Informing low-order models of climate tipping elements using outputs from higher-complexity Earth system models

Bochow, Nils; Krönke, Jonathan; Garbe, Julius; Wunderling, Nico

doi:10.5194/egusphere-2026-614

Preprints

https://doi.org/10.5194/egusphere-2026-614

Preprints

18 Feb 2026

| 18 Feb 2026

Informing low-order models of climate tipping elements using outputs from higher-complexity Earth system models

Nils Bochow, Jonathan Krönke, Julius Garbe, and Nico Wunderling

Abstract. Crossing climate tipping points poses a rising risk under continued global warming. Yet quantitative tipping risk assessments often rely on idealised system dynamics and do not take into account Earth system model (ESM) processes. Here, we present a process-informed, updatable framework that links systematic stability assessments from comprehensive models to transparent low-order dynamical systems for three high-impact climate tipping elements (TEs): the Greenland Ice Sheet (GrIS), the West Antarctic Ice Sheet (WAIS) and the Atlantic Meridional Overturning Circulation (AMOC). We assemble TE experiments from Earth system and Earth system component models, fit element-specific dynamical systems with saddle-node bifurcations that map external forcing to state transitions, and run idealised instantaneous-forcing experiments to show the application of our framework. A simple, modular update protocol allows tipping thresholds and timescales to be revised as new simulations from ESMs become available without refitting the full framework. Applied to current ESM simulations, our emulators reproduce multistability of the GrIS and WAIS and a freshwater-forced weakening of the AMOC, yielding decision-relevant transient and equilibrium behaviour consistent with the underlying ESMs. Our approach provides a transparent bridge between comprehensive simulations and simple dynamical systems, and can be extended to additional climate tipping elements as suitable experiments become available.

Received: 02 Feb 2026 – Discussion started: 18 Feb 2026

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Nils Bochow, Jonathan Krönke, Julius Garbe, and Nico Wunderling

Status: final response (author comments only)

RC1:
'Comment on egusphere-2026-614', Anonymous Referee #1, 30 Mar 2026
The authors fit third order models, representing saddle-node bifurcations, to model data of three tipping elements; the Greenland Ice Sheet (GrIS), West Antarctic Ice Sheet (WAIS) and Atlantic Meridional Overturning Circulation (AMOC). The aim of this approach is to develop simple models representing tipping dynamics that allow for fast simulations, making them suitable for decision making.
The aim of the paper is worthwhile, however the current state does not go far beyond fitting a third order polynomial to model data. I have several suggestions/comments which I believe will strengthen this work and make it more valuable for the tipping community.

Main comments:
Uncertainty. Currently no uncertainty of the emulator-models is given, while uncertainty is key to know how much the results can be trusted. Hence, I think it is key to address the uncertainty question here, and not postpone it to later work. This does not need to be extensive, but a first idea of the reliability of the fit would be very valuable.

Verification. The authors run transient simulations with their fitted models, but do not show any comparison with transient runs from the models to verify how well their framework works. As transient runs are available for at least some models (and used to determine the timescale), it would be valuable to compare the fitted models to those. This would also give insight in the reliability. Something to consider here is also testing the models’ reliability out of sample, as e.g. for the ice sheets you fit it to data up to 3-4 degrees, but do transient simulations up to 6 degrees. What is the reliability of those results?

Modular. In the abstract the authors state their approach is modular. However, this is not discussed in some detail till the discussion, and I am uncertain how exactly it works. As it is a main claim, it needs a improved arguments and discussion.

Specific comments:
I am not convinced by the statement that the method is process-informed. It is fit to physical models, but the model that is fit is not necessarily informed by any physical constraints. For example, in the transient simulations for GrIS the final volume of the ice sheet depends on the level of global warming (i.e. the warmer, the more ice loss), while I would say at a certain point all ice has disappeared, meaning it should no longer depend on the level of warming. Using the current approach this will never be the case (due to the chosen 3rd order model).

