The impact of tides on Antarctic ice shelf melting

Richter, Ole; Gwyther, David E.; King, Matt A.; Galton-Fenzi, Benjamin K.

doi:https://doi.org/10.5194/tc-16-1409-2022

Articles | Volume 16, issue 4

https://doi.org/10.5194/tc-16-1409-2022

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

https://doi.org/10.5194/tc-16-1409-2022

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

Articles | Volume 16, issue 4

Research article

|

21 Apr 2022

Research article |

| 21 Apr 2022

The impact of tides on Antarctic ice shelf melting

Ole Richter, David E. Gwyther, Matt A. King, and Benjamin K. Galton-Fenzi

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Final revised paper (published on 21 Apr 2022)
Preprint (discussion started on 24 Jul 2020)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

RC1: 'Review', Anonymous Referee #1, 03 Aug 2020
- AC1: 'Reply on RC1 & RC2', Ole Richter, 21 May 2021
RC2: 'Review: `Tidal Modulation of Antarctic Ice Shelf Melting’ by Richter et al.', Anonymous Referee #2, 27 Aug 2020
- AC1: 'Reply on RC1 & RC2', Ole Richter, 21 May 2021

Peer-review completion

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

ED: Reconsider after major revisions (further review by editor and referees) (21 May 2021) by Evgeny A. Podolskiy

AR by Ole Richter on behalf of the Authors (23 Jul 2021) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (27 Jul 2021) by Evgeny A. Podolskiy

RR by Anonymous Referee #1 (10 Aug 2021)

Suggestions for revision or reasons for rejection

“Tidal Modulation of Antarctic Ice Shelf Melting”

by Ole Richter, David E. Gwyther, Matt A. King, and Benjamin K. Galton-Fenzi MS No.: tc-2020-169

The authors present an updated version of a manuscript reporting on the effects of including tidal forcing within a circum-Antarctic ice shelf-ocean model. The principal aims of the study was to identify what is lost from models that do not include tides, and what is likely to remain lost when such non-tidally enabled models attempt to include the effect of tides by accounting for the shear induced vertical heat and salt transport.

It seems to this reviewer that the study advances the discussion of the impact of tides on ice shelf basal melt in a useful way. In particular, the authors make a serious effort to identify the weaknesses in the model, and how those weaknesses are likely to have affected the results.

I have attached a marked-up copy of the pdf, which points out a few typographical slips and makes occasional suggestions on how clarity might be improved. I have one main concern that needs to be addressed before the manuscript can be published.

The definition of thermal driving needs to be corrected. At the moment, the authors have used “thermal forcing”, the difference between the mixed layer temperature and the freezing point at the ice-ocean interface. “Thermal driving” is the difference between the mixed layer temperature, and its freezing point calculated at the pressure of the ice base. The ratio of the two numbers is unlikely to change much, and so I imagine it will have no effect on the results of the study. But it needs to be corrected.

The only other major comment I have is about the the description of the interpretation of the results of the decomposition into dynamical, thermodynamic and covariational effects of tidal forcing on simulated melt rate. I like the approach, introduced by Jourdain et al 2019, but I’m unsure about some aspects of the interpretation. I accept this might be a point for discussion (and maybe I need to think harder about it). The relevant text is in lines 129 to 134. I’ve made a few comments below, which might help the authors revise that short piece of text.

The authors start with the second term in (5) (it would be worth going in order of the terms in the equation):

“The dynamical component describes the mean effect of tidal current velocity as well as tidal residual flow (including tide induced buoyant plumes from melting upstream).”

This term is mean(delta_u* x T*_non-tidal). delta_u* is the difference between the friction velocity for tidal and non-tidal runs, and T*_non-tidal is the thermal driving for the non-tidal run. This term contributes to the difference in meltrates between tidal and non-tidal simulations. Does the “mean effect of the tidal current velocity” refer to an oscillatory component that drives shear in the boundary layer, and therefore turbulent exchange of heat to the ice base? I can understand that, if so. “Tidal residual flow” presumably again refers to its notional effect on vertical shear? “Tide induced buoyant plumes” presumably refers to the effect of tidally-induced melting on the buoyancy driven flow in the cavity. As I mention in the comments on the pdf, I think the use of the word “plumes” is confusing. This is a full, 3-D model and any plumes are part of the general buoyancy-driven flow. In general, I think all that needs to be stressed is that the dynamical term refers to the representation of shear-driven turbulent mixing in the three equation model, and any tidally-sourced processes that contribute to the speed of water flow in the cavity. And I would delete mention of plumes.

“Thermodynamical changes account for tidal vertical mixing of heat below the turbulent boundary layer (TBL) as well as upstream thermal effects associated with tides (including tidal modulation of meltwater input).”

