the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 Feb 2026
Comparing calving laws at Greenland’s three largest ice shelves
Abstract. The retreat of Greenlandic glaciers through calving has major implications for the ice sheet's mass balance and future sea-level rise contributions. Despite its importance, the implementation of calving in ice sheet models remains contested, with several calving laws suggested to parametrise this process. While the performance of some of these calving laws has been tested for Antarctic ice shelves and Greenland's grounded outlet glaciers, it is unclear which calving law would best capture the observed behaviour of Greenland's ice shelves. Petermann, Ryder, and Nioghalvfjerdsbræ (79N) glaciers are fronted by Greenland's three largest ice shelves, accounting for 90 % of the remaining floating ice and buttressing ~15 % of the ice sheet's mass. Here we build on other systematic calving studies by comparing five calving laws at Greenland's three largest ice shelves using the Ice-sheet and Sea-level System Model (ISSM). We begin by constraining the performance of each law against observed terminus fluctuations between 2008 and 2024, and continue with projections to 2300 under various climate forcings. When evaluated against observed terminus changes, we recommend the use of a von Mises or Crevasse Depth calving law owing to their consistent performance and similar tuning parameters across the three ice shelves. However, in our extended projection runs, we find that calving parametrisations have little influence on grounding line discharge rates, which are instead driven by the choice of climate forcings. Large ice shelf calving or collapse events are scarce, and only in these rare cases do we find any pronounced grounding line response. Our results indicate either continued buttressing potential from Greenland's ice shelves into the coming centuries or fundamental flaws in the current set of calving laws that involve calibrating to contemporary ice-shelf behaviour.
- Preprint
(26737 KB) - Metadata XML
-
Supplement
(8620 KB) - BibTeX
- EndNote
Status: open (until 18 Mar 2026)
- RC1: 'Comment on egusphere-2026-436', Anonymous Referee #1, 23 Feb 2026 reply
-
RC2: 'Comment on egusphere-2026-436', Ellyn Enderlin, 11 Mar 2026
reply
The study assesses the performance of five calving parameterization at Greenland’s three large ice shelves through a comparison of modeled and observed terminus positions from 2008-2024. The assessment is quite holistic because it considers both the area misfit as well as terminus shape. After identifying the optimal tuning parameters for each calving parameterization, the authors perform sensitivity tests to determine the impact of the choice of calving parameterization on mass loss projections for the ice shelves under three different types of forcings (atmosphere-only, melt at the grounding line, melt across the ice shelf). They find that the Von Mises and Crevasse Depth calving parameterizations are the best suited for modeling the evolution of the ice shelves in recent years but that the calving parameterization has little impact on mass loss projections.
I really enjoyed this paper. It is very well written and the figures are terrific. I have a few minor comments throughout but I commend the authors on a well-formulated study and associated paper.
Minor Comments
Note that as an American I use the spelling “parameterization”, not “parametrisation” as used by the authors, and defer to the editorial team to decide how it should be spelled.
Line 5: Change “are fronted by” with “terminate as” or something similar.
Line 14: By “grounding line response” do you mean a change in discharge across the grounding line or a change in the position of the grounding line, or both?
Line 15: Replace “that involve calibrating to” with “when calibrated to”
Line 28: Replace “SLR” with “sea level rise”
Lines 37-39: This sentence somewhat implies that the shift in calving regime is driven by the accelerated mass loss, not the change in terminus geometry. Please rephrase. I also recommend adding references to publications that analyze calving style, such as Kehrl et al. (2017; https://doi.org/10.1002/2016JF004133) and Bézu and Bartholomaus (2024; https://doi.org/10. 1029/2024GL110224).
Lines 46-51: I recommend that you add a reference to Miele et al. (2023; https://doi.
org/10.1029/2022JF006959) in here where appropriate.
Line 101: I had difficulty visualizing the melt profiles because I have always been under the impression that models need to prescribe zero submarine melting at the grounding line to maintain numerical stability. Either this is untrue for ISSM because of its degree of sophistication or the authors’ description is a bit too simplistic. Please be more specific with your description than “the highest melt rates occur near the grounding line” because this is quite ambiguous. Are the highest melt rates at the mesh nodes just seaward of the grounding line, 10s of meters away, 100s of meters away?
Line 106: When the ice front becomes grounded, presumably this adjustment to the submarine melt parameterization means that it is now a horizontal melt rate rather than a vertical melt rate, correct?
Line 150: Do you use a nearest neighbor approach to estimate R from RACMO for each mesh node? Do you do any interpolation or down-sampling?
Eqn 12: I thought through this equation for quite a while and I still have a difficult time reconciling aspects of it. Can (r-r_c)/(1-r_c) ever be negative? I can see how it could be less than or greater than 1, which explains why the “min” is included in the equation, but I have not been able to think through why the max is included other than simply to guarantee that the calving rate is never negative because that would imply false lengthening of the glacier. Additionally, the results presented in the paper indicate that r_c =1 for Ryder and 79N and that would cause division by zero. Does that mean that the calving rate for these glaciers is simply dictated by M_max because the terms in parentheses default to 1? The authors do not need to massively elaborate on this equation but one or two more sentences to explain it here would be really helpful.