Introduction. There are a number of studies looking at abrupt change in climate models which are relevant, but not referenced. Drijfhout et al. (2015), Terpstra et al. (2025), Harteg et al. (preprint, TOAD), Angevaare and Drijfhout (preprint).

Methods. The reference simulations, timescale function and calibration all need to be explained better. Currently it is hard to know how exactly the fit is done and which choices are made and why. Similarly for the rescaling. I understand it is for computational reasons, but I would suggest to give some more detail on how it’s done in the appendix and how the values to which is rescaled are chosen (order one, but somehow they differ between tipping elements). Specifically:
L111-114 are not clear to me.

Eqn. (2) – suggest making the theta dependence on the rhs explicit.

L121 – Shouldn’t it be z_data instead of x_data? (appreciate it’s the same, but it reads confusing).

Figures. A lot of figures have a normalised state (a.u.) on the y-axis, making them hard to interpret. For example for the AMOC it is not till the end that it is mentioned that Veros and POP have very different AMOC background states, which is key for interpreting the results. This needs to be mentioned earlier, as otherwise the transient simulations are hard to interpret. Changing the figures to physical units can help with this.

By design the tipping thresholds match those of existing literature, as you also mention. So I would not mention that explicitly as a result.

Suggestions to consider for the discussion:
Is there the possibility to use observational constraints in this framework?

You currently have a fit for each climate model. Is there a way to combine these, reflecting the trust we have in them?

Do you expect your emulator to respond realistically to overshoot scenerios?
Citation: https://doi.org/10.5194/egusphere-2026-614-RC1
RC2: 'Comment on egusphere-2026-614', Anonymous Referee #2, 14 Apr 2026

This paper presents a method that fits 1D dynamical systems (double-well potentials with variable control parameter) to data previously obtained from ESM simulations of tipping points in various sub-systems of the climate. Using the obtained models can be useful for conceptual studies of tipping elements, given that the emulated dynamics are reliable when extrapolated beyond the ESM data. But I have major reservations with respect to the motivation and soundness of the mathematical form of the dynamical system used, as well as the overall presentation of the paper.
Major comments
1.
When this was introduced as a “framework”, I was expecting to
a) get uncertainty estimates on the model parameters
b) be able to synthesize information from different ESMs of the same tipping element into one model emulator
This is unfortunately not possible, and instead the method is a particular way of fitting one dynamical system (limited to a 1D fold-fold bifurcation third-order polynomial ODE) for each set of simulations in a given ESM. I think the limitations of the framework need to be highlighted better, and it needs to be explained better how the collection of obtained models can then nevertheless be used to make “decision-relevant” studies of climate tipping risks.

2.
Section 3.1.1, where as part of the method the “timescale” tau is estimated as function of the control parameter (before the actual fitting, if I understand correctly), is in my view misinformed. The purpose seems to be to account for critical slowing down, which gives a power-law divergence of the relaxation time towards equilibrium as a saddle-node bifurcation is approached.
But the form of Eq. 1 using a constant tau already gives rise to a saddle-node bifurcation, and thus will feature critical slowing down in itself. So I don’t see a basis for introducing this additional, duplicate critical slowing down into the equations. Maybe the fitting procedure still works (at least introducing a monotonic tau(p) does not induce additional equilibria), but conceptually it is hard to justify. I find this a major issue, since this timescale function is the only major enhancement with regards to previous work, which simply fits Eq. 1 to data while having a constant tau.
I guess that by using such a simple 1D system, the time scale that could be estimated from fluctuations around equilibrium may yield an emulated “timescale” of the eventual collapse (which is then far from equilibrium) that is far off the actual timescale in the ESM. So I understand that there is a motivation to estimate a constant characteristic time scale using other, transient simulations. That being said, it seems that the actual time scale of the model dynamics (i.e. scaling of parameters [a, c, e]) is afterwards modified anyhow in an unknown way by fitting the polynomial parameters from the equilibrium simulations.

