Part I: A thorough analysis of the stability of the uncoupled Rooth inter-hemispheric 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 defined 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 where the THC is reversed. Fast increases in the moisture flux into the northern high latitude box strongly inhibits the breakdown and can prevent it, in the case of slow increases in the Northern Hemisphere. Similarly, high rates of heat flux increase in the Northern Hemisphere destabilize the system more effectively than low ones, and increases in the heat fluxes in the Southern Hemisphere tend to stabilize the system. (© 2005 American Meteorological Society)

Part II: This study follows a similarly structured analysis on an uncoupled version of the same model presented in Part I. Since we are dealing with a coupled model, a direct representation of the radiative forcing is possible, because the main atmospheric physical processes responsible for freshwater and heat fluxes are formulated separately. Each perturbation to the initial equilibrium is characterized by the total radiative forcing realized, by the rate of increase, and by the North-South asymmetry. Although only weakly asymmetric or symmetric radiative forcings are representative of physically reasonable conditions, we consider general asymmetric forcings, in order to get a more complete picture of the mathematical properties of the system. The choice of suitably defined metrics allows us to determine the boundary dividing the set of radiative 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 where the THC is reversed. We also consider different choices for the atmospheric transport parameterizations and for the ratio between the high latitude to tropical radiative forcing. We generally find that fast forcings are more effective than slow forcings in disrupting the present THC patterns, forcings that are stronger in the northern box are also more effective in destabilizing the system, and that very slow forcings do not destabilize the system whatever their asymmetry, unless the radiative forcings are very asymmetric and the atmospheric transport is a relatively weak function of the meridional temperature gradient; in this latter case we present the analysis of the bifurcations of the system. The changes in the strength of the THC are primarily forced by changes in the latent heat transport in the hemisphere, because of its sensitivity to temperature that arises from the Clausius-Clapeyron relation.