Large-eddy simulations of the ice-shelf–ocean boundary layer near the ice front of Nansen Ice Shelf, Antarctica

Na, Ji Sung; Kim, Taekyun; Jin, Emilia Kyung; Yoon, Seung-Tae; Lee, Won Sang; Yun, Sukyoung; Lee, Jiyeon

doi:https://doi.org/10.5194/tc-16-3451-2022

Articles | Volume 16, issue 9

https://doi.org/10.5194/tc-16-3451-2022

© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/tc-16-3451-2022

© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 16, issue 9

Research article

|

01 Sep 2022

Research article |

| 01 Sep 2022

Large-eddy simulations of the ice-shelf–ocean boundary layer near the ice front of Nansen Ice Shelf, Antarctica

Ji Sung Na, Taekyun Kim, Emilia Kyung Jin, Seung-Tae Yoon, Won Sang Lee, Sukyoung Yun, and Jiyeon Lee

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Final revised paper (published on 01 Sep 2022)
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AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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RC1: 'Referee review', Anonymous Referee #1, 31 Jul 2020
- AC1: 'Author's response for Referee comment (RC1)', Jisung Na, 06 Nov 2020
RC2: 'Review of “Large-eddy simulation of the ice shelf-ocean boundary layer and heterogeneous refreezing rate by sub-ice shelf plume” by Ji Sung Na et al.', Anonymous Referee #2, 31 Aug 2020
- AC2: 'Author's response for Referee comment (RC2)', Jisung Na, 06 Nov 2020

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

ED: Reconsider after major revisions (further review by editor and referees) (20 Nov 2020) by Jan De Rydt

AR by Jisung Na on behalf of the Authors (01 Jan 2021) Author's response

ED: Referee Nomination & Report Request started (13 Jan 2021) by Jan De Rydt

RR by Anonymous Referee #1 (24 Jan 2021)

RR by Anonymous Referee #2 (15 Feb 2021)

Suggestions for revision or reasons for rejection

General comments:

This study uses large-eddy simulations (LES) to examine the effect of turbulence in the ice- shelf-ocean boundary layer (IOBL) of Nansen Ice Shelf. The simulations are based on recent observations of ocean conditions near the Nansen Ice Shelf. The dynamics are forced by a neutrally buoyant plume moving beneath the ice shelf and penetrating into the open ocean. Key results are the basal melt rate of the ice shelf and the freezing occurring at the ocean surface (modelling sea ice formation), both of which increase when the plume is more turbulent. The authors also attempt to discuss some interesting heterogenous structures in terms of Ekman layer dynamics, but I did not follow this explanation as it stands.

The study is of some interest and has been improved from the previous iteration. The new simulations have an idealised velocity input condition to model a plume with four different levels of turbulence. The temperature and salinity input conditions are broadly based on observations taken further away from the ice shelf. The scientific premise (what happens when turbulence is increased?) is much clearer. There are few LES of sub-ice shelf flow, in particular with the aim to match observations. I think that the study has potential for publication, but I have some comments that I would like to see addressed first.

Specific comments:

1. The authors vary only the shape of the input velocity profiles across the four runs. As the set-up is so constrained (in terms of setting specific input profiles of velocity, temperature and salinity) I wonder what portion of the results are caused by the input conditions versus the dynamics in the system. What do the authors expect would happen if there was no basal melt? Would there still be plenty of mixing in the sub-ice shelf flow, and would we still see the increase in surface freezing at the ice edge? Similarly, if the surface freezing was turned off, how would this change the outflowing plume dynamics?

2. I disagree with (or perhaps I did not understand) the Ekman layer explanation for the heterogeneity seen in the strong turbulence cases. I agree that stronger velocities beneath the ice shelf could lead to a stronger Ekman layer, but why wouldn’t this be a homogenous response underneath the whole ice shelf? What is constraining the length scale of the heterogeneity? (E.g. could it alternatively be a baroclinic eddy with a Rossby radius of deformation?) I would appreciate more discussion on these points and an in-depth explanation of the physical mechanisms.

3. I think more can be done to compare against other cases, in particular Naveira Garabato et al. (2017). (Side note: this study seemed to be missing from the citation list in the manuscript.) The only comparison with the Naveira Garabato et al. study was L321 “These physics with the Ekman layer and the upwelling behavior of PISW are similar to centrifugal overturning instability and lateral shear proposed by Naveira Garabato et al. (2017).” I was confused by this. Are the authors saying that the mechanisms are similar? And if so, how similar and what are the differences? Again, I would appreciate a more in-depth explanation of the exciting phenomena that is noted in this study. I think this would really strengthen our understanding of the phenomena we might expect to see sub-ice shelf and on the ice edge.