3.
In many places, it is mentioned that the framework is “modular”, “naturally designed for efficient updating”, “modular update protocol” etc. But the only justification for why this is the case is that the parameter e (constant offset of the bifurcation parameter) can be changed without refitting the model, in the case where new ESM simulations come along that reveal a different critical threshold. First, I don’t see why this is even worth mentioning. Anyone who chooses to do simulations with conceptual models can decide to redefine their control parameter as (p-p0) if they think the critical threshold is in one place or the other, so in what way is this unique to this method? Besides, one would not even need to make new simulations with changed value of e, but can simply relabel any plots with dependence on p → p + e. Second, are there really realistic scenarios where new data from an ESM becomes available and everything about the system stays the same (the exact entire shape of the bifurcation diagram), but the critical threshold is shifted? In my view it would be much better to do actually do a refitting, rather then to postulate the dynamics are the same while only the scale of the bifurcation parameter changed. And furthermore, why would it be a big deal to refit the model with new data? Is the fitting computationally intensive? Finally, how does a shifting of p by e affect the choice of the function tau(p-p_c)? Should Eq. 3 (or the parameter p_c) not also include a dependence on e?
4.
I am not convinced the authors have demonstrated that new scientific results can be achieved with the method, even though it is claimed that it is “decision-relevant” and “physically grounded”. The proposed method simply fits 1-d dynamical systems to ESM data and then hints to using the collection of models (although it remains unclear how to synthesize different models of the same tipping element) to estimate the thresholds (e.g. Sec 4.1) and the time scales of partial or full collapse (e.g. WAIS, Sec. 4.2). This is problematic, since
a) the fit is often simply not good (e.g. SICOPOLIS model), and so it seems to be more robust to simply look at the ESM data to argue for the location of the tipping point, rather then considering the extrapolation of the 1D model, which has visibly clear discrepancies with the ESM data.
b) the estimate of timescales relies on the rationale for the functional dependence of the time scale, which is unclear, see comment #2.
As hinted at in the discussion, I guess that they might use the models in the future for more conceptual studies of coupled tipping elements. But here it would be unclear which of the several 1d models for a given tipping element one should choose. Overall, I would have been more convinced if the authors simply use the method and demonstrate that new scientific results can be obtained.

5.
I find the formulation of the abstract a bit misleading:
They contrast their approach with ones that “rely on idealized system dynamics” and which “do not take into account Earth system model processes”. At the same time it is said that the method fits “saddle-node bifurcations” to ESM model output, stating this makes it process-informed. I find this a bit misleading, since their approach indeed heavily relies on idealized dynamics by shifting and stretching the predefined bifurcation diagram of a one-dimensional system. The functional form of this system is given and not derived from any underlying processes, at least if with processes one refers to physical processes related to the climate system.
Similarly, I would not call the models “low-order” (as already in the title), but “conceptual”. At least in my understanding, low-order is usually used for models of several ODEs that have been formally derived by approximation of the underlying PDEs of, for instance, the fluid dynamics. But I might be wrong here.
They go on to say that the “emulators reproduce multistability of the GrIS and WAIS, …”, but this is the case by definition of the choice of their one-dimensional model.
In general, the language in the paper sounds at times not scientifically precise enough, and rather too much like a sales pitch. Examples are: “process-informed”, “decision-relevant”, “element-specific”, “reduced-complexity”, “domain-specific simulations”, “high-fidelity experiments”, “transparent low-order dynamics”, “traceable”.
Some of these descriptors can of course simply be rephrased and spelled out explicitly in their meaning. For others it can perhaps be motivated more explicitly why they are apt. But many of these descriptors do not really hold up to scrutiny in my opinion, see my other comments.

Minor comments:
2 of 3 example systems have the double two-fold, i.e., tri-stability. Why not attempt to fit a higher-degree polynomial model to it? Then one would not need to postulate that each system with tri-stability consists of two completely independent sub-systems. This postulate is not justified in general, and limits the emulated dynamics as well as the method on the whole.

The discussion does not relate enough to the actual content of the work, i.e., the underlying assumptions as well as benefits with respect to prior work. It is mostly a general discussion on AMOC, WAIS, etc. which are not really informed by this work (e.g. p12 first paragraph).

