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Climate network characterization of the Atlantic Meridional Overturning Circulation edge state

Laure Moinat1,2, Reyk Börner3, Valerio Lucarini4,5, Maura Brunetti1,2, and Henk A. Dijkstra3

Phys. Rev. Research 8, 033268 – Published 3 September, 2026

DOI: https://doi.org/10.1103/q9bd-4h4j

Abstract

This article is part of a Physical Review Collection on the Physics in a Changing Climate.

The Atlantic Meridional Overturning Circulation (AMOC) has been identified as a tipping element in the Earth system. Under the current climate change scenarios, it is urgent to develop robust methods for determining the probability of future AMOC transitions. Recent studies using an Earth system model of intermediate complexity (EMIC) have revealed the importance of an AMOC edge state, located on the boundary of the attraction basin of the collapsed state, in AMOC transitions. Here, we provide a characterization of this edge state through climate networks, using instantaneous temporal correlations between geographical locations to define the network links. We apply the climate network analysis to a set of EMIC simulations with CO2 forcing according to an intermediate climate change scenario (SSP2-4.5), which exhibit qualitatively different AMOC responses as a result of interaction with the edge state. We show that network measures, specifically the normalized degree centrality, reveal the presence of teleconnections across the equator as the AMOC approaches the edge state. A similar result is obtained for an Earth system model (ESM) simulating AMOC collapse or recovery, suggesting that climate networks could be used to detect an AMOC instability in ESMs and observations.

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Physics in a Changing Climate

Climate Science is a growing field that is attracting colleagues from many disciplines. This Collection, a joint effort by Physical Review E, Physical Review Research, and PRX Energy curated by Prof. Justin Burton from Emory University, aims at providing a survey of the diverse range of topics that scientists with a connection to Physics are exploring in this exciting area of research. This includes climate and related geosciences, sustainability, energy, and material science, and may include fundamental as well as applied research.

Every article in this Collection was subjected to a rigorous peer review process, upholding the high standards applied to all papers. The Physical Review E, Physical Review Research, and PRX Energy editorial teams managed the peer review and made all editorial decisions.

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References (58)

