the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 20 Jan 2026
Brief communication: Nye was right!
Abstract. Despite decades of study, predicting crevasses penetration depths remains controversial. Nye provided one of the earliest estimates of crevasse penetration depths. Recently, a new theory, called the horizontal force balance (HFB), challenges Nye's model, suggesting crevasses can penetrate much deeper than predicted by Nye. Here we use a numerical model to show that Nye's estimate remains accurate so long as crevasses are closely spaced, but crevasses penetrate deeper as the spacing increases. Moreover, contrary to many parameterizations of crevasses as damage in depth-integrated models, we find that crevasses do not increase the stress in the intact portion of the ice.
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Status: open (until 03 Mar 2026)
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CC1: 'Comment on egusphere-2025-6384', Donald Slater, 22 Jan 2026
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AC1: 'Reply on CC1', Jeremy Bassis, 23 Jan 2026
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We appreciate the comment by Donald, especially since comments played such a key role in some of the earlier work in this field. In short, Donald’s questions are exactly what we were hoping for when submitting. We can clarify two points immediately since in retrospect we realized our exposition was not clear as we had hoped and we want to avoid these issues plaguing other readers before we have the opportunity to clarify some of the text.
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1. In retrospect, we realize that our prose was more ambiguous than we had hoped, but we did simulate crevasses as discontinuities in the ice and applied ocean pressure as a traction boundary condition on bottom crevasses walls. Our method only superimposes ocean pressure in the region of ice immediately above bottom crevasses that is not yet fractured, but would be water-filled if it did break. We did check that our method of computing crevasse depths was consistent with other estimates, like the energy method that does not depend on these slightly opaque extra steps. There is a slightly embarrassing issue in that we did assume that  the portion of bottom crevasses that penetrate above the water line are air-filled, which is not obviously true if the ice is impermeable. This small, technical issue does not influence our results and allows us to compare directly with other simulations that made the same simplification, but does beg for a more physical description of the fluid-crevasse interaction in the future.
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2. The stress concentration that we examine is indeed the case (ii) described by Donald. Although perhaps not as clear as we had hoped, we computed the average horizontal stress in the region that lies *above* bottom crevasses and *beneath* surface crevasses and compared this average stress to the background deviatoric stress that we imposed as a boundary condition.  The "stress in the uncrevassed portion of the ice shelf between crevasses" was meant to indicate the vertical portion of an ice column above the bottom crevasses and beneath the surface crevasse.   (We should really have included this in a diagram.). This is partly motivated by damage mechanics where damage associated with micro-cracks and voids reduces the load-carrying cross-section of a representative volume element. However, damage mechanics is traditionally applied to small regions of a crack and not to represent the larger scale effect of crevasses on the stress within a column of ice. Our simulations emphasize that so long as crevasses are closely spaced, the stress in the region above bottom crevasses and beneath surface crevasses is completely unaffected by the presence of the crevasses.  In fact, as Nye originally hinted at, there is no stress concentration at all in this case.
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The final issue raised by Donald is also a good one.  We currently only show the total combined depth of crevasses. We did, in fact compute the depth of bottom and surface crevasses independently. The only reason we don’t show these results is because we couldn’t find a way to do it that didn’t make the plots overly busy and the discourse we could provide around this issue didn’t seem to add anything that wasn’t already present in the literature (e.g., Jiménez and Duddu, 2018). We can show these if they are of interest to any readers as additional figures or, perhaps we can rethink the visualization to add more information to the current figures.
