DYNAMICAL PREDICTION OF LARGE-SCALE CONDENSATION 73 
It is well known that in the lowest 100 mb 
next to the Earth’s surface humidities close to 
100% are necessary before condensation is ob- 
served. This of course is due to the relatively in- 
tense mixing in the boundary layer. When surface 
winds are light, condensation in the form of fog 
may occur with lower humidities, but still con- 
siderably higher than in the ‘free’ atmosphere. It 
is of interest that non-industrial haze, which may 
be regarded as low-density fog, also occurs at high 
humidity. Under normal surface wind conditions, 
the intensely mixed layer is capped by an inver- 
sion through which the turbulence subsides al- 
most discontinuously, and it is above the inver- 
sion that some condensation may occur at 
humidities as low as 60%. 
The empirical relations found in no way are 
intended to reflect this discontinuous turbulence 
structure in the 1000-S00 mb layer, but rather 
to give a measure of the integrated effect of tur- 
bulence in the entire layer. To account ade- 
quately for the finer grain structure of turbulence 
would require far greater vertical resolution and 
more refined techniques than have been em- 
ployed here. One could guess as to what Figure 
1 would look like if ‘low clouds’ were stratified 
according to the mean relative humidity (a) be- 
tween 800 mb and cloud base, and (b) between 
cloud base and 1000 mb. For (a) the standard 
deviation of relative humidity would be larger 
than the mean in the 1000-800 mb layer due to 
weaker mixing so that condensation could occur 
at lower mean relative humidities. Curve (a) 
would then intercept the ¢ = 0 axis at h ~ 0.45. 
Since the most intense mixing would be confined 
to the layer next to the ground, the frequency 
distribution of relative humidity would be very 
peaked. The curve (b) would intercept c = 0 at 
h = 0.85 or 0.90. Of course in this boundary 
layer c no longer corresponds to cloud amount 
but rather to the visibility which in the absence 
of industrial pollutants is fairly good measure of 
liquid water content in clouds as well as in fog 
[Houghton and Radford, 1938]. The fact that the 
visibility decreases with increasing relative hu- 
midity for humidities over 70% [see, for example, 
Neiburger and Wurtele, 1949] tends to support 
the above supposition. 
An effective means for demonstrating the 
‘goodness of fit’ of Figure 1 is to deduce cloud 
amount from synoptic radiosonde data only and 
to compare with ‘actual’ cloud observations, rec- 
ognizing that the upper-level clouds when ob- 
scured from below must be estimated. All possible 
data including airways reports were employed. 
The comparisons are shown in Figures 2 and 3, 
for two cases, late spring and late fall. Included 
also are the geopotential fields at the 1000-, 700-, 
and 500-mb levels. The comparisons in the vicin- 
ity of the mountains must be ignored since the 
low-level humidities are fictitious and the ob- 
served cloud layers correspond to lower pressures 
than do sea-level observations. 
The two cases shown in Figures 2 and 3 are 
from wholly independent data. However, the 
empirical linear relations of Figure 1 have been 
found extremely useful as an analysis aid in re- 
gions of sparse radiosonde data such as over the 
oceans. Moreover, even over continental U. 3. 
the radiosonde network is often inadequate to fix 
the phase of smaller-scale distributions of humid- 
ity such as are associated with frontal zones. 
The surprisingly good relation between liquid 
water content and water vapor suggests a means 
for incorporating the cloud stage in the water 
budget, and in fact will lead to a measure of the 
efficiency of moist adiabatic processes in large- 
scale condensation. Since cloud cover is a relative 
two-dimensional measure of liquid water, if we 
assume the vertical extent of large-scale (non- 
convective) clouds to be proportional to a lnear 
measure of the horizontal dimension, then the 
volumetric measure of liquid water W is propor- 
tional to c3/*. Defining Wy as the minimum liquid 
water content necessary for precipitation, which 
according to Fig. 1 corresponds to ¢ = a = 1, 
then 
W = W,c?/2 (2) 
We denote by the subscript 2 the condition 
when h = 1, so that co = 1.38. We may now write 
the continuity equations for mixing ratio 7, mass 
of liquid (cloud) water per unit mass of air W, 
and mass of precipitating water per unit mass of 
air Wp, assuming that water vapor may change 
by expansional condensation or compressional 
evaporation, but that precipitating water does 
not evaporate 
dr Ym {5 = 0 force = 0 
= SOS > (3) 
dt Pp lore <1 for 0 <c =, 
dw m 
AS EG a) ee 
dt Pp 
(4) 
Soe = 0 force < cq orw > 0 
lo < 6* <1 fora <c<candw <0 
dWp Ym 
= —d* — fry 5 
dt p Ae @) 
