Warning of a forthcoming collapse of the Atlantic meridional overturning circulation

The study addresses whether the AMOC is approaching a critical transition (collapse) and, if so, when this tipping might occur. AMOC is a key climate tipping element; its collapse would strongly impact North Atlantic climate. While CMIP5/6 models assessed by IPCC suggest a 21st-century collapse is very unlikely, observed weakening and theory of critical transitions motivate searching for observational early-warning signals (EWS) such as increased variance (loss of resilience) and autocorrelation (critical slowing down). The authors aim to (1) establish statistical significance of observed EWS in an AMOC fingerprint derived from sea surface temperatures (SST) and (2) provide data-driven estimates of the tipping time without assuming a known external control parameter trajectory, only that it approaches the critical threshold quasi-linearly over time.

The paper situates its work within: (a) modeling and paleoclimate evidence linking abrupt Dansgaard–Oeschger events to AMOC bistability and hysteresis, where freshwater forcing can induce saddle-node bifurcations; (b) CMIP5/6 Earth-system model results with large inter-model spread and potential biases that may overestimate AMOC stability (e.g., tuning to historical climate, representation of deep water formation, salinity, glacial runoff); (c) theoretical EWS literature on critical slowing down and variance increase derived from fluctuation–dissipation; (d) observation-based AMOC EWS reports (e.g., Boers 2021); (e) AMOC monitoring since 2004 and longer-term SST-based AMOC fingerprints from the Subpolar Gyre (SG) region supported by model ensembles. The authors note uncertainties in freshwater flux components and the potential use of global mean temperature as a control parameter proxy in prior work, while here they avoid specifying a particular driver beyond quasi-linear approach to a threshold.

Data and AMOC fingerprint: The AMOC strength is proxied using the Subpolar Gyre (SG) SST anomaly minus twice the global mean (GM) SST anomaly from HadISST (monthly, 1870–2020). Seasonal cycles are removed by monthly climatology. The 2× GM subtraction compensates for global warming and polar amplification, calibrated against observational MOC estimates (1957–2004), yielding an optimal factor near 2; robustness is checked using 1× and 3× GM subtractions. Modeling framework: The AMOC fingerprint x(t) is modeled as a stochastic process X following near a saddle-node bifurcation normal form with additive noise: dX = −Λ(X − m)^2 + λ dt + σ dB (Eq. 1), where m, Λ, λ are parameters; the stable state satisfies μ − m = √Λ, a saddle-node signature supported by steady-state curves from ocean and coupled models. The control parameter is assumed to begin ramping linearly at time t0 toward the critical value (λ = 0) per λ(t) = Λ(1 − Θ[t − t0](t − t0)/τr) (Eq. 2), where τr is the ramping time. The approach allows for noise-induced tipping (n-tipping) prior to reaching the deterministic bifurcation. Local linearization and EWS estimation: Within a sliding window Tw (e.g., 50 years), the dynamics are approximated by an Ornstein–Uhlenbeck (OU) process (Eq. 3): dX = −α(λ)(X − μ(λ)) dt + σ dB, with α the inverse correlation time. For fixed Λ, stationary mean μ, variance γ^2 = σ^2/(2α), and lag-1 autocorrelation ρ = exp(−αΔt) (Δt = 1 month). From windowed MLEs of μ, γ^2, and ρ, the parameters relate via α = −log ρ/Δt, σ^2 = 2αγ^2, and Δλ(t) = (σ^2/(4γ^2(t)))^2, enabling inference on the ramping trajectory. Baseline (pre-ramp) EWS values are compared to windowed estimates to detect significant increases. EWS detectability theory: Sampling variances for EWS estimators are approximated (Eq. 4), leading to analytic window-size requirements to detect departures from baseline at confidence level q: Tw > 2q^2/(â0 − â(t))^2 for variance (Eq. 7) and a larger requirement for autocorrelation (Eq. 8). These show variance as a more sensitive EWS than autocorrelation for given data length. Tipping-time estimation: Two complementary approaches are used: - Moment-based estimator: From running-window estimates of α(t) and σ^2(t) (after detrending data within each window), compute γ^2(t) and Δλ(t) = (σ^2/(4γ^2(t)))^2. Fit a linear ramp starting at t0 by least squares, scanning t0 between 1910–1950 and window size Tw, yielding an optimal t0 = 1924 and optimal window Tw = 55 years (Fig. 6e). A linear fit of Δλ(t) provides −Δλ0 = 2.34 yr^−1 and a ramping time τr = 133 years, implying a tipping year tc ≈ 2057. - Approximate maximum likelihood estimation (MLE): Before t0, exact OU MLEs estimate λ0, m, σ^2. After t0, the full nonlinear SDE likelihood is approximated using Strang splitting for transition densities (preferred over Euler–Maruyama for accuracy in nonlinear dynamics). With t0 = 1924, the optimal fit yields the same tc = 2057 with a 95% CI of 2025–2095. Noise-induced tipping and early-warning window: Using Kramers’ escape theory, the mean waiting time for n-tipping is derived, showing that near the bifurcation, n-tipping can precede deterministic tipping, limiting EWS usefulness. Analytical and simulation results delineate a green band of parameter space where increased variance provides reliable early warning for Tw = 50 years, whereas autocorrelation requires longer windows. Uncertainty quantification and model checking: Parametric bootstrap (1000 realizations) of model (1)–(2) with estimated parameters provides empirical confidence intervals for tc and other parameters, accounting for model-approximation uncertainty. The bootstrap mean ⟨tc⟩ ≈ 2050 with 95% CI 2025–2095. Model adequacy is assessed via uniform-to-normal residuals and Q–Q plots, indicating a good fit. Robustness checks using alternative fingerprints (SG − 1×GM, SG − 3×GM) shift the estimate by only years to decades while preserving conclusions.

