Beyond Critical Slowing Down: Slow Modes, Extreme Tails, and Field Decoherence in Tipping Transitions
Abstract
Tipping transitions are abrupt reorganizations between statistical regimes, usually anticipated through critical slowing down: recovery slows, autocorrelation and variance rise, and spectral power shifts toward low frequencies. In noisy, spatially extended systems, however, these signatures alone cannot distinguish weakening resilience, increasingly likely excursions toward a competing state, and spatial reorganization. We address these questions in the stochastic Ghil-Sellers energy balance model, whose ice-albedo feedback supports warm and snowball metastable regimes, through three viewpoints. Reduced Ruelle-Pollicott resonances and Kolmogorov modes diagnose relaxation and response in physically interpretable observables; Extreme Value Theory probes the accessibility and persistence of tail excursions; and Data-Adaptive Harmonic Modes diagnose the frequency-resolved organization of the temperature field. Near tipping, several reduced decay rates slow together and their modes become geometrically harmonized along a common transition direction, while Green functions show delayed recovery and enhanced low-frequency susceptibility only when the response residues are nonzero. Cold extremes become less sharply bounded and more clustered, and the full field becomes less compressible as its phase distribution broadens, even as a dominant low-frequency component emerges. Read jointly, these diagnostics reconcile apparently contrasting signatures and connect statistical indicators to the physical geometry of competing climate states. We further show that a small localized albedo change can create an additional pair of folds, so that a distance to tipping may carry structural as well as statistical uncertainty. The results provide a framework for interpreting early warnings that distinguishes changes in the system's dynamics from uncertainty in the model's bifurcation structure.
Related
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BibTeX
@misc{chekroun2026beyond,
title = {{Beyond Critical Slowing Down: Slow Modes, Extreme Tails, and Field Decoherence in Tipping Transitions}},
author = {Mickaël D. Chekroun and Valerio Lucarini},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.11350},
eprint = {2607.11350},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.11350},
}
RIS
TY - UNPB
TI - Beyond Critical Slowing Down: Slow Modes, Extreme Tails, and Field Decoherence in Tipping Transitions
AU - Mickaël D. Chekroun
AU - Valerio Lucarini
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2607.11350
UR - https://arxiv.org/abs/2607.11350
AB - Tipping transitions are abrupt reorganizations between statistical regimes, usually anticipated through critical slowing down: recovery slows, autocorrelation and variance rise, and spectral power shifts toward low frequencies. In noisy, spatially extended systems, however, these signatures alone cannot distinguish weakening resilience, increasingly likely excursions toward a competing state, and spatial reorganization. We address these questions in the stochastic Ghil-Sellers energy balance model, whose ice-albedo feedback supports warm and snowball metastable regimes, through three viewpoints. Reduced Ruelle-Pollicott resonances and Kolmogorov modes diagnose relaxation and response in physically interpretable observables; Extreme Value Theory probes the accessibility and persistence of tail excursions; and Data-Adaptive Harmonic Modes diagnose the frequency-resolved organization of the temperature field. Near tipping, several reduced decay rates slow together and their modes become geometrically harmonized along a common transition direction, while Green functions show delayed recovery and enhanced low-frequency susceptibility only when the response residues are nonzero. Cold extremes become less sharply bounded and more clustered, and the full field becomes less compressible as its phase distribution broadens, even as a dominant low-frequency component emerges. Read jointly, these diagnostics reconcile apparently contrasting signatures and connect statistical indicators to the physical geometry of competing climate states. We further show that a small localized albedo change can create an additional pair of folds, so that a distance to tipping may carry structural as well as statistical uncertainty. The results provide a framework for interpreting early warnings that distinguishes changes in the system's dynamics from uncertainty in the model's bifurcation structure.
ER -