EXTRATROPICAL CYCLONES 
the stratosphere and the upper half of the troposphere, 
may be an important effect to consider together with 
the divergence effects represented in Fig. 1. A cyclonic 
storm traveling along the jet-stream zone would come 
under the influence of superimposed upper mass diver- 
gence from the time when it passes the place of great- 
est constriction of the upper streamlines. A complete 
theoretical treatment of this case, which calls for a 
combination of the divergence effects of Fig. 1 and 
Fig. 8, is not available; but there seems to be consider- 
able empirical evidence for strong cyclonic deepening 
under the described circumstances. Such synoptic evi- 
dence has mainly been gathered by Scherhag [80]. 
Scherhag points to Ryd [28, 29] as the originator of 
the idea that mass divergence of importance for cyclone 
deepening should occur in upper delta patterns. Ryd’s 
theoretical contributions appeared in 1923 and 1927 
when there were as yet no upper-air maps. 
Returning to Fig. 7, we see that complete inertial 
instability dv,/dn > 20, may at times extend from 150 
mb down towards the 500-mb surface. It may also 
extend over a thousand kilometers’ length of current, 
but the width of the zone of such unstable shear is 
hardly more than three hundred kilometers at any one 
point. Inside that volume of current the geostrophic 
wind, with its superimposed component of isentropic 
upgliding or downgliding, does not represent a stable 
flow. However, with stable neighboring flow on either 
side, no very large unstable deviations from geostrophic 
flow will be able to develop. The most likely system of 
perturbations in the unstable part of the current will 
be helical cellular circulations, as indicated in Fig. 7. 
Such circulations would serve the purpose of exchanging 
momentum across the zone of unstable shear and thus 
lessen that shear. The height of each cell would have 
to be small, probably less than one kilometer, so that 
the solenoid field set up by the cellular circulation should 
not grow strong enough to reverse the initial circulation. 
An indirect indication of the existence of the helical 
cellular circulations is seen in the observed ‘‘multiple 
tropopauses,”’ each one probably representing a cell 
wall between superjacent circulation rolls. According 
to Palmén [22], these multiple tropopauses are quasi- 
isentropic as would be expected if they are formed as 
circulation-cell boundaries. 
SYNOPTIC EXAMPLE OF AN EXTRA- 
TROPICAL CYCLONE 
The weather situation over North America during 
November 7-10, 1948, has been selected to illustrate 
the principles of this article. A large occluded cyclone 
which was located over the Hudson Bay region during 
this period can serve as a model of the most frequent 
structure of old cyclones, while over the central United 
States the atmosphere displays all the successive stages 
of frontogenesis and the early life history of a growing 
frontal wave cyclone. Our description will begin with 
the evolution of the long-wave background pattern of 
the upper layers, represented by a set of 300-mb maps, 
then the advective frontogenesis in the lower tropo- 
587 
sphere will be illustrated by a sequence of ground-level 
and 850-mb maps as well as selected profiles, and finally 
the three-dimensional structure of the frontal wave 
cyclone will be shown by a synoptic set of maps from 
the ground to 300 mb. 
Synoptic Evolution of the Upper Layers. The six 
300-mb maps at 12-hr intervals in Fig. 9 all show the 
semipermanent Hudson Bay cyclone. Through the 
whole troposphere this cyclone is a cold-coré vortex 
and therefore shows up as a deep center on the 300-mb 
maps. Equally permanent is the crest of high pressure 
extending northwards from a warm anticyclone over 
the eastern North Pacific. Both the Hudson Bay low 
and the eastern Pacific high are typical features of the 
general circulation but they have more than average 
strength during November 7—10. The westerly current 
meandering through between them is quite strong over 
a narrow zone, while the pressure gradients in the high 
and the low are quite weak. The trough located over 
the western United States on November 7 moves slowly 
to the central states and deepens gradually from 
November 7 to November 9. This upper-air process 
plays an important role in the formation of the frontal 
cyclone which takes place under the pre-trough south- 
westerly current (without producing any separate low- 
pressure center at 300 mb). 
The deepening of the upper trough may be caused 
in two ways (see equation (1)): either through a sinking 
component of motion at the 300-mb level, or through 
horizontal mass divergence in the column above 300 mb. 
In the former case the temperature in the trough at 300 
mb ought to be rising with time. This is not borne out 
by the observations during November 7-9, so that we 
are left with the horizontal mass divergence as the 
probable cause of the deepening of the trough. The 
mass divergence must be operated through the feeding 
of air into the trough with such a high velocity that the 
Coriolis force and centrifugal force overcompensate the 
initial pressure gradient. The mechanism for producing 
such a strong jet in the northerly current behind the 
trough must be sought on the anticyclonic bend to the 
west. 
The maximum curvature of the 28,400-ft contour 
of the 300-mb surface is represented on the November 
7th map by an are of a circle with radius r;. At the 
same place in western Canada the maximum possible 
curvature of a steady-state anticyclonic current, flow- 
ing under the influence of the observed pressure-gradient 
force, is represented by another are of a circle with 
radius fmin 2 The curvature analysis on the 300-mb 
3. The value of 7min is obtained from the equation of anti- 
eyclonie circular motion 
—v/r = —20,0 — 06/dr = —20.(v — 2), (12) 
in which @ stands for the geopotential in the pressure topogra- 
phy, r and v are positive, —d6/dr is the outward-directed 
pressure gradient, —2Q.v is the inward-directed Coriolis force, 
and —v®/r is the centripetal acceleration. When equation (12) 
is applied to a selected point on the map, ® and d6/dr are 
