the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 06 Oct 2025
Chaotic fluctuations in Greenland outlet glaciers limit predictability of a future ice sheet collapse
Abstract. The future evolution of the Greenland ice sheet (GrIS) depends on the intensity and the speed of climate change. By applying different rates of temperature change in a state-of-the-art comprehensive ice-sheet model coupled to a regional energy-moisture balance atmospheric model, oscillations in the total ice-sheet volume are found under warming magnitudes between 1.0 and 1.3 K above present-day temperatures. These are located in the northwestern drainage basin of the GrIS and are due to two ice streams which alternate between fast and slow basal velocities, manifesting in a build-up/surge variability. These ice streams interact due to their spatial proximity, resulting in irregular periodicity. The ice streams appear in a region where tipping of the entire GrIS begins, leading the oscillations to affect the tipping behaviour. These oscillations directly impact the time it takes before the ice sheet collapses at a given external forcing magnitude by hundreds of thousands of years for an ensemble of rates of forcing and initial conditions. These long tipping times are proposed to be due to chaotic transients. Our results suggest that ice-stream oscillations are a potential source of internal chaotic variability in ice sheets that affect tipping behaviour, thereby complicating prospects of anticipating such a tipping.
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Status: open (until 08 Dec 2025)
- RC1: 'Comment on egusphere-2025-4116', Anonymous Referee #1, 12 Nov 2025 reply
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The authors explore tipping (both bifurcation- and rate-induced) in a three-dimensional model of the Greenland ice sheet coupled to a regional energy-moisture balance model. They find that the ice sheet will tip to a much lower ice state depending on the rate of the forcing and the overall level of the forcing. Considering the rate-induced transitions, they find that the time of tipping appears to relate in a non-monotonic way to the forcing. They conjecture the existence of an intermediate (chaotic edge) state or a boundary crisis to be the reason for this unpredictable time of tipping. Oscillatory behaviour of the system is also explained through the response of the Humboldt and Petermann glaciers and is removed to try to isolate the rate-induced tipping.
I have a couple comments regarding the presentation of the results.
1. Initially I was suspect of the chaotic behaviour claims in the paper. At the end of page 7 it is claimed that there is sensitive dependence on initial conditions, however this is not rigorously justified. Moreover, the model response is then continuously referred to as chaotic. Appendix B, however, has a much stronger argument for the conjecture of chaos in the system, including calculations which aim to verify (reject) the existence of a chaotic attractor (chaotic saddle). While I do not think all of this appendix should be moved into the main text, I strongly feel that some critical conclusions do need to be. In the first mention of chaos. I recommend adding a short discussion detailing your evidence and conjecture for the boundary crisis. Some of the more detailed discussions can still be left in the appendix.
2. The authors claim that there is no critical rate for rate-induced tipping. I find this very questionable. If the system does not tip when forcing is constant and then tips when it is not, there is some critical rate (albeit could be very small). Unless that the authors can prove that the system continues to tip as the rate limits to zero, I recommend softening such statements of no critical rates and acknowledging the critical rate could be smaller than the smallest value tested.
3. The forcing in the model is not well described. I imagine it is some kind of regional temperature anomaly based on its units, but I could not find an explicit description or expression. Additionally, the authors mention that the forcing increase is somehow adapted to equilibration time. This would be nice to see written out explicitly.
4. In general section 2 need to be rewritten so that it is much clearer. I found it very hard to follow the introduction of parameters and governing equations. There is a lot of repetition where a parameter is defined mathematically and then introduced later for its physical interpretation. This can be easily fixed with a careful rephrasing.
5. The terms "tipping time" and "tipping point" seem to be used interchangeably in the text. This is a pedantic comment but important because often they mean different things. Choose one term and clearly state how you are defining it.
6. On page 8 you mention the oscillatory behaviour for the first time. If there is oscillatory behaviour there could be existence of an unstable periodic orbit as a boundary that could potentially explain the irregular transition times which are perhaps more related to crossing this threshold. This also would strengthen your boundary crisis argument as the chaotic attractor can then collide with an unstable periodic orbit at the crisis.
7. Figure 6 appeared to me to have "edge state" or chaotic saddle like dynamics. Again, perhaps a short discussion of the results in the appendix would be useful in the text to clarify why this is not believed to be the case.