FIGURE 5.21. The meridional overturning streamfunction x of the atmosphere in annual mean, DJF, and JJA conditions. [The meridional velocities are related to x by v = - (pa cos y)-1 dx/dz ; w = (pa2 cos y) 1 dx/dy.] Units are in 109 kgs-1, or Sverdrups, as discussed in Section 11.5.2. Flow circulates around positive (negative) centers in a clockwise (anticlockwise) sense. Thus in the annual mean, air rises just north of the equator and sinks around ± 30°.

(weaker) cells, more or less symmetrically arranged about the equator, one branching north and the other south. Not surprisingly, the regions of mean upward motion coincide with the wet regions of the tropics, as evident, for example, in the presence of cold cloud tops in the OLR distribution shown in Fig. 4.26. In contrast, descending regions are very dry and cloud-free. The latter region is the desert belt and is also where the trade inversion discussed in the context of Fig. 4.16b is found.

This vertical motion is accompanied by meridional flow. Except in the tropics, mean northward winds are weak (< 1m s-1) everywhere. In the tropical upper troposphere (near 200mbar, between about 20° N and 20° S) we observe winds directed toward the winter hemisphere at speeds of up to 3 ms-1. There is a return flow in the lower troposphere that is somewhat weaker, and which is directed mostly toward the summer hemisphere. Thus the "easterlies" we deduced from Fig. 5.20 are in fact north-easterlies, north of the equator in northern winter, and south-easterlies, south of the equator in southern winter. These are the trade winds mentioned earlier.

The overturning circulation of the tropical atmosphere evident in Fig. 5.21 is known as the Hadley cell; we will consider its dynamics in Chapter 8. The (much) weaker reverse cells in middle latitudes of each hemisphere are known as Ferrel cells, after William Ferrel (1817-1891), an American meteorologist who developed early theories of the atmospheric circulation.

Eddies and waves

Finally, in case the typical, zonally-averaged, cross sections presented here give the impression that the atmosphere actually looks like this at any given time, note that, in reality, the atmospheric structure is variable in time and three-dimensional. This is evident on any weather map (and from the fact that we need weather forecasts at all). A typical instantaneous 500mbar geopotential height analysis is shown in Fig. 5.22 and should be compared to the (much smoother) monthly average shown in Fig. 5.12. Although the general features of the meridional structure are evident (in particular, the decrease of height of the pressure surface from low to high latitude) there are also many localized highs and lows in the instantaneous structure that, as we shall see, are indicative of the presence of eddies in the flow.8 The atmosphere, especially in the extratropics, is full of eddying winds. As will be discussed in Chapter 8, the eddies are the key agency of meridional heat and moisture transport in the middle to high latitudes.

In summary, in this chapter we have discussed how warming of the tropical atmosphere and cooling over the poles leads, through hydrostatic balance, to a large-scale slope of the pressure surfaces and hence pressure gradient forces directed from equator to pole. It turns out that, as we go on to discuss in detail in Chapters 7 and 8, this pressure gradient force is balanced on the large-scale by Coriolis forces acting on the winds because of the Earth's rotation. In fact the temperature, pressure, and wind fields shown in this chapter are not independent of one another but are intimately connected through basic laws of physics. To take our discussion further and make it quantitative, we must next develop some of the underlying theory of atmospheric dynamics. This is interesting in itself because it involves applying the

Vilhelm Bjerknes (1862-1951), Norwegian meteorologist. His father, Carl, was a professor of hydrodynamics, while his son, Jacob became a famous meteorologist in his own right (see Chapter 12). With Jacob, he created an early network of meteorological observations. Bjerknes was the founder of the ''Bergen school'', where the now-familiar synoptic concepts of cyclones, fronts, and air masses were first established.

FIGURE 5.22. Typical 500mbar height analysis: the height of the 500mbar surface (in decameters) at 12 GMT on June 21, 2003. The contour interval is 6 decameters = 60 m. The minimum height is 516 decameters and occurs in the intense lows over the pole.

laws of mechanics and thermodynamics to a fluid on a rotating Earth; thinking about the importance, or otherwise, of rotation on the fluid motion; and contemplating the motion from different frames of reference, that of the rotating Earth itself and that of an inertial observer out in space looking back on the Earth.

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