The Atlantic Meridional Overturning Circulation (AMOC) is a crucial component of the Earth's climate system, acting as a significant heat transporter. Its potential collapse is a major concern due to the projected severe consequences for the North Atlantic region and global climate patterns. Recent observations suggest a weakening of the AMOC, raising concerns about its stability. However, previous climate model intercomparison projects (CMIP), particularly CMIP5, have indicated a low probability of a full AMOC collapse within the 21st century. This assessment is based on large ensemble simulations, but there is growing concern about model biases and the inherent uncertainties involved in predicting tipping points in complex systems. This paper addresses these uncertainties by applying a rigorous statistical analysis to observed data, focusing on early-warning signals (EWS) to predict the likelihood and timing of an AMOC collapse. The study leverages the concept of early-warning signals (EWSs) which manifest as increased variance (loss of resilience) and increased autocorrelation (critical slowing down) before a critical transition. Recent studies have reported such signals for the AMOC. The primary goal is to provide a statistically robust framework for estimating the time of the tipping point using these EWSs, moving beyond simply observing trends in the EWSs and addressing the inherent statistical uncertainties involved.

Numerous studies, including model simulations and paleoclimatic reconstructions, link abrupt climate fluctuations, such as the Dansgaard-Oeschger events, to the bimodal behavior of the AMOC. Many climate models exhibit hysteresis, where changes in a control parameter (e.g., freshwater input) lead to AMOC bifurcations through saddle-node bifurcations. While state-of-the-art Earth-system models can replicate this behavior, the inter-model spread is substantial, and the critical threshold remains poorly constrained. The AR6 IPCC report, primarily based on CMIP5 models, judged a 21st-century collapse as very unlikely (medium confidence). However, CMIP6 models exhibit a larger spread in AMOC responses to warming, increasing uncertainty. Existing models suffer from biases like overestimated stability (due to tuning to historical data), poor representation of deep-water formation, salinity, and glacial runoff. These biases underscore the need for more robust methods to assess the risk of AMOC collapse.

The study uses an AMOC fingerprint derived from sea surface temperature (SST) data in the Subpolar Gyre (SG) region of the North Atlantic, spanning 1870-2020. This fingerprint is modeled using a stochastic differential equation (SDE) that incorporates a control parameter (Λ) representing the system's stability. The SDE is designed to capture the dynamics near a saddle-node bifurcation, a common characteristic of critical transitions. The authors focus on two early-warning signals: increased variance and increased autocorrelation. These are calculated from the observed AMOC fingerprint within running time windows (τw). Maximum likelihood estimation (MLE) is used to estimate parameters within these windows. The uncertainty in these estimates is quantified to determine the statistical significance of the observed EWSs. Crucially, the study does not assume a known control parameter; instead, it assumes a linear approach towards the critical value. Two independent methods are used to estimate the tipping time: a moment-based estimator (using variance and autocorrelation) and an approximate MLE directly on the nonlinear SDE. Bootstrap methods are employed to determine confidence intervals for the tipping time estimates. The study also calculates the probability of noise-induced tipping (n-tipping), where random fluctuations trigger a transition before the critical value is reached. The model uses a normal form of a co-dimension one saddle-node bifurcation which is supported by climate models showing a square-root dependence of the stable state on the control parameter.

The analysis reveals a statistically significant increase in both variance and autocorrelation in the AMOC fingerprint, starting around 1970. This indicates the system is moving towards a tipping point. Using two independent methods (moment-based estimator and approximate MLE), the study estimates the collapse will occur around 2057. The 95% confidence interval for this estimate is 2025-2095. Variance proves to be a more reliable EWS than autocorrelation, requiring a shorter observation window to detect significant changes. The analysis also considers the time scales involved: autocorrelation time (τac), ramping time (τr) over which the control parameter changes, and the required time window (τw) for detecting changes in EWSs. A linear ramping of the control parameter towards the critical value is assumed and confirmed by a close fit to the AMOC fingerprint data. The probability of noise-induced tipping is also incorporated into the analysis, indicating that the observed variance increase can be considered a reliable EWS within a specified range of control parameter values. Bootstrap analysis using 1000 model realizations provides confidence intervals for the tipping time estimates. The goodness-of-fit of the model is assessed using quantile-quantile plots of residuals, showing good agreement between model and data.

The findings demonstrate the significant risk of an AMOC collapse within the next few decades. This conclusion is supported by the robust statistical analysis of early-warning signals, going beyond simple trend detection and providing confidence intervals for the tipping time. The results have strong implications for climate change projections and mitigation strategies. The study acknowledges limitations, such as the model assumptions and the possibility of only a partial AMOC collapse. While the model captures essential dynamics, the exact nature of the AMOC's governing equations is not known, introducing potential uncertainty. Further research should investigate these aspects and analyze the specific nature of the tipping to determine if the collapse is partial or complete. Nevertheless, the clear statistical signal of an imminent collapse highlights the urgency for decisive action to reduce greenhouse gas emissions.

This study provides compelling evidence for an impending collapse of the AMOC, with a high probability of it occurring by mid-century. The rigorous statistical framework employed, accounting for uncertainties and noise-induced tipping, strengthens the prediction's robustness. While limitations exist regarding model assumptions and the potential for a partial collapse, the findings underscore the urgent need for effective climate change mitigation efforts to avoid this potentially catastrophic event. Future research should focus on refining the models, incorporating additional data sources, and investigating the full range of potential AMOC collapse scenarios. Continuous monitoring of the AMOC is critical to track its evolution and provide timely warnings of impending changes.

The study's main limitations stem from model assumptions. The model used simplifies the complex AMOC dynamics, and the true governing equations are unknown. The assumption of a linear approach to the critical value, while supported by the data, may not perfectly reflect the system's behavior. Additionally, the study focuses primarily on early-warning signals related to variance and autocorrelation, potentially overlooking other relevant indicators. The possibility of only a partial AMOC collapse, instead of a complete shutdown, is also acknowledged as a limitation. These uncertainties underline the importance of continued monitoring and research to refine the predictive capabilities.