600 
Another pomt of importance should be noted here. 
The source region of polar air is smaller in area than 
the source region of tropical air. Therefore any outflow 
of polar air into lower latitudes must have a tendency 
to break up into “streams” embedded in tropical air. 
These streams of polar air often select ‘‘preferred re- 
gions” determined by geographical factors. Several such 
preferred regions for polar outflow can be found in the 
Northern Hemisphere. It is through these regions of 
preferred polar-air outflow that the principal fronto- 
genetical regions on the earth’s surface are determined, 
as Bergeron pointed out in his outlme of dynamic 
climatology [8]. 
Analyses of synoptic charts for different levels indi- 
cate that in the region between two cyclone families, 
where no surface polar front exists, pronounced frontal 
zones appear on the charts for the middle troposphere 
(e.g., at the 700- and 500-mb surfaces). In such cases 
the polar front appears to be interrupted only in the 
surface layers and not at higher levels in the atmos- 
phere (compare Figs. 5 and 6). Since this difference 
between the polar front on the surface and in the free 
atmosphere is essential for an understanding of the 
three-dimensional air movement in cyclones, it is neces- 
sary to discuss the problem of meridional movement of 
air masses before we go further in our description of the 
characteristic structure of the atmosphere. 
If ¢ denotes the vertical component of the relative 
vorticity, ¢ the latitude, © the angular velocity of the 
earth’s rotation, and D the depth of a given air mass 
(here regarded as incompressible), the principle of con- 
servation of potential vorticity, according to Rossby 
[52], can be expressed by the equation 
d /§ + 2Qsin¢\ _ 
=| a =o a) 
From (1) it follows that the individual change of vortic- 
ity 1s 
1dD 
D dt 
d§ _ _ 2Qcos¢ 
cia a ie 
(¢ + 2Q sin ¢), (2) 
where v is the meridional wind component and a the 
radius of the earth. 
The first term on the right in (2) gives the change of 
vorticity due to the meridional motion; the second 
term, the effect resulting from the change in depth of 
the air column. If we assume that the air moves without 
change in depth, the vorticity imcreases for movement 
toward the south. If, in order to simplify the discussion, 
we assume that the increase in vorticity appears as in- 
creasing curvature, the air parcel continuously curves 
to the left if v is negative (north wind). It is then easy 
to show that any air column moving without shrmking 
must ultimately bend back after reaching a lowest lati- 
tude. According to equation (1), this latitude is deter- 
mined by the initial latitude, meridional wind com- 
ponent, and vorticity of the air parcel. 
The change in depth of an air column moving south- 
ward can be computed from equation (2) if the vorticity 
along the trajectory is known. In the special case of a 
MECHANICS OF PRESSURE SYSTEMS 
straight flow without horizontal shear (relative vor- 
ticity ¢ = 0) we obtain 
= == == Gin G, (8) 
a 
This equation determines the shrinking of a polar air 
column moving with the north-south velocity v along 
a trajectory of zero relative vorticity. 
If we use either equation (1) or (3) for ¢ = 0, it is 
possible to compute the depth of a polar air mass at 
different latitudes as a function of its original depth at 
a given latitude. If we assume a depth of 8 km at lati- 
tude 60°N, we obtain the followmg values for D at 
lower latitudes: 
Latitude N (deg) 60 50 40 30 20 10 
Depth (km) 8.0 7.1 5.9 4.6 3.1 1.6 
The foregoing values are very approximate. If we 
permit an increase in relative vorticity, higher values 
of the final depth of the polar air result. On the other 
hand, however, air which descends from the level of 
8 km to, for example, 5 km will undergo a temperature 
increase of about 30C. In other words, the air will no 
longer be very cold at that lower level. Thus there must 
be some limit, determined by the original temperature, 
for the smking of the polar air. 
From the very simplified reasoning above, it follows 
that there must be some southern limit fer the exten- 
sion of characteristic polar air in the upper-air charts. 
This southern limit for the 500-mb level is somewhere 
around latitude 30°N. Systematic analyses of circum- 
polar 500-mb charts indicate that air masses with the 
characteristic polar air temperature very seldom reach 
latitude 30°N, and that 20°-25°N represents the south- 
ernmost limit for real polar air at the 700-mb level.* 
It is now easier to understand the structure of the 
atmosphere in the area between two cyclone families or 
surface polar fronts. The breaks im the surface polar 
front which permit outflow of polar air mto the tropics 
are not necessary at upper levels where the polar air 
flows southward as a subsiding current. At the 500-mb 
level, for example, a southern boundary for the polar air 
can be maintained around the hemisphere, at least in 
principle. 
Many meteorologists who regularly use fronts on 
surface maps are inclined to reject the idea of upper 
fronts existing around the hemisphere. Their opinion is 
founded on the idea that surface friction is necessary 
for the formation of distinct fronts. It is obvious that 
surface friction contributes to the sharpening of fronts. 
Tn the free atmosphere, however, other frontogenetical 
factors can be as effective as those in the surface layer, 
or sometimes even more effective (cf. Bergeron [2] and 
Petiterssen [46]). On the other hand it is evident that 
the great dynamic significance of fronts, confirmed in 
3. In this reasoning the nonadiabatic processes have been 
completely disregarded. A southward-moving polar air mass 
naturally undergoes a gradual change and eventually com- 
pletely loses its polar character because of the heat transfer 
from below. 
