A Model for Antarctic Ice Shelf Hydrology and Stability (MONARCHS v1.0)

Buzzard, Sammie; Elsey, Jonathan; Robel, Alexander

doi:10.5194/egusphere-2026-3247

Preprints

https://doi.org/10.5194/egusphere-2026-3247

Preprints

13 Jul 2026

| 13 Jul 2026

Status: this preprint is open for discussion and under review for Geoscientific Model Development (GMD).

A Model for Antarctic Ice Shelf Hydrology and Stability (MONARCHS v1.0)

Sammie Buzzard, Jonathan Elsey, and Alexander Robel

Abstract. Antarctica's floating ice shelves experience considerable surface melting, leading to the formation of supraglacial melt lakes. The presence of surface meltwater and the formation of these lakes leaves ice shelves vulnerable to meltwater-induced damage. This can lead to the loss of the buttressing effect provided by ice shelves on the grounded ice sheet, thus increasing Antarctica's potential sea level contribution. Understanding the surface hydrology of ice shelves in the present and the future is thus an essential first step to reliably project future vulnerability of Antarctic ice shelves to meltwater-driven hydrofracture and possible collapse events. Therefore, we have developed the first comprehensive 3-D Model for Antarctic Ice Shelf Hydrology and Stability, called MONARCHS.

MONARCHS calculates the surface energy balance of the ice shelf, heat transfer through the ice shelf and the volume of any subsequent meltwater that is produced when the surface energy balance is positive. The model simulates both vertical and lateral movement of this meltwater through the firn, calculating refreezing and saturation of firn air space as well the related changes in temperature and density. When firn is saturated and surface melt lakes can form, the model simulates the full lake lifecycle, including lake depth increases and full refreezing.

We present a case study focused on the George VI Ice Shelf on the Antarctic Peninsula where significant melt lake formation has been observed in recent years. The model shows reasonable agreement in lake extent and depth with observations. Furthermore, we demonstrate that the speed of lateral meltwater percolation through firn, a key uncertainty in firn modelling, has significant consequences for lake extent and depth, suggesting future research should focus on reducing this uncertainty. This community-driven, open-access model has been developed with input from observations, and will allows us to provide new insights into the surface meltwater distribution on Antarctica’s ice shelves.

Received: 04 Jun 2026 – Discussion started: 13 Jul 2026

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.

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Sammie Buzzard, Jonathan Elsey, and Alexander Robel

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RC1: 'Comment on egusphere-2026-3247', Amber Leeson, 24 Sep 2026 reply

I was very pleased to see this paper since I have followed the development of MONARCHS for some time. I think that an open-source model capable of representing both vertical firn hydrology and lateral meltwater transport on Antarctic ice shelves would be a genuinely useful community tool with potentially wide adoption and therefore think this work is, in principle, publishable and worth publishing.
That said, I think the manuscript in its current form needs considerable tightening and more careful checking before publication. I think that the overall concept of MONARCHS is sound, but I have concerns with how the model is documented, justified and evaluated in the paper. In several places I found important aspects of the formulation difficult to reconstruct from the manuscript alone, or which only became clear after looking at the code and places where the interpretation of the results is stronger than I think the validation supports.
For a model-description paper, I think the manuscript needs to be particularly clear about exactly what is being solved, what quantities are prescribed versus calculated, how the vertical and lateral components are coupled and what the main parameter choices and numerical assumptions are. I also think that more needs to be said about how sensitive the results are to those choices. The George VI validation section is good, and adds value as a real-world case study, but it could be made much more convincing by simplifying the comparison with observations and making the spatial and volumetric comparisons more direct.
I have made a fairly large number of detailed comments below, but they are intended to help make the model description more precise and the paper easier for future users of MONARCHS to follow. If the authors take these on board then I think this will be a strong and useful paper.
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Section 1:

Lines 33-35: Reference to Kingslake et al., 2017 over-states what is evidenced by that paper. I don’t think anyone has shown that meltwater can flow to areas thought to be completely dry…
Lines 35-36: You could cite my 2020 paper here as well. I don’t mind if you prefer not to.
Lines 37-38: See also: https://www.nature.com/articles/s41467-026-72724-x and https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2023JF007378.
Lines 47-49: Rather than say ‘study after study’ it would be more meaningful to summarise what these papers say about why this is important, what physical processes are affected and what the potential impacts might be.
Lines 50-53: A bit more detail on the limitations of the earlier model would be helpful.
Line 59: Actually, the SHED model (Gantayat et al.,) does model the complete lake lifecycle over multiple years, albeit in Greenland.
Line 59: Probably unreasonable to say that they don’t account for the full EB, because they do through the RCM forcing. ‘Explicitly model’ probably better.
How does using your own EB compare to using RCM melt fields?
Section 2:
Figure 1 is OK but could be made more visually appealing. It also left me a little unclear on exactly what is taken from the atmospheric forcing and what is recalculated within MONARCHS. Looking at the code, it seems that incoming shortwave/longwave radiation, air temperature, pressure, dew point and wind are prescribed, but sensible and latent heat fluxes are then calculated internally using the MONARCHS surface temperature. If so, could you make this clearer? I can see the reason for recalculating the energy balance in MONARCHS if the intention is to allow the evolving surface state/albedo to feed back onto melt, but I think this set up needs explaining explicitly. Appendix A currently seems to imply that the sensible and latent heat fluxes are provided directly by the forcing data.
I also couldn't find much description of how snowfall is incorporated into the firn column. From the code it looks like new snow changes the column depth and the existing column is conservatively regridded, with different treatment when snow falls onto firn, a lake or a lid. Could you describe this in Section 2.1, including the assumed density and temperature of new snow and how the vertical grid is updated?

I also wondered about the units of the ERA5 snowfall input. In the ERA5 import routine sf is identified as water equivalent and there is a commented-out conversion to snow depth, whereas the snow accumulation routine appears to use the supplied value as a physical snow depth when calculating the added mass. Am I missing a conversion elsewhere?
The vertical model runs on the order of hourly and the lateral routing occurs on the order of daily. Have you tested how sensitive the results are to this coupling frequency? Since lateral transport changes where water is stored and therefore whether lakes and associated albedo feedbacks develop, I wondered whether changing the interval between lateral-routing steps would change the solution.
Section 2.1:

Mathematically fine, based on the 2018 paper, all good. Again, the figures could be made more visually appealing.
I think the actual albedo parameterisation needs to be described here. Figure 3 says that changes in albedo associated with melting and lake formation are represented, but it isn't clear from the text how the model switches between dry snow, wet/saturated firn, water and ice/lids, or how lake albedo varies with depth. Since changes in lake formation and lateral routing can feed back onto melt production, I think this is an important part of the model physics rather than just a parameter listed in the Appendix.
The description of vertical meltwater percolation here could be expanded slightly. At present it sounds as though water simply percolates until it encounters cold firn or pore closure. Looking at the code, however, there is also a finite percolation time, capillary retention and progressive refreezing as the water moves through the column. These processes seem important for determining how quickly water reaches depth and when saturation/lake formation occurs, so I think they should be described in the paper rather than only being apparent from the code.
Section 2.2:

I understand this less.
In the D8 routing it looks like the receiving cell is selected based on the largest difference in water level and the distance to diagonal cells is only accounted for afterwards when calculating the flow speed. Would it be more consistent to choose the flow direction based on the steepest hydraulic gradient, i.e. Δh/l, rather than the largest absolute drop in water level?
In Equation 7, are you really using the density of the firn here? Looking at the code, it seems to be calculated from the solid and liquid fractions; so more like the bulk density of the ice-water mixture. Why use that rather than the density of the water itself, given that it’s the water that is moving? It would be good to clarify this, especially since the results seem quite sensitive to lateral flow speed.
On the subject of flow speed, you describe u as the flow speed in eq 7 which obviously then gets used in eq 8. My understanding is that the standard Darcy expression gives a Darcy flux, whereas converting this to the actual pore-water velocity requires accounting for porosity. Is porosity incorporated somewhere in your definition of permeability or elsewhere in the calculation?
I also noticed that the permeability is given as negative. In the code this seems to cancel with a negative value of g, so I think this is just a sign convention rather than giving a negative flow speed. But permeability itself shouldn’t really be negative, suggest clarifying in the text.
I wondered whether an alternative approach moving the water would be to use the vertically resolved firn model to identify hydraulically connected saturated layers, and then aggregate these into an effective transmissivity/storage layer before applying Darcy flow laterally. This might provide a more physically intuitive representation of transport through a vertically extensive saturated zone than using the properties of a single vertical level. Did you consider this?
In Eq 8 it might be useful to note that w_moveis capped at 1 in the implementation - presumably to conserve mass.

Line 198: what about flow through crevasses and drained lakes? This might be minimal on GVIS due to its compressional stress regime but I think you should mention that the model omits it here.
For lake/surface water you assume effectively instantaneous movement and set w_move=1, but the routing still appears to move water only between neighbouring cells during each lateral timestep. Does this mean that the maximum propagation speed of surface water is effectively set by the grid spacing and lateral-routing frequency? If so, is this reasonable based on modelled flow speeds and have you tested sensitivity to these choices?
I also think it would be useful to clarify how lakes with frozen lids are treated during lateral routing. From the code it looks as though lateral water movement from lidded lakes is disabled, but I couldn’t find this assumption described in the manuscript so maybe I’ve misunderstood.
Section 2.3:

Section 2.3 feels quite detailed for the main text, particularly the discussion of operating systems, compiler requirements, fallback solvers and installation options. I wonder whether some of this could be moved to the supplement or model documentation, leaving the main text to briefly explain the computational design and performance.
I understand the motivation for using Python in terms of accessibility and ease of development, but given that computational performance is clearly important for the intended applications, did you consider using a compiled core (e.g. Fortran/C) with a Python interface? Numba presumably gives you some of the benefits of this approach while keeping the bulk of the code in Python, but it might be useful to discuss this a little.
I also wonder whether most of Section 2.3.1 could be moved to the Supplement. I think it is useful to state in the main text that MONARCHS parallelises well and to give a brief indication of the computational cost/scaling, but the detailed strong- and weak-scaling experiments, discussion of I/O and threading overheads, etc. feel more like supplementary material. This might help keep the main text focused on the model physics and numerical formulation.
It would also be useful to give prospective users a clearer and less technical sense of the computational resources required for different problem sizes. You state that the George VI simulation takes ~6 h on 64 cores, which is helpful, but could you also give the basic hardware specification and perhaps one or two indicative examples of what can reasonably be run on a laptop/workstation versus what would require HPC? This would make the performance section much more useful to users planning their own applications.
Section 3:

I wonder whether Sections 3.1 and 3.2 would fit better within Section 2 as model verification/numerical tests. Both seem to be testing the numerical behaviour of MONARCHS - vertical-resolution convergence in 3.1 and the behaviour/convergence of the lateral-routing implementation in 3.2 - rather than demonstrating a scientific application of the model. I think putting these alongside the model description would make the structure clearer, with the George VI case then becoming the first actual application of MONARCHS. I’d also be interested to see a direct comparison between 1D MONARCHS and the original matlab code alongside these tests.
Section 4:

Line 283: The description of horizontal sampling/resolution is not clear. If REMA is 100 m, how do you get to 1 km resolution?
Line 282: how does the DEM specify firn depth when it is an elevation product?
Figure 9: Would be nice to show filled sinks in the DEM on this figure to get a feel for potential lake size and shape. Might also elucidate the fidelity of the REMA product.
Line 289: why ERA-5?
Line 291: why a 1 hour timestep? Is this for vertical flow? If so then what’s the timestep for lateral?
Lines 297-305: I appreciate that the 37 m value is only used to initialise the density profile, and that this evolves during spin-up. However the value was taken from Larsen C, and George VI has quite different firn conditions. Barnes et al. (2020) estimate firn air content on George VI to be around 1.5 m, which seems quite different from the initial firn state implied by the 37 m transition depth used here. Normally we would spin up until the entire column has been refreshed. Did you do this? If not then have you checked that the George VI firn air content/density profile – and the temperature structure - has actually properly spun up by the period analysed?
Section 5:

I found this section difficult to follow.
Figure 12: this would work better as a single panel with observed lakes superimposed on modelled rather than side by side.
Line 332: Not sure you can say that the modelled lake depths are similar to those observed. They look considerably shallower to me. You also need to bear in mind that Moussavi use the RTE with the red band to calculate depths and that this is known to underestimate (Melling et al., 2024).
Line 337: Not sure I follow this – why don’t you just compare the volume of water in lakes? That would probably be a fairer comparison that depth.
Line 345 and around: This is probably slush, which is filtered out (imperfectly) of both Moussavi and Discherl products. Have you looked at a slush dataset e.g. Becky Dell’s or Emily Glen’s? Oh, I see you raise this as a possibility later. Definitely worth a quick look given how much discussion you give to it.
Line 361: I’m not sure that the observational data need to be converted to a binary lake/no-lake classification on the MONARCHS grid. Would it be fairer to calculate the fractional observed lake coverage within each MONARCHS cell and compare this directly with the binary MONARCHS lake mask? The modelled lake cells could then be overlaid on a map of observed fractional lake coverage (e.g. in revised figure 12), which would make the spatial agreement much clearer and avoid introducing the somewhat arbitrary 30–40% threshold.
Section 5.1

I’m slightly confused by the framing of this sensitivity experiment. Earlier, lateral flow speed is calculated from Darcy’s law and therefore seems to be a modelled quantity rather than an independently prescribed parameter. What is actually being varied here? If you are multiplying the calculated velocity by a constant factor, is this effectively a sensitivity test to the assumed permeability/flow-law coefficient? If so, I think it would be clearer to vary and report the relevant physical parameter directly, ideally over a range justified from observations or the literature, rather than referring to ±10–100% changes in “flow speed”.
Also a typo: the entries in the ‘Lateral Flow speed (m/s)’ column are percentage perturbations rather than flow speeds in m/s.
Section 6:

Section 6 feels rather long relative to the results presented, and there is quite a lot of overlap with the “Future work” material in Section 7. I wonder whether this could be tightened considerably, keeping the Discussion focused on what the George VI experiment and sensitivity tests tell us about MONARCHS, and moving or condensing the more speculative model-development material into Section 7.
Line 402: I fully agree that you have provided the community with the first open-source 3-D model of ice shelf surface hydrology but I am less convinced that you have demonstrated that it is well suited to modelling meltwater transport over ice shelves and melt lake development. I think you have demonstrated that MONARCHS is capable of simulating lateral meltwater transport and lake development, but the comparison with observations still shows some important discrepancies and uncertainties. Perhaps soften this wording.
Line 408: Suggest ‘…in reality water may be able to travel further than we simulated, for example through the development of preferential flow pathways and surface rivers.‘ Current wording suggests that it’s an unknowable quantity when actually it is calculated by your model.
Lines 412-414: suggest rephrasing for clarity. E.g. on line 413: Is 10 cm actually the minimum lake depth that MONARCHS can simulate, or is 0.1 m the threshold you have chosen for classifying a model cell as a lake? Table 2 seems to describe it as the latter.
Line 415: I’m not quite sure what is meant by not representing slush explicitly. MONARCHS already appears able to represent wet/saturated firn and to route water laterally through it, which seems to capture at least some of the hydrological behaviour of slush. Is the missing process specifically the persistence of a saturated surface snow/firn layer before it becomes a free-water lake?
Lines 431–435: I’m not sure MONARCHS in its current form can be described as a model for predicting future firn-air-content loss more generally. It captures FAC changes associated with melt, refreezing and accumulation, but I couldn’t find a description of dry-firn densification/compaction. Could you clarify what processes controlling long-term FAC evolution are represented, and perhaps qualify this statement?
Section 7:

This is good but doesn’t actually have much concluding material in it. Suggest keep section 7 as future work, bring some of the stuff from sect 6 into and add a proper conclusion as section 8. This would ideally provide a clearer summary of what MONARCHS has actually demonstrated in this study, where the validation was successful, where important discrepancies remain, and what the main current limitations are.
Line 438: I think this description undersells it. Suggest something like: ‘We have substantially extended the Buzzard et al. (2018a) 1-D lake model into a 3-D ice-shelf surface hydrology model by coupling multiple vertical columns through topography-dependent lateral meltwater routing.’
Line 446: PFAs have been observed on Antarctic ice shelves. See: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020GL089552, https://www.mdpi.com/2073-4441/13/5/731, https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2024GL109367

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Citation: https://doi.org/10.5194/egusphere-2026-3247-RC1
RC2:
'Comment on egusphere-2026-3247', Anonymous Referee #2, 05 Oct 2026 reply
General comments
I commend the authors on producing a very thorough, well-presented, robust and impactful piece of work. The study is made especially valuable by the combination of a physically justified model, and a thoroughly tested numerical implementation that is completely open source with documentation and welcomes community contributions. The work marks a strong development in surface hydrology modelling, providing the first 3D ice-shelf surface hydrology model that accounts for complete surface-lake evolution, vertical and lateral meltwater transport, and a full surface energy balance, all in one model. Considering its novelty and documented, open-access nature, I believe MONARCHS be well received and used by the ice-sheet/shelf modelling community.
There are, however, a few areas that I think need to be addressed before publication. These mainly concern how the model is presented in the manuscript (in particular the form of Darcy’s law, which I have doubts about), some discussion points which I think could be extended, as well as various smaller points of clarification and structuring. Once these points have been addressed, I believe the manuscript will be worth publishing and ready for publication.

Specific comments
I have three main specific comments, as well as several smaller comments regarding improvements to descriptions and explanations, figures and structure.

Sensitivity to timestep split:
Has the sensitivity of the results to the split between the vertical and horizontal timesteps been investigated? I think it would be worthwhile to add a comment on this sensitivity to the manuscript.

Extended discussion:
I would like to see a discussion of whether and how MONARCHS could be applied to ice sheets (c.f. shelves).

Form of Darcy’s law:
I am slightly unsure that the form of Darcy’s law used for the horizontal water routing (eq. 7) is correct. The form of Darcy’s law I am familiar with (and is relevant here) is
q = u * (1 – phi) * S = - Pi/mu * rho_w * g * dh/dx ,
where q is the volume flux of water relative to the ice, u (m/s) is the “horizontal” (i.e. parallel to the surface slope) velocity of the water, phi is the volume fraction, S is the saturation (i.e. the proportion of the pore space that contains water), Pi is the permeability (m^2, also taking into account the relative permeability), mu (Pa s) is the viscosity of water, rho_w (kg/m^3) is the density of water, g (m/s^2) is acceleration due to gravity, and dh/dx is the (small) surface slope. I have used the same symbols as in the manuscript, apart from for the viscosity, because the viscosity in the manuscript is said to have units Pa/s. Is this correct? Should the units be Pa s?
Rearranging to make the Darcy’s law above look like eq. 7 in the manuscript gives
u = - ( Pi / (eta * (1-phi) * S) ) * rho_w * g * dh/dx ,
which is the same as eq. 7 if:
mu = eta, which is suspect is the case, just with a units error in eta,

DeltaH = - dh/dx, which I think is the case from the definition of DeltaH in line 186 (although I do find the notation DeltaH for a gradient a little confusing – please consider changing this to something that looks more like a gradient term),

rho_firn = rho_w / ( (1-phi) * S) ).

