698 
With T—T, < 1C, it follows that 7 (w — w,) is large 
Pp 
as compared with 7’ — T, except for a rare situation of a 
practically saturated environment. Hence the assump- 
tion of 7 = T, appears a reasonable one for the dis- 
cussion of such factors as liquid-water content and the 
variation of cloud mass with height. With 7 = T, 
and ¥. = Ye, equation (3) becomes 
2 o-wtae. 
cpm dz 1 GB 
Nie Nd = 
Let w./w = H, the relative humidity of the environ- 
ment, and ya — ye = I. If I’ and Z are considered as 
constants between elevations Z) and Z, the integration 
of equation (7) yields 
1/(1—#) Z 
m _ (Wo : Cp T il S| 
mo (=) ep | HO Sp eyo lh 
The variation of the cloud mass with different lapse 
rates and relative humidities is illustrated in Fig. 5. 
| 2 3 4 5 6 
Z-Zo IN KILOMETERS 
Fic. 5.—Dilution of cloud mass with elevation. m/mp is the 
ratio of the actual cloud mass m, at the level Z, to the fractional 
mass mo which originated at the cloud base Z, y- is the lapse 
rate of temperature, and H is the relative humidity. The 
cloud base is at 900 mb and 20C. 
The mass increases more rapidly when the environment 
has a steep lapse rate of temperature and a high relative 
humidity. All these curves pass through a maximum, 
the location of which depends on I’. These maxima 
occur at that height where the moist-adiabatic lapse 
rate becomes equal to y,, as can be seen from equation 
(4) if dm/dz is set equal to zero. 
With the same assumptions equation (6) becomes 
d(mwz)/dz = me, V/L, (9) 
LOCAL CIRCULATIONS 
thus, 
T 
Opes [mae 
Im (10) 
The variation of wz is illustrated in Fig. 6. The liquid- 
water content and cloud mass vary with T and A in a 
manner summarized in Table I. It is suggested that 
these general conclusions on the variation of m and wy 
also hold for the case where the cloud air is slightly 
warmer than the environment; that is, the situation 
where there is a force to accelerate the cloud air upward. 
SL 
O 
LIQUID WATER CONTENT IN GM/KG 
De} 
2 3 4 5 6 
Z-Z) IN KILOMETERS 
Fie. 6.—Variation of the liquid-water content with elevation 
for the same conditions as in Fig. 5 
For the application of the above results to the an- 
alysis of an actual cloud, consideration must be given 
to the horizontal variation of the amount of environ- 
ment mixed with the rising column, the change with 
time of the lapse rate and the relative humidity of the 
TaBLe I, DEPENDENCE or CLoup Mass Aanp LiquiIpD-WATER 
ConTENT UPON LApsE RatTE or TEMPERATURE 
({ = Yz — Y.) AND ReLative Humipitry (H) 
T increasing H increasing 
increases 
m decreases 
decreases 
Wi increases | 
environment, the change with time of the degree of 
mixing, and the significance of the internal circulation 
cells within the cloud. Also it has been assumed that 
the entire liquid-water content is carried upward, there- 
fore the analysis cannot be applied to cases where 
precipitation occurs. 
The graphs in Fig. 5 may suggest a peculiar cloud 
a 
