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The equatorial zone of the earth receives more energy per surface unit from the sun in the form of short-wave radiation than the polar regions because of the spherical form of the earth. The resulting temperature difference between the equator and the poles leads to meridional heat transport by the atmospheric and the oceanic circulation, both parts of the climate system. In its turn this heat transport mitigates the extreme cold and heat, caused by the differential heating by the sun and is responsible for a moderate global climate and a habitable earth.

The oceans cover over 70% of the earth with a relatively thin layer of water. The earth is a slightly flattened sphere with an effective radius of 6371 km. On this sphere topographic relief is present which forms continents and deep basins; the latter contain the oceans. Within the oceans the currents in the upper 1000 to 1500 m are mainly driven by wind stress at the sea surface. The deep cold branch of the THC, below the wind-driven layer, is for a large part constrained and guided by the topography of the ocean basins and their interconnections.

Pressure is the force exerted on a unit surface that is oriented perpendicular to the direction of that force. According to the international system for weights and measures (the SI system) the unit for pressure is Pascal, with symbol Pa, equivalent to N/m^2 (SUN 1985). The pressure in sea is one of the thermodynamic variables of seawater, determining together with temperature and salinity a range of seawater properties, e.g., density, specific heat, sound velocity, etc. (Fofonoff and Millard 1983). The net force, exerted by a pressure gradient on a water parcel, also is one of the main driving forces of the THC. The pressure used in oceanography is generally the sea pressure, P , which is the actual pressure minus one standard atmosphere (= 101 325 Pa). When the oceanic motions are restricted to low frequencies (no surface waves, internal waves, or convective motion), vertical accelerations can be ignored and the vertical momentum equation is to a very high accuracy approximated by the hydrostatic equilibrium: $$ \frac{{\partial P}} {{\partial z}} = - \rho g.(3.1) $$ Here z is the vertical coordinate (upward positive), ρ is the density of seawater and g is the gravitational acceleration. With ρ ≈ 1000 kg/m^3 and g ≈ 10 m/s^2 the pressure in sea increases with about 10,000 Pa for each depth increment of 1 m. In oceanography the use of the non-SI unit decibar (symbol dbar) is allowed. A pressure increase of 1 dbar (10^4 Pa) corresponds numerically with a depth increase of about 1 m.

The THC is essentially a meridional, vertically overturning circulation system with its sources of deep and bottom water at high latitudes, both in the northern and the southern hemisphere. A useful way to study the THC, following the example set by the German oceanographer Georg Wüst (1935), is the analysis of meridional vertical sections of the tracers potential temperature, θ, and salinity, S . Both parameters are conservative, which means that outside the direct influence of air-sea interaction in the upper ocean the salinity and potential temperature of a water particle only change due to mixing. The conservation of potential enthalpy is fundamentally a better approximation of the first law of thermodynamics (Fofonoff 1962; McDougall 2003), but for most oceanographic applications the conservation of potential temperature and of salinity function quite well. The “spreading path” of the cold deepwater, formed in high latitude source regions, often is derived from sections of potential temperature and salinity by a combination of intuition and physical reasoning. In this section we start, as an example, with the distribution of potential temperature and salinity in the Atlantic Ocean, since the main sources of deepwater, both arctic and antarctic, are found in that ocean.

As was described in the previous chapter, the cold branch of the THC in the Atlantic Ocean brings the saline core of NADW to the latitude of the southern tip of Africa (≈35°S) from where it can enter the southern Ocean (Fig. 5.1). The NADW core overlies fresher AABW which appears to spread northward from the Southern Ocean into the Atlantic.

