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https://doi.org/10.5194/egusphere-2026-3507
© 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/egusphere-2026-3507
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
26 Jun 2026
| 26 Jun 2026
To tip or not to tip
Abstract. Tipping points have become a buzzword in Earth sciences, but ambiguous or overly narrow definitions of tipping are causing confusion around the concept. Agreeing on what tipping means, and whether a system tips or not, is important for robust science and communicating tipping risk. Based on a critical evaluation of existing tipping definitions, we propose a revised, general definition that characterizes a tipping event as a persistent nonlinear transition in forced systems. Our definition emphasizes both the phenomenology (observed time series) and cause (feedback mechanism) of a tipping event. Inspired by response theory, our proposition is compatible with more specific mathematical formulations while avoiding challenging notions such as bifurcations, equilibrium states, abruptness and irreversibility – making the definition testable also on transient dynamics in diverse complex systems under time-varying forcing. We showcase its practical use and limitations in a toy model and a case study of Earth system model data.
How to cite. Börner, R. and Dijkstra, H. A.: To tip or not to tip, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2026-3507, 2026.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.
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Status: final response (author comments only)
Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor
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- RC1: 'Comment on egusphere-2026-3507', Anonymous Referee #1, 22 Jul 2026
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RC2: 'Comment on egusphere-2026-3507', Anonymous Referee #2, 03 Sep 2026
Summary: In this manuscript, the authors propose a new, much-needed, general definition of tipping points in the Earth sciences, outline specific criteria for meeting this definition, and provide a mathematical framework for evaluating whether these criteria are met for a given physical system. In my view, the proposed definition itself is clear, robust, and fulfills the authors' stated goal of bridging mathematical intuition on tipping and considerations around practicality/impacts of identifying tipping points, and if adopted would bring a lot of clarity to the field of Earth system tipping dynamics. I have some comments that I hope will strengthen the manuscript by improving the logic of some paragraphs and definitions of some concepts, but I think that overall, this manuscript will be a very useful perspective piece.
Specific comments:
- Line 91: “However, it is often not useful to define a concept via its relevance.” Without further justification, this seems to be a rather vague and subjective statement. I recommend the authors instead say what the risk/downside is of defining a concept by its relevance.
- Line 100: “…arguably not all abrupt changes classify as tipping events.” Here it is not clear what definition of “tipping event” the authors are referring to--- certainly by the Lenton definition, an abrupt change is classified as a tipping point (simply because that is how Lenton has defined a tipping point). From the next clause, it becomes clear that they mean that an abrupt change may not be associated with any of the mathematical principles (bifurcation, multi-stability) that they deem important, so I recommend making the language more specific/clear in this way. In general, any time the authors refer to a “tipping event” or “tipping point” prior to introducing their own definition (e.g., anywhere in sections 1 and 2), they should be careful to say which of the other (insufficient) definitions they’re using or what specific characteristics they’re referring to.
- Line 106—108 (and specifically, “this can result in spurious hysteresis effects…”): I understand here the point the authors are trying to make about irreversibility and spurious hysteresis, but I think the authors should expand these two sentences to explain things a bit more explicitly for a broad audience. For example, I recommend they first define hysteresis as the mathematical concept underpinning “irreversibility” (I don’t believe they do this anywhere in the manuscript, and this should maybe go at the start of the paragraph to explain why it is associated with tipping points in the first place), explain how it conceptualized as a signature of multi-stability/a bifurcation, and then explain how a linear system can also exhibit this signature with the right depending on the magnitudes of inertia/forcing timescale. Then it will be clearer to a general reader why irreversibility/hysteresis is not a reliable indicator of nonlinear change.
- Line 112: Related to comment #2, what is meant by “tipping-like behavior” here? Transient/spurious hysteresis? Abruptness?
- Line 136: This seems like an appropriate/necessary place to add more justification for the focus on the positive-feedback aspect of tipping. How does focusing on this aspect serve the authors’ goals/purpose of a new tipping definition?
- Given that the authors state that the qualitative focus of their definition is on the positive feedback/self-amplifying change (line 136), then the phenomenology they focus on should also be clearly tied to self-amplifying change. Is this the case? In other words, does being in a regime of dominant positive feedbacks always lead to a “persistent nonlinear transition”? If so, then with criterion 2 also being met, there would be a one-to-one relationship between a persistent nonlinear transition and the positive feedback, which would unify the two criteria of tipping around the central concept of positive feedbacks.
- In criterion 1c, the condition that tau_B lasts “at least as long as tau_TH” seems like a rather arbitrary choice/definition for persistence. Can the authors justify this further? In particular, I can imagine that during a “fast” tipping transition (let’s say something that occurs over 5-10 years for the Earth system), only observing 5-10 additional years would be insufficient for establishing that a dynamically distinct and linear regime has been reached.
- Section 3.1.1 Remark #1: Is this special case considered a tipping event by their definition? (and is this classification desirable?)
