the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 02 Aug 2024
Subglacial discharge effects on basal melting of a rotating, idealized ice shelf
Abstract. When subglacial meltwater is discharged into the ocean at the grounding line, it acts as a source of buoyancy, enhancing flow speeds along the ice base that result in higher basal melt rates. The effects of subglacial discharge have been well studied in the context of a Greenland-like, vertical calving front, where Earth's rotation can be neglected. Here we study these effects in the context of Antarctic ice shelves, where rotation is important. We use a numerical model to simulate ocean circulation and basal melting beneath an idealized three-dimensional ice shelf and vary the rate and distribution of subglacial discharge. For channelized discharge, we find that in the rotating case melt rate increases with two-thirds power of the discharge, in contrast with existing non-rotating results for which the melt rate increases with one-third power of the discharge. For distributed discharge, we find that in both rotating and non-rotating cases melt rate increases with two-thirds power of the discharge. Furthermore, in the rotating case, the addition of channelized subglacial discharge can produce either higher or lower ice-shelf basal melt-rate increase than the equivalent amount of distributed discharge, depending on its location along the grounding line relative to the directionality of the Coriolis force. This contrasts with previous results from non-rotating, vertical ice-cliff simulations, where distributed discharge was always found to be more efficient at enhancing terminus-averaged melt rate than channelized discharge. The implication, based on our idealized simulations, is that melt-rate parameterizations attempting to include subglacial discharge effects that are not geometry and rotation aware may produce spatially averaged melt rates that are off by a factor of two or more.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-2297', Anonymous Referee #1, 19 Aug 2024
The authors conducted model experiments for an idealized ice shelf with subglacial discharge for rotating and non-rotating ice shelves. Authors show different sensitivity to subglacial discharge for rotating and non-rotating ice shelves. They also show how earth rotation and subglacial discharge location can impact cavity circulation and the melting of ice shelves. The results are well presented and key conclusions are supported by the model analyses provided in the manuscript. I suggest moderate revision.
Moderate comment
(1) Practically, all ice shelves are influenced by rotation. The meaning for considering non-rotating ice shelves, I assume, is small ice shelves that do not feel the effect of earth rotation. It would be nice to have a paragraph describing the length scale that separates rotating and non-rotating ice shelves. Maybe a discussion involving non-dimensionalized parameters may be helpful.
(2) There is no discussion about vertical resolution and coordination. Is the behavior of ice shelf meltwater strongly impacted by the choice of vertical resolutions? Do you see a similar response even if you double (or half) the vertical resolutions? How sensitive is your overall conclusion to the choice of vertical resolutions?
Minor comment
Lines 103-105: It would be nice if authors could explain somewhere (a Table maybe) in the manuscript what the observed (or estimated) rates of subglacial discharges are for different ice shelves (that helps us understand, for example, figures 2 and 6 better).
Lines 163-169: This text is a bit difficult to follow. Please consider adding arrows to help us where you are talking about in Figures 7e1 and e2.
Citation: https://doi.org/10.5194/egusphere-2024-2297-RC1 -
AC2: 'Rrequired pre-decision reply on RC1', Irena Vankova, 23 Sep 2024
This is a required response to reviewers prior to the editorial decision.
If we are asked to revise and resubmit the paper, we will address the comments of the reviewer in detail. Regarding the major comments, this means including some discussion on length scales (involving Rossby number in this case) and more details on the effects of vertical resolution.
Citation: https://doi.org/10.5194/egusphere-2024-2297-AC2
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AC2: 'Rrequired pre-decision reply on RC1', Irena Vankova, 23 Sep 2024
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RC2: 'Comment on egusphere-2024-2297', Anonymous Referee #2, 30 Aug 2024
This manuscript presents results of idealised modeling experiments on the impact of subglacial discharge on basal melting of ice shelves. The authors vary the magnitude and distribution of subglacial discharge and find a complex set of behaviours. They also explicitly show the difference that rotation makes, which I feel is important because the temptation may be to ignore this when designing parameterisations due to the complexity introduced. They nicely contrast the results to the ‘Greenlandic’ vertical calving front case.
Since there is increasing interest in the role of freshwater discharge on basal melting of ice shelves, but relatively little research has been undertaken to date, I think this paper is timely and important and useful. I also find it to be generally scientifically sound but have some remaining questions and suggestions for improving the presentation. I detail these below in categories of significant comments and minor comments.
