EXTRATROPICAL CYCLONES 
gap. The lifting of a tongue of warm air relative to a 
colder environment, illustrated in Fig. 2, can be as- 
sumed to furnish a great part of the merease in kinetic 
energy during the cyclonic development from wave to 
vortex. 
The tropopause is also shown in the profiles. It has 
a erest over the warm-front surface and a trough over 
the cold-front surface, and the amplitude of the tropo- 
pause oscillation increases with the growth of the cy- 
clone. In Fig. 2d the tropopause has a deep depression 
almost coinciding with the cyclone center, which is at 
that stage surrounded by air of cold origin up through 
the whole troposphere. Details of tropopause structure, 
such as the frequent subdivision into multiple tropo- 
pauses, have been left out:in Fig. 2. 
Hatched areas in Fig. 2 indicate the location of the 
main precipitation areas of the cyclone. The largest 
area is covered by the warm-front rain, where the 
air from the warm tongue climbs the receding wedge of 
cold air and condenses much of its moisture. A more 
narrow zone of precipitation accompanies the cold 
front where some air from the lower part of the warm 
tongue is lifted by the advancing cold wedge. Higher 
portions of the warm tongue move faster than the 
cold-front wedge and are not lifted by it. The described 
upward motion of the warm air next to the frontal 
surfaces should be visualized as being superimposed on 
the general pattern of vertical motion, upward in the 
front half and downward in the rear half of the cy- 
clone (Fig. 1). This general, upward motion is some- 
times sufficient to cause rain where it is not called for 
as a consequence of upgliding on frontal surfaces. Some 
extensive warm-sector rains and also the rain in the 
front half of a cold trough or a cold vortex are prob- 
ably to be explained by the general upward motion 
shown in Fig. 1. 
To complete the precipitation picture of the cyclone 
the air-mass precipitation should also be added, that 
is, the drizzle in the warm moist parts, caused by con- 
densation from low clouds formed by the cooling of the 
warm air over cold surfaces (mainly ocean surfaces), 
and the convective showery precipitation formed 
through the heating from the ground, or through lift- 
ing of convectively unstable air at fronts. 
While the thermal pattern of the cyclone near the 
ground is the result mainly of horizontal advection 
and nonadiabatic gain or loss of heat exchanged with 
the ground, the pattern in the free atmosphere is also 
influenced by the slow but systematic vertical dis- 
placement of the air shown in Fig. 1 and by the heat 
transfer of penetrative convection. However, the dom- 
inant process for the shaping of the upper-tropospheric 
temperature field is horizontal advection. The develop- 
ment of the thermal pattern of the waves in the upper 
westerlies follows roughly the advective scheme shown 
in Fig. 3. A warm tongue forms in the part of the wave 
with advection from the south, and a cold tongue in 
the part with advection from the north. In this early 
stage of the wave the pressure crests and troughs must 
tilt westward, as shown for the pressure trough in 
Fig. 1. In the further development, both warm and 
581 
cold tongues grow in amplitude and move forward 
relative to the pressure wave, because the eastward 
motion of the air exceeds that of the wave. If the 
wave motion were entirely horizontal, a thermal pat- 
tern of permanent structure relative to the moving wave 
would be reached when the isotherms have adapted to 
the shape of the relative streamlines. For the idealized 
case of v, = constant in each level of the sinusoidal 
Fie. 3—Advective formation of the thermal upper wave by 
the winds blowing relative to the moving pressure wave. 
wave pattern, the ratio of the amplitude A, of the 
relative streamline to that of the streamline As would 
be 
Apr a Vz 
As On => Ci 
(4) 
Hence, close to the level where v. is equal to the wave 
speed c, the relative streamlines, and with them the 
advectively transported isotherms, would acquire a 
much greater amplitude than that of the streamline. 
The ratio Az/As will decrease from that level upward 
to the tropopause, where v, has its maximum. 
Under the influence of the upward motion ahead of 
the pressure trough and downward motion behind it, 
the ratio in (4) would be reduced, as shown by Miller 
[20]. Synoptic experience shows that Ar/As stays posi- 
tive in all tropospheric levels where v, > c, also under 
the joimt influence of vertical motion and horizontal 
advection. In other words, after a period of thermal 
transformation of the type shown in Fig. 3, the waves 
in the upper troposphere tend to become thermally 
symmetric, with warm tongues coinciding with pres- 
sure crests and cold tongues with pressure troughs. 
With the reversal of the meridional temperature 
gradient from troposphere to stratosphere, the advec- 
tive effects on temperature in the upper waves are 
also reversed. Hence the stratospheric pressure crests 
are cold and the pressure troughs warm. It then fol- 
lows indirectly that the wave pattern of pressure crests 
and troughs rapidly loses amplitude with height im 
the stratosphere. In the stably stratified stratosphere 
the local warming and cooling through vertical motion 
are stronger than in the troposphere, and are quite 
