Diagnosing the Atlantic Meridional Overturning Circulation under density surfaces is critical in the context of abrupt climate change

The Atlantic Meridional Overturning Circulation (AMOC) is a crucial component of our climate system, influencing water mass formation and transformation. It is driven by buoyancy fluctuations and mixing within the water column. The AMOC is often studied using climate models by calculating strength indexes based on constant depth intervals (z-AMOC). However, at high latitudes, where deep water forms in the Atlantic, isopycnals are much steeper than in subtropical regions. This means that the z-AMOC framework may not fully capture the processes involved in interior ocean ventilation due to its failure to consider density gradients. To address the potential biases of the z-AMOC approach, we calculate the AMOC using density surfaces (ρ-AMOC). We compare the z-AMOC and ρ-AMOC frameworks under three scenarios: Pre-Industrial (PI), historical, and quadrupled PI CO₂ concentrations (4xCO₂). The PI and historical simulations serve as a testbed for evaluating the frameworks, while the 4xCO₂ scenario is crucial for assessing climate sensitivity and natural variability in response to extreme CO₂ levels. We also analyze water mass transformations driven by surface-induced and interior-mixing processes.

Our findings reveal that both the location and strength of AMOC maxima are significantly influenced by the choice of framework. Under constant depth coordinates, the AMOC reaches a maximum transport of 21 Sv at approximately 35^oN, while it achieves around 25 Sv at 55^oN when calculated from density surfaces for both PI and historical climates. In the 4xCO₂ scenario, both frameworks show an abrupt weakening of the AMOC, linked to sea-ice melting and reduced deep convection, followed by a gradual recovery to maximum values of 10-15 Sv due to increased evaporation and salt export to the North Atlantic. Furthermore, we find that the z-AMOC maxima time series correlates more closely with those at 26^oN (r ~ 0.7) than with ρ-AMOC maxima (r ~-0.3). This discrepancy arises from the flatter isopycnals in the z framework, even in the subpolar North Atlantic where isopycnals are actually steeper. Based on these results, we argue that the density framework better represents the physics of AMOC by directly incorporating water mass transformations and their density structure.

We indicate that including the density framework in climate model output configurations enhances our understanding of uncertainties regarding future climate change impacts. The AMOC is a critical climate tipping point, and there is currently no consensus on its future behavior. Calculating ρ-AMOC also becomes especially relevant when considering the 4xCO₂ scenario as the AMOC shutdown and recovery in both frameworks driven by different processes indicates that the z-AMOC depicts the right patterns based on incorrect underlying mechanisms. This inconsistency introduces additional uncertainties to conclusions draw in studies addressing future AMOC strength and variability derived from the z-AMOC framework. Finally, we suggest that analysis across timescales and under different conditions must be performed with density surface outputs as much as possible, to enable a more comprehensive evaluation of these two frameworks and their applications.