Holmes et al. present an Elmer/Ice-based modeling study regarding calving dynamics at Kronebreen, Svalbard, that yielded important insights into the field of calving initiation due to frontal undercutting. I congratulate the authors to this thoroughly performed and discussed modeling study. I have no severe concerns regarding publication of this article. However, in its present form, especially the visualization of the results lacks clarity and needs to be changed/improved in order to make the figure content more easily accessible to the reader. I recommend to accept the manuscript of Holmes et al. for publication in The Cryosphere after a minor revision along the issues outlined below.

Detailed comments:

L15: Maybe Svalbard should also be mentioned here, as the paper is about Svalbard.

L19f: Strictly spoken, "frontal ablation" also contains subaerial melt and sublimation at the calving front and should be mentioned for clarity (see Cogley et al. 2011, Glossary of Glacier Mass Balance, for details).

L24ff: Maybe it would be worth adding Svalbard's tidewater glaciers that have shown retreat over recent decades, which implies substantial calving (e.g. Braun et al. 2011, doi:10.1111/j.1468-0459.2011.00437.x).

L64: "supra-glacial melt" is rather odd, "surface melt" would be the right term (also to be corrected in the following)

Fig. 1: left panel: name the most important currents in the map; right panel: no needs for three decimals (one is enough)

L105: I'm not sure if this is the right location, but in any case it needs to be noted that you do not consider subaerial frontal melt/sublimation in your modelling.

L106-109: Additional information about e.g. mean velocities and errors/uncertainties of the calculated velocities must be presented here. Given the nature of the study, velocities at the front should be given special attention.

L179ff: The position should be mentioned from where the profiles were measured (maybe also indicate them in Figure 1).

Table 2: The term "Large icebergs" should be quantified somehow in the caption so that it can directly be distinguished from "All icebergs".

Fig. 4b/c: I find it very hard to distinguish between "All size" and "Large" in those figures. The presentation of the data should somehow be changed so that a straightforward differentiation is possible. I also think that this kind of plot is inadequate to visualize the results, as +80 and ‑80 cm are located in direct vicinity. A linear bar plot would be correct instead (it would also solve the problem that lines overlap frequently for small numbers of icebergs, which is in parts responsible for the problematic readability of the graphs).

Fig. 5: Same comments as for Figure 4. This needs to be changed here, too.

L264: correct to "... an impact ..."

Discussion section: It might be worth taking a look at another study that analyzed calving at Kronebreen (Sund et al. 2011, TCD, https://tc.copernicus.org/preprints/tc-2010-104/), even if the paper was not accepted for final publication. Maybe it gives some additional insights into the discussion.

Fig. 7: I have some problems with this figure, too: While I like the idea of showing the profiles in perspective, I think this makes visual comparison of the undercut sizes almost impossible. In (a) sizes are given for profiles 2 and 3. It appears that the undercut in profile 2 is about four to five times as large as thin in profile 3, but this is by no means supported by the values given. Moreover, it is strange that profiles 1 and 4 are shown with their numbers, while undercut values are given for profiles 2 and 3. I suggest to change the presentation of the profiles in (a) to individual x (distance from calving front) vs. y (depth) line graphs. This would allow the reader to get the right idea of the sizes of the undercuts.

L345 "We note..." instead of "The authors of this paper note..." ?

L390: It needs to be discussed to which extent the fact that subaerial frontal melt was not considered in the model (only one single simplified overall frontal melt), has an impact on the results. I mean, frontal melt rates are different below and above the water line, which clearly also impacts the creation of undercuts.

It looks like this manuscript already has three expert reviewers and I have little to add to the discussion already underway.  I support publication of the manuscript and detailed reviews already provided.  I will keep my comments brief to avoid torturing the review process.    

My first recommendation is one that I always provide for all numerical studies.  I humbly suggest that the authors consider a numerical convergence study with different element sizes and time step sizes.  A few years ago, Brandon Berg and I ran into some subtle issues with the standard Elmer Ice implementation of no-penetration boundary conditions (Berg and Bassis, 2020).  The effect was subtle and only manifested itself after re-meshing when we removed calved blocks of ice.  However, the fix that we proposed was (I think?) incorporated into Elmer-Ice.  Nonetheless, an important lesson for us based on that is to always do numerical convergence studies to make sure things behave as expected.

The study we were trying to do when we discovered the numerical artifacts was to see if advection of crevasses was important in the process (Berg and Bassis, 2022).  The Nye zero stress crevasse model assumes that glaciers have no fracture memory and that if a crevasse cannot form the detachment boundary of an iceberg, crevasses immediately close leaving no trace.  When we look at glaciers, we clearly see crevasses have initiate upstream and propagated downstream.  Where this is relevant is because, as other reviewers pointed out, the stress near the calving front depends on the shape of the imposed melt profile along the calving front, a small amount of crevasse advection from just upstream of the calving front could have a significant effect on the predictions any crevasse depth model.  One of the conclusions from Berg and Bassis, 2022 was that advection *sometimes* mattered.  The fact that advection *might* be important could be a worthwhile caveat because I wonder if you will end up with slightly different conclusions is you include advection and/or different melt profiles.

I leave these comments at the discretion of the authors to consider and I want to be clear that I am using the two cited studies as examples that illustrate my own experience working on slightly related problems and I am not requesting that the authors cite either of these manuscripts.

Berg, B. and Bassis, J.: Brief communication: Time step dependence (and fixes) in Stokes simulations of calving ice shelves, The Cryosphere, 14, 3209–3213, https://doi.org/10.5194/tc-14-3209-2020, 2020.

Berg, B., & Bassis, J. (2022). Crevasse advection increases glacier calving. Journal of Glaciology, 68(271), 977-986. doi:10.1017/jog.2022.10