The latter point is where the real difference comes in, with rho_firn < rho_w < rho_w / ( (1-phi) * S) ). Is this an error in eq. 7, or is there a reason that the firn density features but not the water density? Looking at the Colbeck (1978) reference, I couldn’t find anything to explain this.
Related to this point, does the density of firn take into account the water within the firn, or not (in which case rho_firn + (1-phi) * rho_ice, where rho_ice is the solid ice density)?
Finally on this point, where does the value of hydraulic permeability come from?

Other comments regarding the model/numerical descriptions:
Is the sign in eq. 1 correct? As it stands, a positive SEB leads to an increase in H. Is that correct? After eq. 1, please also define what H and t are, in which direction z points, and state that T_frz is the freezing/melting point. I think it would also be helpful to show the direction of z in one of the schematics.
Moreover, in the lake SEB (eq. 3), F_sens and F_lat are of the opposite sign to in eq. 1. Please address this inconsistency. Please also state what T_sfc means in eq. 3.
Lines 107-108, 111-112: Is there a particular functional form used for the thermal conductivity and specific heat capacity as functions of the ice and air quantities? If so, what is it?
Page 6-7: Is there a heat equation for the lake missing from the text?
Line 143-153: It might aid understanding of this paragraph if a diagram of the radiation partitioning was included, but I will leave this decision up to the authors.
Section 2.3.1: I think a brief explanation of the difference between strong and weak scaling, and what each is trying to test in particular, would be informative here.
Does number of grid points remained fixed as thickness changes, i.e. meaning dz changes? This was not clear to me, but is based on the ‘Initial dz’ in Table 1. Please clarify.

Structure:
Perhaps consider moving some of the computational details to appendices. To me, it felt like quite a lot of detail for the main text. Having said that, I think the addition of a very brief description of just-in-time (JIT) compilation would be helpful.
I would have liked to have been able to access results from both benchmarking models (e.g. videos) in either an appendix or supplementary information.
Is the last paragraph before the start of section 5.1 (i.e. lines 367-371) necessary, especially the second and third sentences? The ideas within it are repeated in the paragraphs above and in section 5.1 below. Perhaps remove the paragraph (or keep just the first sentence) and add the following reference to section 5.1 above:
Line 357: “large uncertainty and” -> “large uncertainty (investigated in sec. 5.1) and” or similar.

Figures/tables:
Figure 1: Please say in the figure caption and/or a key what the colours in the figure represent.
Figure 2: Does everything in the third box need to be carried out every timestep, or just loading the meteorology? Also, I suggest making the font size a little larger, at least as big as the text in the caption.
Figure 3: I think this figure could be made a little clearer. Mainly, what do the big downward arrows represent? Heat flow and water flow? If so, should one of the arrows stop before the ice lens? Also, perhaps label the water/lake, in the same way that the firn, air etc. have been labelled.
Figures 6 and 7: I think these could be combined into a single figure, with 2 side-by-side subfigures. Regardless, is there a reason for the ‘ideal’ lines being different colours in the two figures? If not, I suggest making them the same colour. If keeping the figures separate, please also add ‘measured’ to the legend in figure 7.
Table 1: I would find it beneficial to have a column for ‘Run time’ added to Table 1 (to support line 262). Please consider this. Perhaps also consider whether Table 1 would be better suited to an appendix.
Figure 8: I suggest changing the colour bar in panel b to ‘Final lake depth (m)’.
Figure 9: I think this figure could be made a little clearer. I find it a little confusing that the model domain appears to be a piece of ocean (with nothing to indicate there is an ice shelf).
Figure 11: I would suggest changing the colour scheme in panel b, to one more like those in the other panels (i.e. light to dark). The current diverging colour scheme gives (unwanted) prominence to about -2.8 degrees C. Moreover, the high and low values colours of the diverging colour scheme look the same in greyscale.
Figure 13: I think it would aid comparison if the first two plots were stuck together along the x-axis (and the x-ranges of the two plots were made the same), with the one of the plots being flipped so it is upside down beneath the first (as if ‘reflected’ in the x-axis). This would make it much easier to compare the locations of the peaks in the two plots.

