Persistent memory and tail-risk amplification in Atlantic Meridional Overturning Circulation variability: a Volterra integral framework calibrated with CMIP6

Abstract

The Atlantic Meridional Overturning Circulation (AMOC) carries multi-decadal memory that ensemble-mean risk projections do not capture. We quantify this memory and its consequences for tail risk with a Volterra integral framework applied to ensemble-mean-subtracted variability in 14 CMIP6 models (1850-2100, three SSP scenarios), so that results reflect intrinsic thermohaline memory rather than the common anthropogenic forcing trend. Four results follow from leave-one-out cross-validation and an annealed-quenched tail decomposition. First, the ensemble-mean DFA1 Hurst exponent is H = 0.781 +/- 0.219, with 12 of 14 models showing long-range dependence (H > 0.5), consistent with thermohaline adjustment timescales near 33 yr. Second, a first-order Volterra model reduces out-of-sample RMSE by 16.8% over the best autoregressive baseline and by 12.3% over an unconstrained 20-lag distributed baseline, both robust to 200 circular-shift placebos (p < 0.05): the physically motivated kernel shape carries genuine predictive advantage. Third, the rolling 30-year lower-tail frequency rises 1.9-3.1x above the historical baseline depending on scenario, and the memory amplification index exceeds 1 in 8 of 14 models under SSP5-8.5 (median 1.15): persistence-driven clustering of weak-AMOC states amplifies tail frequency beyond forcing-only projections. Fourth, model-specific optimal memory horizons (15-52 yr) correlate with thermohaline regime (r = 0.74, p < 0.01), and the ensemble-mean Hurst exponent already exceeds a detection threshold H* = 0.70 in 9 of 14 models, with theoretical lead times to near-tipping conditions of 10-35 yr depending on scenario. These results support trajectory-specific, memory-aware AMOC risk assessment under moderate-to-high forcing and a physically grounded, scenario-conditional early-warning framework.