This paper presents the results from the ISOMIP+ Project, in which a number of ice-shelf-enabled ocean models were compared by running a series of carefully defined experiments.  The details of the experiments have been published elsewhere, and the experiments themselves appear to have been run a while ago, which makes this a slightly unusual review, which can only really cover presentation and not substance.

Many of the model codes have changed a little since the experiments were run, but those updated codes are used frequently for standalone ocean and coupled ice-sheet-ocean experiments, as were the earlier versions, and the results pervade the literature.  This work represents the only direct inter-comparison of those models and is thus incredibly valuable, even if the configurations are now slightly historical.  I commend the authors for pursuing the task of analysing and publishing the results.

The presentation is generally clear and logically structured, and I while I do have comments on substance, I’m not expecting those to be acted on, in terms of redoing analyses, prior to publication.  So, most of my comments should be seen as more philosophical in nature, concerning the broader approach adopted in the work and how it might be built on in future. Normally I dislike papers talking about what should or will be done in future, feeling that it is generally better to focus on what has been done and what has been learnt from that.  However, in this case, the lessons learnt about how to compare models are probably as important (if not more so) than what can actually be learnt about (the historical versions of) the models themselves from this inter-comparison.

It seems to me that the results of the ISOMIP+, or similar, exercises are of potential value in (at least) two ways: to document differences between models and thus provide insight into how the various models behave in separate applications (both realistic and idealised); and to explain model differences with the ultimate goal of adapting codes towards gaining improved (or at least more consistent) results.  Lines 90-91 hint at the latter aim, but the paper really addresses the former, and perhaps that point could be clarified.  Arguably, documentation of the differences is all that can be done at this stage.  Without knowledge of a “correct” solution, more consistency around a potentially incorrect solution might even be a bad thing.  Nevertheless, the community should (in my opinion) be striving towards improved models rather than simply accepting that each implementation will be different and documenting those differences.  So, I think the ongoing inter-comparison efforts should keep that other goal in their sights.

Which brings me to my main point that there is maybe something missing from the paper.  The ISOMIP activity is clearly continuing, and there is much that can be learnt from the successes and problems encountered in this activity.  It would be valuable to briefly discuss those and how they might shape future activities.

For example, there was never a formal comparison of models run on the original ISOMIP configuration, but where results have been presented in different papers, they appear to be far more consistent than the ones presented here.  Why is that?  Does the simpler geometry minimise the differences that arise from discretisation of the topography (see later comments)?  Or was it that modellers were freer to tweak other model settings to match a range of outputs from the original 1997 paper, rather than only alter transfer coefficients to match a prescribed melt rate?  Wouldn’t the answers to those questions be worthwhile exploring, with that second goal in mind?

As it stands, the paper seems to suggest that the ISOMIP and ISOMIP+ configurations are now finished with and the way ahead lies in increasing the complexity still further with an inter-comparison of realistic domains.  But isn’t that likely to throw up even more model diversity and put that second goal even further out of reach?  I guess the argument is that with a realistic domain you have a “known answer”, but is that true?  You have a known answer in terms of the melt rate, but you have no idea of what the complex circulation should look like and only a patchy knowledge of the seabed geometry that has a major influence on it and hence the melt rate.  It’s not clear to me that tuning certain parameters to improve the match with observation when such vital information is so lacking really helps in improving the models.

I’m not saying that such experiments would not be of interest.  They would be really valuable in addressing that first goal of documenting differences on domains that are actually in use for projections.  But if the community is not to lose sight of the second goal of genuinely improving the physical representation of the processes within the models, wouldn’t a return to ISOMIP, and more work on ISOMIP+ be equally valuable?  Running all the current models on ISOMIP would be interesting and you could maybe run three sets: one with a COM-type setup; one with a TYP-type setup; and one with a TYP-TUNE-type setup, where modellers would follow their typical tuning procedure to match the original 1997 results as closely as possible (which is what I assume has been done in the literature to date).  In fact, that last set is arguably what is missing from the experiments in the current paper.  In having the tuned COM experiments defined with most choices constrained, while the unconstrained TYP experiments are not tuned, the authors have arguably done the models a disservice and maximised the discrepancies.  I accept that without knowledge of the “correct” solution there is not really a target that models can be tuned too.  However, therein lies the advantage of ISOMIP.  There is at least an “accepted” solution, even if we don’t know much about its correctness.

