Please note that we have reproduced the first referee's comments below, divided into sections, and written our author responses in bold beneath each section.

General Comments

This manuscript presents an interesting and timely investigation of the role of submesoscale mixed-layer eddies (SMLEs) in modulating the seasonal ocean heat budget and sea ice evolution near the marginal ice zone (MIZ). By comparing eddy-resolving (3D) and non-eddy (2D) MITgcm simulations, the authors isolate the thermodynamical impacts of SMLEs, which are often neglected in coarse-resolution climate models. The study addresses a significant knowledge gap by quantifying how SMLEs influence sea ice melting and freezing processes through heat transport and feedback mechanisms.

The paper is generally well-motivated, clearly written, and scientifically sound. The approach is methodologically appropriate, and the results provide new insights into the coupling between submesoscale dynamics and polar climate processes. The identification of distinct summer and winter responses strengthens the contribution and highlights the necessity of submesoscale parameterization in climate models.

Overall, this is a contribution of interest to the polar oceanography and climate modeling communities. Some clarifications and improvements would further strengthen the manuscript before publication.

We thank the reviewer for their overall positive assessment of the manuscript. We agree that there is room for improving the presentation of the work. We detail the response to the comments below.

Specific Comments

[1] Introduction

The introduction provides a comprehensive overview of submesoscale dynamics and their relevance in polar regions. However, it is somewhat verbose and would benefit from streamlining to emphasize the central research question. The authors may consider shortening the general background on SMLEs, improving transitions between topics, and highlighting the novelty of their thermodynamic focus relative to previous studies.

While observational and modeling studies are well cited, the flow from general submesoscale theory to polar-specific impacts could be smoother. Adding brief linking sentences to connect classical SMLE mechanisms with polar sea ice interactions would enhance readability. Moreover, the main research gap, which involves quantifying the thermodynamic impacts of SMLEs across seasons and background stratifications, should be emphasized earlier, ideally before detailing the study objectives.

We agree the introduction could do with better streamlining. We will link sentences, reference the research gap earlier, and emphasize how the previous research directly links to the new research here, making the transition between paragraphs easier.

[2] Materials and Methods

The description of the model setup contains many technical details in long, complex sentences. For example, information on vertical and horizontal grid spacing, mixing schemes, and viscosity settings could be split into shorter sentences or a table. This would improve readability and make it easier for readers to understand the experimental design.

Following comments also from referee 2, we will move some of the material to an appendix  (the lines 87-101), and the second half of section 2.2, and cite relevant studies (Horvat et al. 2016/Abernathey 2011) for reference, so that this section is shorter. Also, where sentences have become long, we will break them up for ease of reading.

Some parameter choices, such as the Smagorinsky coefficient, horizontal eddy viscosity, and small horizontal diffusivity in winter, are described, but the rationale is brief. It would strengthen the manuscript to explain why these values were selected, particularly how they affect numerical stability and the development of SMLEs, and whether sensitivity tests were conducted.

These values were selected (a higher horizontal viscosity on the divergent part of the flow dv/dy and a lower viscosity on the rotational component of the flow du/dy) to decrease grid point noise, correlated to sea ice formation, on the meridional velocity field whilst not dampening the zonal jet. Sensitivity tests were conducted and these values were found to be the best for this purpose. To reduce the grid-point noise in the thermodynamic fields, the small amount of horizontal diffusion of temperature and salinity was introduced in the model. In addition, a third step to help with this issue was to change the smoothing settings within the KPP package. A few regularisations and smoothing options with the KPP package were investigated. These include reducing the shear mixing when the velocity shear is low and the Richardson number is large. They helped to further reduce the noise in the velocity fields. In 3D we used the same values, whilst acknowledging this could potentially impact the development of SMLEs, by weakening the fronts.

We will add the above description to the appendix along with the other model details.

While the 2D “no eddies” configuration is introduced, the description could clarify explicitly which processes are suppressed (e.g., lateral variations, baroclinic instabilities) and ensure the naming of the experiments is consistent (Arctic/Antarctic, summer/winter). Providing a concise summary table of the main experiments with initial conditions and key parameters would greatly enhance reproducibility.

