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Global warming overshoots increase risks of climate tipping cascades in a network model

Abstract

Current policies and actions make it very likely, at least temporarily, to overshoot the Paris climate targets of 1.5–<2.0 °C above pre-industrial levels. If this global warming range is exceeded, potential tipping elements such as the Greenland Ice Sheet and Amazon rainforest may be at increasing risk of crossing critical thresholds. This raises the question of how much this risk is amplified by increasing overshoot magnitude and duration. Here we investigate the danger for tipping under a range of temperature overshoot scenarios using a stylized network model of four interacting climate tipping elements. Our model analysis reveals that temporary overshoots can increase tipping risks by up to 72% compared with non-overshoot scenarios, even when the long-term equilibrium temperature stabilizes within the Paris range. Our results suggest that avoiding high-end climate risks is possible only for low-temperature overshoots and if long-term temperatures stabilize at or below today’s levels of global warming.

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Fig. 1: Interacting climate tipping elements.
Fig. 2: Effect of overshoot peak temperature.
Fig. 3: Expected number and risk of tipping events at different convergence temperatures.
Fig. 4: Timing and mechanisms of tipping events following temperature overshoots.

Data availability

The data on overshoot trajectories and time series of the 4.455 million individual ensemble members are, due to the very high storage requirements, available from N.W. upon reasonable request.

Code availability

The code leading to the overshoot trajectories and tipping-risk assessments is available within the python modelling package pycascades at https://pypi.org/project/pycascades/, together with a model description paper64. The version of pycascades of the results of this manuscript is stored together with a readme, code of the figure files and intermediate evaluation scripts via https://doi.org/10.6084/m9.figshare.21408243. In case of questions or requests, please contact N.W.

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Acknowledgements

This work has been carried out within the framework of PIK’s FutureLab on Earth Resilience in the Anthropocene. N.W., J.R. and J.F.D. acknowledge support from the European Research Council Advanced Grant project ERA (Earth Resilience in the Anthropocene, ERC-2016-ADG-743080). J.F.D. is grateful for financial support by the project CHANGES funded by the Federal Ministry for Education and Research (BMBF) within the framework ‘PIK_Change’ under grant 01LS2001A. R.W., J.R., D.I.A.M., S.L. and B.S. acknowledge financial support via the Earth Commission, hosted by FutureEarth. The Earth Commission is the science component of the Global Commons Alliance, a sponsored project of Rockefeller Philanthropy Advisors, with support from Oak Foundation, MAVA, Porticus, Gordon and Betty Moore Foundation, Herlin Foundation and the Global Environment Facility. The Earth Commission is also supported by the Global Challenges Foundation. P.D.L.R. acknowledges support from the European Research Council ‘Emergent Constraints on Climate–Land feedbacks in the Earth System (ECCLES)’ project, grant agreement number 742472. The authors gratefully acknowledge the European Regional Development Fund (ERDF), the BMBF and the Land Brandenburg for supporting this project by providing resources on the high-performance computer system at the Potsdam Institute for Climate Impact Research.

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Contributions

R.W., J.R. and J.F.D. conceived the study. N.W. designed the study, performed the simulations and led the writing of the manuscript with input from all authors. N.W., S.L. and B.S. prepared the figures with input from R.W., J.R., P.D.L.R., D.I.A.M., and J.F.D. J.F.D. led the supervision of this study.

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Correspondence to Nico Wunderling or Jonathan F. Donges.

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Nature Climate Change thanks Max Rietkerk, Bregje van der Bolt and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Exemplary overshoot trajectories and their impact on tipping events.

a, Time series of four different exemplary overshoot trajectories in dependence of the global mean surface temperature increase above pre-industrial levels (ΔGMT). Additionally, the four horizontal coloured lines show the critical temperatures of the Greenland Ice Sheet (GIS), the West Antarctic Ice Sheet (WAIS), the AMOC and the Amazon rainforest (AMAZ) for this specific ensemble member (for the entire ensemble of overshoots and tipping element set-ups, see Methods). b-d, The impact on tipping events in response to the applied overshoot scenario. Even though we only show one exemplary ensemble member here, it is apparent that higher temperature stabilisation levels (T_Conv) lead to a higher number of tipped elements (compare scenarios in b, c with scenarios in d, e), but also higher peak temperatures and convergence times have the same effect. The parameter values for this example are (same as in Fig. 1a,b): T_crit,GIS=1.1C, T_crit,AMOC=3.6C, T_crit,WAIS=3.0C, T_crit,AMAZ=4.3C, s_GIS → AMOC=9.2, s_AMOC → GIS=-3.1, s_GIS → AMOC=9.5, s_WAIS → AMOC=1.1, s_WAIS → GIS=1.5, s_GIS → WAIS=1.5, s_AMOC → AMAZ=3.0, τ_GIS=1602 yrs, τ_AMOC=172 yrs, τ_WAIS=1008 yrs and τ_AMAZ=56 yrs. The interaction strength parameter is set to d=0.20. For more details on the parameter values and meaning, see Methods.

