Figure 3.2 shows the original set-up of Stommel’s two-box model for the THC. North-south exchange of water between a low-latitude box (left) and a high latitude box (right) is parameterized as a function of the density difference between the two boxes. H denotes the freshwater forcing, the flux of freshwater through the atmosphere from low latitudes to high latitudes or equivalently, as shown here, the flux of salt through the atmosphere from high latitudes to low latitudes.
The circulation consists of a volume flux q taken to be proportional to the density difference between high and low latitudes. If q > 0, there is poleward surface flow because high-latitude density is greater than low-latitude density, and vice versa. At low latitudes, the ocean gains heat from and loses freshwater to the atmosphere; the opposite is true at high latitudes. Consequently, both temperature and salinity are higher at low latitudes than at high latitudes. This has opposite effects on density. When q > 0, the temperature difference dominates the density difference and drives the circulation, whereas the salinity difference brakes it, and vice versa. The situation q > 0, with sinking implied at high latitudes, is familiar from the North Atlantic and describes today’s active THC.
In a plausible limiting case (Marotzke, 1990), the box temperatures are assumed to be imposed by the atmosphere, as is the surface freshwater exchange. A new addition to the system is horizontal diffusion. It reflects the transport of salinity by the ocean gyres, the systems of ocean circulation characterized by swift currents near the western boundary and slower return flows farther eastward, occurring at virtually the same depth. Understanding the effect of ocean gyres on the stability of the THC is crucial, and the models currently used are likely to distort this influence because of their low spatial resolution.
Two cases are considered here. The “standard” case is the classical THC box model with only very weak diffusion; the other case will be designated “diffusive.” In the example shown, the diffusive case has a different proportionality factor relating density differences to flow strength, such that with the same freshwater forcing, the two cases have very similar strengths of the “normal” North Atlantic THC.
imply that the real THC displays hysteresis and the possibility of abrupt change. Or would any transition be smooth, on the time scale of the forcing change, and be reversible? Simulations with comprehensive three-dimensional GCMs show both types of behavior. An ocean model with relatively large diffusion, caused by the choice of the numerical scheme, exhibits a transient behavior very similar to the upper dashed curve in Figure 3.4 when a slow freshwater flux perturbation is applied to the North Atlantic (Mikolajewicz and Maier-Reimer, 1994). A less-diffusive coupled model