- Statistically significant increases in variance and autocorrelation of the AMOC fingerprint are detected around 1970 relative to baseline, indicating loss of resilience and critical slowing down. - Tipping-time estimates: Best estimate tc ≈ 2057 (moment-based and approximate MLE methods consistent). Bootstrap mean ⟨tc⟩ ≈ 2050 with a 95% confidence interval 2025–2095; 66% CI reported for the main proxy in Table 1 is 2039–2070. - Early-warning signal efficacy: Variance requires shorter data windows than autocorrelation to detect significant changes at the 95% level, making variance the more reliable EWS for AMOC in available records. With a 50-year window, increased variance can be detected when λ(t) ≲ −1.2, whereas autocorrelation detection typically requires longer windows. - Ramping characteristics: Optimal initiation of ramping is estimated at t0 = 1924, with ramping time τr ≈ 133 years to the critical point under current trends. - Noise-induced tipping: As the system nears the bifurcation, the mean waiting time for noise-induced transitions can become shorter than the data window, limiting EWS predictability close to tipping. - Robustness across proxies: Using SG − 1×GM, SG − 2×GM (calibrated optimal), and SG − 3×GM fingerprints yields tipping estimates of 2083 (95% CI 2024–2180), 2057 (95% CI 2025–2095), and 2067 (95% CI 2034–2102), respectively. - Model fit and validation: Nonlinear likelihood with Strang splitting and OU pre-ramp approximation fits the data well (Q–Q residuals close to linear), supporting the modeling approach.

The findings provide evidence that the AMOC is approaching a critical transition, with EWS significantly elevated since about 1970. By translating observed changes in variance and autocorrelation into model parameters under a saddle-node bifurcation framework with a quasi-linear ramping control parameter, the study estimates a likely tipping in mid-21st century. Variance emerges as the more practical EWS given observational constraints, enabling earlier detection than autocorrelation. The integration of analytical detectability theory, rolling-window estimation, and nonlinear likelihood-based inference strengthens confidence in both detection and timing estimates. The results align with theoretical expectations of critical transitions and complement prior observational EWS studies, while offering quantified confidence intervals for tipping time. The study also delineates the limits of EWS utility due to potential noise-induced tipping near the threshold and emphasizes the societal relevance of a possible AMOC collapse, calling for continued monitoring and mitigation efforts.

The paper develops and applies a robust statistical framework to detect early-warning signals and estimate the timing of a critical transition in the AMOC based on an SST-derived fingerprint. It establishes statistical significance for increased variance and autocorrelation and predicts a likely AMOC collapse mid-century, with a best estimate around 2057 and a 95% CI of 2025–2095. The approach shows that variance is a more reliable EWS than autocorrelation for the available data lengths and provides analytical criteria for detectability. The methodology combines windowed OU approximations, nonlinear likelihood with Strang splitting, and bootstrap-based uncertainty quantification, and results are robust across reasonable choices of the SST fingerprint. Future work should apply the method to state-of-the-art model simulations with controlled linear ramping at various rates to assess model-specific predictability and further refine observational EWS strategies. Given the potential impacts, enhanced direct AMOC monitoring and rapid emissions reductions are urged.

- Model approximation: The AMOC fingerprint is modeled via a simplified stochastic normal form (saddle-node) with a quasi-linear ramping control parameter; real climate dynamics may deviate, and the true driver is not explicitly specified. - Proxy-based inference: Conclusions rely on an SST-based AMOC fingerprint (SG − k×GM); while calibrated and tested for robustness, it remains an indirect proxy and subject to SST dataset uncertainties and polar amplification assumptions. - Quasi-stationarity and windowing: EWS theory assumes approximate stationarity within windows; near tipping, this assumption weakens. Detection depends on chosen window size, which trades bias and variance. - Noise-induced and rate-induced tipping: Near the threshold, noise-induced tipping can precede deterministic tipping, limiting EWS predictability; rate-induced tipping could alter timing under faster forcing changes. - Partial tipping possibilities: Some models suggest intermediate or partial tipping states before full shutdown; the analysis cannot rule out partial rather than complete collapse. - Limited direct observations: Continuous direct AMOC observations exist only since 2004, necessitating reliance on longer proxy records for trend detection and timing inference. - Inter-model spread and biases: Known model biases and spread in AMOC stability complicate extrapolation, though the analysis is primarily data-driven.