L11: In the abstract “…we impose velocity’s theoretical profile varying the power-law index.” Consider rephrasing as I did not know what “velocity’s theoretical profile” meant when I first read through. Highlight that the velocity profile is varied and therefore turbulence is also changed.

L35: “Therefore, because driving forces from the ocean and opposite forces by the meltwater merge within the boundary layer (meters to tens of meters) right beneath ice shelf, which is known as the ice shelf–ocean boundary layer (IOBL), we have to investigate the IOBL flow and its structure to reveal the basal melting physics in ice shelves (Holland et al., 2020).” This was a long sentence and a bit unclear. Please consider rephrasing.

L135: The power-law equation U=U_t (z/z_t)^(1/n). Firstly, I assume the x signified multiply and not x-direction (was written in the manuscript as U=U_t x (z/z_t)^(1/n))? Secondly, is z_t the surface roughness? Thirdly, when I quickly plotted this power law I got something that looked different to the Figure 2 inset. So how does this equation directly relate to the profiles in Figure 2 inset? Is there some normalisation coming in to play? Finally, are there other studies (apart from Irwin 1979) that have used these profiles? I am wondering if the justification for the plume shape can be strengthened by citing some more studies that use these profiles.

L152: The wind effect is excluded in the simulations by setting the surface velocity to zero, even though observations showed a non-zero value of wind. In the reply to reviewers there was some justification for the zero velocity condition, would it be possible to have the brief explanation included in the manuscript also?

Section 2: I might have missed this, but what was the surface freezing condition on temperature and salinity? Was it a Dirichlet or flux condition?

L175: How was the large-eddy turnover time calculated here?

Figure 2: There is a lot of variability in this figure, which makes it difficult to determine whether it is in equilibrated state. Are there other results that show the simulations are equilibrated?

Results: Are there any indications of inertial waves present in the simulations, due to having Coriolis parameter (f)? I am wondering if this variability would appear on the friction velocity (Figure 2).

Figure 5: Caption does not seem to be consistent with legend. What is the difference between (a) and (b) figures? If it is n=3 and n=7, then why are these values also varied in the legend?

L239: Could the spatial-averaged freezing rate values also be included here? Perhaps an earlier reference to Table 2 would help (first time you reference Table 2 is in Section 4.2 Discussion)?

L262: “Because turbulence kinetic energy production is proportional to mean shear gradient and turbulent shear stress, turbulent shear forcing is highest in the strong turbulence case.” Could a citation please be included for the first half of this sentence?

Figure 9: There are some negative heat flux values below the positive values in the IOBL. What is causing this?

Section 4.2: There are a few different ideas discussed in this section. Please consider breaking into separate paragraphs.

L324: Please include a definition for the flux Richardson value. How was it calculated in the simulations?

Technical corrections:

L34: “opposite forces” perhaps “opposing forces”?

L70: Here and in several other places there is a “the” missing (e.g. “THE main parameter…”).

L71: “For consistency in experiments, we considered different turbulence state while remaining thermohaline forcing by the melting and freezing.” Was this meant to be more along the lines of: “For consistency in experiments, we considered different turbulence states while keeping the same thermohaline forcing by the melting and freezing.”

L97: Units missing on Coriolis parameter.

L124: “…was used in whole cases.” Should this be “…was used in all cases.”?

L183: Domain center (y=1536m) is different to that stated in Figure 3 caption (y=1728m).

L223: Wavenumber is missing units.

Figure 8, Figure 9a: Are units on (rho u v) correct? Should they be kg m^-1 s^-2?

L257: “Important to not is that a noticeable trend of heterogeneous patterns of melting rate in the meridional direction is not observed.” I think this sentence is saying that the melt rate is homogenous? But it is a bit unclear, please consider rephrasing.

L259: “Freezing rate” should this be “melting rate” as talking about sub-ice flow?

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ED: Reconsider after major revisions (further review by editor and referees) (23 Mar 2021) by Jan De Rydt

AR by Jisung Na on behalf of the Authors (04 May 2021) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (30 Jun 2021) by Jan De Rydt

RR by Anonymous Referee #1 (03 Jul 2021)

Suggestions for revision or reasons for rejection

I appreciate that the authors have made significant additions to the text since the last round. I have indicated major revisions because there are still many aspects of this work that remain unclear. Some of this needed clarification arose due to additions made since last round, and some questions remain from last round so I have tried to be more specific in my comments. My comments this round pertain mostly to the science rather than language. I acknowledge that the authors are likely non-native English speakers. Unfortunately, non-standard grammar and awkwardness of some of the sentences will deter some readers and in cases will contribute to confusion about the science (as they did for me), and consequently reduce the impact of the article. I recommend getting a careful read-through for grammar and awkwardness before the next round.

Given the edits to the manuscript, some reorganization is needed. For instance, much more than validation happens in Section 3.1. The paragraphs should be split in several places to divide distinct topics, as I’ve noted in my comments. Some places also lack adequate transitions between topics.

