THE PHYSICS OF ICH CLOUDS AND MIXED CLOUDS 
both the volume swept by a particle and its rate of fall 
quickly increasing, and the particle becomes a precipi- 
tation element. However, it is important to note that it 
takes an appreciable time for the growth to reach the 
critical stage: if the cloud begins to dissolve in the 
meantime the ice particles will not develop into precipi- 
tation elements, but will disappear with the droplets. 
Observation shows that the summits of cumulus clouds 
are constantly and rapidly replaced from below, fresh 
cloud masses rising only to diverge, sink, and evaporate, 
so that the life of each particle near the cloud tops is 
very brief. It can therefore readily be imagined that 
cumulus, rising some distance above the level at which 
the ice nuclei first act mm significant numbers, have 
summits containing ice crystals which fail to reach the 
critical size which would enable them to sink into the 
bulk of the cloud and continue their growth, thus 
eventually becoming hail or rain. The magnitude of 
this effect is difficult to estimate, but it is likely to be 
most marked in clouds of low liquid-water content, in 
which the rate of growth of the ice particles is least. In 
general the liquid-water content of cumulus varies 
directly with the temperature of the cloud base. This 
may account for the failure of cold-weather cumulus, 
with summit temperatures as low as —20C, to pro- 
duce showers. Such clouds may be wholly below the 
temperature at which the ice nuclei first act, and yet 
show no external trace of the presence of ice particles. 
Valuable data for this problem could easily be ob- 
tained by observing the base- and summit-level tem- 
peratures of convection clouds (noting those clouds 
which produce precipitation) and by attempting to de- 
tect the presence of small ice particles during flight 
through the supercooled tops of cumulus. 
When the critical stage is passed and the ice particles 
have begun their growth as precipitation elements, the 
cumulus becomes transformed into the cumulonimbus. 
If the cloud ceases to grow soon after the critical stage 
is reached, the total number of ice particles formed re- 
mains very small, and slowly dissipating patches of 
water cloud may persist for a time near the summits, 
all the ice particles having fallen out. Usually, however, 
the top of the cumulonimbus becomes an ice cloud of 
considerable density, and it seems that the number 
of crystals finally formed must be substantially in- 
creased by a mechanism which Findeisen has begun to 
investigate [6, 7]. During the growth or evaporation of 
an ice particle, air flowing past it carries away minute 
charged fragments of ice (radius about 20 1). These ice 
“splinters” are produced only by particles which are 
ageregates of small crystals, and are not formed at the 
surfaces of simple crystals or at glassy layers of ice. 
Little is known about the manner in which these 
splinters and their electrical charges arise, but Findeisen 
regards this process as the predominant source of 
thunderstorm electricity, and it must be of great im- 
portance in all ice clouds and mixed clouds as a means 
of ice-crystal reproduction without the aid of special ice 
nuclei. According to Findeisen’s experiments [7], the rate 
of formation of ice splinters during the direct condensa- 
tion of vanour into ice amounts to about 5 sec~* from 
195 
an ice surface of area 50 cm?. At temperatures down to 
about —30C the number of ice particles growing upon 
ice nuclei is not likely to exceed 10% m-*. If one-tenth 
of these have reached a radius of 107! em, after about 
twelve minutes they alone will have produced as many 
ice crystals by the splintering process as were formed on 
the ice nuclei. During the growth of ice particles by 
coagulation with supercooled droplets, however, the 
rate of splinter formation is increased perhaps a thou- 
sand fold, and it therefore becomes clear that this proc- 
ess is of dominating importance in the ice-nucleus econ- 
omy of all mixed clouds. The large numbers of erystals of 
insignificant falling-speed, and therefore of small size, 
which compose the extensive anvils of mature cumu- 
lonimbus are probably almost all produced without the 
aid of special nuclei. The splinter formation may be 
essential to the development of cumulonimbus over the 
oceans in polar air masses whose content of ice nuclei is 
likely to be extremely small. 
Here it may be remarked that as yet little attempt 
has been made to work out in detail the growth con- 
ditions of cumuliform clouds and the modifications 
introduced by the appearance of the ice phase and the 
development of precipitation. Again it will be necessary 
to consider the speed of the condensation and coagula- 
tion processes. The rate of ascent of air in vigorous 
cumulus is of the order of 10 to 20 m sec“!, greatly in 
excess of the speeds assumed by recent writers (e.g. 
Austin [2]), who have developed the concept of entrain- 
ment of air from the environment into the rising cur- 
rents. The present writer doubts whether this materially 
affects the growth of large clouds, and believes that the 
simple parcel method of representing convection may 
still prove the most useful, but that it needs modifica- 
tion in the light of important factors which have been 
ignored so far, such as (1) the short life of individual 
clouds and the effect of their continual dissipation on 
the condition of the environment, (2) the effect of 
evaporation and mixing at the edges of small clouds, 
and (3) the effect of the rate of heating at the bottom of 
the convective layer. It is doubtful, in view of the pre- 
dominant condensation of liquid water in rapidly as- 
cending air, whether the latent heat of fusion plays any 
part in the development of cumulonimbus. The writer 
has shown (in work not yet published) that in dense 
clouds the larger ice particles pick up supercooled water 
at a rate which prevents its complete freezing, so that 
the precipitation elements have wet surfaces and a 
temperature not much below OC. A proportion of the 
latent heat of fusion is thus used in warming the precipi- 
tation and is lost to the cloud. On the other hand, the 
accumulation of precipitation elements in the upper part 
of the cloud leads to the mechanical destruction of the 
updraught, and with the release of the precipitation a 
powerful downcurrent is initiated [3]. There is therefore 
reason to believe that in aerological work the develop- 
ment of cumulonimbus may best be followed on thermo- 
dynamic diagrams constructed wholly with respect to 
liquid water. Such diagrams are also appropriate in con- 
sidering the formation of high ice-clouds, but it is 
advisable also to include lines showing the saturation 
