AEROLOGY OF EXTRATROPICAL DISTURBANCES 
Equation (12) can be written 
=) =-—g]| pdivzvdz 
= Op Op 
= of (u% ar 1 28) dz + (gpw)n. 
In the first approximation we can neglect the second 
term on the right which represents the contribution of 
advection to the pressure change. A pressure tendency 
at the surface of —1 mb hr~ corresponds to an average 
divergence of —0.3 X 10-* sec. Direct measurements 
from wind observation by Houghton and Austin [29] 
and further by Sheppard [1] give values for the diver- 
gence of the order of magnitude of 10~> sec or even 
more for specific levels. The disagreement between the 
average divergence in a whole vertical air column deter- 
mined from pressure changes and the values for the 
divergence in different levels computed from actual 
wind observations shows that vertical circulations are 
essential for an understanding of the atmospheric proc- 
esses. Therefore we can state that the surface pressure 
change is the relatively small sum of two large terms 
with different signs and that the influence of the upper 
divergence must be somewhat greater than the influ- 
ence of the lower convergence if (Op/dt)) < 0. Further- 
more, we can conclude that there must be a certain 
level of nondivergence approximately coinciding with 
the level of maximum vertical wind velocity |w]| . 
We can now use the vorticity equation 
(18) 
=4 — —(¢ + 20sin ¢) diva v (14) 
in order to investigate the influence of the divergence 
field on the upper-air flow above the center of the cy- 
clone. The individual absolute vorticity of the air par- 
cels moving above the cyclonic center decreases under 
the influence of the field of divergence. If we expand the 
expression in equation (14), we obtain 
Use OG Oa a ay 52 
a an Os 0z 
15 
dt ot e) 
where v; is the horizontal velocity component along 
the momentary streamline. The local change 0f./dt 
is, on the average, positive above the surface center of 
the cyclone, since the upper trough is approaching. The 
term wo0f,/dz is small in the upper troposphere where 
|w| is small. Since the cyclone and the upper trough 
west of the surface center are moving slowly compared 
with the upper wind one can put 
(16) 
Thus the absolute vorticity must decrease along stream- 
lines of the upper flow. 
The absolute vorticity can be written in the form 
Ov; 
or’ 
fa = 20 sin @ + > + (17) 
611 
where r is the radius of curvature of a streamline. If we 
neglect the shear, the cyclonic curvature must decrease 
in the direction of a streamline. If the air flow has a 
southerly component, the effect of latitude is negative 
and the decrease of curvature is greater than in cases 
with a northerly component. 
If we could follow the development over an individua 
cyclone, the decrease of vorticity along upper stream- 
les should intensify when the upper divergence field 
intensifies. Since the latitude effect, which is propor- 
tional to the meridional wind component v and to the 
change of the Coriolis parameter with latitude, 2Q cos ¢, 
can easily be computed, the shape of the upper con- 
tour lines over a deepening cyclone can be used for an 
estimate of the upper divergence. Scherhag [56] has 
strongly emphasized the connection between the move- 
ment and the deepening of cyclones and the shape of the 
isobars or contour lines in the upper troposphere.!° 
Figure 7 shows the characteristic pressure distribu- 
tion in the lower and upper troposphere for a wave 
cyclone and for a mature cyclone. The increased num- 
ber of closed isobars in the surface layer is an expression 
of the increased cyclonic circulation due to low-level 
convergence. The deformation of the upper isobars indi- 
cates the influence of the upper-level divergence field 
upon the air moving through the system. In the surface 
layer the convergence field has a much longer time to 
influence the air flow than is the case in the upper 
troposphere where the air moves relatively quickly 
through the system. The warm-sector air, subjected to 
strong convergence in the lower and inner parts of a 
cyclone, leaves this region as a current with decreasing 
vorticity because of the upper-level divergence field. 
The principal ascent of the warm air masses takes place 
in the precipitation region marked in Fig. 7; the ex- 
tension of the area of precipitation to the west along the 
occluded front is therefore not primarily the result of 
the ascent of less cold air moving in from the west or 
southwest. 
In the final stage of occlusion the low at the upper 
level nearly coincides with the surface low, whereas in 
the beginning the axis of lowest pressure slopes to the 
west. Single-station analysis gives a phase displacement 
with height which gradually diminishes during the oc- 
clusion process. The importance of this vertical struc- 
ture of cyclones was originally emphasized by von 
Ficker [21, 22]. The deepening of a cyclone due to the 
occlusion process can formally be considered as the 
result of an interaction between two pressure waves, an 
upper and a lower one, according to Defant [19]; if the 
upper wave moves at a higher speed, it reaches the 
lower wave at the time of maximum depth. 
The divergent flow of the upper air above the frontal 
system has been verified by numerous studies of Euro- 
pean cyclones [8, 9, 10, 40]. The characteristic upper-air 
flow outlined here is also in agreement with well-known 
10. We refer to the very extensive list of references concern- 
ing this problem in Scherhag’s textbook [56]. 