I accept all this is actually something that should form part of a community discussion, but I cannot help thinking that a short paragraph or two devoted to the best route forward and in particular the various merits of increased versus decreased complexity as well as re-running the ISOMIP+ experiments in the light of lessons learnt would be of value.

Specific comments:

Lines 58-59:  This sentence summarises the study of Gwyther et al (2020), but with such abbreviated prose that I think the meaning will remain obscure to anyone lacking a detailed knowledge of melt rate parameterisations.  Perhaps the sentence could be expanded a little for clarity?

Line 60:  What does “melt range convergence” mean?

Line 68:  “Zhou et al. (2024) use two ocean …”

Lines 74-78:  A slightly muddled sentence.  Do you mean “Model developments … realistic domains for future projections of … and guide melt parameterisations for …”

Lines 113-116:  Not easy to follow.  Does the calving front vary between models and differ from the BISICLES ice front?

Lines 126-128:  What was the motivation for keeping the density profile the same between the two experiments?  That choice takes you away from setups that you can really describe as “like” the cold versus warm regimes typical of realistic continental shelves.  The key point is that the cold shelves are cold because the stratification is weak.  Having strong stratification in the cold case is what causes the deep detachment of the melt-laden outflow and lack of freezing, which put you in an atypical regime.

Line 170:  “… it increases to account for …”

Line 223:  “… uses partial cells to represent better the bottom …”

Lines 321-322:  Doesn’t NEMO use a finite volume discretisation?

Line 422:  Describing the circulation as “western-intensified” seems a little misleading for simulations on a f-plane.  Presumably any intensification is a result of water column thickness gradients and, while it may be on the topographic “western” side, any relation to the geographic west will be coincidental.

Figures 7, 8, 9 and 10:  In these figures the ice geometry looks quite different between models.  In particular, differences in 7 and 9 are much more pronounced than in figures 2 and 3.  Presumably this the difference between a central section and a width-averaged view of the geometry and highlights that the topography is significantly different at the margins.  Presumably that is a result of differing interpolation schemes and cut-off values used to infer grounding line and ice edge, but doesn’t it mean that all the models effectively had different distributions ice shelf basal gradient, and hence buoyancy forcing.  Given that, differences in model response aren’t really surprising, are they?  This is a strong argument for using a simpler geometry, where interpolation schemes would not end up giving you such different geometries.  This point is illustrated in the Supplementary material, but could be drawn out more prominently in the main text as it is important for the interpretation of the results.

Lines 451-452:  I don’t see how the results in figure 10 resemble observation.  I don’t know of any observation that is suggestive of a reversed overturning circulation in the upper water column.  Many papers going back to the 1970’s discuss a lower and an upper circulation cell producing Deep (DISW) and Shallow (SISW) forms of Ice Shelf Water, but they all (to my knowledge, at least) suggest that both cells are clockwise (i.e. in at depth and out along the ice shelf base).  The reversed circulation looks odd to me and wouldn’t produce DISW and SISW in any case, but rather a single outflow sourced from waters above and below that level in the water column.  I know of no observations that support that, and I assume it is an artefact of the unrealistic stratification (commented on above).

Line 554:  “Many of these differences …”

Figure 13 (and others):  If I understand correctly (not guaranteed as the description is not completely clear to me), the vertical coordinate is discretised into 5 m bins and measured from the defined ice shelf surface.  So, the absolute depths are consistent between panels.  But wouldn’t it be a fairer comparison of the models to plot results as a function of distance from the discretised ice shelf surface used in each model.  That way the distance from the ice base would be the consistent coordinate between panels.  Isn’t that the key variable?

