Efficiency of Natural Rain 
Raymond WEXLER 
Allied Research Associates, Inc., 45 Leon Street, Boston 15, Massachusetts 
Abstract—The efficiency of cloud in utilizing the water made available by the up- 
draft for precipitation may be derived from a steady state equation involving storage 
and horizontal advection. The efficiency is greatest in the middle of widespread rain 
and least in individual thunderstorms. 
The microscale features are evaluated in the initiation of precipitation. Observations 
indicate that large drop sizes, adequate for growth by the accretion process, are present 
in many clouds which do not precipitate. The important factor is the product of the 
mean effective liquid water content and the cloud depth, which has a critical value of 
about 3 g m™* km. 
Introduction—The efficiency of the rain mech- 
anism is of importance not only for the evalua- 
tion of artificial ram production but also for the 
understanding of natural rain processes. An ini- 
tial analysis was made by Weickmann [1958] who 
showed that the influence of particle concentra- 
tion on the rate of rainfall is of secondary im- 
portance. The particle size adapts itself to the 
available concentration. The primary factor in- 
fluencing rainfall rate is the updraft. Weickmann 
distinguished between a releaser cloud in which 
there is no storage of cloud liquid water and a 
spender cloud in which there is storage. In the 
former case the water vapor made available by 
the updraft 1s deposited directly on the precipita- 
tion and no artificial increase is possible. In the 
latter case an increase in particle concentration 
could cause a temporary increase in the rainfall 
rate at the expense of precipitation downstream. 
In the initiation of rain, probability is a factor 
both on the meso and microseales. On the meso- 
scale, probability enters in the favoring by the 
convergence mechanism of a more vigorous or 
longer lasting updraft in one Cumulus cloud over 
another. On the microscale, the passage of a few 
large drops through regions of relatively high 
liquid content is a probability problem. Prob- 
ability also enters in the appearance of freezing 
nuclei in sufficient concentration in cold clouds. 
The question arises as to the critical conditions on 
both scales for the initiation and maintenance of 
precipitation. It is assumed here that the macro 
or mesoscale features largely control the cloud 
extent and depth (although it has been claimed 
that the sudden release of latent heat in the freez- 
ing of the upper portion of a Cumulus cloud can 
cause precipitous growth). In this paper the eriti- 
158 
cal cloud depth for initiating or maintaining rain 
is analyzed in conjunction with the microphysical 
features. 
The important parameter in the production of 
precipitation from a cloud is the product of the 
mean liquid water content Z and the effective 
cloud depth H which may be defined by 
mf 
where V is the fall velocity of the precipitation, 
w is the updraft and # is the efficiency of catch. 
The integration in this equation follows the ascent 
and descent of a drop within the cloud. Accord- 
ing to the equation, for equal geometric depths, 
warm clouds should be more effective than cold 
clouds in producing rain because of higher L. In 
addition the relation between the updraft and the 
fall speed of the precipitation has a marked effect. 
For updrafts of the same order as the fall speeds 
effective cloud depths may far exceed geometric 
cloud depths; this effect is important in the pro- 
duction of rain or hail from shower clouds as well 
as the production of snow from thin Stratus 
clouds. 
Initiation of precipitation—In clouds over the 
tropical ocean, the percentage of warm rain in- 
creases from near zero for a cloud depth of 5000 
ft to 100% for a cloud depth of about 10,000 ft 
[Battan and Braham, 1956]. At intermediate 
depths, wind shear and the humidity of the en- 
vironment probably have considerable influence 
on cloud liquid water content (hereafter LWC) 
and thus the formation of rain. The observations 
suggest that under the most favorable circum- 
stances a 5000-ft cloud depth provides sufficient 
LWC for large cloud drops to reach raindrop size. 
EVL 
V-—w 
(1) 