This term is mean(u*_non-tidal x delta_T*), where delta_T* is the difference in temperature in the upper boundary layer between tidal and non-tidal simulations. As I said in a comment on the PDF, mention of meltwater input is potentially confusing, as it might be read as meaning sub-glacial discharge at the grounding line. More generally, though, it’s the description I have difficulty with. Tidally-induced vertical mixing into the boundary layer is important, but also the way tidal rectification contributes to the horizontal circulation of heat and salt in the cavity is also relevant (for example). Any tidally-induced change in the distribution of temperature within the cavity will contribute to this term, and that of course includes the effect of chilled meltwater from tidally-induced melting.

One final note (apart from the comments in the pdf). There is a lot of use of the word “modulation” in the text. It's usual to reserve it for something whose strength is being varied in a pseudo-periodic fashion. In a manuscript that is primarily about the effect of tides, I would strongly recommend that the authors reserve the word for tidal modulation. So not the effect of tides being switched on or off, but the effect of the variation within the tidal signal. ie melt rates (for example) being modulated at tidal frequencies, or it could also refer to the spatial modulation of the effects of tides. But not the effect of having tides switched on or off. Perhaps words like "impact", "effect", "consequence" etc might be useful.

Referee Report: PDF

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RR by Anonymous Referee #2 (21 Aug 2021)

Suggestions for revision or reasons for rejection

Review: `Tidal Modulation of Antarctic Ice Shelf Melting, Revision 1’ by Richter et al.

The authors have substantially revised this manuscript in response to the original round of reviews, and overall it has substantially improved. Below I have listed several further comments and questions, largely aimed at clarifying aspects of the manuscript and the caveats to the authors’ modeling approach. My most major comment concerns the authors’ decomposition of the ice shelf melt rate into dynamical and thermodynamical drivers. Specifically, I am concerned that the authors’ decomposition may be strongly sensitive to the order in which the difference is taken between simulations (quantifying the effect of adding tides vs. the effect of removing tides), and thus may be producing a misleading partitioning of the dynamical and thermodynamical contributions. Below I explain this concern in detail and suggest an approach that circumvents this issue. This issue has the potential to require wide-ranging changes to the manuscript’s figures, text and conclusions. While I consider this an important issue, I am confident that the authors can resolve it after another round of revisions.

Comments/questions:

L6-7: I had to read this sentence several times to parse it properly. I suggest rephrasing.

L86-88: The prescribed surface fluxes are “accurate” in the sense that they are consistent with observations, but I am not convinced that this is an “advantage”, as the fluxes may be inconsistent with the simulated state of the ocean. For example, negative heat tendencies may be applied to waters that are already at the surface freezing temperature, producing super-cooled waters (presumably the authors have implemented a fix for this issue). Or surface currents could be accelerated by the imposed momentum fluxes in regions where the sea ice is thick and largely immobile, and should be retarding the near-surface flow. I do see the advantage in ensuring that the area-integrated buoyancy gain and loss is correct in different parts of the continental shelf, but I find it misleading to describe this as “accurate”. The authors should rephrase the text to be more candid about the advantages and disadvantages of this approach.

L87-94: Have the authors compared the buoyancy fluxes that result from these modifications with the buoyancy fluxes derived from Tamura et al. 2011? Do they substantially modify the surface fluxes in any particular regions?

L106: Please specify which month(s) the 30-day analysis period occurs in. The authors should also discuss potential sensitivities to performing this analysis in summer vs. winter months. If the analysis is performed over multiple 30-day periods to span the full simulation duration then this should be stated.

L122: “inset”

L145: I do not understand this sentence: please clarify.

Fig. 2: I suggest using fewer color graduations in the colorbar to make it easier to read values in these plots, particularly panel (b).

Fig. 4: I assume that the barotropic velocity here is defined as the magnitude of the depth-averaged velocity vector - is this correct? In panel (b), how is the continental shelf potential temperature defined - surface, bottom, or depth-average (or something else)?

L180-188: I am concerned that the authors’ formulation of the dynamical/thermodynamical decomposition may be producing misleading results here. The core issue is that their decomposition (eqn. (5)) may produce qualitatively different results depending on whether they subtract the no-tides (nt) case from the tides (t) case or vice versa. Consider these two approaches:

Approach 1, quantifying the change in heat flux due to adding tides:
w_b,t - w_b,nt ~
u_nt (Delta t) <thermodynamical>
+ (Delta u) T_nt <dynamical>
+ (Delta u) (Delta T) <covariational>

Approach 2, quantifying the change in heat flux due to removing tides:
w_b,nt - w_b,t ~
- u_t (Delta T) <thermodynamical>
- (Delta u) T_t <dynamical>
+ (Delta u) (Delta T) <covariational>

In each case Delta u = u_t - u_nt and Delta T = T_t - T_nt.

Clearly the covariational term is insensitive to the order of the subtraction. However, the thermodynamical and dynamical terms may be. For example, in order for the thermodynamical terms to be comparable, we require

u_nt (Delta_t) ~ u_t (Delta_t)
=> u_nt/u_t ~ 1
=> Delta t << u_nt, u_t

However, the addition of tides is likely to create situations in which u_nt is approximately zero, but u_t is on the order of 10 cm/s. In such situations, Approach 1 will yield a very weak thermodynamical contribution (perhaps explaining Fig. 5c), whereas Approach 2 will yield a large thermodynamical contribution.

