Rate-induced tipping in ecosystems and climate: the role of unstable states, basin boundaries and transient dynamics
Abstract. The climate system as well as ecosystems might undergo relatively sudden qualitative changes in the dynamics when environmental parameters or external forcings vary due to anthropogenic influences. The study of these qualitative changes, called tipping phenomena, requires the development of new methodological approaches that allow modeling, analyzing, and predicting observed phenomena in nature, especially concerning the climate crisis and its consequences. Here we briefly review the mechanisms of classical tipping phenomena and investigate in more detail rate-dependent tipping phenomena which occur in non-autonomous systems characterized by multiple timescales. We focus on the mechanism of rate-induced tipping caused by basin boundary crossings. We unravel the mechanism of this transition and analyze, in particular, the role of such basin boundary crossings in non-autonomous systems when a parameter drift induces a saddle-node bifurcation in which new attractors and saddle points emerge, including their basins of attraction. Furthermore, we study the detectability of those bifurcations by monitoring single trajectories in state space and find that depending on the rate of environmental parameter drift, such saddle-node bifurcations might be masked or hidden and they can be detected only if a critical rate of environmental drift is crossed. This analysis reveals that quasi-stationary saddle points in non-autonomous multistable systems are the organizing centers of the global dynamics and need much more attention in future studies.
Status: final response (author comments only)
- RC1: 'Comment on npg-2023-7', Anonymous Referee #1, 11 Apr 2023
- RC2: 'Comment on npg-2023-7', Anonymous Referee #2, 29 Apr 2023
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The manuscript "Rate-induced tipping in ecosystems and climate: the role of unstable states, basin boundaries and transient dynamics" by Ulrike Feudel is an outstanding contribution to the field of tipping phenomena and their characterization in complex systems as the climate and ecosystems. It presents a concise but complete review on the mechanisms of classical tipping phenomena, especially focusing on rate-dependent tippings in non-autonomous multi-scale systems. The manuscript is clear and well written, the length and the references are appropriate, and the topic is timely and of wide interest. I have some minor recommendations to improve some missing concepts (for a wider audience) as outlined below.
As a general comment I would suggest to stress a bit more the question of "predictability" of tippings, especially in relation with the nature of tipping phenomena, since it is a central issue in many natural system and in the description with deterministic-stochastic approaches of natural phenomena.
Furthermore, another important issue to be highlighted could be the role of processes operating at different scales in changing the topology and the geometry of fixed point and attractors, as well as, the role of symmetries and scale-invariance (turbulence is one of the possible examples). Some possible suggested (optional) references are highlighted below.
Suggested (optional) references
Alberti T. et al. Scale dependence of fractal dimension in deterministic and stochastic Lorenz-63 systems. Chaos. 2023 Feb;33(2):023144. doi: 10.1063/5.0106053.
Bastiaansen R. et al. Climate response and sensitivity: time scales and late tipping points. Proc. R. Soc. A. 479:20220483 (2023) http://doi.org/10.1098/rspa.2022.0483.
Charó G. et al. Noise-driven topological changes in chaotic dynamics. Chaos 31, 103115 (2021) https://doi.org/10.1063/5.0059461.
Dubrulle B. Multi-Fractality, Universality and Singularity in Turbulence. Fractal Fract. 2022, 6(10), 613; https://doi.org/10.3390/fractalfract6100613.
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