Different reconstructions of glacial sea-surface temperatures (SST) are used to force a hybrid coupled atmosphereocean model. The resulting glacial states differ in global salinity and temperature distributions, and consequently in the strength of the thermohaline circulation. Stability analysis of the Atlantic Ocean circulation, by means of freshwater-flux hysteresis maps, reveals mono-stability for each glacial background state, which appears to be a robust feature of the glacial ocean. We show that this behaviour is directly linked to the hydrological cycle. A monotonic relation between the freshwater input necessary for reaching the off-mode and the hydrological budget in the Atlantic catchment area, accounts for the sensitivity of the oceanrsquos circulation. The most sensitive part of the hydrological balance appears to be in the tropical and subtropical regions suggesting that the lsquoAchilles heelrsquo of the global conveyor belt circulation is not restricted to the northern North Atlantic where convection occurs.