- Section 3.1.1 Final remark: This scenario seems like a misclassification of a tipping point by their criteria/definition that one would want to avoid. Maybe the authors want to consider adjusting their definition to require a minimum tau that depends on the response timescale of the system, or at least suggest that best practice would be to only apply this tipping analysis over a sufficiently long tau (which again would depend on the response timescale of the system considered)?
- Criteria for rejecting the null model (line 210): Although it is somewhat implicit from the first two criteria that eta(t) increases between tau_A and tau_B, I feel it would add clarity to simply add this as another explicit criterion: that eta(t) surpasses some eta_c during tau_TR.
- The authors might want to consider adding a few sentences at the end of section 3.2.1 connecting the mathematical criteria they have outlined back to the more qualitative criteria they establish in section 3.1. This would help the reader understand that the purpose of constructing a null model and evaluating the time evolution of the residual is to be able to quantitatively assess criteria 1a, 1b, and 1c (~line 155).
- Paragraph 214—221: These are very useful nuanced comments!
- While the authors spend a lot of time establishing a clear framework for evaluating criteria 1a—c (null model, etc.), they do not spend much time explaining how one would establish that criteria #2—that the persistent nonlinear change is physically caused by a positive feedback—has been met. Around line 260, they describe how one can establish the presence of a dominant positive feedback based on the concavity of the stability landscape, but for real/high-dimensional systems, the stability landscape is unknown. A bit of elaboration on practically how to identify a net positive feedback in a system where you don’t a priori know the stability landscape (perhaps using the AMOC as an example) would be helpful.
- Picking null models/applying the tipping test: As the authors acknowledge, accurate tipping classification with this framework requires accurate specification of the null model. For the CESM 0.5ppm/year AMOC case, the authors identify that the previously chosen null model (damped decadal oscillator) was actually a poor choice based on the fact that it led to the classification of the AMOC trajectory as a tipping event when it clearly wasn’t. This led them to re-specify the null model. In essence, this meant they needed to already know whether the trajectory contained a tipping point or not in order to construct the correct null model that would give them the “correct” tipping classification. This begs the question--- can the framework the authors introduce actually be used to classify timeseries/systems as tipping/non-tipping when we don’t already know what they “should” be classified as? In other words, is this just a way of formalizing two different classes of behavior, or can it be used for active prediction/classification? Perhaps a way to answer this is to formulate an example where the tipping/non-tipping classification of a trajectory is truly arbitrary based on the forcing and observable timeseries alone (or where tipping/non-tipping trajectories within the same system are qualitatively similar), but where an accurate formulation of the null model leads to a meaningful classification result.
- How is the interval tau_TR determined in Figures 2/3?
Technical comments:
- Line 56: Should be “In the case of a forcing threshold…”
- Figure 3: I recommend mentioning the frequency used for the null model in the figure caption to avoid confusion with the different null models used in Figure 4.
- Relatedly, it’s a little confusing that the colors blue/orange are used to represent two different null models in Figure 4 (and black is used to represent actual timeseries), while blue and orange (although different shades) are used to represent the different forcing scenarios in Figure 3. It would help to rethink the color schemes/panel layout in Figure 3 to be either more consistent with Figure 4 (even though there’s only one null model in Figure 3) or be completely different from Figure 4. For example, they could consider having a column of panels for each forcing scenario in Figure 3 showing all the desired quantities (as in Figure 4).
Citation: https://doi.org/10.5194/egusphere-2026-3507-RC2
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Institute for Marine and Atmospheric research Utrecht, Department of Physics, Utrecht University, Utrecht, The Netherlands
Centre for Complex Systems Studies, Department of Physics, Utrecht University, Utrecht, The Netherlands
Henk A. Dijkstra
Institute for Marine and Atmospheric research Utrecht, Department of Physics, Utrecht University, Utrecht, The Netherlands
Centre for Complex Systems Studies, Department of Physics, Utrecht University, Utrecht, The Netherlands
Short summary
Tipping points have become a popular concept in earth sciences and for communicating climate change risk. However, there is confusion about what tipping means, caused also by ambiguous definitions of tipping terminology. We propose and exemplify a revised tipping definition, focusing on the observed time series and underlying cause of a tipping event. Our proposition seeks to bridge between narrow mathematical and purely qualitative definitions that often remain unclear and difficult to test.
Tipping points have become a popular concept in earth sciences and for communicating climate...
This paper is a timely and crucial piece highlighting the challenges of tipping points as a conceptional paradigm for global change, and offers solutions for the community to consider. I’ve never had less to say in a review. Absolutely excellent.
For what it’s worth to the authors, I have an extensive background in applications of bifurcation theory (and degrees in math), so I can’t judge very well how accessible the explanations will be to a broader Earth science audience. I found them extremely clear and at least think this is probably an excellent primer on this aspect of dynamical systems for a broader audience though.