72 JOSEPH SMAGORINSKY 
ceeded. However some progress has now been 
achieved in devising a stable system for numeri- 
cally integrating the primitive equations for 
baroclinic flow [Smagorinsky, 1958; Hinkelmann, 
1959] as well as for barotropic flow [Phillips, 
1959]. This experience is now being applied to the 
construction of a near-hemispheric, four-level 
model allowing moist adiabatic processes. This 
model will include the baroclinic as well as baro- 
tropic orographic effects and also a simple ac- 
counting of boundary layer processes. 
It is apparent that the much smaller scale con- 
vective motions pose a special problem. It would, 
of course, be impractical to consider describing 
them by explicit dynamics. Ideally desirable is an 
adequate statistical-dynamical theory of moist 
convection which can define the classes of un- 
stable ambient states and account for the system- 
atic nonlinear interaction between the convective 
motions and the larger scale motions resolvable 
by explicit dynamics. Some work in this direction 
has been done by Malkus and Witt [1958] for dry 
convection. Moist convection, on the other hand, 
seems to be inherently different mechanistically 
and considerably more difficult to cope with. 
However, there is promise that numerical model 
experiments will yield further insight into the 
moist convective process, and work is now being 
undertaken in this direction. 
Some gross properties of the macrophysics of 
condensation and precipitation—Until now the 
limitations of the hydrodynamic contexts did not 
warrant refinements in the assumptions regarding 
the physics of condensation. However, contiguous 
studies have indicated the way toward a some- 
what more adequate linkage of the large-scale 
hydrodynamics and the condensation process. In 
CLOUD AMOUNT, C 
1 2 3 4 5 6 aT 8 2 Lo 
RELATIVE HUMIDITY, h 
Fic. 1—Empirically determined relation of 
mean relative humidity h in the layers 1000-800 
mb, 800-550 mb, and 550-300 mb with cloud 
amount c classed as low, middle, and high, respec- 
tively 
particular, it would be desirable to allow for the 
non-precipitating cloud stage, since until now 
only a distinction between clear sky and precipita- 
tion has been attempted. 
It is generally known that cloudiness and even 
precipitation are found to occur at space-averaged 
relative humidities considerably less than 100%. 
This cannot be dismissed as a purely instrumen- 
tal aberration. Humidity as measured by the 
instrument and averaged from the sounding, rep- 
resents the mean of a frequency distribution of 
smaller-scale humidity variations with consider- 
able standard deviation. This must mean that 
for values of the average humidity considerably 
less than 100%, some condensation may be occur- 
ring due to saturation at the high end of the 
distribution. One would then expect that the 
amount or density of condensation (that is cloudi- 
ness) will increase with increasing mean humid- 
ity. Furthermore, one may view precipitation as 
resulting from sustained and very dense conden- 
sation, sufficient to create large enough particles, 
say for example by coalescence or the ice crystal 
process, to overcome the upward vertical cur- 
rents. 
Indeed one does find empirically that non-con- 
vective cloud amount, classed as low, middle, and 
high, is highly correlated with the average relative 
humidity in the respective layers. Precipitation, 
if interpreted as corresponding to a cloud amount 
somewhat greater than 1.0, also fits such a corre- 
lation. In fact, the simple linear relation 
c=Bh-—a>0 (1) 
for each layer yields an excellent fit. Here c is the 
cloud amount, h is the relative humidity in per 
cent, and @ and @ are empirical coefficients. The 
fact that the instantaneous value of ¢ does not 
appear to depend on the instantaneous vertical 
velocity is not surprising. One would expect non- 
precipitating condensation to depend only on the 
accumulated history of the vertical motion, which 
after all is reflected in the humidity. 
For the purpose of establishing the coefficients 
a and @, it was assumed that the mean relative 
humidity in the 1000-800 mb layer corresponded 
to the span of low cloudiness, 800-550 mb to 
middle cloudiness, and 550-3800 mb to high 
cloudiness. A graph of the linear relations is shown 
in Figure 1. (The writer is grateful to 8. Heller- 
man for his assistance in determining this relation 
from careful analysis of a substantial volume of 
synoptic data.) It is of interest that all three 
levels tend to converge to c = 1.3 forh = 1.0. 