We will add a sentence or two to further the explanation of the 2D experiments, explaining that baroclinic instability is supressed in this set-up. In line with comments by reviewer 2 and the editor, we will change the naming of the Arctic/Antarctic experiments to be a differing stratification test, giving also a more consistent naming of experiments as asked for here. As we have said above, we will move some content to the appendix/reference Horvat et al, (2016) and improve clarity by breaking up sentences, but we don’t necessarily need a table at least in the main text because it could break up the section.

The methods section contains a large amount of technical detail, including grid spacing, viscosity and diffusivity settings, and atmospheric boundary treatments. While these details are important for reproducibility, some of the more intricate numerical specifications could be moved to the Appendix. This would streamline the main text, improve readability, and allow readers to focus on the key experimental design and scientific rationale, while still providing full information for replication.

As mentioned above, we will remove some of the information in the initial paragraph of 2.1 and later parts of 2.2, making references to Horvat et al. (2016) and Abernathey et al. (2011) (and adding some of the technical set-up details as mentioned above to the appendix); this is also in line with reviewer 2.

[3] Results

The Results section 3.1.1 provides a detailed description of SMLE development and their impact on the mixed layer during Arctic summer, including vertical stratification and buoyancy fluxes. While the simulations and analyses appear comprehensive, the presentation could be strengthened by improving the logical flow and emphasizing the physical interpretation. Currently, the text mixes descriptions of forcing, stratification, eddy development, and vertical fluxes in a single narrative, which can make it challenging for readers to follow the causal chain. Reorganizing the section to first describe the atmospheric and oceanic forcing, then the resulting stratification and MLD evolution, and finally the eddy dynamics and their restratifying or destratifying effects would improve clarity.

We will attempt some re-ordering of this section to ensure clearer flow, we did aim for the structure the reviewer has described originally, so since this has become out of line we will rework this. We will also move some summary content from the discussion to the end of each of the results sections, so that the flow of the paper is clearer for the reader and the conclusions are more concise.

The analysis of the ML heat budget and eddy impacts (Section 3.1.2) is thorough and provides valuable insight into the mechanisms by which SMLEs redistribute heat between open and ice-covered regions. However, the presentation could be improved by emphasizing the causal interpretation and quantitative comparisons more clearly. For instance, the roles of MHT and Qnet are described in detail, but it would be helpful to explicitly highlight how the presence of eddies amplifies meridional heat transport compared to the 2D simulation, and how this relates to changes in ice melt or ML warming. Additionally, the text could more clearly distinguish between contributions from shortwave, longwave, and sensible fluxes in both regions, linking them directly to the eddy-induced heat redistribution. This would strengthen the physical interpretation and make the connection between eddies and observed heat budget changes more immediate for the reader.

The information the reviewer has asked for is generally in the section, we aimed for the structure they describe. Obviously, we did not achieve this. We will aim to add clarity and re-work here, and as mentioned above, insert more of a summary paragraph at the end of the section to enhance readability.

The Antarctic results (Section 3.3) are presented clearly, with useful comparisons to Arctic simulations, but the section could benefit from emphasizing the physical interpretation of the differences. For example, the text could more explicitly link the faster ML deepening and weaker stratification in Antarctic winter to the smaller eddy impact on sea ice formation, and clarify why the summer eddy impacts are relatively insensitive to initial stratification. Including brief quantitative comparisons or ratios directly in the text (e.g., differences in MLD deepening or lateral density gradients) would help readers quickly grasp the relative magnitudes. Finally, a short discussion of the potential effects of neglected wind forcing on Antarctic results would strengthen the assessment of model limitations.