The major features of the spreading of deep and bottom water from their source regions can be derived from the distributions of oceanographic tracers, as was illustrated in the previous two chapters. Mass conservation constraints require a return flow at shallower depths to bring the deep and bottom water back to their formation regions. Deep upwelling brings these cold water masses from abyssal depths in the ocean basins to shallower levels, either in the Southern Ocean or in the subtropical and tropical ocean basins and the subarctic, including the Atlantic Ocean. The temperature and salinity will adapt to the shallow boundary conditions by diapycnal mixing with the overlying waters, determined by atmosphere-ocean interaction, and the density of the upwelling waters will decrease. The upwelling in the Southern Ocean brings water directly into the ACC. The ACC enables zonal exchanges of this water between the different basins in the Southern Ocean where AABW and AAIW is formed. In Chapter 5 it was already shown that aged deepwater from the Indian and Pacific oceans is exchanged zonally between the different oceans by the ACC (UCDW). Deepwater that enters the thermocline in the Indian and Pacific oceans by upwelling has to follow another route to reach the source regions of NADW in the North Atlantic Ocean (Gordon 1986). Different pathways have been proposed for the interocean exchange of thermocline water (Gordon 2001).

The high-density water types that contribute to the deep water masses of the THC are primarily formed by air-sea interaction in winter. During this process the sea surface loses heat and warms the atmosphere. The heat loss leads to an increase of the sea surface density. An additional increase of the surface density may be caused by the formation of sea ice. Not all the salt dissolved in the seawater will be incorporated in the newly formed sea ice. The remaining concentrated salt solution — brine — increases the surface salinity and thereby the surface density. The latter process is called “brine rejection”. Due to the increase in surface density by cooling and brine rejection the upper parts of the water column can become unstable and convective mixing sets in, leading to a homogeneous water column extending downward from the sea surface.

In Chapter 3 it was stated that in major parts of the ocean, outside the thin turbulent boundaries near the sea surface and the bottom, the dynamics of the ocean circulation are well described by the geostrophic balance. There the pressure gradient balances the Coriolis force. This even applies in a reasonable approximation to the deep western boundary currents where friction modifies the flow. The pressure gradient, or at least its vertical change, is related to the density distribution and can be derived from observations of temperature and salinity according to Eq. (3.15). In order to maintain a mean meridional flow in the ocean, like in the THC, a zonal pressure gradient is required that will vary with depth, supporting, e.g., in the North Atlantic Ocean an equatorward flow in the NADW core and a poleward flow near the surface.

It has become clear from the oceanic tracer distributions, presented in Chapter 5, that in the deep Pacific and Indian oceans deep and bottom waters move upward to at least the levels of the aged deepwater like NIDW and the upper PDW, the so-called deep upwelling. In the Atlantic Ocean the deep upwelling is less clear. However, the existence of a DWBC and a DNBC in both the Pacific and Atlantic Ocean, in agreement with the Stommel-Arons model, indicate that deep upwelling of poleward flowing deepwater probably occurs in the Atlantic Ocean too. In the abyssal basins, where global upwelling occurs, a balance has developed between vertical advection of heat and salt, due to the upwelling velocity and the vertical turbulent diffusion of heat and salt. We follow in this chapter the reasoning of Munk (1966) and Munk and Wunsch (1998) with regard to this advective -diffusive balance. For any conservative tracer C , e.g., salinity or potential temperature, the conservation equation for a stationary distribution can be written according to (4.1), with the source term, Q , set to zero. This equation is here repeated as $$ u\frac{{\partial C}} {{\partial x}} + v\frac{{\partial C}} {{\partial y}} + w\frac{{\partial C}} {{\partial z}} = \nabla _h \cdot (K_h \nabla _h C) + \frac{\partial } {{\partial z}}\left( {K_v \frac{{\partial C}} {{\partial z}}} \right) \cdot (9.1) $$ The vertical (diapycnal) turbulent diffusivity, K _ν, is known to vary strongly with occasionally extremely high values (> 10^−1 m^2/s) in the benthic boundary layer, which may lead to fully mixed bottom layers with a thickness of the order of 100 m (Munk and Wunsch 1998).

The THC can be schematized in a simplified way as a vertically overturning circulation cell (Fig. 10.1) with a localized downwelling region. There the surface heat loss and/or evaporation to the atmosphere increases the surface density. Global upwelling occurs in the larger part of the ocean, whereby the surface density of the upwelled water is reduced by heating and/or precipitation from the atmosphere. The dense water mass, brought to large depths by the downwelling, spreads to other latitudes (and ocean basins) in the deep branch of the THC. The required return flow to the downwelling region takes place in the near-surface branch of the THC, where the water density increases downstream.