ON THE PHYSICS OF CLOUDS AND PRECIPITATION 
dred microns. In the absence of ice erystals, the collision 
mechanism may initiate the precipitation process if the 
drop-size distribution is broad. Regardless of the process 
of initiation, the further growth of the precipitation 
elements is primarily by collision. This includes colli- 
sions of the precipitation elements with themselves as 
well as with cloud elements. In the case of snow, colli- 
sions between crystals are common, as is evidenced by 
even a casual examination of snowflakes. No process 
depending on the diffusion of water vapor seems to be 
capable of forming raindrops of 1-mm diameter and 
larger in the time available. Such precipitation elements 
must be formed by a collision mechanism. In middle 
latitudes, it is probable that the collisions are primarily 
between ice crystals, forming snowflakes which later 
melt into raindrops. In low latitudes, or in any situation 
mn which a water-drop cloud, of large vertical extent 
exists, once drops of, for example, 100-1 diameter 
appear, collision with the cloud drops is sufficient to 
explain the growth of the precipitation elements. More 
quantitative information on collision processes 1s badly 
needed, particularly on collisions between ice crystals 
and between cloud drops of nearly the same size. 
The question naturally arises as to why all clouds do 
not ultimately release precipitation as a result of colli- 
sions between drops of unequal size. It is well known 
that many clouds produce precipitation which evapo- 
rates before reaching the ground, but this is not the 
complete answer. Langmuir’s computations [34] show 
that for each drop size there is a minimum size of the 
larger drop below which no collisions will occur. For 
example, no drop of less than 45-» diameter will collide 
with drops of 12-u diameter. As the smaller drop diam- 
eter imereases, the minimum diameter of the larger 
drop approaches that of the smaller drop. These results 
unfortunately lie in the region where the computations 
are least reliable. If correct, these results show that 
clouds composed of small drops are stable even when 
the drop-size distribution is broad. Diem’s data [10] 
show that clouds such as fair-weather cumulus and 
stratocumulus contain smaller drops than clouds such 
as nimbostratus and heavy cumulus. Stratus also con- 
tains large drops but is not deep enough to yield more 
than drizzle. Houghton [20] and others have also sug- 
gested that a unipolar electric charge on the cloud 
drops might serve to inhibit collisions. 
Snow. For the most part the discussion above has 
assumed the initial presence of a water-drop cloud. 
Tt may be that snow is often initiated m this way, but 
it is probable that snow also occurs in the absence of a 
water cloud. Also, a water cloud will not ordinarily 
exist for more than a short time in the presence of 
snow. It has been stated earlier that ice crystals do 
not form until saturation with respect to water is 
approached. Apparently few freezing or sublimation 
nuclei are active at temperatures above —10C, and 
lower temperatures are generally required. On the other 
hand, there is evidence that the top of a snow cloud 
may be warmer than —10C. This suggests that once 
snow is initiated, nuclei are produced which are active 
at higher temperatures. An important contribution to 
177 
this problem was made by Findeisen [15], who found 
that the more delicate forms of crystals (stellar or 
dendritic) shed tiny splinters of ice as they fall. These 
splinters would serve as sublimation nuclei for new 
crystals at any temperature below freezing. 
Approximate computations of the rate of growth of 
ice crystals suggest that the vapor pressure must be 
nearer saturation with respect to water than to ice if 
the observed sizes are to be attained. In this respect 
the process is quite different from condensation on 
liquid drops, where the vapor is only very slightly 
supersaturated with respect to the condensed phase. 
This difference is due to the much smaller number of 
ice crystals. The supersaturation mereases as required 
to cause sublimation to proceed at the rate prescribed 
by the lifting, saturation with respect to water setting 
the upper limit. 
Nakaya and collaborators in Japan [40, 41, 42] have 
made outstanding contributions to our knowledge of 
the formation of snow crystals. In one paper Nakaya 
and Terada [42] have presented useful data on the 
mass, physical dimensions, and velocity of fall of several 
types of natural snow crystals. In general, the maximum 
masses of the crystals are equivalent to a solid sphere 
of several hundred microns diameter while the velocities 
of fall are much smaller than those of solid spheres of 
equivalent mass. Nakaya and collaborators [40, 41] 
have succeeded in producing im the laboratory all of 
the types of erystals observed in nature. The two 
fundamental parameters determining the crystal type 
are temperature and degree of supersaturation. In gen- 
eral, the more compact crystal forms such as columns, 
prisms, and plates are formed at low supersaturations 
and the more open types such as needles and stellar 
or dendritic crystals are formed at the higher super- 
saturations. The dependence on temperature was not 
clearly established in the references, all of which were 
published before World War II. Dr. Nakaya was able 
to contmue his researches during and after the war, 
but these results have been published only im Japanese. 
However, he has prepared all of his material in book 
form in English, and early publication is anticipated. 
Weickmann [55] collected and photographed ice crys- 
tals in the free atmosphere. He summarized his ob- 
servations as follows: In the lower troposphere, the 
nimbostratus region, there is slight ice supersaturation, 
the temperature ranges from 0 to —15C, and the 
crystals are in the form of thin plates and stars; in the 
middle troposphere or the altocumulus and altostratus 
region, there is moderate ice supersaturation, the tem- 
perature ranges from —15 to —30C, and the crystals 
are mainly thick plates and prisms; in the cirrus region 
or the upper troposphere, the temperature ranges from 
—30 to —60C, and the ice crystals are principally 
hollow prisms often combined as twins or clusters. 
Size of Raindrops. All of the published data on rain- 
drop size were obtained at the surface. A considerable 
number of such measurements have been published but 
it will suffice to refer to the rather recent measurements 
of Laws and Parsons [36]. They used the flour-pellet 
technique and found that the volume-median diameter 
