## The Ocean Heat Budget And Transport

We now turn to the role of the ocean circulation in meridional heat transport. To maintain an approximately steady climate, the ocean and atmosphere must move excess heat from the tropics to the polar regions. We saw back in Fig. 8.13 that the atmosphere

FIGURE 11.24. Observations of CFCs at a depth of 2 km (contoured). Superimposed in red is a snap-shot for 1983 of the CFC distribution at a depth of 2 km in the North Atlantic, as simulated by a numerical model of ocean circulation and tracer transport. The model results are courtesy of Mick Follows (MIT), the data courtesy of Ray Weiss (Scripps).

FIGURE 11.24. Observations of CFCs at a depth of 2 km (contoured). Superimposed in red is a snap-shot for 1983 of the CFC distribution at a depth of 2 km in the North Atlantic, as simulated by a numerical model of ocean circulation and tracer transport. The model results are courtesy of Mick Follows (MIT), the data courtesy of Ray Weiss (Scripps).

transports the larger part of the poleward heat transport with the ocean carrying the remainder. To obtain a quantitative estimate of the role of the ocean in meridional heat transport we must write an equation for the ocean heat budget.

The heat budget for a column of ocean is obtained by integrating Eq. 11-2 vertically over the depth of the ocean:

Vh ' H ocean , by ocean currents

where heat content = prefCw top

Tdz bottom is the heat stored in the column, Qnet is given by Eq. ll-5, Ho prefcw J¡

top bottom uTdz is the

(vector) horizontal heat flux by ocean currents integrated over the vertical column, and Vh is the horizontal divergence operator. Equation 11-11 says that changes in heat stored in a column of the ocean are induced by fluxes of heat through the sea surface and the horizontal divergence of heat carried by ocean currents. If there is to be a steady state, the global integral of the air-sea flux must vanish (see Section 11.1), because ocean currents can only carry heat from one place to another, redistributing it around the globe.

11.5.1. Meridional heat transport —1

Let us define Hocean as the heat flux across a vertical plane extending from the bottom of the ocean to the surface and from the western coast of an ocean basin to the

Float displacements at 2.5 km

FIGURE 11.25. Net float displacements over a time of 600—800d at a depth of 2.5km, showing the movement of North Atlantic Deep Water in the south Atlantic. Eastward displacements are marked in red, westward in blue, and southward in green. Courtesy of Nelson Hogg, WHOI.

FIGURE 11.25. Net float displacements over a time of 600—800d at a depth of 2.5km, showing the movement of North Atlantic Deep Water in the south Atlantic. Eastward displacements are marked in red, westward in blue, and southward in green. Courtesy of Nelson Hogg, WHOI.

eastern coast (cf. Eq. 8-15 for the analogous

expression for the total energy flux, Hatmos, in the atmosphere):

Hocean = Prefcwa cos V

'top vTdz di, bottom where the geometrical factor a cos cpd! is the distance along a latitude circle over an arc d1 (see Fig. 6.19). To take account of (slight) compressibility effects, we interpret T in the above expression as the potential temperature.

Hocean is difficult to measure and not precisely known. However, it can be inferred as follows:

1. as a residual, using atmospheric analyses of velocity and temperature to calculate the heat transport in the atmosphere, which is then subtracted from the total meridional transport calculated from the top-of-the-atmosphere heat flux (incoming solar minus outgoing long-wave radiation) observed directly by satellite.

2. by integrating estimates of air-sea heat fluxes, such as those shown in Fig. 11.4, to obtain the zonal average of the meridional heat flux (an example is shown in Fig. 11.2). If a steady state prevails, the meridional integral of the zonal average of Qnet must be balanced by heat transport in the ocean (see

Eq. 11-11) and so yields an estimate of meridional ocean heat transport at latitude p thus:

Vl J

QnetdidV, (11-12)

where the latitude is chosen so that —1

Hocean (p1 ) = 0. Equation 11-12 simply says that in the steady state the heat flux through the sea surface integrated over an area bounded by two latitude circles and meridional coasts, must be balanced by a horizontal heat flux into (or out of) the region, as depicted in Fig. 11.26. Essentially this is how the ocean-ographic contribution to Fig. 8.13 was computed. Note that if Qnet < 0, then -1

3. by attempting to directly measure Ho from in situ ocean observations making use of hydrographic sections, such as Fig. 11.23.

