the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 03 Jun 2025
SWIIFT v0.10: a numerical model of wave-induced sea ice breakup based on an energy criterion
Abstract. The wave-induced breakup of sea ice contributes to the formation of the marginal ice zone in the polar oceans. Understanding how waves fragment the ice cover into individual ice floes is thus instrumental for accurate numerical simulations of the sea ice extent and its evolution, both for operational and climate research purposes. Yet, there is currently no consensus on the appropriate fracturing criterion, which should constitute the starting point of a physically sound wave–ice model. While fracture by waves is commonly treated within a hydroelastic framework and parameterised with a maximum strain-based criterion, in this study we explore a different, energy-based, approach to fracturing. We introduce SWIIFT (Surface Wave Impact on sea Ice—Fracture Toolkit), a one-dimensional model, based on linear plate theory, into which we incorporate this energy fracture criterion. We demonstrate it with simple simulations that reproduce existing laboratory wave-induced breaking experiments of an analogue material, allowing qualitative comparisons. We find that under some wave conditions, identified by a dimensionless wavenumber, corresponding to in situ or laboratory wave-induced fracture, the model does not predict fracture at constant curvature, thereby calling into question a maximum strain criterion.
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RC1: 'Comment on egusphere-2025-1831', Anonymous Referee #1, 03 Jul 2025
- AC1: 'Reply on RC1', Nicolas Mokus, 12 Sep 2025
- AC4: 'Reply on RC1', Nicolas Mokus, 22 Oct 2025
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RC2: 'Comment on egusphere-2025-1831', Anonymous Referee #2, 01 Oct 2025
This paper describes a method for determining ocean wave induced sea ice breakup patterns using the total bending energy, rather than a local maximum strain criterion. The authors simplify the model by assuming quasi-static bending and by only considering a pseudo one-way coupling from the fluid to the ice deformation. (I say pseudo one-way coupling because the authors still use a sea-ice specific dispersion relation and a model for attenuation by sea ice, although the fluid displacement appears in the equations as a forcing term rather than as an unknown.) Of course, simplifications such as these are necessary, but I would have liked to have seen a little more discussion around these modelling decisions in section 2.1.
The results section is built around comparison with the experimental data of Auvity et al. (2025). I would have also liked to see a numerical comparison with the critical strain fracture criterion. For instance, by imposing an incident wave, the proposed energy method and the strain criterion method would lead to different breakup patterns, and I am left wondering what the qualitative differences between these might be. I don't think addressing this point is necessary for publication of this paper, but it would strengthen the current paper or be an interesting question to address in a follow up work.
With those issues pointed out, I must conclude by saying that the paper addresses an important point in the sea-ice breakup literature with a novel idea. It is very well written and well presented with excellent figures, and I recommend it for publication once the issues raised in this review have been addressed.
Some more minor issues are listed below:
Line 41: be->been
It should be noted that equation (1) is Archimedes' principle.
Is the energy release rate G for ice floes/other materials known or easy to measure?
Figure 2 is very helpful for understanding the fracture process. I would suggest adding a little further discussion about this figure at line 174. For instance:
- It would be helpful to demystify the algorithmic/procedural steps. E.g. if I understand correctly, for each fracture location, the bending must be computed from (6), before the energies can be calculated.
- Is it correct to say (in a simplified sense) that the right fragment energy is generally decreasing in 2a because the right fragment is becoming shorter.Line 222: Please define a semi-normal kernel
When discussing Auvity et al. (2025) in section 3.2, can the authors elaborate on what is meant by the requirement of fracture on nonlinear waves? What kind of nonlinearities are they referring to?
Citation: https://doi.org/10.5194/egusphere-2025-1831-RC2 - AC2: 'Reply on RC2', Nicolas Mokus, 22 Oct 2025
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RC3: 'Comment on egusphere-2025-1831', Anonymous Referee #3, 06 Oct 2025
In this manuscript, the authors discuss a novel wave-induced sea ice criterion / fracture model. I think this is a generally interesting and well written study, and I am, in general, supportive of publication. I have a few comments that I would like the authors to consider and I think that the manuscript should be published once these are addressed.
- regarding section 2.1: while this is definitely interesting, I wonder how big the effect of solving the ice motion, not just assuming that the ice follows the waves (which I agree is strictly speaking incorrect), is. If I understand correctly, the results from 2.1 are used in all the following? I would be curious to see (either as additional lines in some plots, or as an appendix), a quick analysis / comparison of how much difference there is between the results using the "floes following the water" vs. the "floes moving following a balance between buoyancy and flexure" approximations. Is this a large meaningful difference in "standard" waves in ice swell conditions, or just a minor "distraction"?