Extended Data Fig. 2 The effect of time scales in overshoot scenarios on the risk for tipping events.

In the left column, the probability of zero, one, two, three, or four tipped elements are shown for peak temperatures between T_Peak=2.0C (lowest scenario) up to T_Peak=6.0C (highest scenario). The right column breaks down the respective elements, which are responsible for the respective average number of tipped elements from the left column. The three parallel drawn bars in each panel detail the time scale of tipping into three scenarios. The left bar shows the result in equilibrium simulations (after 50,000 simulation years, long-term tipping), the bar in the middle shows the tipping events after 1,000 simulation years (mid-term tipping), and the right bar after 100 simulation years (short-term tipping). We depict the average over the entire ensemble as the bar height and the error bars show the standard deviation.

Extended Data Fig. 3 The effect of the convergence time on the risk for tipping events.

In the left column, the probability of zero, one, two, three, or four tipped elements are shown for convergence times of t_Conv=100 years (uppermost row) up to t_Conv=1,000 years (lowermost row). The right column breaks down the respective elements, which are responsible for the respective average number of tipped elements from the left column. We depict the average of the equilibrium run (long-term tipping after 50,000 simulation years) over the entire ensemble as the bar height and the error bars show the standard deviation.

Extended Data Fig. 4 Expected number and risk of tipping events at low convergence temperatures.

Same as in Fig. 3 in the main manuscript, where the average number of tipped elements is shown for a set of convergence times and peak temperatures at a convergence temperature of a, 0.0C (return to pre-industrial levels) and b, 0.5C. The respective tipping risk that at least one tipping element ends up in the tipped regime is shown in panels c, d. Note that the high climate risk zone commences at higher peak and convergence times as compared to Fig. 3d in the main manuscript.

Extended Data Fig. 5 Expected number and risk of tipping events for high-end temperature overshoots.

Same as in Fig. 3 in the main manuscript, where the average number of tipped elements is shown for a set of convergence times and peak temperatures at a convergence temperature of a, 1.0C, b, 1.5C, and c, 2.0C. The respective tipping risk that at least one tipping element ends up in the tipped regime is shown in panels d, e, f. For all high-end scenarios, the tipping risk for one tipping event to occur ~ 75% if final convergence temperatures are between 1.5 − 2. 0C above pre-industrial levels.

Extended Data Fig. 6 Expected number and risk of tipping events for high-end temperature overshoots at low convergence temperatures.

Same as in Extended Data Fig. 3, where the average number of tipped elements is shown for a set of convergence times and peak temperatures at a convergence temperature of a, 0.0C (return to pre-industrial levels) and b, 0.5C. The respective tippivng risk that at least one tipping element ends up in the tipped regime is shown in panels c, d.

Extended Data Fig. 7 Mechanism for tipping following a temperature overshoot for low T_Conv.

Same as Fig. 4 of the main manuscript, but for lower convergence temperatures of 0.0, 0.5 and 1.0C. To depict the tipping risk visually as the size of the pie charts, the reason (baseline or overshoot tipping) for tipping is depicted in the respective pie charts.

Extended Data Fig. 8 Mechanism and timing of tipping events following a high-end temperature overshoot.

Same as in Fig. 4 of the main manuscript, but for higher temperature overshoot trajectories peaking between 4.5 − 6. 0C. In these cases, tipping also plays a very important role at shorter timescale of 100 years, see the increasing fraction of the dark red part in the pie charts. a, Convergence temperature of 1.5C, b, Convergence temperature of 2.0C.

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Wunderling, N., Winkelmann, R., Rockström, J. et al. Global warming overshoots increase risks of climate tipping cascades in a network model. Nat. Clim. Chang. 13, 75–82 (2023). https://doi.org/10.1038/s41558-022-01545-9

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