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Fig. 6.5
Schematic 500-hPa contours (heavy solid lines), 1000-hPa contours (thin lines), and 1000-
500 hPa thickness (dashed) for a developing baroclinic wave at three stages of development.
(After Palmen and Newton, 1969.)
level and surface flows; strong cold advection is seen to occur west of the trough
at the surface, with weaker warm advection to the east. This pattern of thermal
advection is a direct consequence of the fact that the trough at 500 hPa lags (lies
to the west of ) the surface trough so that the mean geostrophic wind in the 1000-
to 500-hPa layer is directed across the 1000- to 500-hPa thickness lines toward
larger thickness west of the surface trough and toward smaller thickness east of
the surface trough. This dependence of the phase of the disturbance on height is
better illustrated by Fig. 6.6, which shows a schematic downstream (or west-east)
cross section through an idealized developing baroclinic system. Throughout the
troposphere the trough and ridge axes tilt westward (or upstream) with height, 1
whereas the axes of warmest and coldest air are observed to have the opposite tilt.
As shown later, the westward tilt of the troughs and ridges is necessary in order
that the mean flow transfers potential energy to the developing wave. In the mature
stage (not shown in Fig. 6.5) the troughs at 500 and 1000 hPa are nearly in phase.
As a consequence, the thermal advection and energy conversion are quite weak.
6.2
THE QUASI-GEOSTROPHIC APPROXIMATION
The main goal of this chapter is to show how the observed structure of midlatitude
synoptic systems can be interpreted in terms of the constraints imposed on synoptic-
scale motions by the dynamical equations. Specifically we show that for motions
that are hydrostatic and nearly geostrophic, the three-dimensional flow field is
determined approximately by the isobaric distribution of geopotential [(x, y,
p, t)]. For this analysis, it is convenient to use the isobaric coordinate system both
1
In reality, the phase tilts tend to be concentrated below the 700-hPa level.
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