Melting and fragmentation laws from the evolution of two large Southern Ocean icebergs estimated from satellite data

Bouhier, Nicolas; Tournadre, Jean; Rémy, Frédérique; Gourves-Cousin, Rozenn

doi:https://doi.org/10.5194/tc-12-2267-2018

Articles | Volume 12, issue 7

https://doi.org/10.5194/tc-12-2267-2018

© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/tc-12-2267-2018

© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 12, issue 7

Research article

|

12 Jul 2018

Research article |

| 12 Jul 2018

Melting and fragmentation laws from the evolution of two large Southern Ocean icebergs estimated from satellite data

Nicolas Bouhier, Jean Tournadre, Frédérique Rémy, and Rozenn Gourves-Cousin

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Final revised paper (published on 12 Jul 2018)
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Preprint (discussion started on 14 Nov 2017)
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Interactive discussion

Status: closed

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

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RC1: 'Interesting study---presentation can be improved.', Anonymous Referee #1, 14 Dec 2017
RC2: 'Report', Anonymous Referee #2, 20 Dec 2017
AC1: 'reply to referee's comments', Jean Tournadre, 13 Feb 2018

Peer-review completion

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

AR by Jean Tournadre on behalf of the Authors (13 Mar 2018) Author's response Manuscript

ED: Referee Nomination & Report Request started (23 Mar 2018) by Lars Kaleschke

RR by Anonymous Referee #1 (05 Apr 2018)

RR by Anonymous Referee #3 (30 Apr 2018)

Suggestions for revision or reasons for rejection

Bouhier and co-authors present an in-depth study of the melting and fragmentation of two large Antarctic icebergs. The study is concerned with an important topic in climate and cryospheric physics; a topic which has seen a recent surge of interest. The ideas and methods underlying this study are a good fit for The Cryosphere. However, I have a few major and more minor concerns that I believe should be addressed before this manuscript is accepted for publication.

Major Comments:

- I am aware that the authors have had somebody proof-read the language of the manuscript. However, there are still a large number of grammatical errors, typos, and formatting issues in this revised version. This has made reading and reviewing the manuscript unnecessarily difficult. I want to illustrate this with just the first lines of the introduction:

l.16: misplaced superscript "3"
l.17: "(1.500 km^3 yr^-1 ~80%)" -> "(1500 km^3 yr^-1, ~80%)"
l.17: "Tournadre et al. (2016)" -> "(Tournadre et al., 2016)"
l.18: "as a reservoir to transport ice" -> "as reservoirs transporting ice"
l.18: "Antarctic Coastline" -> "Antarctic coastline"
l.19: "diffuse" -> "diffusive"
l.20: "the ter input" -> "the water input"

I could go on. I would keenly urge the authors to revise the language and format to bring it up to the high standard appropriate for The Cryosphere. I would advise to consult a native English speaker once more.

- P.11 Estimation of V_w and T_i: As far as I understand the method here, the authors use one equation (eq 3) to determine two unknowns (V_w and T_i). This system is thus underconstrained, no? Please explain your

- P.11, P.15, P.17: I'm confused about the "99.9% correlation" between the models and observations (and reviewer #2 has hinted at this, without a satisfactory answer, in my opinion). Since the models are fitted to the observations (over small time steps) isn't a high correlation guaranteed by design? Or rather, can you speak of "correlation" in the typical sense here? I see this issue with all 3 models that are discussed.
Furthermore, If I understand this correctly I would have to disagree with the first line of the discussion (p.15 l.25): the authors have merely fitted V_w and T_i (in an underconstrained way(?)) such that the modeled loss of thickness matches the observed. P.15 l.25 reads as if the model ran independently from the observations and recovered the same thickness evolution. This is certainly not the case.

- On closer inspection it becomes clear that the two models of eq (3) and eq (5) are not that unlike each other. Both depend (slightly non-linearly) on relative velocities and linearly on the relative temperature difference between ice and water. However, a direct comparison between the two models is made difficult by the different notations used. The models should be formulated as similarly as possible to make a comparison more intuitive. Also, there are some issues with units (e.g. unit of the 0.58 prefactor in (3), unit of water viscosity (p.12, l.25)?). It would be informative to see how the two models compare for standard values of the drag and material coefficients. I'd suggest a plot for M_b as functions of V_w-V_i for both models (although V_w is presumably a different velocity in eq (5), or as functions of T_w-T_i (or T_b-T_w). Furthermore what values of S_w and P_w are used? (If they are taken to be constant, it might make sense to just give T_b as a constant). Overall, section 4.2 appears to be more or less copied from previous work without putting it into the context of the present study.

