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Fig. 8.1
A schematic picture of cyclogenesis associated with the arrival of an upper-level positive
vorticity perturbation over a lower-level baroclinic region. (a) Lower-level cyclonic vortic-
ity induced by the upper-level vorticity anomaly. The circulation induced by the vorticity
anomaly is shown by the solid arrows, and potential temperature contours are shown at the
lower boundary. The advection of potential temperature by the induced lower-level circula-
tion leads to a warm anomaly slightly east of the upper-level vorticity anomaly. This in turn
will induce a cyclonic circulation as shown by the open arrows in (b). The induced upper-level
circulation will reinforce the original upper-level anomaly and can lead to amplification of
the disturbance. (After Hoskins et al., 1985.)
A strong dependence of cyclogenesis on initial conditions occurs when a large-
amplitude upper-level potential vorticity anomaly is advected into a region where
there is a preexisting meridional temperature gradient at the surface. In that case,
as shown schematically in Fig. 8.1, the circulation induced by the upper-level
anomaly (which extends downward, as discussed in Section 6.3) leads to temper-
ature advection at the surface; this induces a potential vorticity anomaly near the
surface, which in turn reinforces the upper-level anomaly. Under some conditions
the surface and upper-level potential vorticity anomalies can become locked in
phase so that the induced circulations produce a very rapid amplification of the
anomaly pattern. Detailed discussion of the initial value approach to cyclogenesis
is beyond the scope of this text. Here we concentrate primarily on the simplest
normal mode instability models.
8.2
NORMAL MODE BAROCLINIC INSTABILITY: A TWO-LAYER
MODEL
Even for a highly idealized mean-flow profile, the mathematical treatment of baro-
clinic instability in a continuously stratified atmosphere is rather complicated.
Before considering such a model we first focus on the simplest model that can
incorporate baroclinic processes. The atmosphere is represented by two discrete
layers bounded by surfaces numbered 0, 2, and 4 (generally taken to be the 0-, 500-,
and 1000-hPa surfaces, respectively) as shown in Fig. 8.2. The quasi-geostrophic
