The Instability of the Thermohaline Circulation in a Low-Order Model

Although the instability of the thermohaline circulation has been widely observed in numerical ocean models, theoretical advances have been hindered by the nonlinearity of heat and salt transports, a circulation governed by lateral temperature, and salinity gradients. Because the instability occurs initially in polar waters through the formation of haloclines and the halt of convection, any explanatory model must have at least a surface and a deep layer. The model proposed here (two surface boxes above a deep one) reduces to a 2 degrees-of-freedom dynamical system when convection is active and 3 degrees when it is interrupted. The instability that is induced by a negative freshwater perturbation in polar waters has three stages. The first stage is a rapid 5-yr adjustment to a transient thermal attractor that results from an approximate balance between heat advection and air–sea heat fluxes. The second stage is a slow evolution that self-organizes near this attractor, which preconditions the instability, as it can be shown that the circulation becomes more sensitive to changes in salinity gradients than in temperature gradients. The slow O(100 yr) growth of salinity in the subtropics is the critical precursor of the instability while at the same time the subpolar salinity rises against the initial perturbation to stabilize the system by increasing the overturning and restoring convection. When the overturning becomes smaller than the value at the unstable fixed point, the third stage occurs, which is when the subpolar salinity decreases at last on a fast O(10 yr) time scale, precipitating the fall of the overturning. During the last two stages of the instability, the horizontal thermal gradient increases, but its stabilizing effect is just barely unable to prevent the outcome. The return to stability occurs frequently through a regime of multidecadal oscillations with intermittent convection. The hypothesis of mixed boundary conditions has been relaxed by coupling the ocean box model to an atmospheric energy balance model to show that the coupling increases the stability of the oceanic circulation; however, the precursors of the instability are unchanged.