It’s clear to me now what the definition of PISW is. However, I do believe that the definition of IOBL will be misleading. I would have expected that the IOBL would include all of the PISW thickness and that the 5% heat flux definition would have been used for IOBL bottom and not its top. It’s not clear to me in what sense that would be considered a boundary layer (if not related somehow to shear at the boundary) or what the bottom of the IOBL is. I might have missed it, but I don’t think it’s stated explicitly what you mean by sub-shelf plume. My best guess was the full-cavity depth outflow. If that’s right, I think that would also be confusing for readers, as plume usually denotes flow driven by buoyancy whereas this seems to be a geostrophic flow. If you decide to keep this notation, it should be clear what these terms mean.

There are a few instances where the choice of terminology could be improved. I’m not thrilled with the choice to call the different initial and boundary conditions different “turbulent states” as that seems to imply that there is a transition in the mode of turbulence or the kinds of instabilities that occur. There are also instances where the authors use a “downward force” framing, which doesn’t reveal what specifically is influencing the relative buoyancy of water masses. See also a later comment about more specific terminology for “ice front circulations.”

Some aspects of the ice-shelf front circulation remain unclear. Are there convective downwellings throughout the outer cell or only at the convergence of the two cells? You show the horizontal velocity but there is no way for the readers to gauge the strength of these circulatory cells. A streamfunction plot would be the most clear but a vertical velocity plot might work if it’s easily interpretable.

Furthermore, it’s unclear in the text why you think that the outer circulation should be a cell. Why would there be upward velocity at the outermost edge of the domain given that there is a radiation boundary condition? What would set the size of this cell in the real world? (I appreciate that the authors added more discussion of length scales with respect to the ice-front circulation.)

I’d like to see you explain more thoroughly how these simulations relate to the real world a bit better given that understanding observations is given as the main motivation. Are your simulation conditions specific to a season? I assume the observations are from summer, so is there sea-ice freezing here year-round? How does your choice of SST of -1.9 degC relate to observations and season? If there were these two circulation cells, wouldn’t you see a signature in sea ice advection including convergence and ridging or do you not expect these features to be long-lived or to migrate? Besides oceanographic observations, what might validation look like? I appreciate that the authors added a citation to basal melting observations but they say it’s from a channel. Are there no satellite estimates of basal melt on broader scales? Was Nansen not included in the Adusumilli et al. 2020 dataset https://doi.org/10.6075/J04Q7SHT?

I appreciate that the authors added some text pertaining to wind stress forcing, but I do believe that there should be more discussion of how this might affect the strength of the inner overturning cell since that is one of the main results of the paper.

I appreciate the caveat the authors added for frazil ice dynamics, but I strongly feel that there should be more discussion (at least a few sentences) of how inclusion of frazil dynamics might change your key findings. Unless it is the case that you don’t get pockets of supercooled water, in which case that should be stated.

The main remaining gap in the Methods is the determination of heat and salt transfer coefficients. This is crucial to the interpretation of freezing and melting rates. It should also be made more clear in Section 2.2 why you choose the initial and inflow velocity profile you do and how it varies with depth in and outside of the cavity.

I don’t like to harp on this, but I’m still confused by the flux profiles shown in Figure 9. The sub-grid fluxes should increase at the boundary because the turbulent lengthscales decrease near the boundary. Instead it looks like both resolved and sub-grid fluxes go to 0 at the boundary. If I just can’t see the values, perhaps an inset for the PISW would be helpful. Figure S4 also appears to show 0 buoyancy fluxes at the boundary.