Significant comments
Vertical mixing. In general, the rate of entrainment of ambient water into a rising plume is a strong control on its dynamics – higher entrainment means the plume warms up but slows down quickly, while lower entrainment means a faster but generally colder plume. You touch on this in the paragraph beginning on L133. In your model, since the plume is travelling mostly horizontally, the mixing between plume and ambient cavity occurs in the vertical. But I saw very little discussion of vertical mixing in the methods or results. Some details that would be good to include and discuss: (i) what is the typical vertical resolution of the model near the ice base?, (ii) what is the vertical mixing scheme in the model (for both momentum and tracers)?, (iii) does this vertical mixing scheme have a strong bearing on the results?, (iv) can you say any more about the impact of the choices of vertically-averaging over cells within 10m of the ice (L87) and distributing the meltwater into the ocean based on an exponential profile (L88) – I imagine these could influence the results?
Presentation. I found the manuscript quite hard to follow because within the first short results section (L126-149) you had already referred to 5 different results figures, each of which has a significant amount of information. As the results go on, there is a lot of jumping back and forth between figures, often when only a small detail from the figure is relevant. Having first referenced Fig. 2 at the very start of the results (L127), Fig. 2 panels b and c are then not discussed until the very end of the results (L215), so that when I was on L127 and reading the caption to Fig. 2, I had to go looking for what Eq. 1 was. I also found it a bit confusing to keep switching between ‘melt rate summary figures’ (Figs. 2, 6, 9) and ‘simulation output details figures’ (Figs. 3-5, 7, 8). At some point I found it easier to look through the figures on their own rather than trying to read the text and go to the relevant figure. I am not exactly sure how, but it would be great if there was a way of presenting this information in a more linear fashion that was easier for the reader to follow. Some ideas: could you discuss and present the simulation output details figures first, then culminate with the melt rate summary figures which provide the main conclusions of the paper? At least bringing figures 2, 6 and 9 together would make sense I think.
Overall importance of subglacial discharge to ice shelf melt rates and parameterisation of ice shelf melt rates. Fig. 3, left hand column, suggests that the influence of subglacial discharge is quite limited to the region close to where it is being discharged. If this is true for all reasonable values of subglacial discharge then although this was mentioned in the text, I feel that more could be made of this in the discussion and potentially the abstract. In particular in the discussion, because it feels very relevant to how we might parameterise the influence of subglacial discharge on ice shelf basal melt rates. Given the effect appears to be very localised, is a parameterisation for the area-average influence (such as Eq. 1) particularly useful? Won’t Eq. 1 be sensitive to how big the ice shelf is while also not capturing the spatial variability? Does it make more sense to produce a version of Eq. 1 for some region close to the discharge location?
Minor comments
L84 – what is the horizontal viscosity scheme? Can you add a little more detail?
L104 – could you add what specific values of Fs you used?
L116-124 – the set of experiments where you vary where to apply Fs in the vertical. I didn’t see these mentioned in the results or discussion, but saw them plotted on Fig. 6c, where it seems this doesn’t make much difference. I feel this is quite a technical, model-specific thing that has limited relevance to the dynamics of ice shelves, so perhaps move to an appendix or supporting information (and discuss the results of what it showed)? This additional complexity would help to streamline the paper.
L150 – “figures 3, 7, 4, 8 and 5” – it’s not important but having these numbers out of order doesn’t help with the reader being overwhelmed with swapping back and forth between figures.
L223 (Eq. 1) – should k have 10^(-5) instead of 10^5? Also the units of k look correct for n=1/3 rather than 2/3. I presume this should give melt rates in m/s? If so that is probably worth stating since people will be used to thinking in m/yr.
L241 – nice paragraph and discussion. The other part that is potentially relevant and could be discussed here is the influence of plume rise height. The higher the plume rises, the more ice-ocean area over which it increases the friction velocity. And since the plume will rise higher with higher discharge, this can contribute to a higher exponent n when we look at melt rates averaged over a fixed, larger area like an ice shelf. I don’t know to what extent this is relevant for your results?
Localised vs area-averaged melt rates (see also significant comment 3). I really liked Fig. 9, where you restricted to the area close to discharge outlets. I feel that the distinction between area-averaged and localised melt is perhaps not given enough attention in the manuscript. The discussion focuses a lot on the area-averaged melt rates, but for the reasons you give at the end of the discussion it may be that melt rates very close to the grounding line are particularly important. Is it worth bringing up there your results from Fig. 9 that suggest a closer to 1/3 power law dependence when close to the grounding line? And also mentioning this in the abstract?
