Thermohaline circulation stability: a box model study - Part I:   uncoupled model
  A thorough analysis of the stability of the uncoupled Rooth interhemispheric 3-box model of thermohaline circulation (THC) is presented. The model consists of a northern high latitudes box, a tropical box, and a southern high latitudes box, which respectively correspond to the northern, tropical and southern Atlantic ocean. We adopt restoring boundary conditions for the temperature variables and flux boundary conditions for the salinity variables. We study how the strength of THC changes when the system undergoes forcings that are analogous to those of global warming conditions by applying to the equilibrium state perturbations to the moisture and heat fluxes into the three boxes. In each class of experiments, we determine, using suitably de- fined metrics, the boundary dividing the set of forcing scenarios that lead the system to equilibria characterized by a THC pattern similar to the present one, from those that drive the system to equilibria with a reversed THC. Fast increases in the moisture flux into the northern high-latitude box are more effective than slow increases in leading the THC to a breakdown, while the increases of moisture flux into the southern high-latitude box strongly inhibits the breakdown and can prevent it, in the case of slow increases in the Northern Hemisphere. High rates of heat flux increase in the North Hemisphere destabilize the system more effectively than low ones, and increases in the heat fluxes in the Southern Hemisphere tend to stabilize the system. 
Valerio Lucarini, Peter H. Stone