u, below which growth pro- 
ceeds entirely by diffusion. 
Results—Houghton [1950] has compared drop- 
let growth by coalescence in 1 gm m™ cloud with 
the sublimational growth of ice crystals, and 
found the latter to be more rapid for masses up 
to about 10 pgm (melted radius 130 p), a result 
in substantial agreement with the present caleu- 
lations when the coalescence rate in 1 gm m~® 
cloud is compared with the low-density sublima- 
tion rate. But the present study provides the 
means of comparing growth of liquid drops with 
growth of frozen drops by sublimation and ac- 
cretion, and over a wide range of density. 
Considering growth in 4 gm m™ Cumulus, the 
frozen droplet will have the advantage over the 
unfrozen one for masses up to about 1 pgm 
(melted radius 60 ,) (Figs. 2 and 4). In 1 gm 
m~ cloud the advantage persists for masses up 
to 10 pgm (melted radius 130 »), and in Alto- 
stratus of 0.1 gm m™, up to masses of at least 
10* pgm (melted radius > 600 »). The less dense 
accretion particle has a slight advantage over the 
more dense one (Fig. 4). If liquid drops freeze 
at smaller sizes than those noted above, they 
will continue growth more rapidly than their 
unfrozen neighbours, but if freezing is postponed 
until larger sizes are reached, the frozen particle 
loses most of this advantage. Hast [1957] shows 
that the initiation of the all-water coalescence 
precipitation process follows closely upon the 
appearance of 50 p», radius droplets in 4 gm m™ 
Cumulus. But if droplets of lesser radius should 
freeze before any have reached 50 p, these frozen 
particles can compete vigorously with the un- 
frozen remainder, and _ precipitation growth 
through the ice phase is competitive with that 
through the all-water process. This applies only 
to summer Cumulus of the temperate regions, in 
which cloud water contents of 4 gm m™ are at- 
tained above the freezing level. With higher 
cloud contents such as may be achieved in 
warmer Cumulus, the advantage of the all-ice 
growth process over coalescence may be greatly 
reduced, since accretion ‘cuts in’ at a smaller 
particle size the greater the cloud water content. 
The effectiveness of the growing particles in 
removing the cloud water content is best defined 
as the mass collected per unit distance fallen. 
While Figure 4 shows the approximate equality 
of growth rates (within a factor of 2) at various 
particle densities, the less dense particle, falling 
more slowly, collects more cloud water per unit 
distance fallen. Thus, in falling through a unit 
depth of cloud, the less dense particle sweeps up 
more cloud water than a denser particle of the 
same mass. In the three types of cloud considered 
here, particles of density 0.05 may in this sense 
be up to six times as effective as those of den- 
sity 0.9; thus low density accretional growth 1s 
the more potent cloud-consuming process. 
In cloud of low water content (0.1 gm m™*) 
growth to the stage where accretion becomes the 
dominant mechanism requires times in excess of 
half an hour, and cloud depths from 3000 to 8000 
ft for low- and high-density particles, respec- 
tively. Unless cloud exists in such depth, the 
emergent precipitation particles will be more of 
the nature of sublimation elements (snow) 
rather than graupel; with cloud layers of rea- 
sonable thicknesses, only the lowest density 
eraupel is likely to emerge. As cloud water con- 
tent increases, and accretion is increasingly 
favored, the likelihood of accretion elements in- 
creases, and conditions for significant higher- 
density growth improve. In cold Cumulus, the 
dense undiluted core may be favorable for 
graupel growth, while the dilute cloud bound- 
aries will yield sublimation elements, or snow; 
such precipitation of both graupel and snow is 
occasionally observed from small Cumulus dur- 
ing the cold seasons of the temperate regions. 
In denser cloud of 4 gm m™, accretion becomes 
predominant at masses of the order of 1 pgm, 
which may be achieved within the first four min- 
utes of growth; particles of 1 em diameter are 
grown within an additional twelve minutes. Ob- 