- I dont have any major concerns about the results presented from a "mathematical" point of view. However, this field of study has had (in my opinion, but this may be controversial) a history of offering "mathematically rigorous" explanations and models that may have actually turned out to be "physically wrong" because in the real world, a different physical mechanism dominates. Since we are in a branch of applied physics, the ground truth we should compare to is field data, and a model per se, independently of its elegance and mathematical correctness, has no real value unless it explains the real world data better that similar or higher complexity competing models. I understand that the authors compare their results to idealized experiments, but there are so many issues with scaling, ice conditions and formation and structure, etc, that in my experience experiments often have a limited power of proof in this field - for example, the relative scaling between mechanisms and the dominating physics may be different between the field and the laboratory. In this regard, I would like to see more discussion about the following:
- though I understand this may be discussed in the reference provided, I believe that an in-depth discussion of the experimental conditions, ice conditions, etc, from Auvity et al, would be useful, being "self critical / self skeptical" and making it clear what the possible limitations are, would be useful
- can you present simple scaling analysis between your experimental data and typical field conditions, focusing on non dimensional groups that are relevant / appear in your model? Do this seem to scale the same (in which case, one can reasonably hope that the present model may be transferable to real world field data if there are no surprises (other physics) happening), or do these have large mismatches (in which case, there would still be a significant burden of proof)? Compiling all of this in a discussion and dedicated table would be useful.- As discussed above, at the end of the day, field observations and field data are the "ultimate arbiter" of what is correct or not / happening in real life or not / a good model or not (the classical "all models are wrong, but some are useful"). I think this is maybe the biggest "criticism" I have at present - if I understand correctly, this work is based on a mathematical model (and while I agree that the mathematics seem correct, I think it is fair as discussed above to ask if this is really what happens in real life) and a single, very "special case" / "idealized", experiment. I believe that to really be convinced of the applicability of the results of this paper, beyond "just" being a neat mathematical exercise, I would need to see a comparison to field data. I see two possibilities here: either 1) use existing already processed field data, directly from some of the references provided (for example Voermans et al that is referred there and may have been relying on open data / provide enough data to ensure reproducibility of the results, or some of the other references), or 2) perform your own such comparison with your own methodology from scratch based on data you have gathered, or that are publicly available. However, I understand that this is possibly a significant amount of work (maybe not for 1 if there is a smart way to reuse the data analysis previously performed, but definitely with 2), so I dont really feel that I can "require" the authors to do so in this paper. Still, I think that the authors should either go through the (possibly significant amount of work) task of doing such a comparison, or if not, at least have a very clear discussion about the fact that there is still a significant "burden of proof" on the present method to demonstrate its applicability to real world data, putting more weight on the possible limitations of the present model, and suggesting how to test this model.
- The authors discuss quite a bit previous, existing parameterization methods in the introduction. I would like to see this thread picked up more in the results and discussion, and ideally a comparison of both the mathematical behavior of these pre existing parameterizations vs. your present model (typical scaling - is it the same? different? in scaling itself, or prefactors?), and possibly theory prediction power comparisons. Are you predictions significantly different from previous parameterizations? If not, what is the added value of your model? If yes, given that in particular the "empirical criterion based" methods seem to do a reasonable work at fitting observations with ad hoc tuning, do you trust that your model is right and previous parameterizations fitted on field data are wrong / how do you do better with your present model than the previous fitted parameterizations?
Citation: https://doi.org/10.5194/egusphere-2025-1831-RC3 - AC3: 'Reply on RC3', Nicolas Mokus, 22 Oct 2025
Data sets
Fracture threshold, stationary waves Nicolas G. A. Mokus https://github.com/sasip-climate/ff1d-ftsw-pub/tree/v1.0.1
Model code and software
SWIIFT Nicolas G. A. Mokus https://github.com/sasip-climate/swiift
Interactive computing environment
Fracture threshold, stationary waves, ICE Nicolas G. A. Mokus https://github.com/sasip-climate/ff1d-ftsw-pub-ice
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- 1
SWIIFT v0.10 presents an algorithm to predict wave-induced breakup of sea ice floes. Contrary to the most widespread assumption of a critical strain for breakup, the authors implement a different physical mechanism based on energy. I do feel that the model is appropriately described and assumptions are physically justified making it very valuable contribution to the active field of research on waves and sea ice, however some statements need to be recalibrated in view of recent literature, which in parts is omitted, and to avoid overstating the value of the present contribution.