11: It is unclear how imposing a velocity profile is related to different turbulent states
12: The flow of the abstract needs improvement. “To resolve” and “to simulate” make it unclear how these objectives are related.
14: State more clearly which properties are used to validate findings.
16: It is unclear what the distinct features are.
18: It is unclear how this sentence is related to the previous sentence.
19: Writing needs improvement here.
31: I think you mean shear generated by tides.
32: “thermohaline process” is always unclear to me. I’d prefer that you specify melting or thermohaline stratification, mixing, or something else.
36: I wouldn’t say that these processes make it difficult to investigate, just a complex problem.
58-60: Improve the logical flow of these sentences
61: More realistic than what?
67: Citations needed.
74: I think you mean that the melting/freezing boundary condition is the same but the way you’ve written it makes it sound as if you impose the same melt/freeze rate in all runs.
74: Keep the language consistent. I prefer that you stick with “turbulence intensity” rather than switching to “turbulence state” for clarity.
86: Only mentioning “refreezing” here implies there isn’t melting
110: It would be best to specify in the text what H_k, S_k, K_h, K_m are. I might have missed it, but there should also be an explanation for the primes.
114: Specify z here.
115: Relate the filter length to the model resolution.
Figure 1. It think it would be helpful if the velocity profile looked more like the initial or mean profile. Can you label IOBL and sub-ice plume separately?
128: This is confusing since wind stresses are 0 in your simulations, right? Also, the friction velocity should be determined based on the difference in velocity of air and water at the surface. I assume you’ve done this but it should be stated.
136: It’s unclear how the transfer coefficients are determined.
139: It’s hard to believe that melting is negligible unless thermal driving is extremely low since IOBL is rapidly rising along the front.
140: I don’t see the sea surface boundary condition described in this section. The scalar flux boundary condition is in Figure 1 but it should be stated here as well. Is the velocity boundary condition no stress/free-stream? I think it would be helpful to readers to explicitly state that wind affects scalar fluxes but not momentum fluxes.
145: cite Figure 2
145: Mention that the profile is vertically symmetric and z is the distance from the boundary, justify that choice in relation to observations and mention the depth interval over which it’s applied. It’s unclear here what the initial velocity is above the ice shelf base.
145: Discuss this choice in relation to ice-shelf cavity overturning circulation. Is there reason to believe that the baroclinic velocity is small under Nansen? If the IOBL does rise along the ice front, then the velocity structure due to the IOBL will not be reflected in the profile you implement.
145: Generating momentum through an inflow boundary condition may affect the flow differently than imposing geostrophic flow through pressure gradients. I’d like to see you at least acknowledge possible limitations.
197: When after 14h is the averaging ocurring?
198: This paragraph could be broken into several. I recommend describing the circulation and PISW generally, then discussing differences between the cases.
198: In this paragraph there should be more references to panels within Figure 3.
199: Use “end-member” instead of “extreme” unless you believe those n values are extreme in the sense that they are unlikely to be realized in the real world.
202: Would “two overturning cells” be an appropriate description? “Ice-front circulations” and “ocean circulations” are quite general and it’s strange to have circulation in the plural.
203: You might want to reconsider where it makes most sense to present melting and freezing fields. You mention sea ice formation without presenting Figure 6.
205: Might be helpful to the readers to specify that the downward force due to salt flux is the negative buoyancy flux.
207: Stratification line is unclear. Can you provide the pycnocline contour or something similar in Figure 3?
210: To me, this indicates that your simulation results are sensitive to the inflow boundary condition, even far from that inflow condition. This should be clearly stated and why this is the case should be discussed a bit more.
214: The sentence beginning “Positive buoyancy” is a rough transition from the previous sentence. I was expecting you to elaborate on the magnitude and scale of those circulatory cells next. PISW would be better introduced in a new paragraph
214: Rather than the arrow for PISW shown in Figure 3, can you contour this water mass on all panels? I imagine it’s mostly the blue contour in salinity but the reader would need density in order to understand which regions are positively buoyant. I would also appreciate a contour for the IOBL.
217: Cite Figure 7
218: Outer ocean is a confusing term. Do you just mean open ocean?
219: rephrase to avoid “-2 degC of potential temperature.” It’s unclear how this detail is important. It would be more meaningful in relation to the surface freezing point.
221: Sentence beginning “Below 400m” and the following sentence together are unclear.
223: This paragraph could also be broken into several.
225: It’s unclear at this point how varying the velocity profiles helps you evaluate the cause of the ice-front circulation patterns.
227: I think you need to be more clear about what exactly the CTD, ADCP data show. Here the reader might think that the data suggest the circulation cells you simulate, but I don’t think they establish those cells.
230: It’s more clear in the text to use directions (toward or away from ice-shelf front) rather than positive/negative. And what is this difference (stronger in observations or simulations)?
