ISENTROPIC ANALYSIS 
The particular isentropic surface or 
surfaces to be analyzed may be 
sketched immediately in the cross 
sections, and the positions of troughs 
or ridges may thus be determined and 
indicated on the isentropic map.* In 
sketching the isentropes on the cross 
sections, one should bear in mind that 
in the case of adiabatic lapse rates, 
(i.e., d 6/dz =0) the isentropes run 
vertically. In general, one can deter- 
mine the lapse rate directly from the 
isentropes by making use of the fol- 
lowing simple derivation. As an ap- 
proximation we may write: 
G— le ’ 
where T is the temperature and z the 
height above sea level expressed in 
hundreds of meters. Differentiating 
with respect to elevation we obtain: 
(on) Or ule 06 
+ 1, or 
Oz Oz 02 OZ 
If one chooses for dz a unit dis- 
—1. 
Das 
, is the 
Zz 
lapse rate, determined by simply noting 
the difference of potential tempera- 
ture in the vertical range; or the dis- 
tance between two successive isen- 
io) 
tance, say 1000 m, then 5 
tropes may be estimated, and 
z 
guickly determined. This method is 
especially helpful when lapse-rate dia- 
grams are not at hand. 
The domes and ridges in the isen- 
tropic surfaces are found in regions 
occupied by cold air masses, and the 
troughs in the isentropic surfaces are 
found in the warm air masses. To the 
extent that the surface pressure 
changes are due to advection of cold 
and warm masses, the slope of the 
isentropic surfaces will be greatest 
above the isallobaric maxima. 
Fronts on the surface weather map 
also offer a great deal of information 
*Prof. Spilhaus has suggested a more re- 
fined technique for drawing the isentropes 
(Bulletin Amer. Met. Soc., June, 1940). 
141 
about the structure and pattern of 
the contour lines. Regions. in the 
vicinity of well marked fronts are 
characterized by a crowding of the 
contour lines. Since cold fronts are 
generally much sharper and steeper 
than warm fronts, this steep gradient 
of contour lines on the isentropic 
chart is usually at its maximum just 
behind cold fronts. Moreover, as is 
to be expected, the contour lines usu- 
ally run parallel to the surface fronts. 
Experience shows that most well-de- 
fined fronts are characterized by con- 
stant, or almost constant, potential 
temperature, so that the frontal sur- 
faces have a marked tendency to 
coincide with the isentropic surfaces. 
Moreover, since a frontal surface is 
characterized by stable stratification, 
5 would have a maximum within 
z 
the transition zone. Since lateral mix- 
ing occurs mainly along isentropic 
surfaces, it follows that frontal sur- 
faces which are parallel to isentropic 
surfaces will not be destroyed by 
mixing. On the other hand, frontal 
surfaces which intersect the isentropic 
surfaces will dissolve on account of 
lateral mixing, unless the front is 
situated in a field of motion which is 
pronouncedly frontogenetical. When 
the front is associated with large 
areas of precipitation, the process is 
no longer isentropic, and lateral mix- 
ing does not take place along isen- 
tropes, but along surfaces of con- 
stant equivalent-potential tempera- 
ture or surfaces of constant saturated 
potential wet bulb temperature. In 
such cases the isentropic surfaces will 
cross the frontal surfaces. At cold 
fronts, however, the area of precipita- 
tion is normally relatively narrow so 
that, in most cases, cold fronts le 
along isentropic surfaces above the 
frictional layer. The warmest air is 
normally found just ahead of the sur- 
