A thorough analysis of the inter-hemispheric uncoupled Rooth 3-box model of Thermohaline Circulation (THC) is performed by perturbing separately the equilibrium moisture fluxes between the equatorial box and the two mid-high latitudes boxes and the target temperatures of the latter ones. The newly established equilibrium of the system is either qualitatively similar to the initial one, i.e. a northern sinking equilibrium, or radically different, i.e. presenting reversed THC.

High rates of increase in the northward moisture flux lead to a THC breakdown at smaller final increases than low rates, while the presence of southward moisture flux increases strongly inhibit the breakdown

Similarly, fast target temperature increases in the North Hemisphere destabilize the system more effectively than slow ones, and again the target temperature increases in the Southern Hemisphere tend to drive the system towards stability.

The lines describing the phase transitions of the system from the northern sinking to the southern sinking equilibrium are drawn in the parameters space analyzed for moisture fluxes (Figure 1) and target temperatures (Figure 2) perturbations. This provides an extensional of the usual quasi-static studies to the dynamical domain.

While increasing the ratio of the southward/northward moisture flux increase changes dramatically the overall shape of the phase transition line in such a way that thresholds appears, this is not the case for perturbations in the target temperatures; this provides evidence that the thermal and saline way of destabilizing the THC are not fully equivalent.