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

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.

• The paper demonstrates that the effectiveness of early-warning signals is highly sensitive to the choice and projection of observables onto the system’s critical slow manifold.
• A three-box model reveals that AMOC collapse can occur in both full and partial regimes through distinct bifurcation pathways driven by heterogeneous convection sites.
• Statistical extrapolations using conventional metrics often misestimate tipping times, underscoring the need for operator-theoretically informed observable construction.

Conceptual and Statistical Challenges in Early Warning for AMOC Collapse

Introduction

The paper "On early-warning of full versus partial Atlantic overturning circulation collapse" (2512.17142) critically examines the prospects and challenges of using early-warning signals (EWS) to anticipate tipping points (TPs) in the Atlantic Meridional Overturning Circulation (AMOC). It departs from the classical paradigm of singular, saddle-node bifurcation-induced collapse by considering a more physically representative scenario: a system with two spatially separated and heterogeneously forced deep water formation sites, allowing for intermediate (partial) collapses. The work demonstrates that the effectiveness and interpretability of EWS critically depend on the dynamical structure of the underlying model, the pathway of collapse, and most essentially, the choice and projection of observables.

Observational and Modeling Context

The AMOC is a dominant mode of oceanic heat transport impacting hemispheric climate, but long-term observational data are equivocal regarding its trend over the past century (Figure 1). Direct measurements (e.g., RAPID-MOCHA, OSNAP), proxy reconstructions (based on sea level and SST fingerprints), and paleoceanographic evidence provide weak, sometimes contradictory, signals regarding historical AMOC weakening. Numerical climate models ensemble projections exhibit a broad spread, attributable to both internal variability and model biases—in particular, biases that systematically favor AMOC stability due to an underestimation of critical positive feedbacks like salt-advection.

Figure 1: Observational time series and SST fingerprint proxies display substantial variability and limited trend robustness for AMOC strength.

Freshwater forcing (primarily from Greenland melt) remains the principal control parameter for tipping in canonical models, but estimates of the threshold required (0.2–0.5 Sv) vary considerably across model structures and resolutions. Recent eddy-resolving simulations suggest lower thresholds, amplifying uncertainty. The risk of collapse under plausible emission scenarios cannot be robustly excluded. This motivates non-model-dependent approaches, such as statistical early-warning via critical slowing down (CSD).

Conceptual Model: Distributed Convection and Partial Collapse

The study introduces a three-box model variant (Figure 2), explicitly distinguishing two northern convection sites with heterogeneous temperature and salinity atmospheric forcing. Unlike the classical single-site Stommel model, this setup enables both full and partial collapse regimes, with bistable or tristable state branches, depending on parameter choices.

Figure 2: Schematic AMOC box model with two polar convection sites, illustrating possible partial and full collapse flow regimes.

Bifurcation analysis (Figure 3, Figure 4) reveals regimes where an increase in freshwater forcing (parameter $\eta_2$) can induce sequential collapse: first, one convection cell reverses (partial collapse, PC), followed by the second, yielding a full collapse. Alternatively, the collapse can bypass intermediate PC states, depending on the interplay of coupled temperature and salinity gradients ($\delta_T$, $\delta_S$).

Figure 3: Bifurcation diagrams for different polar temperature heterogeneities demonstrate emergence of ON, OFF, and partial collapse branches.

Figure 4: Bifurcation projections for global and local observables, showing that ON, PC, and OFF states connect via distinct TPs depending on scenario.

Statistical Early-Warning Signals and Choice of Observable

EWS are predicated on the dynamical phenomenon of CSD, where system recovery rates to perturbations vanish near a saddle-node bifurcation (Figure 5). In multivariate systems, only observables that project significantly onto the critical direction associated with this vanishing eigenvalue will manifest measurable EWS.

Figure 5: The potential landscape flattens near the saddle-node, amplifying variance and autocorrelation of fluctuations.

Phase-space projections (Figure 6) clarify that noise-driven fluctuations become strongly anisotropic, primarily stretched along the direction linking the stable node to the saddle (edge state). Observables orthogonal to this direction (such as $q_1 = T_1 - S_1$, the density gradient in box 1) may fail to signal the upcoming collapse except extremely close to the TP.

Figure 6: Near-tipping, phase-space trajectories align with the slow manifold, and only select linear combinations ($T_1 + S_1$) capture amplified fluctuations.