In Fig. 11.27 we show estimates of Hocean for the world ocean and by ocean basin, computed as a residual using method 1 (note the error bars can reach 0.5 PW). The total peaks at about ±2PW at ±20°, with the magnitude of the northward flux in the northern hemisphere exceeding, somewhat, the southward flux in the southern hemisphere. In the northern hemisphere, both the Atlantic and Pacific Oceans make large contributions. In the southern hemisphere,

FIGURE 11.26. Schematic of the computation of meridional ocean heat transport from net air-sea heat flux, Eq. 11-12. The sea surface is at the top, the ocean bottom at the bottom. At the latitude p it is supposed that the meridional heat flux vanishes.

heat is transported poleward by the Pacific and Indian Oceans, but equatorward by the Atlantic!

Figure 11.27 suggests that:

1. the overall magnitude of Hocean is a significant fraction (perhaps 1/4 to 1/3) of the pole-equator heat transport (see Section 11.5.2 below), but

2. the three major ocean basins—the Atlantic, the Pacific, and the Indian Ocean—differ fundamentally in their contribution to H^cean.

In the Pacific Ocean, the heat flux is symmetric about the equator and directed poleward in both hemispheres. In the Indian Ocean (which does not exist north of 25° N) the heat transport is southwards on both sides of the equator. In the Atlantic, however, the heat transport is northward everywhere, implying that in the south Atlantic heat is transported equatorward, up the large-scale temperature gradient. Remarkably, in the Atlantic there is a cross-equatorial heat transport of about 0.5 PW (cf. Fig. 8.13) and convergence of heat transport in the North Atlantic. Indeed poleward of 40° N the Atlantic Ocean is much warmer (by as much as 3°C) than the Pacific (see the map of sea-surface temperature in Fig. 9.3).

Why are heat transports and SST so different in the Atlantic and Pacific sectors? It is thought to be a consequence of the presence of a vigorous overturning circulation in the Atlantic which is largely absent in the Pacific. To see this consider Fig. 11.28 (top) which presents a quantitative estimate of the circulation of the global ocean separated into 3 layers: shallow (top km), deep (2 to 4 km), and bottom (>4 km). The arrows represent the horizontal volume transport (in Sv) in each of the layers across the sections marked. The circles indicate (© for upwelling, ® for downwelling) the vertical transport out of the layer in question marked in Sv. Thus, for example, 15 Sv of fluid sinks out of the shallow layer in the northern North Atlantic: 23 Sv of fluid travel south i

FIGURE 11.27. Northward heat transport in the world ocean, Hocean, and by ocean basin calculated by the residual method using atmospheric heat transport from ECMWF and top of the atmosphere heat fluxes from the Earth Radiation Budget Experiment satellite. The vertical bars are estimates of uncertainty. From Houghton et al. (1996), using data from Trenberth and Solomon (1994).

FIGURE 11.27. Northward heat transport in the world ocean, Hocean, and by ocean basin calculated by the residual method using atmospheric heat transport from ECMWF and top of the atmosphere heat fluxes from the Earth Radiation Budget Experiment satellite. The vertical bars are estimates of uncertainty. From Houghton et al. (1996), using data from Trenberth and Solomon (1994).

in the deep layer across 25S in the Atlantic Ocean. Around Antarctica 8 Sv of deep water upwells to the shallow layer, while 21 Sv sinks in to the bottom layer. We see that the Antarctic Circumpolar Current carries a zonal transport of around 140 Sv, evenly distributed between the layers. Note the much weaker overturning circulation in the Pacific with no sinking of fluid in the northern North Pacific.

Figure 11.28 (bottom) is a gross but useful cartoon of the upper branch (shallow to deep) overturning circulation highlighting the asymmetry between the Atlantic and the Pacific and between the northern and southern hemispheres. We see that a major pathway accomplishing northward heat transport in the Atlantic is the advec-tion of warm, near-surface water northward across the equator (see the northward flowing western boundary current crossing the equator in Fig. 10.13, bottom), cooling and sinking in the northern North Atlantic, and thence southwards flow of colder fluid as North Atlantic Deep Water. In contrast, the Pacific Ocean does not support a significant overturning cell induced by polar sinking. This is the key to understanding the different nature of heat transport in the basins evident in Fig. 11.27.

11.5.2. Mechanisms of ocean heat transport and the partition of heat transport between the atmosphere and ocean

Heat is transported poleward by the ocean if, on the average, waters moving polewards are compensated by equator-ward flow at colder temperatures. It is useful to imagine integrating the complex three-dimensional ocean circulation horizontally, from one coast to the other, thus mapping it out in a meridional plane, as sketched in Fig. 11.29. If surface waters moving poleward are warmer than the equatorial return flow beneath, then a poleward flux of heat will be achieved.

To make our discussion more quantitative we write down the meridional advection of heat thus (integration across the ocean is implied):

■top drefvôdz bottom top dTO

bottom dz

Vodd.

batttm.

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