1200 
entire layer is thoroughly mixed adiabatically, the 
liquid-water concentration would be given by equation 
(3). In actual clouds, however, the observed values of 
liquid-water concentration are less than the calculated 
values, usually averaging from one-fourth to one-half 
and rarely exceeding three-fourths of the calculated 
value. In most cases the liquid-water concentration 
increases approximately linearly from near zero at the 
cloud base to a maximum just below the top. The dif- 
ference between the observed and theoretical values of 
liquid-water content may be attributed to incomplete 
mixing within the layer and to the downward mixing 
of some dry air from above the cloud. 
Ice crystals may form within a turbulent layer cloud 
or may fall into it from an overlying altostratus cloud. 
In the former case, the precipitation is usually light 
and the concentration of liquid water decreases quite 
slowly near the top and more rapidly in the lower parts 
of the layer. This process leads to a gradual dissipation 
of the cloud, proceeding from the bottom upward. In 
the latter case, the intensity of precipitation is fre- 
quently great enough to cause the rapid dissipation 
of the entire cloud layer. 
Clouds Formed Primarily by Horizontal Convergence 
(Altostratus, Altocumulus, and Altocumulus- Altostratus). 
Horizontal convergence in the wind-velocity field at 
low altitudes is accompanied by relatively slow lifting 
of large masses of air. This is the type of liftmg which 
ordinarily takes place in the forward and central por- 
tions of moving cyclones and leads to the formation of 
very deep and extensive cloud systems predominantly 
of the altostratus type. Observations have shown that 
supercooled liquid-water is ordinarily almost com- 
pletely absent from the main altostratus portions of 
such cloud systems, since these are composed almost 
entirely of ice crystals. Around the edges of these 
cloud systems, however, a complex pattern of alto- 
cumulus layers at various levels frequently occurs, 
composed predominantly of liquid water. When these 
layers form in stable air, they are lenticular and usually 
rather low in water content. When certain layers be- 
come unstable as a result of the lifting process, alto- 
cumulus of the turbulence type, resembling high strato- 
cumulus, may be formed. The concentration of liquid 
water in these clouds depends on temperature and 
cloud thickness, as noted in the preceding paragraph. 
Freezing Rain and Freezing Drizzle. The meteoro- 
logical conditions ordinarily required for the formation 
of freezing rain are an inversion, usually frontal, with 
temperatures above freezing in the warm air above 
the mversion and temperatures below freezing in the 
cold air below the inversion. The temperature range 
of the occurrence of freezing rain is rather small, since 
the raindrops freeze and become sleet (U. S. Weather 
Bureau definition) at temperatures only a few degrees 
below freezing. Unfortunately, measurements of the 
concentration of liquid water in freezing rain are not 
available. Estimates can be made, however, since it is 
known that freezing rain generally consists of relatively 
light, uniform precipitation over a fairly large area. 
If a precipitation rate of 0.1 in. hr and a drop diam- 
CLOUDS, FOG, AND AIRCRAFT ICING 
eter of one millimeter are assumed, the liquid-water 
concentration would be about 0.15 g m=, which is less 
than is usually found in clouds. 
Because freezing drizzle is only rarely encountered 
and the methods used to measure drop size in flight 
are not reliable for drops of drizzle size (thus making 
the correct identification of drizzle difficult), very little 
information is available concerning its liquid-water con- 
tent. Unlike freezing rain, freezing drizzle is not limited 
in its occurrence to frontal conditions but may form 
in a variety of meteorological situations and over a 
wide range of temperature and altitude. The fact that 
large values of cloud drop size tend to occur only with 
small values of liquid-water concentration would sug- 
gest that low values of liquid-water content would be 
expected in freezing drizzle. 
Statistical Data on Liquid-W ater Concentration. A sub- 
stantial amount of data on liquid-water concentration 
and drop size in clouds in the United States is available 
as a result of flight measurements by various organiza- 
tions. Most of these observations were made by the 
National Advisory Committee for Aeronautics [13-15]. 
A considerable number were also made by the Air 
Materiel Command Aeronautical Ice Research Labo- 
ratory [4], and a limited number by United Air Lines, 
American Airlines, and the Douglas Aircraft Company. 
All these measurements were made by the rotating- 
cylinder method and represent average values over time 
intervals varying from about 30 sec to 10 min. The 
average exposure interval was about 1 min in cumuli- 
form clouds and 3-5 min in stratiform clouds. Data 
from all the above-mentioned sources have been in- 
cluded in Tables III and IV. 
Tasie II]. OBSERVED FREQUENCY OF VARIOUS VALUES OF 
Liquip-WATER CONCENTRATION IN CLOUDS 
Liquid-water concentration BSE Ses Ae AGds Cun Gh 
gms % % % 
0.00-0.09 12 50 31 
0.10-0.19 32 32 
0.20-0.29 22 13 26 
0.30-0.39 16 4 
0.40-0.49 12 1 29 
0.50-0.59 5 0 
0.60-0.69 0.3 0 10 
0.70-0.79 0.6 0 
0.80-0.89 0.3 0 7 
0.90-0.99 0 (0) 
1.00-1.19 0 0 2 
1.20-1.39 0 0 1.0 
1.40-1.59 0 0 0 
1.60-1.79 0 0 0.7 
gm gm gms 
Lower quartile........ 0.13 0.05 0.15 
IMGCUEIN 6 6ccc00 00.0008 0.22 0.10 0.34 
Upper quartile........ 0.35 0.17 0.55 
Maximum............. 0.80 0.41 1.71 
Table III gives frequency distributions of values 
of liquid-water concentration observed in three prin- 
cipal cloud types: cumulus and cumulonimbus, stratus 