Citation: https://doi.org/10.5194/egusphere-2024-2297-RC2 -
AC1: 'Rrequired pre-decision reply on RC2', Irena Vankova, 23 Sep 2024
This is a required response to reviewers prior to the editorial decision.
If we are asked to revise and resubmit the paper, we will address the comments of the reviewer in detail. Regarding the major comments, this means including more details on the vertical mixing scheme choices and effects, making the flow of the paper smoother, and highlighting differences in the local vs ice-shelf averaged effects of melt rate increase with subglacial discharge.
Citation: https://doi.org/10.5194/egusphere-2024-2297-AC1
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AC1: 'Rrequired pre-decision reply on RC2', Irena Vankova, 23 Sep 2024
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-2297', Anonymous Referee #1, 19 Aug 2024
The authors conducted model experiments for an idealized ice shelf with subglacial discharge for rotating and non-rotating ice shelves. Authors show different sensitivity to subglacial discharge for rotating and non-rotating ice shelves. They also show how earth rotation and subglacial discharge location can impact cavity circulation and the melting of ice shelves. The results are well presented and key conclusions are supported by the model analyses provided in the manuscript. I suggest moderate revision.
Moderate comment
(1) Practically, all ice shelves are influenced by rotation. The meaning for considering non-rotating ice shelves, I assume, is small ice shelves that do not feel the effect of earth rotation. It would be nice to have a paragraph describing the length scale that separates rotating and non-rotating ice shelves. Maybe a discussion involving non-dimensionalized parameters may be helpful.
(2) There is no discussion about vertical resolution and coordination. Is the behavior of ice shelf meltwater strongly impacted by the choice of vertical resolutions? Do you see a similar response even if you double (or half) the vertical resolutions? How sensitive is your overall conclusion to the choice of vertical resolutions?
Minor comment
Lines 103-105: It would be nice if authors could explain somewhere (a Table maybe) in the manuscript what the observed (or estimated) rates of subglacial discharges are for different ice shelves (that helps us understand, for example, figures 2 and 6 better).
Lines 163-169: This text is a bit difficult to follow. Please consider adding arrows to help us where you are talking about in Figures 7e1 and e2.
Citation: https://doi.org/10.5194/egusphere-2024-2297-RC1 -
AC2: 'Rrequired pre-decision reply on RC1', Irena Vankova, 23 Sep 2024
This is a required response to reviewers prior to the editorial decision.
If we are asked to revise and resubmit the paper, we will address the comments of the reviewer in detail. Regarding the major comments, this means including some discussion on length scales (involving Rossby number in this case) and more details on the effects of vertical resolution.
Citation: https://doi.org/10.5194/egusphere-2024-2297-AC2
-
AC2: 'Rrequired pre-decision reply on RC1', Irena Vankova, 23 Sep 2024
-
RC2: 'Comment on egusphere-2024-2297', Anonymous Referee #2, 30 Aug 2024
This manuscript presents results of idealised modeling experiments on the impact of subglacial discharge on basal melting of ice shelves. The authors vary the magnitude and distribution of subglacial discharge and find a complex set of behaviours. They also explicitly show the difference that rotation makes, which I feel is important because the temptation may be to ignore this when designing parameterisations due to the complexity introduced. They nicely contrast the results to the ‘Greenlandic’ vertical calving front case.
Since there is increasing interest in the role of freshwater discharge on basal melting of ice shelves, but relatively little research has been undertaken to date, I think this paper is timely and important and useful. I also find it to be generally scientifically sound but have some remaining questions and suggestions for improving the presentation. I detail these below in categories of significant comments and minor comments.
Significant comments
Vertical mixing. In general, the rate of entrainment of ambient water into a rising plume is a strong control on its dynamics – higher entrainment means the plume warms up but slows down quickly, while lower entrainment means a faster but generally colder plume. You touch on this in the paragraph beginning on L133. In your model, since the plume is travelling mostly horizontally, the mixing between plume and ambient cavity occurs in the vertical. But I saw very little discussion of vertical mixing in the methods or results. Some details that would be good to include and discuss: (i) what is the typical vertical resolution of the model near the ice base?, (ii) what is the vertical mixing scheme in the model (for both momentum and tracers)?, (iii) does this vertical mixing scheme have a strong bearing on the results?, (iv) can you say any more about the impact of the choices of vertically-averaging over cells within 10m of the ice (L87) and distributing the meltwater into the ocean based on an exponential profile (L88) – I imagine these could influence the results?