Lines 677-679:  So, does that suggest that the target melt rate in the COM experiments was too high?  How was it set?

Review of:  Results of the second Ice Shelf-Ocean Model Intercomparison Project (ISOMIP+)

Authors:  Claire K. Yung et al.

This study reports model output from the ISOMIP+ study, which consisted of 12 different ocean model configurations simulating ocean circulation and ice-shelf melt rates in idealized ice-shelf cavities. The simulations consist of 20-year runs in two different configurations: (i) an initially cold-shelf cavity transitioning to a warm shelf regime due to a far-field sponge-layer forcing and (ii) an initially warm-shelf cavity transitioning to a cold-shelf regime due to a far-field sponge-layer forcing. The warm experiments (warm far-field properties) are mostly equilibrated while the cold experiments appear to still be in a stage of transient adjustment after 20 years. The study reports differences in ice-shelf cavity hydrographic properties, circulation properties, and melt rates. The choice of vertical grid appears to have one of the largest impacts on variations across the models because of the representation of ocean thermal and velocity properties near the ice-ocean interface.

We greatly appreciate the effort that has been undertaken by this group of modelers to run these simulations and to bring the output together for this comparison. This study will make a nice contribution to the literature and will be an important resource in developing the next generation of coupled ocean-ice shelf models. There are two major suggestions, described in more detail below. First, the manuscript would benefit from a more concise summary of where this group of authors perceives that future model development and model choices will have the greatest impact in improving numerical representations of ice shelf-ocean interactions. Second, the lack of information and discussion of the density structure and stratification in the main text is a significant omission in this manuscript.

We recommend major revisions because of the number of comments that are provided below, but I do not anticipate that these will be too hard to address. 

*** This is a joint review from a senior and an early career researcher. ***

Major comments

• As an overall comment, this manuscript would benefit from a clearer statement about how these results inform priorities for future model development or model design choices. The degree to which a more synthetic interpretation of the model results could be provided would make this paper more valuable to the scientific community interested in ice-ocean interactions. The group of authors that contributed to this manuscript are the leading experts in this field — it would be great to have a more nuanced (and more opinionated!) discussion of these simulations in the Discussion section.

A related comment:  At the moment, each simulation is presented as an equally valid realization of ocean circulation in the cavity.  It is clear, however, that certain simulations are well outside of the expected behavior.  For a general reader, it would be helpful to provide some critical assessment of which models perform more realistically and perhaps more importantly, why certain models seem to be failing.  This is not a criticism of any model, but a way to learn what impacts model fidelity. It would be nice to capture this in the Discussion section.

• The absence of any information about the structure of the density field, specifically the ocean stratification, is a significant omission in this study. In terms of controls on circulation and near-ice-shelf transport properties, recent work has highlighted the importance of ocean stratification. This is particularly true for the gyre and overturning circulations—both controlled by geostrophic shear. The density will be determined by the salinity field, rather than the temperature field. I realize that salinity information is contained in the supplementary material, but I suggest moving a discussion of ocean/cavity stratification to the main text.

• It would be helpful to have the overturning circulation diagnosed and presented in density coordinates, rather than in depth coordinates (the Eulerian overturning). Using a density framework provides a better assessment of water mass transformation processes in these simulations, which offers more physical insight into controls on the overturning. I appreciate that the output required for this calculation may not be available for all, or any, of the models. If this is not possible, it would helpful to have a more nuanced discussion of what the overturning represents in these models (adiabatic vs. diabatic processes). See the comment below about transient stratification adjustment and inferred vertical velocities.

• I am concerned that most of the variations across the cold-shelf simulations are due to the fact that the models are at different stages of adjustment to a new equilibrium. This is strongly suggested by the model results as well as the discussion in the manuscript. This is quite different from the warm shelf experiments, where multi-model variations are more likely due to different representations of boundary layers, geometry, vertical coordinate schemes, etc. The authors should think critically about whether the cold-shelf experiments provide insight into how model differences influence cavity properties and ice-shelf melt. While the authors are clear about the transient nature of these experiments, perhaps a shorter paper focused on the warm-shelf experiments would be more appropriate (and still worthy of publication).

