Ocean Gyres and Abrupt Change in the Thermohaline Circulation: A Conceptual Analysis

The implications are investigated of representing ocean gyre circulations by a diffusion term in the Stommel and Rooth box models of the thermohaline circulation (THC) in one and two hemispheres, respectively. The approach includes mostly analytical solution and study of the bifurcation structure, but also numerical integration and feedback analysis. Sufficient diffusion (gyre strength) eliminates multiple equilibria from either model, highlighting the need for accurate gyre circulation strength in general circulation models (GCMs) when considering the potential for abrupt climate change associated with THC shutdown. With diffusion, steady-state flow strength in the Rooth model depends on freshwater forcing (i.e., implied atmospheric water vapor transport) in both hemispheres, not only on that in the upwelling hemisphere, as in the nondiffusive case. With asymmetric freshwater forcing, two solutions (strong stable and weak unstable) are found with sinking in the hemisphere with stronger forcing and one solution with sinking in the other hemisphere. Under increased freshwater forcing the two solutions in the hemisphere with stronger forcing meet in a saddle-node bifurcation (if diffusion is sufficiently strong to prevent a subcritical Hopf bifurcation first), followed by flow reversal. Thus, the bifurcation structure with respect to freshwater forcing of the diffusive Rooth model of two-hemisphere THC is similar to that of the Stommel model of single-hemisphere THC, albeit with a very different dynamical interpretation. Gyre circulations stabilize high-latitude sinking in the Stommel model. In the Rooth model, gyre circulations only stabilize highlatitude sinking if the freshwater forcing is weaker in the sinking hemisphere than in the upwelling hemisphere, by an amount that increases with diffusion. The values of diffusion and freshwater forcing at which qualitative change in behavior occurs correspond to the range of the values used in and obtained with GCMs, suggesting that this analysis can provide a conceptual foundation for analyzing the stability of the interhemispheric THC, and also for the potential of the Atlantic THC to undergo abrupt change.