These comments are in line with those of reviewer 2, both have asked for a re-work of this section. There is actually a similar impact to sea ice under Antarctic-like conditions, so we will clarify that this deeper MLD in the Antarctic-like weaker stratification doesn’t lead to a significantly different impact on sea ice formation (+/- 3%). We will clarify the insensitivity to summer stratification. In the discussion, we will add more information too. Again, the summaries to be inserted will clarify all this before the discussion. We will quantify some more specific values of MLD and lateral buoyancy gradients (and give more specific references to the figure in section 3.3). We touch on potential effects of neglected wind forcing overall, then we will expand to why this matters more in the Antarctic (stronger winds). We will also reference other locational differences that we don’t consider here that could alter the impact of SMLEs in different environments such as the Antarctic environment, suggested by reviewer 2, like atmospheric forcing or topographic constraints.  

Technical Corrections

In Section 2, “Materials and Methods,” it is recommended to split the content into two subsections for clarity: 2.1 “Model setup” and 2.2 “Residual-mean framework.” This would improve the organization and make it easier for readers to follow the methods.

Agreed, done.

Please note that we have reproduced the second referee’s comments below, divided into sections or bullet points, and provided our author responses in bold beneath each section.

Referee comment on “Seasonal impact of submesoscale eddies on the ocean heat budget near the sea ice edge”

Greig & Ferreira is a well-written and topical study that will be a useful contribution to the community. They show that submesoscale mixed layer eddies play a key role in the heat and sea ice budgets of the marginal ice zone, and investigate the sensitivity to background stratification and seasonal forcing. I think there are many interesting results, however I find the overall framing of the Arctic/Antarctic conditions to be a bit strange. The only difference between the “Arctic” and “Antarctic” simulations is the initial stratification. So why not just frame the study as testing the sensitivity to background stratification?

There are so many differences between the Arctic and Antarctic marginal ice zones in the real world: the forcing, large-scale circulation, winds, ice type/thickness, etc. Of course, these things are not represented in your idealized setup, which is fine. But I just think it’s a bit misleading to present these simulations as representing an Arctic/Antarctic contrast. If this is your intent, then why choose these specific locations from EN4 to initialize the model (there can be very significant regional differences in the mean density structure within the Arctic and Antarctic, respectively)? My point is just that I think the results would be more accurately framed as testing the sensitivity to background stratification. This is a very valid and useful thing to do, and it’s great to mention how this links broadly to the Arctic versus Antarctic, but I think this could be done with a bit more nuance (and I think these results are actually useful outside the context of comparing the Arctic to the Antarctic).

 Again, we thank the reviewer for their overall positive assessment of the manuscript and agree that there is room for improving the presentation and clarity of the work. We detail the response to the comments below.

We did aim to phrase these Arctic/Antarctic experiments as sensitivity to a background stratification, however we acknowledge this now reads as simply locationally different experiments. We will rephrase this throughout the paper, renaming these 2 experiments (previously named “Antarctic summer/winter” as a sensitivity test to differing stratification, with Antarctic-like stratification used for both seasons. We will contrast this with the main experiments that most of the paper focuses on (i.e., summer and winter Arctic-like stratification). We will then also emphasise (in section 2.3 as well as in the discussion) that these results could be further applicable outside of the Arctic-Antarctic comparison.

Also, to clarify, you are using the standard MITgcm sea ice package without any representation of sea ice floes? I feel this needs to be addressed directly. Sea ice floes in the marginal ice zone have similar length scales to submesoscale ocean flows, so most idealized modeling studies that deal with submesoscale sea ice-ocean interactions use either a simplistic representation of floes or a discrete element sea ice model. And typically, the relevant dynamics that are identified relate explicitly to floe-flow or floe-floe interactions. This needs to be discussed as it is important to understanding how your results relate to previous work.

Indeed, we did not include representation of sea ice floes as some effects of ice floes have been explored in previous studies and we aimed to isolate the thermodynamical ocean-ice processes. We will address this limitation in the discussion (e.g., how floe distributions tie into future work, how this could affect our results, etc).

All this said, I want to emphasize that I think these are interesting simulations and it’s a very nice paper dealing with an important subject!

More detailed comments are provided below:

Detailed comments:

Line 22-26: Perhaps also worth mentioning that ocean heat has been invoked as a leading driver of the recent, rapid Antarctic sea ice loss (e.g. Purich & Doddridge, 2023).

