### Tropopause Temperature Maps

__Map construction:__

The contours on these tropopause temperature maps are constructed by
plotting the spatial location of the intersection of the 2.0 PVU surface with a
particular isentrope. This
method of construction is different from simply plotting the potential temperature as a
single-valued function of *q*, because it allows folds in the tropopause to
be seen as crossing contours.

__Interpreting
the maps:__

Tropopause
temperature maps are useful in interpreting tropospheric dynamics because of the
association between boundary temperature anomalies and potential vorticity (PV)
anomalies. In particular, quasi-geostrophic theory can be used to show
that temperature anomalies on the upper and lower boundaries of a fluid can be
thought of as collocated PV anomalies. On a lower boundary, the PV anomaly
has the same sign as the temperature anomaly, while on an upper boundary the
anomalies have opposite signs.

For
example, a cold region of the tropopause is typically low in height and
correlated with an underlying positive PV anomaly. A warm region at 850 mb
(i.e. a region of anomalously high saturation equivalent potential temperature) is associated with an
overlying positive
PV anomaly. The distribution of tropopause and 850 mb temperatures can
thus be thought of as distributions of PV on the upper and lower boundaries of
the troposphere.

The
vertical penetration depth of a particular boundary PV anomaly determines
whether it can influence the properties of the other boundary.
Extratropical cyclogenesis can be thought of as the interaction of upper- and
lower-tropospheric PV anomalies (in the sense of the classical Eady model).

In the real atmosphere, PV is created
and destroyed by diabatic processes. Some insight can be gained by
examining the satellite images corresponding to a particular tropopause
temperature map and noting how the tropopause temperatures evolve over time in
both regions of active convection and regions of strong radiative cooling.