  1. D. I. Armstrong McKay, A. Staal, J. F. Abrams, R. Winkelmann, B. Sakschewski, S. Loriani, I. Fetzer, S. E. Cornell, J. Rockström, and T. M. Lenton, Exceeding 1.5°C global warming could trigger multiple climate tipping points, Science 377, eabn7950 (2022).
  2. S. Rahmstorf, Is the Atlantic overturning circulation approaching a tipping point? Oceanography 37, 16 (2024).
  3. N. Wunderling, A. S. von der Heydt, Y. Aksenov, S. Barker, R. Bastiaansen, V. Brovkin, M. Brunetti, V. Couplet, T. Kleinen, C. H. Lear, et al., Climate tipping point interactions and cascades: A review, Earth Syst. Dynam. 15, 41 (2024).
  4. L. Caesar, S. Rahmstorf, A. Robinson, G. Feulner, and V. Saba, Observed fingerprint of a weakening Atlantic Ocean overturning circulation, Nature 556, 191 (2018).
  5. K. Y. Li and W. Liu, Weakened Atlantic meridional overturning circulation causes the historical North Atlantic warming hole, Commun. Earth Environ. 6, 416 (2025).
  6. S. L. L. Michel, H. A. Dijkstra, F. Guardamagna, V. Jacques-Dumas, R. M. van Westen, and A. S. von der Heydt, Deep learning based reconstructions of the Atlantic meridional overturning circulation confirm twenty-first century decline, Environ. Res. Lett. 20, 064036 (2025).
  7. R. M. van Westen, M. Kliphuis, and H. A. Dijkstra, Physics-based early warning signal shows that AMOC is on tipping course, Sci. Adv. 10, eadk1189 (2024).
  8. W. Liu, S.-P. Xie, Z. Liu, and J. Zhu, Overlooked possibility of a collapsed Atlantic meridional overturning circulation in warming climate, Sci. Adv. 3, e1601666 (2017).
  9. H. A. Dijkstra, B. Krauskopf, R. Börner, and R. M. van Westen, Transitions of the Atlantic Ocean circulation, Nat. Rev. Phys. 8, 410 (2026).
  10. R. Börner, O. Mehling, J. von Hardenberg, and V. Lucarini, Global stability of the Atlantic overturning circulation: Edge state, long transients and boundary crisis under CO2 forcing, Philos. Trans. R. Soc. A 384, 20250087 (2026).
  11. A. Romanou, D. Rind, J. Jonas, R. Miller, M. Kelley, G. Russell, C. Orbe, L. Nazarenko, R. Latto, and G. A. Schmidt, Stochastic bifurcation of the North Atlantic circulation under a midrange future climate scenario with the NASA-GISS model, J. Clim. 36, 6141 (2023).
  12. S. Drijfhout, J. R. Angevaare, J. Mecking, R. M. van Westen, and S. Rahmstorf, Shutdown of northern Atlantic overturning after 2100 following deep mixing collapse in CMIP6 projections, Environ. Res. Lett. 20, 094062 (2025).
  13. J.-H. Oh, J.-S. Kug, Y. Shin, X. Geng, S. Wang, F.-F. Jin, S.-I. An, S.-P. Xie, and W. Liu, Noise-induced tipping of Atlantic meridional overturning circulation under climate mitigation scenarios, Nat. Commun. 16, 11515 (2025).
  14. H. Stommel, Thermohaline convection with two stable regimes of flow, Tellus 13, 224 (1961).
  15. P. Cessi, A simple box model of stochastically forced thermohaline flow, J. Phys. Oceanogr. 24, 1911 (1994).
  16. J. R. Scott, J. Marotzke, and P. H. Stone, Interhemispheric thermohaline circulation in a coupled box model, J. Phys. Oceanogr. 29, 351 (1999).
  17. V. Lucarini, S. Calmanti, and V. Artale, Destabilization of the thermohaline circulation by transient changes in the hydrological cycle, Clim. Dyn. 24, 253 (2005).
  18. A. A. Cimatoribus, S. S. Drijfhout, and H. A. Dijkstra, Meridional overturning circulation: Stability and ocean feedbacks in a box model, Clim. Dyn. 42, 311 (2014).
  19. J. Marotzke and J. Willebrand, Multiple equilibria of the global thermohaline circulation, J. Phys. Oceanogr. 21, 1372 (1991).
  20. S. Rahmstorf, M. Crucifix, A. Ganopolski, H. Goosse, I. Kamenkovich, R. Knutti, G. Lohmann, R. Marsh, L. A. Mysak, Z. Wang, and A. J. Weaver, Thermohaline circulation hysteresis: A model intercomparison, Geophys. Res. Lett. 32, 2005GL023655 (2005).
  21. H. A. Dijkstra, Characterization of the multiple equilibria regime in a global ocean model, Tellus A: Dyn. Meteorol. Oceanogr. 59, 695 (2007).
  22. M. Hofmann and S. Rahmstorf, On the stability of the Atlantic meridional overturning circulation, Proc. Natl. Acad. Sci. USA 106, 20584 (2009).
  23. E. Hawkins, R. S. Smith, L. C. Allison, J. M. Gregory, T. J. Woollings, H. Pohlmann, and B. de Cuevas, Bistability of the Atlantic overturning circulation in a global climate model and links to ocean freshwater transport, Geophys. Res. Lett. 38 (2011).
  24. R. M. van Westen and H. A. Dijkstra, Asymmetry of AMOC hysteresis in a state-of-the-art global climate model, Geophys. Res. Lett. 50, e2023GL106088 (2023).
  25. S. Manabe and R. J. Stouffer, Two stable equilibria of a coupled ocean-atmosphere model, J. Clim. 1, 841 (1988).
  26. V. Lucarini and T. Bódai, Edge states in the climate system: Exploring global instabilities and critical transitions, Nonlinearity 30, R32 (2017).
  27. O. Mehling, R. Börner, and V. Lucarini, Limits to predictability of the asymptotic state of the Atlantic meridional overturning circulation in a conceptual climate model, Physica D 459, 134043 (2024).
  28. J. Lohmann, H. A. Dijkstra, M. Jochum, V. Lucarini, and P. D. Ditlevsen, Multistability and intermediate tipping of the Atlantic Ocean circulation, Sci. Adv. 10, eadi4253 (2024).
  29. P. M. Battelino, C. Grebogi, E. Ott, J. A. Yorke, and E. D. Yorke, Multiple coexisting attractors, basin boundaries and basic sets, Physica D 32, 296 (1988).