Minor comments

• Abstract:  It is always nice to have a few quantitative statements in the abstract.  You might consider putting some values on the range of variability of key parameters. 

• Line 21:  You might consider some earlier citations here as it has been well known for some time that AABW formation impacts the global overturning, e.g. Purkey and Johnson papers, Talley 2013, or earlier studies.

• Line 30:  “discrepancies among different models” consider providing a few examples.

• Line 55: “higher spatial resolution”  Be quantitative here if possible — by how much did the resolution increase?

• Line 62:  “incorporating the unresolved effect of stratification due to buoyant meltwater,” Consider adding additional details here since previous models do represent vertical temperature and salinity profiles (and thus stratification).

• Introduction:  The introduction captures the range of studies that have attempted to model ice-shelf cavities, but it mostly lists these papers. It would be nice to provide some synthesis about key outcomes as well as remaining gaps in modeling capabilities and future priorities (at least as perceived by this group of authors).

• I realize that these simulations are now ~20 years old, but the manuscript needs a better justification of starting the warm experiments with a cold shelf and vice versa, especially as the focus of this study is on steady state behavior. 

• Figure 1 caption:  Ocean 1 and Ocean 2 in the text are referred to warm and cold, respectively, because of the boundary forcing. In the caption, Ocean 1 and Ocean 2 are referred to as a cold and warm, respectively, because of the initial condition.  Please make sure these are consistent.  Also, the text indicates that the domain is 480 km long, but only 400 km are shown — is the other 80 km the sponge layer?  It would be helpful to indicate in the caption that the transects in the right-hand panels were taken at y=40 km.

• Line 126:  “By making use of the experiment’s linear equation of state, the cold and warm profiles are designed to have the same density profile.” This choice should be justified further — the density structure outside of ice-shelf cavities of warm and cold shelves are typically have very different density structures. 

• Line 158:  You might make is clearer there is only a single parameter that is tuned (\Gamma_T) although presumably the melt rate depends on both \Gamma_T and \Gamma_S.

• Line 225: How does a “a full step representation” reduce velocity noise?  Naively this sounds like a steppier bathymetry and ice-shelf draft.

• Line 239:  Here and elsewhere in the text, the authors state that certain models were not able to reach the target melt rate. It would be nice to provide some additional information about why this melt rate was not achieved.  Did the model crash with large transfer coefficients or did the melt rates saturate?

• Line 244:  “the coupled ice–ocean framework as described in Jordan et al. (2018)” Can you confirm that the ice-shelf/sheet is stationary in this configuration, i.e. there is no grounding line migration?  It appears that there is water inland of the grounding zone in Figure 2d for this configuration — this would be worth commenting on.

• Section 3:  While I appreciate that it is important to provide some details of each model used in this inter-comparison, the authors might consider whether key information could be provided more succinctly with a table.  For instance, there seems to be a few key differences between models, e.g. where T/S values are diagnosed for estimating melt rates, the spatial scale of the ice-shelf geometry and bathymetry, etc., that have a strong impact on model differences. Summarizing these for the reader would make this section more readable. Also, a summary of what seem to be particularly sensitive or critical parameters at the end of the section would be valuable. The authors may consider moving model details to the supplementary material.

Line 312:  “The fluxes are adjusted each month to match the freshwater flux from melting averaged over the previous 3 months.” Please provide some justification for this choice; it was not clear why this was implemented.

• Figure 2:  Some of the differences between the temperature distributions are quite subtle. The authors might consider showing a multi-mean and then deviations away from this mean for each model. This might highlight differences between the simulations more clearly.  The contours are not described in the caption.

• Line 395:  “where the thermal and haline driving is larger due to the salinity stratification” I did not understand why salinity stratification leads to larger forcing of the ice-shelf. Above, the manuscript discusses how stratification shields the ice shelf from warm water.  Do these models capture the effects of entrainment by meltwater plumes?