- Regarding firn compaction: I agree that it is important to mention this in the main text and to provide the 2-5% error estimate. However,I would argue that it doesn't need to get a full appendix (the error is small and the matter is rather tangential to the story). I thus recommend just removing Appendix A.

Minor Comments:

P.3

l.13: "area, size, and shape" - What's the distinction between area and size here? Does size refer to longest horizontal dimension(s)? Please clarify.

l.21: "The first section" - The Introduction is really the first section. You should probably refer to the sections by the numbers they are given.

Figure 1:
- mark grounding sites
- change time labels on legends to Jan 2014, Feb 2014, ...

P.4

L.6: delete "(latitude, longitude)"
L.9: "Altimeter data can"
L.17: "final detectable collapse"

Figure 2:
- add a legend with "* - MODIS, o - Altimeter"

P.5 Section header: "2.3 Environmental data"

P.7

L.14 So the +- 0.9m represents the standard deviation of the standard deviation? I would just report the std as +- 3m. Or am I misunderstanding?

L.18 It's difficult to reconcile these numbers with Fig. 4a. There seems to be a faster melt period between Sept '14 and Nov '14? The melt appears to be slowing down again after May '15?. If you want to give these three regimes you should probably indicate the slopes with dashed lines?

L.23 Stern et al (2016), "Wind‐driven upwelling around grounded tabular icebergs" talks particularly about the unbalanced forces around grounded icebergs.

Last paragraph: If I understand this calculation correctly it assumes that all sidewall erosion is due to fracture and all bottom erosion is due to melt. I agree that this is a good approximation, but it should be stated explicitly.

Equation 1: This has a dimensional issue. The right hand side is M = dV/dt = m^3.d^-1? The l.h.s is m^2*m. I guess you assume dT has units m.d^-1. You should probably write something like
M = \Delta V/ \Delta t = S* \Delta T/ \Delta t,
where \Delta t = 1 day. I'd argue for the use of \Delta T, rather than dT, since you're looking at finite intervals.

Equation 2: Similar arguments as for eq (1)

Figure 4
- panel a. The caption doesn't match the colors of the figure. Also, maybe make the stars the same color as the continuous lines (red and blue?)

Equation 4: what do the different terms represent physically?

P.16

L.20 delete parentheses

L.23: what are the 63% and 64% values? Correlation coefficient r?

P.17

L.1: "a-dimensional loss" -> "relative volume loss"

Equation 8: While the form of eq (7) makes obvious sense, I don't have an intuition of why a second dependence on V_i should be of the multiplying form (1+exp(...V)). Could the authors explain this choice?

Figure 8. I find it hard to see anything in this figure. The panels should be substantially revised and rethought. To start out with, I suggest two columns, with column 1 for C19a and column 2 for B17a.

Figure 9. I would put these on a log-lin scale (by construction of equations (7) and (8) this seems, no?). Furthermore, I'd suggest a plot where the B17a and C19a curves are laid on top of each other to compare the two melt rates visually.

Fig 11. Some of the labels appear to be messed up, although I'm not entirely sure which ones.

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ED: Reconsider after major revisions (02 May 2018) by Lars Kaleschke

AR by Jean Tournadre on behalf of the Authors (13 Jun 2018) Author's response Manuscript

ED: Publish subject to minor revisions (review by editor) (20 Jun 2018) by Lars Kaleschke

AR by Jean Tournadre on behalf of the Authors (21 Jun 2018) Author's response Manuscript

ED: Publish subject to technical corrections (22 Jun 2018) by Lars Kaleschke

AR by Jean Tournadre on behalf of the Authors (22 Jun 2018) Manuscript

Short summary

The evolution of two large Southern Ocean icebergs, in terms of area and thickness, are used to study the melting and fragmentation laws of icebergs. The area and thickness are estimated by the mean of satellite images and radar altimeter data. Two classical formulations of melting are tested and a fragmentation law depending on the sea temperature and iceberg velocity is proposed and tested. The size distribution of the pieces generated by fragmentation is also estimated.