  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.