Numerical simulation of stationary variance as a function of forcing (Figure 7) illustrates this dependency. Only observables aligned with the critical direction (e.g., $X_1 = T_1 + S_1$) show monotonic, strong increases in variance approaching the TP. Conventional choice observables (global $q$, local $q_1$, $q_2$) can exhibit weak, plateaued, or even non-monotonic EWS trends, particularly on branches bounded by multiple bifurcations or in scenarios with intermediate tipping.

Figure 7: Normalized variance vs. freshwater forcing for different observables showing pronounced trends only for carefully aligned observables.

Challenges in Extrapolating Tipping from EWS

Previous literature posited that time-to-bifurcation can be forecasted by extrapolating lag-1 autocorrelation (or variance) trends, implicitly assuming saddle-node normal form scaling ($\lambda^2 \propto \mu$) for the linearized restoring rate $\lambda$ (Figure 8). This assumption strictly holds only when extremely close to the TP and for observables which isolate the critical slow mode.

Figure 8: Linearization scaling for restoring rates; departure from normal form (concave/convex deviation) leads to systematic bias in extrapolated tipping time.

Both univariate and multivariate systems commonly violate this normal form scaling away from TP, resulting in systematically premature or delayed tipping predictions. For complex observables, or in systems where the TP is bounded on both sides (e.g., partial collapse branch), EWS trends are inconsistent, and extrapolation becomes unreliable or structurally biased.

Detailed ensemble-based simulations (Figure 9) confirm these theoretical expectations: predictions using poorly projected observables either fail to predict, predict with large uncertainty, or exhibit arbitrarily large estimation biases in both directions. Only observables that yield high signal-to-noise EWS near TP (typically, physically motivated or operator-theoretically constructed linear combinations) yield reduced uncertainty.

Figure 9: Practical extrapolation of tipping time using autocorrelation—accuracy and reliability grossly depend on chosen observable and regime.

Implications, Limitations, and Future Directions

The findings underscore the critical dependence of EWS-based collapse prediction on the physical and mathematical construction of observables. Deriving representative observables for CSD requires explicit knowledge of system dynamics—possibly via operator approaches, phase space analysis, or adjoint methods—rather than defaulting to global mean state metrics.

Partial collapse scenarios, multi-site deep convection, and spatio-temporal heterogeneity produce multiple branches, edge states, and intermediate TPs. These phenomena invalidate the assumption that EWS necessarily predict full system collapse. In situations where collapse is distributed or migratory, observed EWS may reflect local transitions (e.g., shutdown of Labrador Sea convection) rather than basin-wide AMOC reduction.

Moreover, bifurcation topology—multiple branches bounded by TPs—allows for non-monotonic EWS trends, further challenging extrapolation and interpretation. Statistical uncertainty in predicted tipping time, arising from normal form violation and observable projection ambiguity, can be unbounded unless system-specific constraints are imposed.

Theoretical extrapolation skills might improve with further development of machine-learned collective variables, operator-theoretic basis selection, and enhanced dynamical systems identification from data. Additionally, future climate model development should address the representation of critical feedbacks (e.g., salt-advection, convective, subpolar gyre) and resolve model biases that affect the stability and threshold estimation of the AMOC.

Conclusion

This paper demonstrates, via a conceptual multi-site box model and associated stochastic simulations, that:

• The existence and strength of statistical early-warning signals are highly dependent on the chosen observable. Observables that project onto the critical slow manifold capture CSD; default metrics (e.g., AMOC strength) often do not.
• Complex bifurcation structures permit intermediate and partial collapse states. EWS in standard observables cannot reliably distinguish whether a forthcoming TP results in full or partial AMOC collapse.
• Monotonicity and scaling assumptions underlying EWS extrapolation are generically violated in realistic, multivariate systems. Quantitative prediction of tipping time from EWS, absent observable optimality and sufficient proximity to TP, is precarious.
• Structural statistical uncertainty and ambiguity in EWS interpretation challenge their exclusive use for AMOC risk assessment.

These results establish the necessity for physically and operator-theoretically informed observable construction when applying EWS approaches to climate system tipping. Future research may focus on improved identification of critical variables, further fragmentation of deep convection zones, and reconciliation of model bifurcation structure with observational signatures.