Purich, A., E.W. Doddridge (2023). Record low Antarctic sea ice coverage indicates a new sea ice state. Communications Earth & Environment, 4, 314.

Agreed, added.

Line 46: You are citing the pre-print rather than the actual published paper for Giddy et al. (the year should be 2021, not 2020).

Giddy, I., et al. (2021). Stirring of sea-ice meltwater enhances submesoscale fronts in the Southern Ocean. Journal of Geophysical Research: Oceans, 126, e2020JC016814.

Thanks, amended the reference.

Line 51 (and throughout): Need to be clearer about whether you’re referring to lateral or vertical heat transport by SMLEs.

In this paper we mostly refer to lateral transport by SMLEs, as we don’t quantify vertical here. We will clarify this in-line here and elsewhere, as well as when explaining how the ML heat budget was calculated (following the final MLD so there aren’t significant SMLE vertical heat fluxes across it).

Lines 70-71: Yes, I agree that more studies on submesoscale sea ice-ocean interactions have focused on mechanical effects. But Horvat et al. (2016) highlighted thermodynamic melt of sea ice floes by submesoscale eddies, and Gupta & Thompson (2022) considered both thermodynamic and mechanical interactions. These papers are cited elsewhere in the manuscript, but should at least be acknowledged.

Agree, we have cited these papers above in thermodynamic paragraph of the introduction as the reviewer mentions, and as suggested we will also re-cite references when talking about how the thermodynamic aspect relates directly to the specific research gap on these lines.

Another highly relevant paper to this work, which is not cited, is Brenner et al. (2023). Brenner, S., et al. (2023). Scale-dependent air-sea exchange in the polar oceans: Floe-floe coupling in the generation of ice-ocean boundary layer turbulence. Geophysical Research Letters, 50, e2023GL105703.

Indeed, this is a highly relevant paper and builds specifically on the Cohanim paper referenced. We will also add this reference in the previous work section.

Introduction: a general comment on the introduction is that you do not do much to distinguish between the Arctic and Antarctic. Yet, a major focus of the simulations is comparing Arctic and Antarctic conditions. As I mentioned at the start, I’m a bit hesitant about this framing. But if you are going to proceed with this, then you should at least outline some of the differences between the poles in the introduction (and this could still be discussed briefly even if you do alter the framing around background stratification).

As in our response above, we have now shifted the focus and wording throughout the paper to a sensitivity to background stratification experiment.

Lines 87-101: Since the model setup is essentially the same as Horvat et al. (2016) and much of this paragraph is just paraphrased from that paper, I think it is fine to condense this a bit and cite their paper for the details (or move to an appendix).

We will condense this and cite their paper., as well as moving some more information to the appendix on the model parameters, as suggested by reviewer 1.

Lines 107-110: See my initial comments about the framing of these simulations as Arctic versus Antarctic.

Agreed, amended text.

Line 113: Does ERA5 have MLD as an output?

No, it doesn’t because it is only atmospheric data (no ocean component, SST and sea ice concentration are prescribed by observations). However, we did also do a sensitivity analysis to the MLD in section 3.4, to show how this choice matters.

 Line 119: How are the surface fluxes computed in the sea ice-covered part of the domain?

We will add an explanation of surface heat fluxes under the ice, which is essentially a conduction and latent heat flux as well as shortwave penetration through the ice. However, for full details we will reference the MITgcm manual thsice section, and the sea ice model by Winton (Winton, M., A Reformulated Three-Layer Sea Ice Model,  Journal of Atmospheric and Oceanic Technology, 2000). (8.6.1. THSICE: The Thermodynamic Sea Ice Package — MITgcm checkpoint69i-2-ge6feef6 documentation, section 8.6.1.1.3 subroutine ICE_THERM)

Section 2.1: First off, this could be Section 2.2 and you could have the earlier part of the Methods section be “Section 2.1 Model Set-up.” But more importantly, this section needs to be introduced better. You need to start by stating what you are doing and why. i.e. you are using the isopycnal streamfunction and EOS to isolate the eddy-induced circulation, etc. Otherwise the section begins very abruptly and it’s not even clear how this relates to the aims of the study until the end of subsection.

