An inconsistency between two classical models of the ocean buoyancy driven circulation

A 2-layer version of the Stommel-Arons model of the abyssal circulation is shown to be inconsistent with the closure scheme used in Stommel's conceptual box model of the thermohaline circulation. The closure relates the strength of the exchange between 2 boxes, taken to represent the meridional overturning cell in the ocean, to the density difference between the boxes. Here, the Stommel-Arons model is used to argue that the difference in density, averaged over regions corresponding to Stommel's boxes, is not indicative of the rate of exchange between these regions. More generally, it is argued that to a good approximation, the zonally-averaged density field in the Stommel-Arons model is independent of both the sense and structure of the meridional overturning cell or cells. The reason for this is that, although the western boundary currents make an O(1)contribution to the zonally-averaged meridional transport, they have only a very small influence on the zonally averaged density field.