231: “The difference is from...” How do you know this? How can you exclude wind forcing as the reason? By downward force, do you mean that the freezing rates are stronger/weaker or that the water mass properties are different and thus the relative buoyancy is different?
Figure 4: Explain why simulated velocity profiles look so similar. Also, it’s unclear
233: Explain why the differences in ML temperature and salinity can be attributed to differences in ice-shelf melting from observations rather than differences in PISW dynamics.
240: Here I think you’re arguing that your LES results explain a feature in the observations. This should be stated explicitly. However, if this is the cause then this process has a weaker effect in the simulation than in reality because the pycnocline is not depressed enough. Do you need these large-scale circulation cells to explain the observations or would regular small-scale convective mixing from sea ice formation suffice?
Figure 4 makes it clear that the simulated thermocline is too weak relative to observations. This should be discussed.
241: If PISW upwelling can explain the temperature and salinity excursions in the mixed layer, then why don’t we see it in Figure 4? I imagine this could be because the simulated profiles are time-averaged. Do you ever see such features in the instantaneous profiles? If not, why might this be?
241: “the comparison of quantity and its characteristics ” this is too vague.
250: This wavenumber seems too precise
Figure 5 would be easier to interpret if the points were colored on a linear scale with distance from the inlet boundary
251: To say that these spectra follow a -5/3 slope feels like a stretch. Also, are you analyzing wavenumbers that are too large here for your resolution? It would be helpful to have marked the transition between resolved and sub-grid turbulence.
255: How do these factors suppress turbulence?
270: What is the origin of these baroclinic eddies? Are they convective instabilities associated with salt flux or something else?
280: I think it would be better to say “caused by melting”
290-294: I found these sentences confusing. Do we only know melt rates in a basal channel? How can your thermal driving values be so different from observations?
Figure 8: it’s hard to tell the difference between u and v lines.
296: This doesn’t look like a high-speed current to me.
Figure 9: The Ekman lengthscale looks super large.
Figure S2: These differences in the Ro radius don’t appear to be large enough to explain differences in flow heterogeneity.
310: this makes it sound like buoyancy and momentum are directly related rather than indirectly related.
312: It’s unclear to me how you determine the PISW top and why it wouldn’t be coincident with the ice base.
313: I was expecting the 5% heat flux to determine the IOBL bottom.
325: I would have expected you to bring your study into this paragraph. You have a HSSW-dominated regime and yet only ice-shelf melting and not freezing.
325-344: I think you spend too much time reiterating topics already laid out in the introduction.
345: oceanic region >> open ocean?
346: the way this is worded it makes it sound like the far-field values are derived from the interfacial values rather than vice versa
348: what do you mean by trend here?
353: “change in plume characteristics” change with what? Maybe just that inclusion of frazil dynamics changes plume characteristics, which requires rephrasing this sentence.
358: I would think that heat and salt exchange would be less vigorous in the stably stratified IOBL than in a convecting ML. I imagine that some readers would be thinking the same and it would be helpful to address why this is the case.
360: I don’t understand how you get circulation cells over the same depths that the velocity is set to 0. I don’t remember this from the Methods either. Is this text correct? Is this only an initial condition, because here it sounds like it’s fixed for all time?
364: Again, I don’t see evidence for high speed currents
367: “Assumed” >> “calculated”
368: “This denotes that…” means that the location of the salt maximum would indicate driving forces and I don’t think you intend to say that.
370: The wedge mechanism needs more introduction.
371: I don’t think that the existence of an Ekman layer needs to be brought up in the discussion, as it is expected.
376: It’s unclear whether the baroclinic eddies mentioned here are the same or different (i.e., in scale) from the baroclinic eddies at the Rossby radius.
378: This paragraph needs to be split. You go from talking about Ri_f to a list of model limitations.
379: I don’t know what you mean by “turbulence” here (what features?) or where in the column you’re computing the Ri_f and stratification.
381: It’s unclear what you mean by negative feedback here, though I assume you’re talking about the degree of stratification generated by enhanced buoyancy fluxes. It should be clarified for the reader.
384: “This limitation can be solved using a dynamic SGS model” implies that you didn’t use a dynamic SGS model. This sentence should be edited.
385: What is the “claimed mechanism”?
385: When you say “fill the gaps” I’m picturing a physics-informed interpolation or state estimate whereas here it’s more of an extrapolation from one point at the ice-shelf front into the cavity. Please rephrase.
387: I appreciate the clarification in the parenthetical. However, it is still awkward to say “and their feedback.”
397: inlet >> inflow boundary condition
399: “fluctuation” is ambiguous because it could be turbulent fluctuations or fluctuations in the mean flow.
403: “agree well” I think this sentence should acknowledge the primary misfit(s) with observations.
412: This sentence is unclear to me. The 4 turbulence cases should have different levels of shear yet similar stratification so how does this indicate that “the stratified forcing by PISW varies according to the flow shear caused by turbulence”?
413: What exactly should be investigated further? Controls on stratification of the IOBL?