We’ve added section 2.1 and 2.2, plus introduced the section more clearly.

Also, this technique is pretty widely used to diagnose eddy transports so you can probably condense some of the detail and just cite past work (e.g. Abernathey et al. 2011) or move to an appendix.

We aim to move the latter part of this section to an appendix, since it contains a lot of technical details of calculations.

Lines 186-187: This is interesting, and what does this mean for the heat transport? If the front is salinity-dominated then the sign of the buoyancy flux is not necessarily the same as the sign of the heat flux.

Yes indeed the heat transport is from open ocean under ice (heat budget, section 3.1.2 and figure 6), whilst the front is salinity dominated near the surface and heat dominated below that (line 174).

Equation 5 & Lines 219-221: As I asked before, how are the surface fluxes computed in the icecovered part of the domain? This is important to interpreting the heat budget.

See above response to this query, and the details of the surface heat flux under ice will be referenced again in this section to add interpretation.

Lines 242-243: The main narrative thread has gotten a bit lost by this point. So just to clarify, the 3-D simulation has a lower sea ice volume due to the meridional heat transport by SMLEs (rather than the vertical heat transport)? I think it’s important to clarify lateral versus vertical fluxes.

Yes, we will clarify this in this section, and as mentioned in response to reviewer 1: add summaries to the end of sections to aid the reader, as well as explaining we are talking about lateral heat fluxes due to SMLEs.

Lines 267-268: I think this is important, lateral temperature gradients are weak because the temperature is near the freezing point, so you can have eddy buoyancy fluxes that are not accompanied by significant heat fluxes.

Yes, we will re-work this sentence to emphasise that here.

Line 331: “temporal” changes sounds more natural than “time” changes to me.

Agreed, changed.

 Lines 351-353: This gets at my initial comment about framing this as Arctic versus Antarctic. If the initial stratification is similar in summer at both poles, then these simulations will show similar results. But in the real world, there are many things that could contribute to differences in SMLE activity between the poles (forcing, winds, ice characteristics, topographic constraints, etc). In particular, the winds are very different. I know these things aren’t represented in your simulations, but it seems like you’re stating that the effect of SMLEs is the same at both poles in summer, and I think this is misleading. You address this a bit in lines 359-361, which is great. But I think you could expand upon this. Winds are known to be much stronger in the Antarctic, so you could state this directly, or even speculate on how this might manifest in the SMLE story.

As well as the changes in wording of the section as mentioned in above responses (changing Antarctic section to different stratification), we will also add relevant text to this section to refer to further differences between the Arctic/Antarctic environments that are present and haven’t been specifically represented here.

Lines 379-381: This is interesting. If we assume that the APE reservoir scales with the MLD and lateral buoyancy gradient, then we might expect the eddy-induced overturning to be greater in the “Antarctic” i.e. deeper MLD case. So why is streamfunction weaker in the Antarctic setup? Is the lateral buoyancy gradient weaker?

The lateral buoyancy gradients are of similar magnitude in both seasons, but indeed MLD is deeper in Antarctic. This doesn’t scale exactly with the FK parameterization scaling, this could be due to a number of reasons, but there also could be an effect of the transient component here (due to the non-steady state, stronger in the Antarctic than for the Arctic as the state of the ML responds more rapidly for the weaker, Antarctic-like stratification). This could result in a larger cancelling of the SF than in the Arctic case.

Lines 418-450: I think it’s really nice to list the key outcomes, but these are a bit dense. I think you should include all of this information in the Conclusions section, but you could consider putting some of this in the text (rather than bullet points) and really consolidating your key bullet points to 3-4 streamlined takeaways.

We previously had these points mostly in text rather than bullets, but were advised to add the bullets for more impact. It would be difficult to streamline them without adding an additional paragraph at the end. However as said above, we will add some of the information earlier in the paper, into the results, which will allow us to streamline a little this discussion section and that would also add the precision and readability asked for here.

