The Atlantic Meridional Overturning Circulation (AMOC) constitutes a central component of the global climate system, influencing large-scale heat transport, regional climate variability, and long-term climate stability. Recent observational and modeling studies increasingly suggest that the AMOC may be approaching a critical transition, potentially associated with nonlinear dynamical behavior and abrupt weakening. This study synthesizes observation-based methodologies for detecting early-warning signals of AMOC instability using global and regional temperature datasets, statistical indicators of critical slowing down, and advanced spectral estimation techniques. Drawing on surface temperature reconstructions such as GISTEMP and HadCRUT5, the analysis emphasizes the role of variance, autocorrelation, and low-frequency spectral power as indicators of reduced system resilience. Particular attention is given to methodological challenges arising from non-stationarity, seasonal effects, and heteroscedasticity in climate time series. By integrating maximum entropy spectral analysis with heteroscedasticity-robust estimators of serial dependence, this work contributes to a more nuanced interpretation of emerging early-warning signals reported in recent literature. The results indicate that multiple independent indicators consistently point toward a long-term destabilization of the AMOC, although substantial uncertainty remains regarding the timing and magnitude of potential transitions. The study underscores the importance of combining physically informed climate understanding with statistically robust monitoring frameworks to improve early detection of large-scale climate tipping dynamics. These findings are relevant for climate risk assessment and for refining observational strategies aimed at monitoring critical components of the Earth system.

Atlantic Meridional, Overturning Circulation, early-warning signals, climate tipping points, spectral analysis, global temperature variability, critical slowing down

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