DYNAMICAL PREDICTION OF LARGE-SCALE CONDENSATION TH 
larger than the threshold liquid water content 
below which precipitation cannot occur. There is 
some empirical evidence [aufm Kampe and 
Weickmann, 1957; Mason, 1957, p. 231] that such 
a maximum exists, its value depending on the 
type of cloud. This is reasonable since the pre- 
cipitation drop size and hence W, should depend 
on the characteristic magnitude of the vertical 
velocities working against gravity. For  strati- 
form clouds, with a characteristic vertical velocity 
of 5 cm see, pW. ~ 0.5 gm m-* (p is the air 
density); while for Cumulus clouds, with vertical 
velocities of the order of 50m sec, pW. ~ 5 gm 
m~*. Komabayast [1957] suggests that pl. var- 
ies as the 14 power of the vertical velocity. We 
have then for stratiform clouds that pW, ~ 0.3 
gm m-~*. 
One would expect pV. for non-convective 
clouds to be a maximum in mid-troposphere 
(+550 mb) where w is a maximum in the large 
scale; this is consistent with the findings of aufm 
Kampe and Weickmann [1957], who report much 
lower liquid water contents at the Cirrus level. 
However, for the purpose of estimating the varia- 
tion of 6 with h in different cloud layers we use 
an average value of pV; = 0.3 gm m~*, and 
furthermore assume the temperature to vary as 
in the standard atmosphere. The corresponding 
values of the parameters occurring in (1), (19), 
(20), and (21) are given in Table 1. Figure 4 
shows 6 as a function of h and ¢ for each of the 
three tropospheric layers for which a and 8 have 
been determined empirically. Figure 4 indicates 
that for ascending motion the maximum rate of 
increase of liquid water, which is proportional to 
6 — 6*, is attained just as precipitation begins. 
As the mean relative humidity increases beyond 
this point, 6 — 6* decreases until dW /dt = 0 at 
h = 1. Under continued upward motion the con- 
densing water is directly precipitated. On the 
other hand for downward motion of an existing 
cloud the rate of conversion of liquid water to 
water vapor, which is proportional to 6, has a 
maximum at = 1 and decreases monotonically 
toc = 0. 
The net effect is a process analogous to that 
resulting from entrainment in Cumulus develop- 
ment, but on a smaller scale. The fact that mean 
relative humidities of 100% are not often ob- 
served even from precipitating clouds must mean 
a significant dilution of the moist adiabatic proc- 
ess during precipitation. Hence even larger up- 
ward vertical velocities than calculated on the 
assumption of no dilution (6 = 6* = 1) are neces- 
TaBLE 1—Values of parameters used 
in constructing Figure 4 
Layer | a | B p rs va | Ym 
rs % 
| lee : 
mb | ream | fe 
550-300 | 0.433 | 1.733 | 0.6 Het 6221508 
(high) | 
800-550 0.70 | 2.0 ORO eset eoO 229 
(mid- | 
dle) | | 
1000-800 | 2.0 3.338 | 1.1 | 7.9 | 4.6 | 2.4 
(low) | | | 
HIGH eee Py ray a eT 
c § MIODLE DDR enc aaa wen Meee Sn ee Cee oeoty 
LOW 
Fra. 4—The percentage of mass undergoing 
moist adiabatic processes 6 as a function of rela- 
tive humidity h for low, middle, and high clouds; 
the corresponding cloud amount c is given along 
the upper abscissa; solid lines are for the non- 
precipitating stage, dashed lines are for the pre- 
cipitating stage; for 0 < ¢ < 1.0, each curve is 
valid for w S 0; for 1.0 < ¢ < 1.8 the solid line is 
valid for w > 0 and the dashed line for w < 0 
sary to explain the amounts of large-scale precipi- 
tation observed. 
REFERENCES 
AUBERT, E. J., On the release of latent heat as a 
factor in large scale atmospheric motions, J. 
Met., 14, 527-542, 1957. 
Aurm Kamer, H. J., anp H. K. WrIcKMANN, 
Physics of clouds, Met. Res. Rev., 1951-55, Met. 
Monographs, Amer. Met. Soc., 3, 182-225, 1957. 
HINKELMANN, K., Ein numerisches Experiment 
mit den primitiven Gleichungen, C.-G. Rossby 
Memorial Volume, Esselte A. B., Stockholm, 
1959. 
Hovuenton, H. G., anp W. H. Raprorp, On the 
measurement of drop size and liquid water con- 
tent in fogs and clouds, Papers Phys. Oceanogr. 
Met., Mass. Inst. Tech. and Woods Hole Oceanog. 
Inst., 4, 31 pp., 1938. 
Komapayast, M., Some aspects of rain formation 
in warm cloud (II), Liquid water content as a 
function of upward velocity, J. Met. Soc. Japan, 
35, 266-277, 1957. 
