Global stability of the Atlantic overturning circulation: Edge state, long transients and boundary crisis under CO$_2$ forcing

Abstract

The Atlantic Meridional Overturning Circulation (AMOC), a crucial ocean current system, could transition to a weak state. Despite severe associated climate impacts, assessing the AMOC's response under global warming and its proximity to possible critical thresholds remains difficult. To understand future Earth system stability, a global dynamical view is needed beyond the local stability analysis underlying classical early-warning methods. Using an intermediate-complexity climate model, we explore the stability landscape of the AMOC for different atmospheric CO$_2$ concentrations. We explicitly compute the edge state (or Melancholia state), a chaotic saddle on the basin boundary separating the strong and weak AMOC attractors found in the model. While being unstable, the edge state can govern the transient climate for centuries, supporting centennial AMOC oscillations driven by atmosphere-ice-ocean interactions in the North Atlantic. At increased CO$_2$ levels projected for the near future, we reveal a boundary crisis where the current AMOC attractor disappears by colliding with the edge state. Under crisis overshoot, long chaotic transients due to "ghost states" lead to diverging ensemble trajectories under time-varying forcing. Rooted in dynamical systems theory, our results offer an explanation of large ensemble variance and apparent "stochastic bifurcations" observed in earth system models under intermediate forcing scenarios.

Figures (18)

• Figure 1: AMOC bistability in PlaSim-LSG at CO$_2$. (a) and (b) show the Atlantic meridional overturning streamfunction for ON and OFF, respectively. (c)-(h) show anomalies of OFF relative to ON for (c) surface air temperature, (d) precipitation, (e) zonal wind speed in the mid-troposphere (around 300-800 hPa), (f) sea surface temperature, (g) sea surface salinity, and (h) oceanic convection depth. All panels are computed from 1000-year time averages.
• Figure 2: Edge tracking method, illustrated (a) in the schematic quasipotential landscape of a bistable AMOC and (b) as idealised timeseries projected onto the coordinate $u$ (in our context, the AMOC strength). The landscape shows the basins of attraction of the attractors $\bm x_A$ (orange shading) and $\bm x_B$ (blue shading), separated by the basin boundary (green dashed). Starting from $\bm x_a$ and $\bm x_b$, three exemplary iterations (as numbered) yield a pseudotrajectory (green solid line) that leads close to the edge state $\bm x_M$. Gray dashed lines indicate the bisections.
• Figure 3: Edge tracking and AMOC states at 360ppm CO$_2$. (a) Interpolating initial conditions between the ON (orange) and OFF (blue) AMOC state allows locating the basin boundary. (b) Iterations 2-5 of the edge tracking algorithm, showing the trajectories that converge to ON (orange) and OFF (blue), respectively. The edge pseudotrajectory (green) is constructed from segments of these trajectories. (c) Edge trajectory (green) and trajectories on the ON (orange) and OFF (blue) attractors. The AMOC strength is measured between 46-66$^\circ$N.
• Figure 4: State space projection onto the meridional SG, vertical SG, and salinity anomaly in the deep North Atlantic (below 1000 m, north of $50^\circ$S). Faint orange (blue) lines show trajectories relaxing from near the edge state to the ON (OFF) state. Arrows indicate the time direction.
• Figure 5: Energetics of the climate states. (a) Imbalance of top of the atmosphere radiation (left) and heat flux at the sea surface (right), integrated over the globe for ON, OFF and Edge (negative imbalance means the Earth/ocean is losing energy). (b) Oceanic enter of mass anomaly $\Delta h$ (relative to 1970.3126 m below sea level) for years 200-1400 of the edge trajectory and corresponding time intervals for ON and OFF. The 400-year long relaxation paths from Edge$\to$ON (beige) and Edge$\to$OFF (light blue, plotted in reverse time) are shown for one of the edge tracking iterations. (c) Northward meridional heat transport, showing the total from atmosphere and oceans (for ON, orange) and the oceanic contribution (all states, dotted). Bottom inset: Difference in total (solid) and oceanic (dashed) heat transport for OFF (blue) and Edge (green) relative to ON. (d) Oceanic heat transport in the Atlantic basin only, showing the variability of the AMOC oscillation on the Edge state (green band).