• Line 404:  “also have cold temperature transects”  Can you provide more details here?

• Line 405:  “These variations demonstrate that models can achieve similar cavity-averaged melt rates (the tuning target melt rate below 300m is achieved by all models except ROMS and FVCOM) with very different spatial distributions of melting. These differences in melt rate patterns, particularly near the grounding line and side walls, have implications for ice sheet evolution in coupled ice sheet–ocean models.”  This is a really interesting result!  It would be nice to go into a bit more detail — mechanistically, what is happening at the grounding zone and side walls that are different between models. Also, can you explicitly state why this would matter in more realistic coupled ice sheet-ocean models.

• Paragraph starting on line 420:  I was somewhat surprised that the barotropic circulation within the cavity was the same magnitude as the overturning circulation. For the continental shelf circulation the barotropic gyres are typically an order of magnitude stronger (see Webber et al. 2019 for example). Is this because the barotropic gyres are weaker in the cavity or is this a result of estimating the overturning circulation in depth coordinates, rather than density coordinates?

• Line 422:  “clockwise” — you should also state that these are “cyclonic” gyres.

• Line 472:  “The area-averaged melt rates over the entire ice shelf for the Ocean1 and Ocean2 experiments demonstrate the dependence of melt rate on temperature (Fig. 11).”  The statement should be more precise here — melt rates also depend on the circulation structure.

• Figure 7:  Why does the overturning circulation extend into the ice shelf in some of these panels?

• Figure 9:  The overturning circulation in the cold regime experiments show a clockwise circulation at depth, supported by ice-shelf melt, and a shallower counter-clockwise circulation. This upper cell must be supported by waters becoming denser in the ice-shelf cavity and it was not clear what process is responsible for this. Is the ocean water freezing back on to the ice shelf in these simulations?  This freezing is typically associated with waters becoming supercooled when they rise from depth, but that does not seem to be consistent with the streamfunctions here. Another possibility is that these simulations are not in steady state — in simulations where the density surface are evolving with time, the overturning streamfunction will produce vertical velocities that are not associated with diapycnal transports.

• Line 445:  “Return flow above and below this depth is created by the modifications made by the restoring forcing to the fluid’s buoyancy at the x = 800 km wall boundary.”  This does not explain what process provides the source of mid-depth outflow from shallower depths (from the upper counter-clockwise cell).

• Figure 11:  It is nice to show the collapse of the melt rate evolution when normalizing!

• Figure 12:  I would suggest removing the COCO simulation from this figure. It is well outside the range of all the other experiments and makes it difficult to assess differences between the other 11 simulations. It would also be helpful to indicate the position of the final state (the time average of the 20th year) in each panel.

• Line 532:  “If the ice shelf cavity flow is driven only by buoyancy, the magnitude of melt would be expected to be proportional to the near-ice velocity, which in turn should approximately scale with overturning circulation strength (e.g. MacAyeal, 1984; Jourdain et al., 2017).”  I did not understand this statement.  The strength of the overturning is governed by the rate of water mass transformation, which depends on both the magnitude of the buoyancy flux at the ocean-ice shelf interface as well as the density gradient. The velocity field arise to move water across the stratification at a rate to balance the buoyancy-driven transformation. The magnitude of melt would only be proportional to the near-ice velocity if the buoyancy gradient is uniform.

• Figure 13:  It would be nice to produce this figure as a function of density on the y-axis, rather than depth.  The discussion around Figure 13 would benefit from assessing differences in the stratification between these different models.  What does “transect averaged” mean in the caption?  

• Line 520:  “The deviation from the quadratic scaling is consistent with Holland (2017), who show that warm-to-cold transitions (i.e. Ocean2) better match the equilibrium response compared with cold-to-warm transitions (i.e. Ocean1).”  This statement was unclear, can you please clarify.

