On early-warning of full versus partial Atlantic overturning circulation collapse

TL;DR

The paper introduces a minimal Stommel-type three-box AMOC model with two convection sites to study how spatial heterogeneity can lead to sequential tipping events and how early-warning signals depend on the monitored observable. It demonstrates that critical slowing down indicators are highly observable-dependent and may be non-monotonic, complicating predictions of tipping times and whether a collapse is partial or full. It also shows that extrapolating tipping times using saddle-node normal-form scaling can be unreliable in multivariate, non-normal settings, though observables aligned with the edge-state direction can yield more informative warnings near the bifurcation. Overall, the work highlights fundamental limitations of EWS for real-world AMOC tipping and underscores the need for physically informed observables and more complex multi-location dynamics.

Abstract

Climate models indicate a possible collapse of the Atlantic Meridional Overturning Circulation (AMOC) even for moderate climate change scenarios. There is considerable uncertainty in its likelihood for a given scenario and the critical global warming threshold. An alternative are early-warning signals (EWS) in AMOC fingerprints, which leverage generic statistical properties before destabilization of a steady state (a saddle-node bifurcation). But an AMOC collapse may be a sequence of partial collapses with shutdown of deep water formation in distinct regions. A conceptual model is presented featuring a sequential shutdown in two deep water formation regions. Multiple tipping points are present that do not follow the saddle-node normal form. As a result, the choice of the observable used to monitor EWS dramatically influences the prediction of the collapse via EWS. Various trends in EWS for different observables make it hard to determine what type of collapse (partial or full) will follow.

Figures (9)

• Figure 1: a Time series of observed and reconstructed changes in the AMOC circulation strength. Included are direct AMOC strength measurements from the RAPID array (red) and five hydrographic sections (blue dots) BRY05KAN10, as well as a reconstruction based on sea level anomalies (green) FRA15. The longest time series (black) is the sea surface temperature fingerprint RAH15 sometimes used as proxy for AMOC strength. Shown is the anomaly of sea surface temperatures in the North Atlantic subpolar gyre with twice the global mean sea surface temperature anomaly to correct for global warming and polar amplification, as was used in DIT23. b Climatology of the mixed layer depth for the month of March from the GLORYS reanalysis (period 1993 to 2024).
• Figure 2: Schematic of the three-box AMOC model. In the foreground is the larger equatorial box, and in the background are two northern polar boxes. The overturning flow $q_1$ and $q_2$ between the boxes at the bottom and surface is represented by the red arrows. The direction of the arrows represents the present-day, temperature-driven AMOC 'ON' state with $q_1>0$ and $q_2>0$. As in Stommel's model STO61, a reversed and weaker salinity-driven circulation state can exist for either of the polar boxes, in which case $q_i<0$ and the arrows to and from a given polar box are reversed. If the circulation is reversed for both polar boxes it corresponds to a fully collapsed AMOC 'OFF' state. If only reversed for one polar box it is a partially-collapsed (PC) state.
• Figure 3: Bifurcation diagrams of the box model with respect to the freshwater forcing parameter $\eta_2$, for five different values of the heterogeneity in surface temperature forcing $\delta_T$. Solid (dashed) lines are stable (unstable or saddle) fixed points. Open circles mark saddle-node bifurcations, or, as found in d, fold bifurcations of two saddle points.
• Figure 4: Bifurcation diagrams with respect to the freshwater forcing parameter $\eta_2$ for the three observables $q$, $q_1$, and $q_2$. For scenario I ( a-c) $\delta_T = -0.15$ is chosen, i.e., box 1 is forced fresher and warmer than box 2. In scenario II ( d-f) $\delta_T = 0.02$ is chosen, such that box 1 is forced fresher but slightly cooler.
• Figure 5: Changing potential landscape $V_{\mu}(x)$ for a one-dimensional system described by the saddle-node normal form $\dot{x} = -\partial_x V_{\mu}(x) = x^2 + \mu$. As $\mu$ is increased, the stable node (red) and the saddle point (green triangles) approach each other, and at the critical value $\mu_c = 0$ they collide and no more fixed point exists. If the system is perturbed away from the stable node, it takes increasingly long to relax back (purple balls). When driven by small, random perturbations, the fluctuations around the stable node become increasingly large and correlated (see red timeseries).