Line 183: I’m not sure if you mean that you explored values for K between the two numbers that are listed or you somehow used a varying interval across a range of explored values. Please clarify.
Line 189: Replace “kept fix” with “kept fixed”
Line 201: If you only increase melt at the grounding line, does that mean there is a big spike in the melt profile followed by the same linear decrease in melt with depth that was prescribed in the relaxation runs? Or did you increase the melt at the grounding line and adjust the linear melt curve so that melt is now increased nearly everywhere but the amount of the increase decreases with depth until it matches the initial value at the waterline?
Figure 3: I was initially confused by the “ in the figure legend. My interpretation is that the grounding line positions are identical for all the calving parameterizations based on the caption, but that is not immediately clear when looking at the figure. I’d consider replacing those marks with an orange dashed line to make it more explicit that the grounding line in orange is valid for all the calving parameterizations like in Figure 4.
Line 284: Replace “sees discharge rates decline” with “drives a decline in discharge rates”
Line 369: Add a reference to Enderlin and Bartholomaus (2020; https://doi.org/10.5194/tc-14-4121-2020) in this section. They found that up to tens of meters of water would need to be added to crevasses in the CD parameterization to match observed crevasse depths. For Ryder they estimated 6.1 m of water would be needed, which is more than but comparable to your results. Although Zachariæ Isstrøm is not included in your study, it abuts 79N and they obtained a similar water depth there (3.2 m) as you estimated for 79N.
Line 435: Replace “sees a greater” with “produces a greater” or something similar.
Citation: https://doi.org/10.5194/egusphere-2026-436-RC2
Viewed
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 223 | 136 | 17 | 376 | 53 | 44 | 23 |
- HTML: 223
- PDF: 136
- XML: 17
- Total: 376
- Supplement: 53
- BibTeX: 44
- EndNote: 23
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
Overall, I find the manuscript to be a very well written and clearly presented investigation into the impact of using one of five different calving on the future behaviour of the calving front of three Greenlandic ice shelves. This is a very topical and impactful area of research, as our ability to simulate ice shelf calving is a known area of uncertainty when making predictions for how ice sheets will respond to a warming climate. I am happy to recommend publication, provided my comments can be addressed.
My first comment is that the calibration exercise does not currently show the impact of calving front shape on ice discharge (although this can be inferred from time 0 on Fig7). It might be good to have a figure showing this.
Currently you are tuning to minimise the misfit in total shelf area. Potentially, this could result in a shelf front being greatly advanced on one side of the domain whilst retreated by the same amount on the other. This is likely to have a quite different amount of buttressing when compared to a shelf position that is everywhere on the observed position, despite similar misfits. It can also potentially ignore an ice shelf that has detached from a lateral boundary. For example, the observed position of Petermann in Fig 2(i) compared to the MT law on the left hand boundary. Perhaps incorporating a comparison to observed discharge rates in combination with the area match might be a better metric for calibration?
My second comment is in regard to the melt profiles used for forcing. My understanding is that all simulations have a minimum melt layer that never experiences any melting near the surface. Whilst I gather this is a good match to present day observations, can you comment on how likely this is to continue in a warming climate? Do you see any evidence of ice thickness at the calving front being strongly linked to your choice of this minimum melt layer (is it ~110m at Ryder to match the minimum melt depth, for example)? Perhaps a figure showing flow line profiles of ice thickness could help here. Do you results appear unduly influenced by the choice of the size of this melt layer?
Line comments/typos below.
L103: Can you comment on the different melt profiles used for Petermann and Ryder, despite them being so geographically close to each other? Are the different profiles assumed to be a result of differences in ocean forcing or due to the shape of each ice shelves cavity?
L111: How often is this limiting maximum migration rate used in the simulations? For an example, is there an approximate percentage of time for the run where this maximum is reached?
L115: For clarity, define whether a positive calving rate advances or retreat the front position.
L115: In which direction is this calving rate applied? Perpendicular to ice geometry at the calving front, or antiparallel to ice velocity at the calving front?
L130: For the Crevasse Depth and Minimum thickness laws. Are these applied at every model time step or some longer interval? (Monthly, Yearly, etc)
L189: "kept fixed in our"
L200: To clarify, does this mean that all simulations still maintain their minimum melt sections of 0 melting during these warming scenarios? If so, the term oceanFull may be a little misleading.
L209: Are there any cases where you chose a parameter that gave you a qualitatively better match to ice front position even if the quantitative misfit value was worse?
L295: In the static case for Petermann, VM has a greater front retreat rate than CD during the 2100s, and yet CD has a greater retreat of the grounding line. Can you comment on this?
L328: Should velocities be ice discharge here?
L331: VM and EC appear the best on average, but do noticeable worse on Petermann. Can you comment on this?
L395: Is it unreasonable to calibrate for individual Glaciers in large scale ice sheet simulations? It will certainly be more work, and will require some technical challenges around the boundaries between different glaciers, but I don't foresee any absolute barriers to doing so. Your results from just three glaciers already imply differences in how each law performs at different glaciers.
L448 able to parameterise