Articles | Volume 33, issue 3
https://doi.org/10.5194/npg-33-385-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-33-385-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
06 Aug 2026
Research article |
| 06 Aug 2026
| 06 Aug 2026
A simple dynamical system for representing climate tipping points with hysteresis
UK Centre for Ecology and Hydrology, Benson Lane, Wallingford, Oxfordshire, OX10 8BB, UK
Paul D. L. Ritchie
Department of Mathematics and Statistics, Faculty of Environment, Science and Economy, University of Exeter, North Park Road, Exeter, EX4 4QE, UK
Global Systems Institute, Faculty of Environment, Science and Economy, University of Exeter, North Park Road, Exeter, EX4 4QE, UK
Joseph Clarke
Department of Mathematics and Statistics, Faculty of Environment, Science and Economy, University of Exeter, North Park Road, Exeter, EX4 4QE, UK
Global Systems Institute, Faculty of Environment, Science and Economy, University of Exeter, North Park Road, Exeter, EX4 4QE, UK
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Tipping points are abrupt, rapid, and sometimes irreversible changes, and numerous approaches have been proposed to detect them in advance. Such approaches have been termed early warning signals and represent a set of methods for identifying changes in the underlying behaviour of a system across time or space that might indicate an approaching tipping point. Here, we review the literature to explore where, how, and which early warnings have been used in real-world case studies so far.
Mark S. Williamson, Peter M. Cox, Chris Huntingford, and Femke J. M. M. Nijsse
Earth Syst. Dynam., 15, 829–852, https://doi.org/10.5194/esd-15-829-2024, https://doi.org/10.5194/esd-15-829-2024, 2024
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Emma L. Robinson, Chris Huntingford, Valyaveetil Shamsudheen Semeena, and James M. Bullock
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Short summary
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Paul D. L. Ritchie, Hassan Alkhayuon, Peter M. Cox, and Sebastian Wieczorek
Earth Syst. Dynam., 14, 669–683, https://doi.org/10.5194/esd-14-669-2023, https://doi.org/10.5194/esd-14-669-2023, 2023
Short summary
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Complex systems can undergo abrupt changes or tipping points when external forcing crosses a critical level and are of increasing concern because of their severe impacts. However, tipping points can also occur when the external forcing changes too quickly without crossing any critical levels, which is very relevant for Earth’s systems and contemporary climate. We give an intuitive explanation of such rate-induced tipping and provide illustrative examples from natural and human systems.
Chris Huntingford, Peter M. Cox, Mark S. Williamson, Joseph J. Clarke, and Paul D. L. Ritchie
Earth Syst. Dynam., 14, 433–442, https://doi.org/10.5194/esd-14-433-2023, https://doi.org/10.5194/esd-14-433-2023, 2023
Short summary
Short summary
Emergent constraints (ECs) reduce the spread of projections between climate models. ECs estimate changes to climate features impacting adaptation policy, and with this high profile, the method is under scrutiny. Asking
What is an EC?, we suggest they are often the discovery of parameters that characterise hidden large-scale equations that climate models solve implicitly. We present this conceptually via two examples. Our analysis implies possible new paths to link ECs and physical processes.
Gang Liu, Shushi Peng, Chris Huntingford, and Yi Xi
Geosci. Model Dev., 16, 1277–1296, https://doi.org/10.5194/gmd-16-1277-2023, https://doi.org/10.5194/gmd-16-1277-2023, 2023
Short summary
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Isobel M. Parry, Paul D. L. Ritchie, and Peter M. Cox
Earth Syst. Dynam., 13, 1667–1675, https://doi.org/10.5194/esd-13-1667-2022, https://doi.org/10.5194/esd-13-1667-2022, 2022
Short summary
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Despite little evidence of regional Amazon rainforest dieback, many localised abrupt dieback events are observed in the latest state-of-the-art global climate models under anthropogenic climate change. The detected dieback events would still cause severe consequences for local communities and ecosystems. This study suggests that 7 ± 5 % of the northern South America region would experience abrupt downward shifts in vegetation carbon for every degree of global warming past 1.5 °C.
Louise J. Slater, Chris Huntingford, Richard F. Pywell, John W. Redhead, and Elizabeth J. Kendon
Earth Syst. Dynam., 13, 1377–1396, https://doi.org/10.5194/esd-13-1377-2022, https://doi.org/10.5194/esd-13-1377-2022, 2022
Short summary
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Rebecca J. Oliver, Lina M. Mercado, Doug B. Clark, Chris Huntingford, Christopher M. Taylor, Pier Luigi Vidale, Patrick C. McGuire, Markus Todt, Sonja Folwell, Valiyaveetil Shamsudheen Semeena, and Belinda E. Medlyn
Geosci. Model Dev., 15, 5567–5592, https://doi.org/10.5194/gmd-15-5567-2022, https://doi.org/10.5194/gmd-15-5567-2022, 2022
Short summary
Short summary
We introduce new representations of plant physiological processes into a land surface model. Including new biological understanding improves modelled carbon and water fluxes for the present in tropical and northern-latitude forests. Future climate simulations demonstrate the sensitivity of photosynthesis to temperature is important for modelling carbon cycle dynamics in a warming world. Accurate representation of these processes in models is necessary for robust predictions of climate change.
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Short summary
The risk of climate change triggering tipping points is a concern. While Earth System Models (ESMs) predict these points, their timing often varies. Equations of nonlinear dynamical systems can model tipping, hysteresis, and inertia, enabling comparison with ESMs. We propose a method to map tipping timing estimates onto a dynamical system that simulates a full hysteresis loop. We focus on solutions to the equation under overshoot forcing in global temperature and different inertia levels.
The risk of climate change triggering tipping points is a concern. While Earth System Models...