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RR by Anonymous Referee #3 (22 Oct 2021)

Suggestions for revision or reasons for rejection

This paper reports on large-eddy simulations of an ice shelf-edge region, inspired by observations made in front of Nansen Ice Shelf, Antarctica. The simulations are run with an idealised geometry and boundary/initial conditions for temperature, salinity and velocity that are inspired by observations. The velocity boundary condition beneath the ice shelf is varied to simulate four different regimes with varying levels of turbulence. The velocity profile between the ice shelf and the continental shelf below is modelled using a power-law velocity profile, where the power-law relationship is varied to simulate varying degrees of turbulence. A three-equation model is used to model the basal melting of the ice shelf, where changes in ice shelf geometry, volume flux input and lateral ice shelf melt are excluded. In the open-ocean portion of the simulation domain, a rigid sea-ice lid is assumed, where the freezing rates are calculated using a three-equation model. Constant heat and salt exchange coefficients are used for the sea-ice region and varying coefficients, calculated using Monin-Obukhov similarity theory, are used in the ice shelf region (this needs to be clarified, as I may have got this wrong?). The high turbulence simulations show an increased basal melt rate and a stronger Ekman layer, resulting in a modified circulation pattern in the open-ocean region.
I found these simulations to be interesting and I think this paper is of interest to the community. Some changes and clarifications need to be made however before I would be comfortable with publication. Specifically, I think further reference to the existing literature needs to be made. I think the ice front region is a particularly interesting region, not least because it is relatively easy to observe compared with the grounding line. Your simulations are relatively idealised, but I think you should still be able to link your work to previous work in the ice shelf front region, even if the conclusion is that elements of your simulations make comparison difficult. Most importantly, the reader needs to be left with an understanding of what the implications of your simulations are for studies of the ice shelf region. In Garabato et al. (2017), they make the point that the intrusion depth of the ice shelf plume has important ramifications for the effect of ice shelf melt on the Southern Ocean (specifically in simulations). I think motivating your study with this scientific question (or some other broad question) would help clarify the point of your work to the reader.
I have a series of other clarifications and edits to the text that I would like to see which are listed below:
1. It needs to be clear that you are studying an ice front throughout the abstract and the introduction. The geometry of your situation is key to the physics of interest, so must avoid trying to say too much about generic IOBL plumes. i.e. I would revise the sentence in the abstract:
“In this study, we utilize a large-eddy simulation to investigate the role of the turbulence within the IOBL flow with sub-ice shelf plume”
To something involving explicitly focused on ocean dynamics at the edge of an ice shelf.
2. This line in the abstract:
“This demonstrates that the larger baroclinic eddies enforces heterogeneous distribution of positively buoyant meltwater upwelling”
Is confusing to me. How does a larger melt rate demonstrate that there is a heterogeneous distribution of meltwater upwelling? Surely the melt rate could be homogeneous but larger? This point about heterogenous/homogenous response needs to be explained more fully in the text (or excluded, as I am not totally sure what it adds to the conclusions of the paper).
3. Lines 32-35 “Shear force generated by tidal mixing and the thermohaline process during sea ice formation are the basal melting driving forces in cold water cavity (e.g., high salinity shelf water), whereas the intrusion of circumpolar deep water (CDW), which is the water well above the local freezing temperature, is the main driving force for basal melting in the warm-water cavity (Davis and Nicholls, 2019; Jacobs et al., 1992; Yoon et al., 2020).”
Needs to be split up into two sentences maybe. One saying shear forces drive turbulent mixing of T and S through the IOBL, and another saying that shear is generated by tidal mixing or by circulation, where the source of temperature and salinity mixed up to the ice base is HSSW or CDW
4. Line 67 : This would be a great opportunity to introduce the novelty of your geometry e.g. However, applications of the LES to IOBL at sub-ice shelf environment are quite limited. The geometry and scales of ice-ocean interaction may be qualitatively different for an ice shelf, particularly when considering the ice front. Ice shelves typically have a thickness of 100s of metres compared with the O(1 m) scales of sea ice.
5. Line 68 : “In this study, we performed LES experiments for the IOBL and oceanic flow including freezing effect at sea surface and the basal melting process with neutrally buoyant sub-ice shelf plume near ice front.”
Split into two sentences, first saying that you are studying the ice shelf plume at the ice front, then saying the effects you are including within your study.
6. Introduction: Paragraph on what would we expect of this flow? Cite observations of this near ice shelf region and the ideas that people use (i.e. Garabato instability work, ice front blocking work from Wahlin et al, 2020?)
7. Line 86: “To simulate the oceanic flow with refreezing”
maybe expand on this, melting is included as well as refreezing so that’s worth noting
8. Sa is confusing notationally, it might be better just as S
