On the Dynamical Prediction of Large-Scale 
Condensation 
by Numerical Methods 
JosEPH SMAGORINSKY 
U.S. Weather Bureau, Washington 25, D.C. 
Abstract—The paper discusses properties of the hydrothermodynamic frameworks 
thus far employed, the approximations regarding the microphysics of precipitation, the 
quality of results of numerical integrations for different models, further work in the 
construction of more sophisticated dynamical models, and investigations of the relation 
of large-scale liquid water content and of water vapor, and the implications for the 
dynamical prediction of cloud formation and dissipation. 
A brief survey of the state of the art—Attempts 
to make dynamical precipitation forecasts by 
numerical means began over 5 years ago. The 
first efforts were merely to employ the vertical 
motions calculated during the course of baroclinic 
numerical forecasts [Smagorinsky and Collins, 
1955; Miyakoda, 1956; and Smebye, 1958]. The 
hydrodynamics were quasi-geostrophic, the baro- 
clinic structure was described by information at 
three levels, and the potential vorticity was lin- 
earized when it appeared undifferentiated. Fur- 
thermore, the released latent heat was not per- 
mitted to add energy to the system. 
It was assumed that precipitation occurred 
upon attaining saturation, but it was already 
realized that the space-averaged relative humid- 
ity need not be 100% for condensation or precipi- 
tation to oecur. The possibility of supersatura- 
tion, supercooling, evaporation from falling drops, 
or inadequate nucleation was ignored. The results 
were reasonably encouraging, but further work 
suggested that departures from observation were 
to a large extent a result of errors in the large- 
scale hydrothermodynamics. The most obvious 
defect was the neglect of released latent heat, 
which is a destabilizing effect [Smagorinsky, 1956; 
Aubert, 1957]. This alone can amplify the large- 
scale upward vertical motions by as much as an 
order of magnitude giving maxima as large as 
50 cm/sec. The degree of destabilization increases 
with decreasing scale and decreasing static stabil- 
ity. 
It was also possible to remove the mathemati- 
cal limitations of quasi-linearization and to add 
the barotropic effects of large-scale mountains. 
Since these models now possessed energy sources 
and moisture sinks it was desirable to provide a 
pseudo-boundary layer which would allow for 
71 
surface friction and evaporation depending on 
land or sea. The quasi-geostrophic model equa- 
tions have been recast to be governed instead by 
the balance (or quasi-non-divergent) condition 
[Smagorinsky and collaborators, 1959]. The results 
are often better, especially in the movement of 
the systems, but also suffer because of new limita- 
tions introduced. The relatively smaller charac- 
teristic scale of moisture distributions present 
special difficulties and somewhat special numeri- 
cal techniques have been devised to reduce trun- 
cation error. 
Although very distinct progress has been made, 
the remaining hydrodynamic degeneracies leave 
24-hour precipitation forecasts with much to be 
desired. It is quite obvious that the geostrophic 
approximation as well as the balance condition 
are really valid for the very large-scale quasi- 
barotropic components of the motion. Much of 
the validity is lost when trying to describe the 
dynamies of the smaller-scale baroclinic develop- 
ments which occur sporadically as extratropical 
cyclogenesis. This is probably the major reason 
why geostrophic and balanced baroclinic models 
on the average give no better wind forecasts at 
500 mb than do barotropic models. The effects 
of released latent heat are on still a smaller scale, 
and the inertial-gravitational modes of atmos- 
pheric motion become even more important, if 
not essential. The divergent components appear 
to be of consequence not only in dynamical inter- 
actions but also for a proper accounting of the 
moisture budget. 
There therefore seems to be no question that 
further progress will depend on our ability to 
construct an adequate dynamical framework. 
Until quite recently, attempts to integrate nu- 
merically the primitive equations had not suc- 
