the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 May 2026
The implementation and effectiveness of Calving Algorithms in numerical ice models (CalvingMIP)
Abstract. Ice calving plays a significant role in ice sheet mass loss. Predictions of future ice sheet mass balance require accurate representations of the calving process in numerical ice models to determine rates of future global mean sea level rise. Whilst calving has recently begun to have been implemented in numerical models there has not been a systematic investigation into how this implementation compares between different ice flow models. The Calving Model Intercomparison Project (CalvingMIP) has been established to address this question by providing a framework of experiments to investigate the accuracy of simulated calving rates and how simulated properties at the calving front evolve over time. Our initial focus has been on how calving is implemented in models, therefore focusing on calving algorithms, rather than on how much ice should be calved at a particular time (calving law). Our results, from thirteen different numerical modelling groups, show that the majority of calving algorithms implemented are able to accurately implement a given calving rate with an ice front that evolves smoothly throughout the calving process. These results show that we can have confidence in the models capacity to accurately implement calving laws in the future.
Competing interests: At least one of the (co-)authors is a member of the editorial board of The Cryosphere.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-1962', Anonymous Referee #1, 23 Jun 2026
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RC2: 'Comment on egusphere-2026-1962', Anonymous Referee #2, 15 Jul 2026
This paper presents an inter-comparison of several ice sheet models on a pair of test cases for calving algorithms. The goal is to assess the ability of numerical models to implement calving algorithms with a fixed law for how the terminus evolves as a step towards studying the physics of calving. This is an important first step. If numerical methods for simulating terminus evolution are not reliable, then that problem has to be solved before making claims about physics based on simulation results.
The paper succeeds in getting a comparison among many different ice sheet models and in improving calving algorithms during the process. I think this is a valuable contribution to the collective knowledge and should be published. I have a few reservations. I think the authors make a few claims that are not justified by the results. I also think there was a missed opportunity to probe further at the characteristics of the different numerical methods that were used.
The focus on continuous terminus evolution makes sense given the simulation techniques we have today (typically level-set methods). But the paper makes statements about several places about its applicability to Antarctic calving. Continuous evolution of the terminus is a good approximation for Greenland but it is well established that much of the calving mass loss in Antarctica is due to massive calving events that occur every few decades. That timescale is longer than a typical timestep used in a numerical model. The paper claims that its results lend confidence in models' ability to simulate calving. I would walk this claim back to saying that its results lend confidence in models' ability to simulate one type of calving. This is not to impugn this (very important) work; arguably it isn't reasonable to expect models to be able to do large infrequent tabular calving events with today's numerical methods.
My other criticism is that the authors make a few statements to the effect that there is broad agreement among the models. The paper is still valuable even if the models don't broadly agree: a negative result is still a result. I think the results, which the authors communicate and illustrate very well, don't justify these statements. For example, figures 9 and 10 show (to my eye) substantial behavior differences between the models. Again, this is a significant result in itself -- it means that numerical modelers have more work to do! I think it would be better to say for example that figure 9b shows that the models relax to the same end state but that some of their trajectories differ rather than claiming that there is broad agreement.
Many of the figures (4, 9, 10) show substantial differences between how smooth the model trajectories are. I would have liked to see some more in-depth analysis as to why some show clear stair-step patterns and others do not. For example, if the results show that level-set methods or anisotropic meshes can give smoother trajectories than other schemes, then that is valuable information guiding how future models should be constructed. In the discussion section, the authors state that there were not systematic differences attributable to the scheme but rather argue that the more extreme results are due to how they were interpolated to a regular 5km grid. If that's the case then it's not clear whether the project is an intercomparison of the accuracy of calving algorithms or of interpolation methods.
Specific comments:
22-25, "widely varying spatial and temporal scales": I think it's more fair to say that the reason for this simplification is because free boundary problems are demonic and most people don't want to deal with them if they can avoid it.
25-27: I agree if you make this statement about Antarctica but it's harder to make the claim for Greenland.
38-39: This is more of a philosophical debate but if you believe that stochasticity is important then it's a good question to ask whether a hypothetical calving model should exactly reproduce an individual observed trajectory or whether we need different ways to evaluate hypothetical models.
77-78: Is it possible that some desirable properties of the model cannot be achieve with a rectilinear grid? For example, if you try and compute the perimeter of a circle but you discretize the interior/exterior on a regular grid then you never get the right answer.
362: Should this be a melt rate equal to the local ice thickness divided by the model timestep? A melt rate has to have units of thickness / time.
401-410: What's going on with UFEMISM here? This looks like a sampling error which could unfairly make that model look worse than it is.
Figure 8: These look near identical in the eyeball norm, it would be better to plot the differences against some baseline (e.g. the average thickness among all models) with a diverging color map.
435, "good general agreement": these look noticeably different, I'd say the final states agree but the trajectories differ
451: The absolute magnitudes are close enough but there are noticeable differences among the models. Some are oscillating, others are smooth. If we could rule out the possibility that this was a sampling or interpolation artifact then those oscillations looks like a numerical artifacts. That's understandable when simulating such a challenging system but it's hard to draw a conclusion one way or the other if, as the authors say, this might just be because of interpolation.
Citation: https://doi.org/10.5194/egusphere-2026-1962-RC2
Data sets
CalvingMIP – Calving algorithm simulations James R. Jordan, Frank Pattyn, and The CalvingMIP Team https://zenodo.org/records/20041205
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This is a valuable community paper and an important first step for systematic evaluation of calving in numerical ice-sheet models. The manuscript is well motivated, the experimental design is appropriate for a phase-1 algorithm-focused MIP, and the results will be useful for model developers and users. I recommend publication after following revision.
1. Line 245, "floating cells adjacent to ....", does this mean CISM only capture floating shelf calving? Can it capture grounded glacier calving activity?
2. Table3, there is a clear resolution mismatch for IMAU UFEMISM (20km) coarser than all the other models. Can results be replaced with 5km resolution simulation instead? In fact, shouldn't IMAU be consistent with NCAR CISM's results with the same resolution (at least for circular domain where calving rate direction doesn't make diffrence)?
3. Have all these models conducted convergence analysis on grid size? Might be a good idea to put it in SI and make sure the paper presents converged result from each model.
4. In conclusion text, the author claims calving algorithm does not make a noticeable difference for the result. To justify that, the author should first justify in table3, other variations do not skew simulation results. (for instance, is it safe to claim in current configureation, HO and SSA has similar results, any scaling argument to justify this? The author has already justified for the circular domain, calving rate direction shouldn't make any difference on the results)
5. Line 385, when interpreting Figure3, I can see the outliers are IMAU & AWI YELMO, is it a typo that the author emphasize PIK PISM intead?
6. Fig.3 and Fig.9 are not consistent. The outlier changes from IMAU & AWI YELMO to IMAU & PIK PISM, why?
7. For each figure, after stating which models deviate from theory/other models, the authors can add more explanation of why that happens, and mitigation strategies to fix that (if possible).
8. The project is very valuable as stated by the author "whilst undertaking the work for this project most models significatnly imporved their results for those initially submitted, both in terms of accuracy as well as spotting previously unnoticed errors in their code". Can the author highlight what bugs in the code for different models were fixed during this project (maybe summarize in a table and attach as SI)? I think the list of "common mistakes to make" is very valuable for students who just start learning ice sheet models. The table can also highlight the mitigation strategy to be implemented in the future, for those models that exhibit limitations during this project.