9. Line 116: you’ve introduced the governing equations and the turbulent closure which is great. I think this paragraph could do with a sentence that summarises the key positives and drawbacks of your chosen sub-grid scale model. For instance, I don’t imagine it works well for regions where the flow becomes laminar?
10. Elaboration is needed on the melt/freeze condition that you apply. My understanding is that you apply a three equation model with constant coefficients in the open-ocean/freezing region, and a three equation model with exchange coefficients calculated using Monin-Obukhov theory for the ice shelf region. Is this correct? If so you need to state this explicitly
11. You include citations for your three-equation model values in the table, but I think mentioning your sources in the text would be beneficial for the reader
12. Line 135: “where u* is the friction velocity which is calculated by the velocity at first node and roughness length”, are you saying that you infer the friction velocity using a drag coefficient, using the relation U^2 = C_d u*^2 ? If so, you should state this explicitly including your value for C_d and your source for that number. The true drag coefficient is defined using the vertical shear at the boundary; however, I don’t think you would resolve those scales in your simulations, so I presume you are using a drag coefficient.
13. Line 157 : “Initial profiles were set in the variation range of vertical profiles of our 24 CTD and 23 LADCP observations conducted near the ice front of the NIS.” I don’t understand this sentence. Are you saying that the initial profiles are taken as a mean of the vertical profiles or a smoothed version? Can you detail the exact method for choosing your idealised profiles?
14. Line 158-159: “The outlet boundary condition was determined to match the radiation boundary condition (extrapolation)”, could you elaborate further on this boundary condition? I do not understand which radiation you are referring to and what the form of the boundary condition is? This is important for determining the utility of your inferred circulation
15. Line 160-162: Your Dirichlet boundary condition for velocity implies that you have a rigid lid. Your satellite imagery shows a region of ice-free ocean at the edge of the ice shelf. You have assumed essentially that it is ice-covered and the ice does not move (similar to land-fast sea ice). I do not think this is necessarily a problem, but it should be pointed out when you introduce your boundary condition. Are you simulating a winter-version of this ice front region?
16. Line 221: “Below 400 m depth, a well-stratification features appear in salinity distribution.” I do not know what this sentence refers to, please clarify.
17. Line 246 : “it is necessary to confirm that the turbulence characteristics of the LES result are similar to the turbulence characteristics of inertial subrange in which energy cascading occurred with few dissipations”, I understand most of this sentence but I do not understand the last three words. Are you just saying it is necessary to confirm that the resolved turbulence in your model follows a inertial scaling?
18. You should include details of how you calculated the 1D energy spectra, perhaps including the equation for your calculation. Specifically, I’m wondering whether it’s calculated along a single line in the y-direction for instance? I’m slightly confused as to why you have so many fewer points at the high wavenumber end of your plot than at the low wavenumber end. Usually, power spectra show the opposite trend, as you have more points to evaluate small wavelengths with, you get a higher density of points at the high wavenumber end. If you tried calculating your spectra using a numerical method such as the Welch method, you might also get a smoother result, as currently it’s difficult to determine whether the presented spectra do indeed show a -5/3 slope or not. Also, I don’t think it’s a problem if they do not show a -5/3 spectrum, as you are simulating an anisotropic flow, so you might not expect a classic inertial subrange. Your SGS model may assume homogeneous isotropic turbulence, but your resolved turbulence does not need to.
19. Line 317 : “Negative heat flux at 320–400 m depths denotes that some of the entrained heat by the intrusion of the outer ocean is transferred to the downward direction.” I don’t understand this argument. In your temperature and salinity plots, the profiles seem to be increasing with depth in the sub-ice shelf region, so why would the heat flux be negative? I think this needs further explanation
20. Your first discussion section seems more like introduction than discussion to me. Your results aren’t discussed, rather the broad field and approach is discussed. I suggest including the key points from this section in a paragraph or two in the introduction then removing the section.
21. If you wanted to make the point about the two circulations more convincing to the reader, you could include a snapshot of vorticity as well as zonal velocity (which doesn’t show us the vertical velocities that complete your overturning.
22. You mention the work of Garabato et al. 2017, and I think you could explore the connections here further. If you claim that the mechanism in your simulations is similar, then you need to provide evidence of this fact. I suggest calculating some of the metrics used in Garabato et al. 2017, specifically the Richardson angle (Thomas et al. 2013).
23. Turbulence intensity is a confusing metric, could you instead show dissipation rate? This would make your work more directly comparable to the observations in Garabato et al. 2017.
24. Should we expect any ice front blocking effect in your simulations as in the work of Wahlin et al. 2020? If not, why not? This paper would be worth discussing with reference to your simulations.
25. Ensure your list of references is consistent (specifically the placement of the year)

