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  Quantifying resilience in non-autonomous and stochastic Earth system dynamics with application to glacial-interglacial cycles

Harteg, J., Wunderling, N., Donges, J. F. (2026): Quantifying resilience in non-autonomous and stochastic Earth system dynamics with application to glacial-interglacial cycles. - Earth System Dynamics, 17, 3, 673-686.
https://doi.org/10.5194/esd-17-673-2026

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https://doi.org/10.5281/zenodo.16603222 (Code)
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 Urheber:
Harteg, Jakob1, Autor                 
Wunderling, Nico1, Autor                 
Donges, Jonathan Friedemann1, Autor                 
Affiliations:
1Potsdam Institute for Climate Impact Research, Potsdam, ou_persistent13              

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 Zusammenfassung: Understanding Earth resilience—the capacity of the Earth system to absorb and regenerate from perturbations—is key to assessing risks from anthropogenic pressures and sustaining a safe operating space for humanity within planetary boundaries. Classical resilience indicators are designed for autonomous systems with fixed attractors, but the Earth system is fundamentally non-autonomous and out of equilibrium, calling for new ways of defining and quantifying resilience.

Here, we introduce a path-resilience approach that assesses how perturbations deviate from and return to a reference trajectory of a conceptual climate model replicating the glacial-interglacial cycles of the Late Pleistocene. We generate two types of perturbation ensembles: a stochastic ensemble and a single-event ensemble, and compute two complementary metrics: the Reference Adherence Ratio (RAR)—defined as the fraction of stochastic trajectories that remain within a narrow band around the unperturbed trajectory—and return time—defined as the time a single perturbed trajectory takes to return to the reference path. Together, these metrics reveal strong temporal variation in resilience across the glacial-interglacial cycles. We find that RAR increases markedly during deglaciations and peaks in interglacial periods, while return times generally shorten as the system approaches interglacial conditions—indicating that certain phases of the cycles act as convergence zones and potential anchors of Earth system stability. As the Earth system departs from such stable interglacial regimes under ongoing anthropogenic forcing, understanding the resilience of these trajectories—and what it may take to return to them—becomes increasingly important.

These results highlight that resilience in non-autonomous systems is inherently path-dependent and illustrate a promising first step toward its quantification. Further research is needed to develop more general resilience indicators suitable for complex, forced dynamical systems.

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Sprache(n): eng - English
 Datum: 2025-11-282026-05-142026-06-012026-06-01
 Publikationsstatus: Final veröffentlicht
 Seiten: 14
 Ort, Verlag, Ausgabe: -
 Inhaltsverzeichnis: -
 Art der Begutachtung: Expertenbegutachtung
 Identifikatoren: MDB-ID: No MDB - stored outside PIK (see locators/paper)
PIKDOMAIN: Earth Resilience Science Unit - ERSU
Organisational keyword: Earth Resilience Science Unit - ERSU
PIKDOMAIN: RD1 - Earth System Analysis
Organisational keyword: RD1 - Earth System Analysis
Research topic keyword: Ice
Research topic keyword: Nonlinear Dynamics
Regional keyword: Global
Model / method: Quantitative Methods
Research topic keyword: Paleoclimate
OATYPE: Gold - Copernicus
DOI: 10.5194/esd-17-673-2026
 Art des Abschluß: -

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Titel: Earth System Dynamics
Genre der Quelle: Zeitschrift, SCI, Scopus, p3, oa
 Urheber:
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Ort, Verlag, Ausgabe: -
Seiten: - Band / Heft: 17 (3) Artikelnummer: - Start- / Endseite: 673 - 686 Identifikator: CoNE: https://publications.pik-potsdam.de/cone/journals/resource/1402282
Publisher: Copernicus