Presentation. I found the manuscript quite hard to follow because within the first short results section (L126-149) you had already referred to 5 different results figures, each of which has a significant amount of information. As the results go on, there is a lot of jumping back and forth between figures, often when only a small detail from the figure is relevant. Having first referenced Fig. 2 at the very start of the results (L127), Fig. 2 panels b and c are then not discussed until the very end of the results (L215), so that when I was on L127 and reading the caption to Fig. 2, I had to go looking for what Eq. 1 was. I also found it a bit confusing to keep switching between ‘melt rate summary figures’ (Figs. 2, 6, 9) and ‘simulation output details figures’ (Figs. 3-5, 7, 8). At some point I found it easier to look through the figures on their own rather than trying to read the text and go to the relevant figure. I am not exactly sure how, but it would be great if there was a way of presenting this information in a more linear fashion that was easier for the reader to follow. Some ideas: could you discuss and present the simulation output details figures first, then culminate with the melt rate summary figures which provide the main conclusions of the paper? At least bringing figures 2, 6 and 9 together would make sense I think.
Overall importance of subglacial discharge to ice shelf melt rates and parameterisation of ice shelf melt rates. Fig. 3, left hand column, suggests that the influence of subglacial discharge is quite limited to the region close to where it is being discharged. If this is true for all reasonable values of subglacial discharge then although this was mentioned in the text, I feel that more could be made of this in the discussion and potentially the abstract. In particular in the discussion, because it feels very relevant to how we might parameterise the influence of subglacial discharge on ice shelf basal melt rates. Given the effect appears to be very localised, is a parameterisation for the area-average influence (such as Eq. 1) particularly useful? Won’t Eq. 1 be sensitive to how big the ice shelf is while also not capturing the spatial variability? Does it make more sense to produce a version of Eq. 1 for some region close to the discharge location?
Minor comments
L84 – what is the horizontal viscosity scheme? Can you add a little more detail?
L104 – could you add what specific values of Fs you used?
L116-124 – the set of experiments where you vary where to apply Fs in the vertical. I didn’t see these mentioned in the results or discussion, but saw them plotted on Fig. 6c, where it seems this doesn’t make much difference. I feel this is quite a technical, model-specific thing that has limited relevance to the dynamics of ice shelves, so perhaps move to an appendix or supporting information (and discuss the results of what it showed)? This additional complexity would help to streamline the paper.
L150 – “figures 3, 7, 4, 8 and 5” – it’s not important but having these numbers out of order doesn’t help with the reader being overwhelmed with swapping back and forth between figures.
L223 (Eq. 1) – should k have 10^(-5) instead of 10^5? Also the units of k look correct for n=1/3 rather than 2/3. I presume this should give melt rates in m/s? If so that is probably worth stating since people will be used to thinking in m/yr.
L241 – nice paragraph and discussion. The other part that is potentially relevant and could be discussed here is the influence of plume rise height. The higher the plume rises, the more ice-ocean area over which it increases the friction velocity. And since the plume will rise higher with higher discharge, this can contribute to a higher exponent n when we look at melt rates averaged over a fixed, larger area like an ice shelf. I don’t know to what extent this is relevant for your results?
Localised vs area-averaged melt rates (see also significant comment 3). I really liked Fig. 9, where you restricted to the area close to discharge outlets. I feel that the distinction between area-averaged and localised melt is perhaps not given enough attention in the manuscript. The discussion focuses a lot on the area-averaged melt rates, but for the reasons you give at the end of the discussion it may be that melt rates very close to the grounding line are particularly important. Is it worth bringing up there your results from Fig. 9 that suggest a closer to 1/3 power law dependence when close to the grounding line? And also mentioning this in the abstract?
Citation: https://doi.org/10.5194/egusphere-2024-2297-RC2 -
AC1: 'Rrequired pre-decision reply on RC2', Irena Vankova, 23 Sep 2024
This is a required response to reviewers prior to the editorial decision.
If we are asked to revise and resubmit the paper, we will address the comments of the reviewer in detail. Regarding the major comments, this means including more details on the vertical mixing scheme choices and effects, making the flow of the paper smoother, and highlighting differences in the local vs ice-shelf averaged effects of melt rate increase with subglacial discharge.
Citation: https://doi.org/10.5194/egusphere-2024-2297-AC1
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AC1: 'Rrequired pre-decision reply on RC2', Irena Vankova, 23 Sep 2024
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Irena Vaňková
Xylar Asay-Davis
Carolyn Branecky Begeman
Darin Comeau
Alexander Hager
Matthew Hoffman
Stephen F. Price
Jonathan Wolfe
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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