Garabato, A. C. N., Forryan, A., Dutrieux, P., Brannigan, L., Biddle, L. C., Heywood, K. J., Jeknins, A., Firing, Y. L., Kimura, S. 2017, Vigorous lateral export of the meltwater outflow from beneath an Antarctic ice shelf. Nature, 542(7640), 219–222
Wåhlin, Anna K., Nadine Steiger, Elin Darelius, Karen M. Assmann, Mirjam S. Glessmer, Ho Kyung Ha, Laura Herraiz-Borreguero et al. "Ice front blocking of ocean heat transport to an Antarctic ice shelf." Nature 578, no. 7796 (2020): 568-571.
Thomas, L. N., Taylor, J. R., Ferrari, R. & Joyce, T. M. Symmetric instability in the Gulf Stream. Deep-Sea Res. Part II 91, 96–110 (2013)

Referee Report: PDF

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ED: Publish subject to revisions (further review by editor and referees) (29 Oct 2021) by Jan De Rydt

AR by Jisung Na on behalf of the Authors (10 Dec 2021) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (23 Dec 2021) by Jan De Rydt

RR by Anonymous Referee #3 (07 Apr 2022)

Suggestions for revision or reasons for rejection

The authors have made some significant improvements on the previous iteration of this article, and I think it could be close to being of publishable quality. My main reservations are still the ways in which this study links to other studies of the ice shelf edge specifically. The paragraph discussing the work of Garabato et al. (2017) and Malyarenko et al. (2018) is good, but these two works should be discussed in detail in your introduction as they are very relevant to the situation you are describing, and I think your work links with those studies very well. You mention that your work agrees with the picture presented by Garabato et al. (2017), whereby centrifugal instability causes turbulent mixing which changes the settling depth of the ice shelf plume. I am not totally convinced that you are seeing this mechanism, so I suggest that you assess the potential instability from your simulations (i.e. look at the vorticity and compare it to the criteria for centrifugal instability). You could also check the Potential Vorticity to see if you are likely to see any symmetric instability which was ruled out by Garabato et al. (2017). You could also show a plot of the spatial variability of the dissipation rate, or the TKE, to demonstrate whether enhanced turbulence is associated with the plume reaching the ice shelf edge. I think you should expand on how these simulations would change if you included winds, with reference to Malyarenko et al. (2018) who discuss this scenario.
I have a series of smaller points which I also think need to be addressed:
4. “Coherent structure of the ocean dynamics near the ice front” needs rephrasing, I think this is not the correct use of the phrase coherent structure
5. Change to “to simulate the varying turbulent intensities”
23. “Frazil ice” is misused throughout the manuscript. Frazil ice refers to ice that forms due to the supercooling of water, where the water pressure has increased and so the freezing temperature has increased, so ice begins to form within water that is below its own freezing point. I think you mean to refer to sea-ice formation, or simply generic freezing.
52. “well-mixed feature (20–30 m) of the temperature and salinity induced by a strong tidal forcing and a weak stratification structure was observed” needs rephrasing e.g. “a well-mixed boundary layer was observed in both temperature and salinity, induced by a strong tidal forcing and a weak stratification. A moderate melt rate was observed, despite the low thermal driving, due to the observed shear-driven turbulence.”
79. You have not used Monin-Obukhov similarity theory in your set up – just the standard three equation model. Monin-Obukhov theory would give a correction to the dependence of heat and salt flux on the difference between far-field temperatures/salinities and those at the ice base, as discussed in Vreugdenhil et al (2019). You have only included a linear dependence for your heat and salt fluxes, so I would not term that Monin-Obukhov similarity theory.
166. 1/Gamma_T, 1/Gamma_S, usually these are defined as Gamma_T and Gamma_S, why have you used the inverse?
270. Your discussion of the ‘baroclinic eddy’ needs more clarity. I think you could remove the whole paragraph starting from “this PISW layer blocks an intrusion of the outer ocean” to line 274.
274. A comparison of the scale of your spatial patterns to the Rossby radius of deformation is useful, but you should first define the Rossby radius of deformation and make it clear how you have calculated it.
Figure 6. I think you should plot lines rather than a scatter, to better show the power spectra. You should also list in the caption how exactly these spectra were calculated i.e. was it a single point velocity measurement through time? Or was it a spatial assessment of the entire velocity field? The spectra are very noisy, so it’s difficult to see the slope – if you average spectra across multiple times, or some spatial average, then you will get smoother spectra which may be more useful.
Figure 6. Your second plot seems to show shallower slopes than k^(-5/3)? Is this a k^(-1) slope? Please include the slope on this plot. If it is k^(-1) then that could be indicative of a Batchelor style regime rather than an inertial subrange, which would be worth commenting on.
344. I think the way you are calculating thermal driving is different from the method given in Wray (2019). You have temperatures and salinities taken from ocean observations, so that should not give a significantly different thermal driving. I imagine that the main differences between your simulations and the observations in terms of melt rate is associated with the lack of winds in your simulations, but there are so many idealisations in your simulations that could be the cause of this disparity.

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ED: Publish subject to minor revisions (review by editor) (08 Apr 2022) by Jan De Rydt

AR by Jisung Na on behalf of the Authors (18 Apr 2022) Author's response Author's tracked changes Manuscript

ED: Publish subject to minor revisions (review by editor) (24 Jun 2022) by Jan De Rydt

AR by Jisung Na on behalf of the Authors (12 Jul 2022) Author's response Author's tracked changes Manuscript

ED: Publish as is (12 Aug 2022) by Jan De Rydt

AR by Jisung Na on behalf of the Authors (16 Aug 2022)

Short summary

Beneath the Antarctic ice shelf, sub-ice-shelf plume flow that can cause turbulent mixing exists. In this study, we investigate how this flow affects ocean dynamics and ice melting near the ice front. Our results obtained by validated simulation show that higher turbulence intensity results in vigorous ice melting due to the high heat entrainment. Moreover, this flow with meltwater created by this flow highly affects the ocean overturning circulations near the ice front.