the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 11 May 2026
Consistent ridging and opening coefficients for multi-category sea ice models with modified viscous-plastic rheologies
Abstract. In multi-thickness category sea ice models, subgrid-scale ridging and the opening of leads are represented by a redistribution function. This function modifies the thickness distribution based on grid-scale strain rates. There is a physical link between sea ice rheology and redistribution by assuming that the work done by internal stresses in deforming sea ice is equal to the change in potential energy and frictional loss during the formation of ridges. Hence, modifications of the rheology require changes to the redistribution function to be consistent. For the special case of an elliptical yield curve and a non-normal flow rule, associated consistent ridging and opening coefficients can be formulated such that they reduce to the standard ones in the case of a normal flow rule. It is further demonstrated that the coefficients are independent of biaxial tensile strength. Satisfying specific criteria for the yield curve and plastic potential aspect ratios ensures that the ridging and opening coefficients are bounded by 0 and 1.
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Status: open (until 07 Jul 2026)
- RC1: 'Comment on egusphere-2026-1362', Anonymous Referee #1, 25 Jun 2026 reply
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This paper presents modifications to the standard ice thickness redistribution formulation to make it compatible with VP rheologies that use a non-normal flow rule. The authors also demonstrate that no modifications to the redistribution formulation are required when tensile strength is introduced. The paper is well written and organised, and the results are presented clearly and concisely. The work is interesting, if somewhat niche.
My only major concern is motivation and context for the results. Since the paper has been submitted for publication in The Cryosphere, I would expect a broader discussion of the potential impact these numerical changes may have on our understanding of the physical system. As it stands, the paper is a better fit for, e.g., GMD, where I would probably only have asked for minor revisions. However, with some not-very-major revisions, I think the paper would be fit for publication in The Cryosphere.
Introduction: The authors need to expand substantially on why using a non-normal flow rule is of interest. At the moment, only the use of tensile strength is properly motivated. Still, since the default formulation for it is already valid, I would even skip discussing it in the introduction (the paragraph starting at line 40). Also, a brief explanation of what the phrase "non-normal flow" means could be useful in the introduction (even if a more detailed explanation comes later).
Discussion and concluding remarks: There is no mention here of the impact on simulated volume and ice growth, but this is what a more general (The Cryosphere) audience is interested in. If I understand the paper correctly, your results show that the impact of using a non-normal flow rule is substantially smaller than that reported by Lemieux et al. (2025). Is that correct? This should be highlighted in this section. You should then also discuss the relevance of using a non-normal flow rule for large-scale modelling. If the conclusion is that using a non-normal flow rule has a very limited effect, then that may feel counterproductive, but it's still very important for the community to know. A strong conclusion like that would also make this paper much more interesting than it looks in its current version and significantly improve its impact.
Minor comments:
L65: I understand that you're implementing your ideas into CICE, but I'd always mention Lipscomb et al. (2007) first and only put CICE in parentheses.
Eq 14: I think it would help the reader to point out that this is the same equation as Eq (3) with \alpha_0 (\theta) P_o |\dot\varepsilon| added
L180: Why introduce the second incorrect formulation? You show INC1 because that's what Lemieux et al. (2025) did, but INC2 is not well motivated.
L248: Shouldn't the limit on e_F = e_G be \sqrt{3}/2 and not 1? As per eq (36). This is a nice result that deserves better highlighting in the discussion and conclusions. Does this also mean that in a model without an ITD, we should only use e > \sqrt{3}/2?