For a concrete example, take
u_t = 0.11 m/s
u_nt = 0.01 m/s
T_t = 0.5 deg C above freezing
T_nt = 0.3 deg C above freezing
Delta u = 0.1 m/s
Delta T = 0.2 deg C

Approach 1 yields
<thermodynamical>: 0.002
<dynamical>: 0.03
<covariational> 0.02
Total: 0.052

Approach 2 yields
<thermodynamical>: - 0.022
<dynamical>: - 0.05
<covariational> 0.02
Total: - 0.052

With approach 1, we conclude that <thermodynamical> is an order of magnitude weaker than the other contributions. With approach 2, we conclude that <thermodynamical> is comparable to the other contributions.

It is not clear whether the authors have considered this, so I would ask that they revisit their decomposition in this in mind as they revise the manuscript. My suggestion would be that they decompose the heat flux by defining

u_m = (u_t + u_nt)/2 and T_m = (T_t + T_nt)/2,

and

w_b,t - w_b,nt ~ (u_m + Delta U/2)(T_m + Delta T/2) - (u_m - Delta U/2)(T_m - Delta T/2)
= u_m (Delta T) <thermodynamical>
+ (Delta u) T_m <dynamical>

This eliminates the covariational component and ensures that the thermodynamical and dynamical components are insensitive to the order of subtraction.

L189: “dipol”

L209: “While circum-Antarctic total melt is small” - is it? Did the authors mean to refer to the change in melt due to tides instead?

L213: “strongest changes” - meaning changes due to the introduction of tides? This needs to be clarified because as currently written this is likely to be misinterpreted as changes with time.

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ED: Reconsider after major revisions (further review by editor and referees) (24 Aug 2021) by Evgeny A. Podolskiy

AR by Ole Richter on behalf of the Authors (11 Jan 2022) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (13 Jan 2022) by Evgeny A. Podolskiy

RR by Anonymous Referee #1 (19 Jan 2022)

RR by Anonymous Referee #2 (02 Feb 2022)

ED: Publish subject to minor revisions (review by editor) (03 Feb 2022) by Evgeny A. Podolskiy

Dear Dr. Richter,

your manuscript has been seen by the same two referees who had evaluated it initially. Based on their positive recommendations, I am prepared to accept your manuscript pending final revisions pointed by both referees, which are shown in annotated pdf of Referee#1 and appended below (together with technical remarks from me). As you address these minor revisions, your manuscript will be accepted.

I look forward to seeing the final version of your manuscript.

Yours sincerely,
Evgeny Podolskiy

***

REMARKS

Referee #1:

“My only significant remark is that I'm unsure how much Appendix C adds to the manuscript, but I don't feel strongly either way and leave it as an editorial decision.”

-> Editor: Appendix C describes a quite nuanced choice of the reference state, which might be different in other studies. Since there are no issues with limited space, I suggest leaving Appendix C as it is after incorporating slight modifications suggested by the Referee.

“Annotated pdf contains a set of minor comments and corrections”.

Referee #2:

“L53 and elsewhere: The authors will likely remember this anyway, but the reference to Richter et al. should be updated to reflect that the study has now been published.”

“L158: I do not understand this sentence - isn’t 4km the resolution of the model used in this study? Please clarify.”

Editor:

Line 64
A well{-}known feature

Fig 1.
[western] East Antarctica
-> is it common to refer this way? should be just East Antarctica?

Line 125
Eqn{.} 32

Table 1
Tide{-}induced

Line 195

I am not sure it is obvious what is meant by “cold and warm regimes”. Perhaps, some definition or clarification would be helpful.

“in the supplemental material as Figure B1”
->
in Appendix B as Figure B1

Fig. 4 caption
Tide{-}induced
redundant parenthesis after … No-Tides))

Line 215
tide{-}induced

Line 226
please define what is AABW

Line 244/5
tide{-}driven

Line 245
far{-}field tides

Line 249
(Jacobs, 2004, e.g.)
->
(e.g., Jacobs, 2004)

Line 253
tide{-}driven

Line 263
(see Fig{s}. 5 and 6)

Lines 280, 296
tide{-}driven

Line 298
tide{-}induced

Lines 304, 308
Since this is a summary, for a non-specialist I suggest avoiding acronyms and writing in full “TBL” and “AABW”.

Fig. C1 caption
in equation C1, C2 ->
in equation{s} …

***

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AR by Ole Richter on behalf of the Authors (18 Feb 2022) Author's response Author's tracked changes Manuscript

ED: Publish as is (22 Feb 2022) by Evgeny A. Podolskiy

Short summary

Tidal currents may play an important role in Antarctic ice sheet retreat by changing the rate at which the ocean melts glaciers. Here, using a computational ocean model, we derive the first estimate of present-day tidal melting that covers all of Antarctica. Our results suggest that large-scale ocean models aiming to accurately predict ice melt rates will need to account for the effects of tides. The inclusion of tide-induced friction at the ice–ocean interface should be prioritized.