Technical corrections
Title: I would consider capitalising the letters of the acronym in the title, as is done in some but not all places in the manuscript. Either way, I suggest choosing a consistent capitalisation throughout.
Line 48: “study after study” – consider using a less colloquial alternative.
Line 50: Consider replacing the two commas with hyphens.
Line 52: I think it is slightly unclear what “this” refers to.
Line 72: Isolated bracket: “Section 2.1)”
Line 89: I suggest adding a comma after “heat diffusivity”, to make the long sentence clearer.
Line 98: “During each timestep MONOARCHS is run” -> “During each timestep in which MONCARCHS is run”
Eq. 1, line 103: rho_ice is used in the equation but rho is used in the text beneath.
Figure 3, line 1: “surface energy balance is calculated” -> “surface energy balance, calculated”, to be consistent with the other numbers in the list.
Eq. 2: Please make the brackets bigger, e.g. \bigg(
Line 123: Consider including a (e.g. textbook) citation for the “four-thirds law for turbulent convection”.
Line 125: I would suggest using \mathrm{sgn} (i.e. no italics), so that it doesn’t look like s*g*n.
Line 133: “equation 6” -> “equation 5”
Line 177: “height water” -> “height, water”
Fig. 4: Please change the colour of the arrows; currently the arrows are not visible on top of the dry firn when viewed in greyscale.
Line 190: Why is there a “*” included for multiplication here (but not in the other equations)?
Line 221: “column case MONARCHS” -> “column case, MONARCHS”
Line 226: I would consider replacing “embarrassingly” with something less informal.
Line 310: “movement with” -> “movement, with”
Line 328: “(top right)” -> “(top left)”
Line 330-331: Perhaps clarify briefly here that the percentage comparisons are for only the North West section (i.e. that shown in fig. 12).
Line 410-411: Consider rewording “and the consequences of this” to make it clearer what “this” refers to.
Line 412: “case study a large” -> “case study, a large”
Line 414: “increased” -> “increase”
Line 456: “documentation/ user manual” – remove the space after the slash.
Table A1: Please check and correct several small inconsistencies that appear in this table:
The use of subscripts in the air temperature and thermal diffusivity model parameters (which I think should instead be T_air and k_air, or similar).

When writing units, there should be spaces between the units, e.g. “Pa s”, not Pas”. This is currently done inconsistently.

Also check whether the unit of viscosity is correct (as already mentioned). Should it in fact be Pa s?

Some of the units are written in italics – please correct this to make them upright.

Ensure all the entries in the “Example Value” column begin with capital letters.

In the liquid fraction row, use “N/A” instead of “n/a”.

Remove the space after the slash in “Sfrac/ Lfrac”

Use “or” instead of “/” in the albedo (to make clear there is no division here).

Be consistent with using “Varies between 0-1” and “Ranges from 0 to 1”. If choosing the former, please replace with “Varies between 0 and 1”.

The table lists phi_firn as the density of firn, but the density of firn is represented in the main text as rho_firn in some places and rho in others.

General comment on notation: This is a point of personal preference, but I would recommend changing all the variable subscripts that refer to words (e.g. “ice”) to upright, rather than italics. This would prevent the subscripts from looking like mathematical symbols (e.g. i * c * e).
General comment on capitalisation: Please be consistent with the capitalisation used in the titles and subtitles. Sometimes only the first word is capitalised, sometimes all words, and sometimes something in between (e.g. line 436).

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Citation: https://doi.org/10.5194/egusphere-2026-3247-RC2

Sammie Buzzard, Jonathan Elsey, and Alexander Robel

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Short summary

Melting ice on the surface of Antarctica's floating ice shelves can have important consequences for their stability. Meltwater can form lakes on the surface of the ice, which may cause the ice shelf to become unstable. Here we present the first 3-D model for the creation and movement of meltwater on ice shelf surfaces. We demonstrate the model's capabilities through a case study on the George VI Ice Shelf, Antarctica, and validate the results against satellite observations.


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