Rate-Dependent Hysteresis of the Atlantic Meridional Overturning Circulation System and Its Asymmetric Loop

Abrupt climate changes have occurred repeatedly in the past when the Earth climate system was forced across a threshold. A hysteresis with saddle nodes is the best means to explain the abruptness of a climate system. Here, we study the dynamic hysteresis of the Atlantic Meridional Overturning Circulation (AMOC) with a Stommel's box model and an Earth system model subject to a freshwater flux forcing (FWF). In Stommel's box model, the area of the hysteresis loop increases with increasing FWF frequency, and thus an abrupt transition from the off-state to the on-state of the AMOC (opposite) occurs at lower (higher) FWF than in static hysteresis, referring a “lagged tipping.” In the Earth system model, the expansion/contraction of the hysteresis loop area as a function of FWF frequency is also observed. However, abruptness in the hysteresis is highly distinct in the off-to-on state than the on-to-off state due to asymmetric salt-advection feedback.