I also feel you need to more directly highlight the lateral versus vertical transports when discussing the eddy heat fluxes. Is it correct to say that the eddy heat transport is primarily lateral in summer and vertical in winter? Or is the meridional heat transport just weaker in winter compared to summer (but still larger than the vertical fluxes)?

We will clarify vertical versus lateral heat transport in-line. As above mentioned, here, we talk about SMLE lateral heat transport when we reference the results. In winter, lateral eddy transport is counteracted by eddy-modified vertical heat transport, which in turn is dominated by the convection process of MLD deepening and heat lost at the surface. We will clarify these details, especially in section 3.1.2, as mentioned above.

Lines 456-467: These seems a slightly odd note to end on. I agree that we need SMLE parametrizations that are designed for (or optimized for) the polar regions. But this work has not dealt directly with parameterizations. I think it’s useful to speculate about the implications of the results for parameterization development, but this would make more sense earlier on in this section rather than as the final sentences. In my opinion, it’s more impactful to end with a strong statement about the significance of this work, rather than invoking some other unpublished work that the reader does not have access to.

We agree, we will place this earlier on, and end on a different note, more relating specifically to the impact of the results of this paper.

Lines 470-474: It’s a bit random to me to have such a small appendix given how much detail you gave about the model setup in the main text. If you’re going to keep all of that detail in the Methods section, then you may as well just include these two sentences there. Or alternatively, you could move a more significant amount of those details here and streamline the Methods section in the main text.

Agreed, we have removed the old information in the appendix. However as mentioned above we will keep an appendix for details of the model set-up as recommended by reviewer 1 (the start of section 2.1), as well as some of the technical details of section 2.2, as recommended by reviewer 2.

We thank the editor for their additional comments. Note, we have reproduced their comments again below, and written our responses in bold beneath each bullet point.

Having received two referee reports now, I would recommend authors proceed with doing replies and also preparing revised manuscript for a further review.

Below are some additional comments that mostly echoes what the referees have said already, in no particular order:

• Appendix is short to the point of it being redundant. Would suggest getting rid of it and assimilating the material into the main text (in line with referee 2), or move some of the content in the body to here (in line with both referees). I have no strong opinions either way; I would have gone for the first option personally, but this isn't my paper (I think the readability is fine as is, disagreeing with referee 1 on that front).

Agreed, we actually realised the material in the previous appendix was already in the main text, so we have removed it from the appendix. 

• I agree with referee 2 about "Arctic + Antarctic" grouping to "differing stratification" or similar. I think the authors can keep this general rather than locking themselves into the grouping by geographical location, especially when that grouping reads quite unbalanced at the moment in terms of length (the "Antarctic" subsection is quite short, and the "Antarctic Summer" subsubsection sticks out unnecessarily like the Appendix).

We did intend for the ‘Arctic/Antarctic’ grouping to reference a differing background stratification sensitivity test. We will rework the wording to make this clearer, and the simulations using the Arctic-like or Antarctic-like stratifications will be referred to as such, with the section being titled ‘Background stratification sensitivity’ or very similar, as we agree we don’t want to limit ourselves.

• Fig. 2 to me is taking up a lot of space and not adding very much. Consider shrinking this a bit.

We will shrink this figure.

• Would recommend adding background grid lines in the line plots, partly to help the reader, but also to break up the blocks of white space.

We will aim to add grid lines to the line plots.

• There are some in-line referencing format that doesn't work, e.g. line 146, 468, 479, where you probably want \cite rather than \citep (no brackets, since the object is the article itself).

We have amended these in-line citations using \cite.

• The spelling is a internally inconsistent at the moment (e.g. 457 vs 464, "parameteriSation" vs "parameteriZation"). Copernicus type-setting might change it at some point, but would push for internal consistency for now, with all the "S"s or "Z"s etc. (unless you want to go with the Oxford spelling distinguishing Latin or Greek roots...)

We have amended the ‘parameteriSation’ cases, so that is it consistently ‘parameteriZation’ throughout.