The authors focus on wave induced breakup. This is one of the possible mechanisms leading to the formation of the MIZ but not the only one, and this should be made clearer in the abstract and introduction. For example, internal stresses can be induced by wind and current forcing, and the weakening of the ice cover that promotes breakup to thermodynamic effects (e.g. melting). Moreover, to my understanding, the paper focuses on the condition in which the floes are comparable to the wavelength. While I appreciate that in this condition waves “build” the MIZ via breakup, this is only true in particular seasons and locations. The authors overlook the formation of the MIZ via for example the pancake ice cycle (in which floes much smaller than the wavelength) and is linked both to the agitation induced by the waves (mechanical process) and thermodynamic freezing.
One of the claims, as highlighted in the abstract, is that maximum strain might not be the dominant mechanism. While the energetic criterion proposed might be physically sound, a more throughout comparison with different breaking modes as discussed in a recent paper by Saddier et al (https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.094302?ft=1) should have been considered. Moreover, the calling in the question the maximum strain criterion is not completely novel. For example, in Passerotti et al, that the authors discuss, it was already shown that existing criteria do not match experimental observations.
The authors make a thorough comparison to the experiments of Auvity, a preprint. The experiments are done for a standing wave, which is an unlikely condition to be observed in the ocean where waves are likely to propagate from the open ocean towards the sea ice. I wonder why a greater effort has not been made to make a comparison to laboratory experiments of Passerotti that the author mentions (noting that these encompass a more complex random sea state). Moreover, striking is the absence in their work of mention to the work of Saddier et al that, in my view, closely resembles the one of Auvity, albeit with few notable differences (e.g. propagating waves vs standing waves, and also random waves). In addition, I feel that the authors oversell the model agreement with the experiments (Fig 8).
As a further suggestion, I believe that a working example with propagating ocean waves and a random sea state could be added to the manuscript and it would strengthen the paper.
Additional detailed comments are listed below.
In their modelling paradigm, the energy release rate G is introduced. Can the authors please explain and or suggest how its value can be evaluated in the field and lab experiments. Otherwise, this remains as a fitting parameter.
The numerical experiments are done with a brittle layer of varnish (L268), I wonder if the hypothesis of elastic plate applies to a material that the authors define brittle.
2.1 there are a couple of hypotheses in the modelling framework that, in my opinion, should be better highlighted. The plate is elastic (also the coefficients are those for a quasi-static model) and the ice does not drift.
2.3.2 the attenuation is parameterized as in Sutherland (eq 20). Can the author better justify this modelling choice and explain why other approaches have not been considered. For example an emerging trend is the ones in DeSanti et al and Yu et al (https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2018JC013865; https://www.sciencedirect.com/science/article/pii/S0165232X2200101X
). Can the author please explain/comment on how different attenuation might affect their results.
2.3.3 I do not understand the opening statement. This is reinforced by the choice of the authors of choosing a wave expressed as a variable of the x, whereas in ocean wave applications the more common approach is to provide a time series at the edge of the domain and let it evolve along the x coordinate.
3.2 The authors make the assumption of linearity. There is no discussion on the possible effect of capillarity. In the wave regime explored in the paper (small wavelength) capillarity effect might affect the wave dispersion relation.
Fig 4 the kL axis only spans one order of magnitude and I wonder if the log scale is really needed. Moreover, in the discussion the authors state that they only look at the plate between 0:L/2 because of symmetries. When a breakup occurs how do the authors make sure that this is in the first half of the plate and not in the second half? Is there a reason to believe that the floe breaks synchronously at two points (one in 0:L/2 and one in L/2:L) therefore forming 3 smaller floes.
L21 I feel that in addition to the reference to Auclair there is observational evidence showing that the marginal ice zone affected by waves is close to free drift regime and therefore substantially different from the interior. Addition of appropriate references would strengthen the statement. Moreover, in addition to reference to Thomson, I suggest adding the recent work by Toyota et al (https://www.sciencedirect.com/science/article/pii/S1873965225000520
).
L35 I find this sentence unclear.
L137 for the readership benefit, can the author state what it means unstretchable.
L255 can the value of Y and nu be explicitly specified?
L264 the relationship for polychromatic cases should be explicitly stated for clarity.
L420 can the author better clarify why the definition of the relaxation length differs from Auvity. Can the two be reconciled?
L515 the example does not refer to “typical field conditions” as this is a transient ship wake and not a MIZ formed by open ocean waves.