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tropospheric flow is less than that carried equatorward at lower altitudes. Therefore the net heat transport—the first term in Eq. 8-16—is equatorward. The Hadley circulation carries heat toward the hot equator from the cooler subtropics! This does not seem very sensible. However, now let us add in the second term in Eq. 8-16, the potential energy density gz, to obtain the flux of dry static energy v[cpT + gz). Note that the vertical gradient of dry static energy is d (cpT + gz) /dz = cpdT/dz + g. For an atmosphere (like ours) that is generally stable to dry convection, dT/dz + g/cp > 0 (as discussed in Section 4.3.1) and so the dry static energy increases with height. Therefore the poleward flow at high altitude carries more dry static energy poleward than the low-level flow takes equatorward, and the net transport is poleward, as we might expect.

To compute the total energy flux we must include all the terms in Eq. 8-16. The latent heat flux contribution is equatorward, since (see Fig. 5.15) q decreases rapidly with height, and so the equatorward flowing air in the lower troposphere carries more moisture than the poleward moving branch aloft. In fact, this term almost cancels the dry static energy flux. This is because the gross vertical gradient of moist static energy cpT + gz + Lq, a first integral of Eq. 4-26 under hydrostatic motion, is weak in the tropics. This is just another way of saying that the tropical atmosphere is almost neutral to moist convection, a state that moist convection itself helps to bring about. This is clearly seen in the profiles of moist potential temperature shown in Fig. 5.9. Thus the equatorward and poleward branches of the circulation carry almost the same amount in each direction. In the net, then, the annually averaged energy flux by the Hadley cell is poleward, but weakly so. In fact, as can be seen in Fig. 8.13 and discussed further in Section 11.5, the heat transport by the ocean exceeds that of the atmosphere in the tropics up to 15° or so, particularly in the northern hemisphere.

The relative contributions of the various components of the energy flux are different in the extratropics, where the mean circulation is weak and the greater part of the transport is carried out by midlatitude eddies. In these motions, the poleward and equatorward flows occur at almost the same altitude, and so the strong vertical gradients of gz and Lq are not so important. Although these components of the energy flux are not negligible (and must be accounted for in any detailed calculation), we can use the heat flux alone to obtain an order of magnitude estimate of the net flux. So in middle latitudes we can represent Eq. 8-15 by

Hmid-lat ~

2n— cos p ps [v][T], g where [v] is a typical northward wind velocity (dominated by the eddy component in middle latitudes), and [T] is the typical magnitude of the temperature fluctuations in the presence of the eddies—the temperature difference between equatorward and poleward flowing air. Given a = 6371 km, cp = 1005 J kg-1 K-1, g = 9.81 m s-2, ps ^ 105 Pa, then if we take typical values of [v] ~ 10 ms-1 and [T] ~ 3 K at a latitude of 45°, we —1

estimate Hmid-iat ~ 8 PW. As discussed earlier in Section 5.1.3 and in more detail later, this is of the same order as implied by the radiative imbalance.

In cartoon form, our picture of the low-and high-latitude energy balance is therefore as shown in Fig. 8.12 (left). In the tropics energy is transported poleward by the Hadley circulation; in higher latitudes, eddies are the principal agency of heat transport.

The results of more complete calculations, making use of top of the atmosphere radiation measurements and analyzed atmospheric fields, of heat fluxes in the atmosphere and ocean are shown in Fig. 8.13. The bulk of the required transport is carried by the atmosphere in middle and high latitudes, but the ocean makes up a considerable fraction, particularly in the

Latitude

FIGURE 8.13. The ocean (thin) and atmospheric (dotted) contributions to the total northwards heat flux (thick) based on the NCEP reanalysis and top of the atmosphere radiation measurements (in PW = 1015 W) by (i) estimating the net surface heat flux over the ocean, (ii) the associated oceanic contribution, correcting for heat storage associated with global warming and constraining the ocean heat transport to be -0.1 PW at 68° S, and (iii) deducing the atmospheric contribution as a residual. The total meridional heat flux, as in Fig. 5.6, is also plotted (thick). From Trenberth and Caron (2001).

Latitude

FIGURE 8.13. The ocean (thin) and atmospheric (dotted) contributions to the total northwards heat flux (thick) based on the NCEP reanalysis and top of the atmosphere radiation measurements (in PW = 1015 W) by (i) estimating the net surface heat flux over the ocean, (ii) the associated oceanic contribution, correcting for heat storage associated with global warming and constraining the ocean heat transport to be -0.1 PW at 68° S, and (iii) deducing the atmospheric contribution as a residual. The total meridional heat flux, as in Fig. 5.6, is also plotted (thick). From Trenberth and Caron (2001).

tropics where (as we have seen) atmospheric energy transport is weak. The role of the ocean in meridional heat transport, and the partition of heat transport between the atmosphere and ocean, are discussed in some detail in Section 11.5.2.

### 8.4.2. Momentum transport

In addition to transporting heat, the general circulation also transports angular momentum. In the Hadley circulation, as we have seen, the upper, poleward-flowing, branch is associated with strong westerly winds. Thus westerly momentum is carried poleward. The lower branch, on the other hand, is associated with easterlies that are weakened by surface friction; the equator-ward flow carries weak easterly momentum equatorward. The net effect is a poleward transport of westerly angular momentum. Midlatitude eddies also transport angular momentum (albeit for less obvious and, in fact, quite subtle reasons, as sketched in Fig. 8.14), again mostly transporting eastward angular momentum poleward. This has the effect of modifying the surface winds from that sketched in Fig. 8.5, by shifting the low latitude westerlies into middle latitudes.

The atmospheric angular momentum budget may therefore be depicted as in Fig. 8.12 (right). Because there is a net export of momentum out of low latitudes, there must be a supply of momentum into this region; the only place it can come from is the surface, through friction acting on the low level winds. For the friction to supply angular momentum to the atmosphere (and yet act as a brake on the low level winds), the low level winds in the tropics must be easterly, consistent with that deduced for the Hadley circulation here. The balancing loss of westerly momentum from the atmosphere—which must be associated

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