The fitting routine needs to be explained better. From the notation it does not become clear whether all data, including at different control parameter values, is fitted/optimized at the same time. It is also not clear to me from the text whether the time scale function is determined before or after doing the main fit (I am assuming before).

L43:
What are “highly idealized tipping frameworks”, and in what way does the present paper go beyond that? It seems the authors argue their method falls into the class of “tipping-element emulators”, and thereby bridges the gap toward fully coupled ESMs. If the authors believe that fitting parameters of the double-well potential (or other conceptual systems) to ESM data makes it an emulator, it would be good if they explicitly state this, and at the same time state what type of approach would fall even lower on the modeling hierarchy. I guess this would be using the same type of model, but without any calibration of the parameters to an ESM or observations.

L45:
Similarly, what are “reduced-complexity climate frameworks”?

Eq 1: f(z,p,t)

Regarding Eq. 1 and Eq. 2:
Does the model not include a noise-term? Eq. 1 as it stands is deterministic and only allows for monotonic relaxation towards a fixed point. The ESM simulations on the other hand feature oscillations and quasi-stochastic variability. Comparing (in squared difference sense) time increments of the deterministic 1D model (where the time increments go to zero as it equilibrates) to those of the ESMs (time increments should reach some stationary distribution with zero average to zero, but only if perfectly equilibrated) seems not very reasonable. Or are you only predicting with Eq. 1 one step ahead, i.e. you take the ESM value at time i and predict one time step ahead to get your model increment? This is not clear from the provided text.

L128-135:
This paragraph mixes up the response of the system to perturbations before a bifurcation (critical slowing down) with the relaxation time scale after a bifurcation (as in the example of faster GrIS melt for strong warming above a threshold). It needs to be made clear that there are two different things. Also, I think it is a bit fuzzy to say the “timescale” of a system depends on its state. What is meant by timescale? The relaxation towards an equilibrium would be characterized (in the linear regime) by some e-folding time scale, but this does not depend on the state. Of course the momentary rate of a system state’s movement is given by the right-hand side of the underlying differential equation and does depends on the position in phase space (the state). In case this rate of change varies arbitrarily in phase space, in my opinion this implies that there is no characteristic timescale, as opposed to a “state-dependent” timescale. It would be perhaps better to only say – and this is in line with how the state-dependent timescale is used later - that there can be different characteristic time scales of local relaxation for different attractors.

L189:
“we utilise the results from three independent ice sheet models to fit a dynamical system to the GrIS” → To me this makes it seem like the method allows to derive a single dynamical system from three independent ESMs, whereas in reality one independent dynamical system is obtained for each ESM. Similarly, and even more strongly, this is suggested in line 307 too.

L281-282:
I am not sure about the justification for filtering the high-frequency variability. If the authors are interested in the quasi-equilibrium state, they could just fit the fixed points of Eq. 1 to the average states in the ESM equilibria (as a function of p). What is the effect of filtering, and why is it done?

L289-301:
This relates to the previous point and to the major comment #2:
Why can the characteristic timescales not simply be estimated from the fluctuations around the equilibria from the quasi-equilibrium runs? Why is it necessary to first specify an arbitrary timescale k, and then afterwards fit the parameters [a,c,e] based on the ESM timeseries, which can override the choice of k? Perhaps it would be possible for the authors to demonstrate that choosing a value for k is really necessary in order to obtain a fit.

Citation: https://doi.org/10.5194/egusphere-2026-614-RC2

Nils Bochow, Jonathan Krönke, Julius Garbe, and Nico Wunderling

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Short summary

We provide a simple, updateable tool that turns comprehensive simulations into fast dynamical models for the three major tipping elements; the Greenland Ice Sheet, the West Antarctic Ice Sheet, and the Atlantic Meridional Overturning circulation. By fitting our framework to existing comprehensive simulations, it matches both short-term change and long-term stable states. This helps produce more consistent, policy-ready risk estimates as new simulations arrive.


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