Stability of the interhemispheric thermohaline circulation in a coupled box model

The coupled atmosphere–ocean box model of the interhemispheric thermohaline circulation (THC) formulated by Scott et al. [Scott, J.R., Marotzke, J., Stone, P.H., 1999. Interhemispheric THC in a coupled box model. J. Phys. Oceanogr., 29, 351–365.] is solved analytically, by introducing the approximation that the time variations of salinity in the ocean are much slower than the time variations in the temperature. The analytic solution shows that there is an unstable limit cycle near the bifurcation where the flow becomes unstable, as suggested by Scott et al.'s numerical solutions. The solution also leads to an analytic expression for the conditions under which the instability discovered by Scott et al. sets in, which is more general than that found by Scott et al. In particular, it includes the effect of coupling the THC to the atmospheric meridional transports of heat and moisture. It shows that the stability of THC is much more sensitive to the representation of the atmospheric heat transport, i.e., to how it depends on the meridional temperature gradient, than it is in hemispheric models. In particular, it shows that interhemispheric ocean models that use mixed boundary conditions, or couple the ocean to a diffusive representation of the atmospheric heat transport, are less susceptible to this kind of instability than when the ocean is coupled to a representation of the atmospheric meridional heat transport which is more sensitive to the meridional temperature gradient, as is implied by observations and theory.