Citation: https://doi.org/10.5194/egusphere-2025-6384-AC1
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AC1: 'Reply on CC1', Jeremy Bassis, 23 Jan 2026
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RC1: 'Comment on egusphere-2025-6384', W. Roger Buck, 28 Jan 2026
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Nye was right to make several simplifying assumptions to give the first estimate of the depth of crevasse opening (Nye, 1955). A key simplifying assumption of Nye (1955) is that opening of closely spaced crevasses does not change the stress in the un-crevassed ice. As noted in Buck (2023) this assumption requires that the horizontal forces are not balanced when crevasses open in an ice shelf. The paper submitted by Bassis et al. considers whether Nye’s approximate solution applies to the case of penetration of crevasses through an un-buttressed ice shelf. They present results from an impressive array of numerical cases that simulate the opening of multiple crevasses within a wide domain of either elastic or viscous floating layers. They report the fraction of the layer cut by imposed, co-located surface and basal crevasses. This fraction is shown to depend on the spacing of the crevasses; with a single isolated crevasse pair cutting nearly through the layer; while for crevasses spaced closer than the layer thickness the crevasses cut about halfway through the layer.
The reported results imply that the crevasse spacing somehow changes the average force in the shelf. Given that no horizontal tractions are applied to the sides, top and bottom of the layer (with the exception of the small tractions related to flexural deflections of the layer) this result at first appears to violate Newton’s second law. One would expect the horizontal forces to balance and be uniform at all horizontal positions in an un-buttressed shelf (e.g. Buck, 2023; Coffey et al., 2024; Slater and Wagner, 2025; Coffey and Lai, 2025). Bassis et al. conclude that their results mean that the force balance does not apply to this problem. The numerical calculations appear to be done correctly, but the unphysical results stem from use of boundary conditions that are wrong for the problem considered.
The correct boundary conditions on the seaward end of a floating ice shelf are normal stresses applied by water, as has been accepted since the earliest analysis of stresses in an ice shelf (Weertman, 1957). Bassis et al. use this boundary condition only for cases with a single crevasse. The bulk of the model cases reported in the manuscript use fixed displacement (or fixed velocity for the viscous cases) boundary conditions on the seaward end of the layers, instead of stress conditions. The boundary condition is chosen to result in the correct average stresses (or horizontal force) when the ice shelf is un-crevassed. The problem is that with fixed displacement boundary locations, crevasse opening changes the horizontal stress (and force) in a layer. Thus, a numerical solution with a fixed displacement condition leads to a horizontal force that depends on the number of assumed crevasse locations. This is not the case for fixed stress boundary conditions.
A thought experiment considering a stretched rubber band, in lieu of an ice shelf, illustrates the boundary condition problem. First, stretch a long band (with a length 10 or more times the width, w, of the band) and nail down the ends. The force required to do this depends on the elastic properties of the band and on its width, thickness and the amount of displacement of the ends. Then, cut half way through the width of the band at one point far from the ends of the band and the band stretches a little more around this point. To keep the band the same length, given the pinned ends, the band has to stretch a bit less everywhere else. This results in a small reduction in force required to stretch the band, but the stress in the part of the band above the cut has nearly doubled. Next, make many identical vertical cuts half way through the initial width that are close together compared to w. Effectively, the band then behaves like a uniform band with half the initial width. Given the fixed displacement boundary conditions the strain is everywhere equal to the initial strain of the uncut layer. Thus, the horizontal stress in the band is the same as it was before the cutting, but the force (which equals the average stress times the width) on the securing nails is reduced to half of its original value.
Doing the same experiment, but with a constant force on the end of the band would give a very different result and one more applicable to ice shelves. Imagine that a weight is attached to the bottom end of a vertical rubber band that is pinned at the top. In this analogy, the weight represents constant normal stress from seawater. Next, cut half way through the width of the band at one place along its length. Then the band will slightly lengthen but the force everywhere says the same. Adding more cuts does not change the force maintained by the band, but does change its length. The more cuts we make the more the band will lengthen. As before closely spaced cuts that each cut halfway through the layer means that the band then acts like band with a width w/2.  In that limit, the displacement of the end attached to the weight will be double the initial displacement. Thus, the strain and so the stress in the band has doubled, but the force (that equals twice the initial stress times half the initial width) has not changed. Clearly, the fixed force boundary condition gives a very different result for the stress in the uncut part of the rubber band than does the fixed initial displacement condition. Using the correspondence principle, a similar argument also holds for the case of a viscous layer with fixed velocity boundary conditions.
