Spectral-Gap Diagnostics for Greenland Ice Stability

Greenland ice-sheet stability reflects a fast–slow hierarchy: rapid seasonal and interannual variability in melt and outlet discharge occurs within slower geometric and thermodynamic feedbacks that can generate thresholds for long-run mass loss. Recent reconstructions and simulations report early-warning-like behavior in parts of Greenland, but tipping claims are hard to interpret because transitions may unfold over timescales longer than the satellite era and because observational products mix surface mass balance (SMB), dynamic thinning, and ice–ocean forcing differently. We apply the Trojan Universality Class (TUC) by framing Greenland resilience as a spectral-gap problem in a fast–slow stochastic system. Fast anomalies in melt rate, elevation change, and discharge are treated as perturbations that relax toward a slowly drifting background state governed by geometry (elevation and slope), firn condition, and ocean–atmosphere forcing. The analysis estimates a fast recovery rate from OU/AR(1) fits to detrended, phase-conditioned residuals, and a slow drift rate from sustained trends in SMB and geometry-linked proxies, including indicators tied to melt–elevation feedback. These are combined into a resilience margin that tracks how recovery competes with background drift. We also compute a regime-change statistic to detect structural shifts in forcing-to-response sensitivity, and an explicit observability score capturing record length, product dependence, residual-model adequacy, and instrument-era homogeneity. Calibrated in process-based model ensembles and mapped to observations with transparent observability reporting, the Greenland TUC atlas identifies where resilience loss is inferable, where it remains ambiguous, and which basins show the strongest evidence for destabilization.