The Spectral-Gap View of AMOC Resilience

The Atlantic Meridional Overturning Circulation (AMOC) is a central component of the climate system and a prominent candidate for abrupt transition under sustained forcing. Continuous trans-basin observations at 26.5°N from the RAPID-MOCHA-WBTS array (since April 2004) and complementary subpolar measurements from OSNAP (deployed since summer 2014) provide unprecedented access to variability on subannual-to-interannual timescales, but they remain short relative to the multi-decadal processes believed to control long-run stability. Existing early-warning approaches fall broadly into two categories: (i) statistical early warning signals (EWS) that infer resilience loss from increasing autocorrelation and variance consistent with critical slowing down, and (ii) physics-based stability diagnostics that connect AMOC vulnerability to freshwater-transport and salt-advection feedback mechanisms, including the proposal that the AMOC-induced freshwater transport at the southern boundary exhibits a minimum close to collapse in targeted model experiments. Both approaches face a common obstacle: observational and reanalysis records are nonstationary, noisy, and method-dependent, and the climate literature has increasingly emphasized that "early warning" inferences can be ambiguous without explicit treatment of confounding mechanisms and data limitations. We introduce a unifying diagnostic framework that treats AMOC resilience as a spectral-gap problem in a fast-slow stochastic system: fast AMOC anomalies relax toward a slowly drifting manifold whose drift is controlled by freshwater forcing and stratification. We estimate a fast recovery rate () from an OU/AR(1) model fit to detrended AMOC residuals, define a slow drift rate () from the evolution of slow control proxies, and combine them into a dimensionless "gap margin" () = ()/(() +). We additionally compute (i) a resonance index () that detects increasing narrow-band/oscillatory concentration in AMOC residual variability, (ii) a regime-shift statistic () that flags changes in the forcing→response gain, and (iii) an observability score () that explicitly encodes whether the data support any early-warning inference. This pipeline provides a common coordinate system for comparing RAPID, OSNAP, fingerprint indices, and reanalysis products; it also clarifies which kinds of "warnings" correspond to genuine loss of timescale separation versus artifacts of nonstationarity or observability failure.