  30. J. D. Skufca, J. A. Yorke, and B. Eckhardt, Edge of chaos in a parallel shear flow, Phys. Rev. Lett. 96, 174101 (2006).
  31. J. Lohmann, A. Hansen, A. Lovo, R. Chapman, F. Bouchet, and V. Lucarini, The role of edge states for early warning of tipping points, Proc. R. Soc. A 481, 20240753 (2025).
  32. H. A. Dijkstra, E. Hernández-García, C. Masoller, and M. Barreiro, Networks in Climate (Cambridge University Press, Cambridge, 2019).
  33. J. F. Donges, Y. Zou, N. Marwan, and J. Kurths, The backbone of the climate network, Europhys. Lett. 87, 48007 (2009).
  34. J. F. Donges, J. Heitzig, B. Beronov, M. Wiedermann, J. Runge, Q. Y. Feng, L. Tupikina, V. Stolbova, R. V. Donner, N. Marwan, H. A. Dijkstra, and J. Kurths, Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package, Chaos 25, 113101 (2015).
  35. J. Donges, Y. Zou, N. Marwan, et al., Complex networks in climate dynamics: Comparing linear and nonlinear network construction methods, Eur. Phys. J. Spec. Top. 174, 157 (2009).
  36. F. M. Strnad, J. Schlör, C. Fröhlich, and B. Goswami, Teleconnection patterns of different El Niño types revealed by climate network curvature, Geophys. Res. Lett. 49, e2022GL098571 (2022).
  37. M. van der Mheen, H. A. Dijkstra, A. Gozolchiani, M. den Toom, Q. Feng, J. Kurths, and E. Hernandez-Garcia, Interaction network based early warning indicators for the Atlantic MOC collapse, Geophys. Res. Lett. 40, 2714 (2013).
  38. A. Radebach, R. V. Donner, J. Runge, J. F. Donges, and J. Kurths, Disentangling different types of El Niño episodes by evolving climate network analysis, Phys. Rev. E 88, 052807 (2013).
  39. L. Moinat, J. Kasparian, and M. Brunetti, Tipping detection using climate networks, Chaos 34, 123161 (2024).
  40. Q. Y. Feng, J. P. Viebahn, and H. A. Dijkstra, Deep ocean early warning signals of an Atlantic MOC collapse, Geophys. Res. Lett. 41, 6009 (2014),.
  41. V. Lucarini and T. Bódai, Global stability properties of the climate: Melancholia states, invariant measures, and phase transitions, Nonlinearity 33, R59 (2020).
  42. R. Börner, R. Deeley, R. Römer, T. Grafke, V. Lucarini, and U. Feudel, Saddle avoidance of noise-induced transitions in multiscale systems, Phys. Rev. Res. 6, L042053 (2024).
  43. M. Angeloni, Climate variability in an Earth system model of intermediate complexity: From interannual to centennial timescales, Ph.D. dissertation, Alma Mater Studiorum—Università di Bologna, 2022, dottorato di Ricerca in Geofisica, 34th Cycle.
  44. M. Meinshausen, Z. R. J. Nicholls, J. Lewis, M. J. Gidden, E. Vogel, M. Freund, U. Beyerle, C. Gessner, A. Nauels, N. Bauer, et al., The shared socio-economic pathway (SSP) greenhouse gas concentrations and their extensions to 2500, Geosci. Model Dev. 13, 3571 (2020).
  45. E. de Boisséson, M. A. Balmaseda, and M. Mayer, Ocean heat content variability in an ensemble of twentieth century ocean reanalyses, Clim. Dyn. 50, 3783 (2018).
  46. Y. Zou, R. V. Donner, N. Marwan, J. F. Donges, and J. Kurths, Complex network approaches to nonlinear time series analysis, Phys. Rep. 787, 1 (2019).
  47. L. C. Freeman, Centrality in social networks conceptual clarification, Social Networks 1, 215 (1978).
  48. O. Mehling, K. Bellomo, and J. von Hardenberg, Centennial-scale variability of the atlantic meridional overturning circulation in cmip6 models shaped by arctic–north atlantic interactions and sea ice biases, Geophys. Res. Lett. 51, e2024GL110791 (2024).
  49. P. de Vries and S. L. Weber, The Atlantic freshwater budget as a diagnostic for the existence of a stable shut down of the meridional overturning circulation, Geophys. Res. Lett. 32, 2004GL021450 (2005).
  50. R. M. van Westen and H. A. Dijkstra, Persistent climate model biases in the Atlantic Ocean’s freshwater transport, Ocean Sci. 20, 549 (2024).
  51. V. Lucarini and P. H. Stone, Thermohaline circulation stability: A box model study. Part II: Coupled atmosphere–ocean model, J. Clim. 18, 514 (2005).
  52. V. Dakos, E. H. van Nes, R. Donangelo, H. Fort, and M. Scheffer, Spatial correlation as leading indicator of catastrophic shifts, Theor. Ecol. 3, 163 (2010).
  53. N. Zagli, V. Lucarini, and G. A. Pavliotis, Spectroscopy of phase transitions for multiagent systems, Chaos 31, 061103 (2021).
  54. N. Zagli, V. Lucarini, and G. A. Pavliotis, Response theory identifies reaction coordinates and explains critical phenomena in noisy interacting systems, J. Phys. A: Math. Theor. 57, 325004 (2024).
  55. T. M. Lenton, J. F. Abrams, A. Bartsch, S. Bathiany, C. A. Boulton, J. E. Buxton, A. Conversi, A. M. Cunliffe, S. Hebden, T. Lavergne, et al., Remotely sensing potential climate change tipping points across scales, Nat. Commun. 15, 343 (2024).
  56. L. Moinat, R. Börner, V. Lucarini, M. Brunetti, and H. Dijkstra, Climate network characterization of the AMOC edge state [Data set], Zenodo, 2026, https://doi.org/10.5281/zenodo.20285996.
  57. R. Börner, O. Mehling, J. von Hardenberg, and V. Lucarini, Dataset: AMOC edge state and transient simulations in PlaSim-LSG (Part I) [Data set], Zenodo, 2025, https://doi.org/10.5281/zenodo.17053348.
  58. R. Börner, Dataset: AMOC edge state and transient simulations in PlaSim-LSG (Part II) [Data set], Zenodo, 2026, https://doi.org/10.5281/zenodo.20270589.

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