Climate tipping points are large-scale subsystems of Earth that can abruptly shift to a different state once temperature thresholds are crossed. Five such elements (Greenland and West Antarctic ice sheets, AMOC, ENSO, and Amazon rainforest) are linked by physical processes, but their interactions are poorly understood. Existing studies have examined individual elements and some pairwise links, but a comprehensive stability analysis of the whole network that accounts for uncertainties had not been done. This work fills that gap by combining a conceptual model with nonlinear dynamics methods.
The authors used a system of nonlinear differential equations, where each element is described by a cubic equation with two stable states (a fold bifurcation). Interactions between elements were set as linear couplings with strengths drawn from expert estimates. For stability analysis, they applied basin stability: initial states and model parameters were varied randomly, and the system's convergence to attractors was tracked. Over 3.5 billion simulations were run, covering a warming range from 0 to 8°C and interaction strengths from 0 to 1. Additionally, a new method, Monte Carlo Basin Bifurcation Analysis, was used to detect oscillatory regimes.
For warming above 4°C, a state with four or five tipped elements dominates. Under moderate warming (1–4°C), states that include collapsed Greenland and West Antarctic ice sheets have the largest basin volumes. This points to a special role for ice sheets in the stability of the climate system. In 0.6% of all ensemble members, limit cycles were found: oscillations between the Greenland ice sheet and AMOC arising from their negative feedback. Such oscillations may be analogous to paleoclimate glacial–interglacial cycles.
This work differs from neighboring studies in that it considers not individual tipping points but the entire network of interactions, using basin stability in a multidimensional parameter space. This allows estimating how likely different scenarios are for a given level of warming and coupling strength. The results underscore the importance of ice sheets as key elements that can initiate tipping cascades. The methodology can be extended to other climate systems as knowledge about their interactions grows.
The model could be improved by including more climate elements and refining the interaction structure based on new expert assessments. It is also possible to apply more detailed Earth system models to test the conceptual model's predictions. The study of limit cycles between Greenland and AMOC may stimulate searches for similar oscillations in paleoclimate records.
The results are important for climate science because they provide quantitative estimates of the likelihood of cascading transitions. They can also inform mitigation strategies that account for nonlinear interactions.
Conduct a new expert elicitation on interactions between climate elements to refine model parameters. Develop more detailed models capable of reproducing the nonlinear dynamics of ice sheets and ocean circulation.
This work is directly relevant to predicting climate tipping points and cascades. It shows that even under moderate warming, states with collapsed ice sheets are possible, raising questions about the attainability of Paris Agreement goals.
The model ran over 3.5 billion simulations: if one simulation were executed per second, it would take more than 110 years.
The idea of cascading climate transitions echoes Kim Stanley Robinson's novel 'The Ministry for the Future,' which describes chain reactions in the climate system.