156 
describing the changes in the at- 
mosphere. While at present it is not 
possible to chart exactly substantial 
surfaces, there is much evidence to 
indicate that isentropic surfaces do 
not depart appreciably from substan- 
tial surfaces. Thus, the isentropic 
method of analysis is essentially a 
Lagrangian method. In a study of 
subsidence Namias [20] has shown 
that the potential temperatures at the 
bases and at the tops of subsidence in- 
versions remain fairly constant from 
day to day. Thus, if, in such cases, 
isentropic surfaces are used, it is 
reasonably certain that we are deal- 
ing with the same sheet of air parti- 
cles from day to day. Moreover, it 
is frequently observed that sand- 
wiched layers of dry and moist air 
remain within the same isentropic 
sheets for several days. From these 
observations it appears that, as a 
first approximation, we may consider 
isentropic surfaces as substantial sur- 
faces. 
Nevertheless, there are always at 
work non-adiabatic processes which 
tend to destroy the conservatism of 
isentropic surfaces and to raise or 
lower the isentropes relative to the 
5.0 1015 qe" 
600 
290 300 
Fic. 13.—Illustrating the influence of non- 
adiabatic cooling on the elevation of an isen- 
tropic surface. 
AIR MASS ANALYSIS 
substantial surfaces and also tend 
to transport moisture across the 
isentropic surfaces. These non-adi- 
abatic processes are mainly due to: 
(a) radiation, (b) evaporation and 
condensation, and (c) convection. 
While the influences of these pro- 
cesses may be appreciable over 
lengthy intervals of time, they are 
usually insufficient for disrupting the 
fundamental isentropic flow patterns 
from one day to the next. 
The influence of radiative cooling is 
ulustrated in fig. 13. As _ cooling 
proceeds, the temperature distribution 
changes from A to B to C. The sub- 
stantial surfaces do not change eleva- 
tion but since the temperature de- 
creases, the height of any given isen- 
tropic surface increases from day to 
day. Since the normal moisture dis- 
tribution is one in which mixing ratio 
decreases with elevation, the mixing 
ratio observed in a given isentropic 
surface decreases with time. Since 
the rate of radiational cooling in the 
free atmosphere is usually small com- 
pared with the adiabatic cooling, it 
does not destroy the essential char- 
acter of the flow pattern. This slow 
rate of free-air cooling is indicated 
by the cooling curves computed by 
Moller [21], which suggest that the 
mean temperature change resulting 
from the radiative unbalance in the 
atmosphere hardly exceeds 1.5C° per 
day,* which with normal lapse rate 
corresponds to a vertical displacement 
*Elsasser (Unpublished MS) has recomputed 
such cooling curves on the basis of newer data 
on the water vapor absorption spectrum. In 
general his values do not differ excessively 
from Modller’s. However, both Moller’s and 
Elsasser’s curves are based on monthly means 
of upper-air conditions. On individual days 
the cooling must be much greater sometimes, 
perhaps as much as 10° or 15° C per day from 
a saturated warm stratum with a deep dry 
inversion above it. The figure 1.5° C quoted 
is for mid-latitudes; Elsasser’s’ (Bull. Amer. 
Met. Soc., May 1940) mean values for Florida 
soundings even in winter show over 2.0° C per 
day cooling at moderate elevations. Elsasser 
has published a radiation chart with which 
radiation in individual soundings ean be com- 
puted (Calif. Inst. Techn. 1939).—R. G. Stone. 