• Line 527: “Additionally, the multi-model mean gradients of the overturning and barotropic streamfunction as a function of melt have the same order of magnitude, indicating barotropic and overturning circulation have similar magnitudes.”  I was confused by this statement because Figure 12 does not show streamfunction gradients — you might mean change in volume transport with melt rates, but this would have a slope or trend, rather than a magnitude.

• Line 565:  “show warmer water at depth”  Perhaps be more quantitative here.

• Line 579:  “Sharp differences in temperature along the meltwater layer suggest that the z-coordinate resolution is partially responsible.” Explain why z-coordinate is responsible — presumably it is because terrain-following coordinates resolve the boundary layer better?

• Line 581:  “POP2x also has a very cold boundary layer, likely related to its large melt rate transfer coefficient (Table 2) compared to other z-coordinate models.” Shouldn’t the melt rate matter more than the value of the transfer coefficient?  

• Line 620:  “z-level models are expected to require smaller transfer coefficients to achieve the same tuned melt rate, since the lower vertical resolution near the ice and greater thermal driving sampling and freshwater flux distribution distances result in larger melt rates compared with higher resolution terrain-following configurations (Gwyther et al., 2020).”  This sentence was confusing, consider re-phrasing:  perhaps “near the ice and greater thermal driving sampling” should be “near the ice implies greater thermal driving sampling” 

• Line 645:  “and a significant fraction of the available heat for melting is advected out of the cavity by the buoyancy-driven overturning.”  This is an example where the manuscript would benefit from a clearer statement of the circulations that are diagnosed.  I would have expected the barotropic, or gyre, circulations to carry heat into and back out of the cavity.  The buoyancy-driven circulation, on the other hand, would be associated with heat loss (melting) that converts water from one density class to another.  However, if density surfaces are tilted, there could also be a sheared, baroclinic, circulation that is also adiabatic and contributes to the inefficiency of the available heat to melt the ice shelf.

• Line 669:  “The T–S space results indicate that water mass analysis is effective for model verification.”  State why the T-S plots were useful for model verification — verification of what?

• Section 4.5:  In a manuscript that is already long, I would suggest removing some of the details of the TYP experiment (or moving it to supplementary) and shifting the focus of this section to specifically addressing what additional insight was gained from these suite of experiments.  The last paragraph attempts to provide a summary, but there is no attempt at addressing why these simulations differed (admittedly hard!). 

• The Discussion does a nice job of highlighting key aspects of the model that led to inter-model differences, such as the importance of vertical coordinates and vertical resolution near the ice-ocean boundary.  It would be great to have a short paragraph on how this would influence future model development priorities.

Technical comments/suggestions

• Line 50: It would be clearer to break this into two sentences.

• Line 68:  A verb is missing after “Zhou et al. (2024)  …”

• Line 88:  “drivers” should be “drivers of melt”

• Line 122:  “vary uniformly with depth” I think the authors mean, “vary with depth but hare horizontally uniform.”

• Table 1:  \rho_ref should be a reference density 

• Line 189:  “states” should be “ocean states”

• Line 232:  “advected” should be “horizontally advected”

• Line 331:  “spread vertically” — I assume means “spread uniformly over the upper 20 m”?

• Line 348:  “topography”:  Here and throughout, please be consistent — “bed topography,” “ice shelf topography,” “ice draft,” and “bathymetry” are all used so sometimes it is not clear what is being referred to.

• Line 367:  Suggest modify “difference and drivers of melt” to “differences of melt along with its drivers”

• x-label in Figure 11c,d:  This could have a clearer description, e.g. “Time since the half-maximum melt rate (yr)”

• Line 513:  “melt rates” should be area-averaged melt rates”

• Line 567:  “Upslope” — suggest “seaward”

• Line 617:  “transfer coefficients” should be “thermal transfer coefficients”

• Line 692:  Add compared to COM after less in Ocean 2”

• Line 723:  “similar ocean profiles” should be “similar hydrographic profiles”

• Line 791:  “tuning and development of the melt parameterisation” You might be clear here whether tuning/development of existing parameterizations is sufficient or whether new parameterizations are required.