EFFICIENCY OF NATURAL RAIN 159 
Assuming an efficiency of catch of 0.8, a large 
cloud drop released at the cloud top could at- 
tain a diameter of 1.1 mm at the base of the 
cloud. Over the land, the critical cloud depths are 
about 10,000 ft in central United States and 
12,500 ft in southwestern United States. With 
colder cloud temperatures the maximum mean 
LWC is about 2.5 g m™® but evaporation caused 
by greater turbulent mixing with an environment 
of lower humidity could easily cause a 50% re- 
duction in the effective LWC. Under such condi- 
tions a drop diameter of 1.5 mm could be attained 
at the base of the cloud. The important factor for 
rain formation is the product of the mean effec- 
tive LWC and the cloud depth, which the ob- 
servations indicate to have a critical value of 
about 3 g¢ m® km. Cloud duration of about an 
hour is required in order for the drops to rise 
from the cloud base to top and then to descend 
again. 
It has been observed over land and ocean that 
cloud drop sizes in Cumulus are somewhat greater 
in Cumulus clouds which subsequently develop 
echoes (rain) than those which do not [Battan 
and Reitan, 1957]. For example, at concentra- 
tions of 100 per liter the drop diameters in echo- 
producing clouds over the ocean was 67 pas com- 
pared to 64 » in non-echo producing clouds; 
over the land the respective drop sizes were 62 p 
and 58 ».. However, it may easily be shown that 
only several meters of fall im a cloud containing 
1 g m* would suffice for the 64 drops to grow 
to 67 » or for the 58 » drops to grow to 62 yp. 
It is apparent, therefore, that it is not for the 
lack of large drops that the non-echo clouds 
failed to produce rain. It appears more likely 
that mesoscale features controlling the duration 
and strength of the updraft are responsible for 
the favoring of one cloud over another in the 
subsequent development of rain. As for the oc- 
currence of rain from clouds of smaller depth 
over the ocean than over the land, drop size 
again is evidently not the deciding factor since 
clouds which did not develop rain over the ocean 
had a greater concentration of large drops than 
clouds which did develop rain over the land. 
The critical depth for the production of pre- 
cipitation via the ice phase in Cumulus clouds 
is smaller than that using the water phase in 
warm clouds. There are numerous instances of 
snow over the Great Lakes from Cumulus clouds 
less than 5000 ft in depth. Evidence from the 
radar indicates the existence of snow from gener- 
ating cells, 2000 to 4000 ft deep and wide, with 
vertical velocities of the order of 1 m see-’. Many 
instances of precipitation involving the ice phase 
from a cloud with top warmer than —12°C sug- 
gest that when the depth and duration of the 
updraft is sufficient, growth of precipitation 
somehow occurs either by the sublimation proc- 
ess initiated from freezing nuclei or by the ac- 
cretion process followed by the freezing of drops 
when they are sufficiently large. 
Drizzle has been observed to fall from layer 
clouds about 3000 ft in depth. The important 
factor in the production of drizzle is the dura- 
tion of the cloud, or rather the duration of the up- 
draft, so that drops aided by turbulent motion 
have a path length sufficient to accrete to a size 
of a few hundred microns. 
The efficiency of rain—The efficiency of rain 
production #, may be defined as the per cent of 
water produced by the updraft that falls to the 
surface 
JS pwdq 
R 
where p denotes the density of the air, qg is the 
specific humidity and R the precipitation rate. 
Integration is from the top to the base of the 
cloud. 
A steady state equation for the continuity of 
moisture in a cloud may be written as follows 
oR oq ol (a) (a) 
+ w =w-—-4 u +u 
Oz Oz Oz Ox oy 
Er = (2) 
(3) 
z xs Ou av 
(L + NM) + NM (# a *) 
Ox oy 
where R = NM (V — w) is the precipitation 
rate, N the number of drops of mass M/. The 
second term on the left-hand side is the rate at 
which liquid water is provided by the updraft. 
On the right-hand side, the first term represents 
storage of cloud liquid water, the second is hori- 
zontal advection (which may include evaporation 
due to the mixing of the cloud with drier air), 
and the third represents changes in the concen- 
tration of the precipitation due to the vertical 
wind shear (from the equation of continuity). 
It is readily seen that a measure of the efficiency 
of rain defined by (2) can be derived from this 
equation. 
In the middle of a widespread uniform rain, 
where the fall speeds of the precipitation particles 
are large compared to the updraft, all the terms 
on the right-hand side of (3) may be neglected 
except the first. In this case it is found [Wealer 
