## Info FIGURE 5.11. The geometry of pressure surfaces (surfaces of constants pi, p2 , p3, P4, where pi > p2 > p3 > Pi) in the vicinity of a horizontal pressure minimum. FIGURE 5.12. The mean height of the 500mbar surface in January, 2003 (monthly mean). The contour interval is 6 decameters = 60 m. The surface is 5.88 km high in the tropics and 4.98 km high over the pole. Latitude circles are marked every 10°, longitude every 30°.

Zonal-Average Geopotential Height Anomaly (m) FIGURE 5.13. Zonal-mean geopotential height (m) for annual mean conditions. Values are departures from a horizontally uniform reference profile.

pressure surface is proportional to the mean temperature between that pressure surface and the ground. So where temperatures are cold (warm), air columns contract (expand) and geopotential heights are low (high).

We can estimate the expected tilt of a pressure surface as follows. For an atmosphere in which T varies in the horizontal but is vertically isothermal, the difference in the height of an isobaric surface, p, between warm and cold latitudes, Az^^, is, using Eq. 3-8, act

where ps is the pressure at the surface. If ATwdm = 40°C in the climatology, inserting numbers into the above, we find that the 500 mbar surface drops by Azwodm = 811 m, as is evident in Figs. 5.12 and 5.13.

Finally, it is useful to define the thickness of an atmospheric layer, sandwiched between two pressure surfaces, such as p1 and p2 in Fig. 5.14. From Eq. 5-2 we have:

rpi T dp

which depends on T averaged over the layer. Atmospheric layers are ''thick'' in tropical regions, because they are warm, and ''thin'' in polar regions, because they are cold, leading to the large-scale slope of pressure surfaces seen in Fig. 5.12. Moreover, if tropical columns are warmer than polar columns at all levels, then the tilt of the pressure surfaces must increase with height, as sketched in Fig. 5.14 and seen in the observations, Fig. 5.13. We will see the importance of this fact when we discuss the distribution of atmospheric winds in Chapter 7. 