772 
maps, Petterssen has reported how the percentage fre- 
quency of cyclones and cyclogenesis is distributed over 
the whole Northern Hemisphere [62, Figs. 14-21]. He 
has also given the rate of alternation between cyclones 
and anticyclones, indicating the distribution of travel- 
ing disturbances [62, Figs. 22-23]. 
The frontogenesis builds up cyclonic shear vorticity 
which is transferred into vorticity of cyclonically curved 
flow at the apex of the frontal wave. Large initial 
frontal shear is therefore a sign of “stored” kinetic 
energy which, in being transformed to curvature vor- 
ticity, favors the evolution of the wave into a cyclone. 
The intensity of the frontal cyclogenesis may partly 
be conjectured by the forecaster from the observed 
horizontal velocity differences between the air masses. 
In particular, under the assumption of a normal air- 
mass stratification, sufficiently long waves are usually 
unstable provided that—according to an old rule—the 
wind shear along the front m knots is greater than 
four times the temperature discontinuity in centigrade 
degrees. 
Qualitative examples of such reasoning concerning 
eyclogenesis due to the individual change of vorticity 
of travelmg particles are demonstrated in Fig. 2. The 
FRICTIONAL EFFECT 
wyiysla TILT INCREASING 
wry TILT DECREASING 
wow SO SHARP FRONT 
sy---w DIFFUSE FRONT 
=» I-KM ISOHYPSE OF FRONT 
———— 2-KMISOHYPSE OF FRONT 
CYCLOGENETIC 
FRONT ACTIVITY 
WY ACTIVE 
Wv>-y MEDIUM 
—Y—7- PASSIVE 
va _-~KATAFRONT 
—wa ~ANAFRONT 
activity and passivity 
Fie. 2.—Frontal 
Bergeron, and vorticity dynamics of cyclones according to 
Bjerknes [33]. 
according to 
cold air sample a moves equatorward and partakes in 
the general convergence typical for the forward half of 
a cyclone. For both reasons cyclonic relative vorticity 
is acquired, which at first shows up on the surface 
map mainly as a horizontal cyclonic shear inside the 
cold air along the warm front. In passing the wave 
apex, this air maintains its cyclonic relative vorticity, 
which then is manifested as curvature vorticity. With- 
in the strongly cyclonically curving easterly branch 6 
of the cold current, a low-layer frictional convergence 
and lifting of the polar air contributes toward in- 
creasing the slope of the advancing cold front surface 
as shown by the frontal topography in the figure. 
WEATHER FORECASTING 
Farther behind the apex the cold air samples c and d 
are 1m a region of horizontal divergence strong enough 
to make their cyclonic vorticity decrease or change 
into anticyclonic vorticity despite the southward dis- 
placement. During the growth of the cyclone, more 
and more of the cold air is able to maintain its cyclonic 
vorticity after passing the wave apex, such as repre- 
sented by the life history a—b. Within the anticy- 
clonically curving westerly branch d the low-layer sub- 
sidence combines with the effect of ground friction 
to decrease the slope of the front, as shown through 
frontal isohypses in Fig. 2. The samples e and f, al- 
though moving poleward into their respective cyclones, 
experience sufficient horizontal convergence to acquire 
some cyclonic vorticity. The warm air samples g and h, 
passing at greater distances from their respective 
centers, do not have enough horizontal convergence to 
prevent their acquiring anticyclonic vorticity through 
poleward displacement. Warm air also ascends to the 
base of the westerly jet stream aloft and at the same 
time arrives at the poleward edge of the region of 
maximum frontal upgliding. Hence, this warm air also 
gains anticyclonic vorticity from the effect of the ver- 
tical velocity terms, which under these conditions is 
appreciable even in comparison with the effects of 
both poleward motion and divergence. 
Already in 1934 Scherhag [71] had poimted out that 
a cyclone with strong upper winds deepens. The 
stronger the upper westerlies have been built up during 
the frontogenetical period, the more they are apt to 
form unstable upper waves. A check on the possible 
occurrence of unstable anticyclonic curvature upwind 
from the cyclogenetic area will often give a clue to the 
deepening of the upper cold trough over the rear part 
of the cyclone. This shows up in the surface map as a 
deepening of the nonfrontal cold trough and the central 
part of the cyclone. (For more details, see pp. 587-597 
in “Extratropical Cyclones” by J. Bjerknes in this 
Compendium.) 
The instability of the wave varies also with the 
‘difference in the static stability of the adjacent air 
masses. In this connection we may mention that, mm 
general, waves on a polar front are more often unstable 
than those on an arctic front. Since imcreasing im- 
stability of an air mass favors cyclonic deepening, 
cyclones can deepen in winter by motion from land 
out over the sea. Moreover, where (in the analyzed 
upper-air maps) both the absolute isohypses® and the 
total relative isohypses’ are close together and the two 
sets of lines intersect approximately at right angles, 
cyclogenesis is often occurring in the region of higher 
relative height? and lower absolute height, according to 
synoptic experience. In particular, if the spacing of 
the relative isohypses on the rear side of the low is 
less than that on the forward side—and this is the 
normal case—then, according to Pogade [64], the cy- 
clone will deepen. (In the next subsection, we mention 
Petterssen’s rule that the cyclones also tend to mi- 
grate toward this anterior concentration of horizontal, 
5. For definition see Table I. 