An impetus for the Bassis et al. study is that the horizontal force balance appears to imply that an un-buttressed shelf should break apart via calving, as crevasses cut through the shelf. The fact that un-buttressed ice shelves do exist is taken to mean that a such a force balance cannot be correct. However, in a recent abstract and talk at the Fall meeting of the American Geophysical Union I describe how a strong vertical variation in viscosity through a shelf can prevent such calving. A paper on the effect of viscosity variations on predicted calving assuming forces balance is in preparation.
This paper could be a useful contribution if the authors were to re-run their models with the correct and accepted (stress) boundary conditions for all their cases. The authors could then and show how the stress boundary condition changes the results compared to the cases with fixed displacement (or fixed velocity for the viscous case) horizontal boundary conditions done so far.
References
Buck, W. R. (2023) The role of fresh water in driving ice shelf crevassing, rifting and calving, Earth and Planetary Science Letters 624, 118 444, https://doi.org/10.1016/j.epsl.2023.118444, 2023.
Buck, W. R. (2025) How Basal Melting Can Cause Calving of Ice Shelves (C31A-04) presented at the 2025 AGU Fall Meeting.
Coffey, N. B., Lai, C.-Y., Wang, Y., Buck, W. R., Surawy-Stepney, T., and Hogg, A. E (2024) Theoretical stability of ice shelf basal crevasses with a vertical temperature profile, Journal of Glaciology 70, https://doi.org/10.1017/jog.2024.52.
Coffey, N. B. and Lai, C.-Y. (2025) Horizontal force balance calving laws: Ice shelves, marine- and land-terminating glaciers, Journal of Glaciology 71, 1-23.Â
Nye, J. F. (1955) Comments on Dr. Loewe’s letter and notes on crevasses, Journal of Glaciology 2, 512–514, 1955.
Slater, D. A. and Wagner, T. J. W. (2025) Calving driven by horizontal forces in a revised crevasse-depth framework, The Cryosphere 19, 2475–2493, https://doi.org/10.5194/tc-19-2475-2025, 2025.
Weertman (1957) Deformation of floating ice shelves, Journal of Glaciology 3, 38–42.
Citation: https://doi.org/10.5194/egusphere-2025-6384-RC1
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I thank the authors for this succinct and thought-provoking manuscript that I have enjoyed reading and reflecting on. I am not in the habit of posting Cryosphere comments and wonder if my thoughts are worthy of a comment or more the sort of questions I'd like to discuss over lunch; still, I'm sufficiently interested that here we go.
I'm unsure what the boundary conditions imposed on the crevasse walls in the numerical simulations are. In particular, is there water pressure imposed on the walls of the basal crevasse? (I note the text on L140 here but that didn't totally clear this up for me). If I'm following correctly, the use of the horizontal effective stress to estimate crevasse depths suggests the water pressure is accounted for only after the numerics have run. If so, could your results change if you did have water pressure imposed on the walls of the basal crevasses, because then that water pressure could impact the simulated stress field?
I understand that the simulations have both basal and surface crevasses, and that these depths were varied in different simulations. The results report only the crevasse penetration ratio r, which is the normalised sum of the surface and basal crevasse depth. This makes me wonder how, for a given r, you chose the relative size of the basal and surface crevasses and whether that matters?
Lastly, I was interested to see the results on the stress concentration. But, I ended up doubting what is meant by "stress in the uncrevassed portion of the ice shelf between crevasses", "intact portion" etc throughout this section. Looking at e.g., Fig. 1, does this refer to (i) the intact ice that has full thickness between adjacent surface crevasses, or (ii) the intact ice that sits between a vertically-aligned surface and basal crevasse? If (i) - as the word "uncrevassed" might suggest to me - is that the most relevant place to consider the stress concentration? At least within the HFB framework, it is the stress concentration in definition (ii) that leads to larger crevasses than the Nye definition.
Best regards,
Donald Slater