Bifurcation analysis of a nonlinear Filippov Atlantic Meridional overturning circulation under variable forcing

The Atlantic Meridional Overturning Circulation (AMOC) is integral to regulating the Northern Hemisphere’s climate. It moves warm surface water northward to the subpolar regions. There, the water cools, downwells, and flows southward as a deep current. Despite its importance, modeling the AMOC remains a major challenge. To address this, we propose a nonlinear Filippov model to simulate the progression of salinity and temperature in two vertical boxes representing the North Atlantic. The model formulates the net freshwater flux as a function of surface salinity and temperature, using the aerodynamic method. This flux represents the imbalance between evaporation and precipitation. Our approach provides a more realistic characterization of the AMOC dynamics. Filippov’s convex method is employed to identify the dynamics of the discontinuity boundary and establish the conditions for its various regions. We apply advanced bifurcation theories for Filippov systems to capture the model’s dynamic complexity. Furthermore, we conduct a bifurcation analysis via deriving analytical expressions for each bifurcation, yielding a bifurcation diagram that maps all dynamic possibilities. These findings are visualized by phase portraits showing typical behaviors and transitions, highlighting regions characterized by oscillations, bi-stability, and tri-stability. A previously unknown type of bifurcation, termed the double boundary fold bifurcation, is discovered. Our findings contribute to understanding and predicting the feedback mechanisms between climate change and variations in the AMOC. These insights are crucial for improving climate models and anticipating future climate variability influenced by AMOC dynamics.