Geothermal heat flux is the dominant source of uncertainty in englacial-temperature-based dating of ice-rise formation

Montelli, Aleksandr; Kingslake, Jonathan

doi:https://doi.org/10.5194/egusphere-2022-236

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https://doi.org/10.5194/egusphere-2022-236

Preprints

23 May 2022

| 23 May 2022

Geothermal heat flux is the dominant source of uncertainty in englacial-temperature-based dating of ice-rise formation

Aleksandr Montelli and Jonathan Kingslake

Abstract. Ice rises are areas of locally grounded, slow-moving ice adjacent to floating ice shelves. Temperature profiles measured through ice rises contain information regarding changes to their dynamic evolution and external forcings, such as past surface temperatures, past accumulation rates and geothermal heat flux. While previous work has used borehole temperature-depth measurements to infer one or two such parameters, there has been no systematic investigation of parameter sensitivity to the interplay of multiple external forcings and dynamic changes. A one-dimensional vertical heat flow forward model developed here examines how changing forcings affect temperature profiles. Further, using both synthetic data and previous measurements from the Crary Ice Rise in Antarctica, we use our model in a Markov Chain Monte-Carlo inversion to demonstrate that this method has potential as a useful dating technique that can be implemented at ice rises across Antarctica. However, we also highlight the non-uniqueness of previous ice rise formation dating based on temperature profiles, showing that using nominal values for forcing parameters, without taking into account their realistic uncertainties, can lead to underestimation of dating uncertainty. In particular, geothermal heat flux represents the dominant source of uncertainty in ice-rise age estimation. For instance, in Crary Ice Rise higher heat flux values (i.e., about 90 mW m^-2) yield grounding timing of 1400±800 years, whereas lower heat flux of around 60 mW m^-2 implies earlier ice rise formation and lower uncertainties in the ice rise age estimations (500±250 years). We discuss the utility of this method in choosing future ice drilling sites and conclude that integrating this technique with other indirect dating methods can provide useful constraints on past forcings and changing boundary conditions from in-situ temperature-depth measurements.

Received: 20 Apr 2022 – Discussion started: 23 May 2022

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Journal article(s) based on this preprint

16 Jan 2023

Geothermal heat flux is the dominant source of uncertainty in englacial-temperature-based dating of ice rise formation

Aleksandr Montelli and Jonathan Kingslake

The Cryosphere, 17, 195–210, https://doi.org/10.5194/tc-17-195-2023,https://doi.org/10.5194/tc-17-195-2023, 2023

Short summary

Aleksandr Montelli and Jonathan Kingslake

Interactive discussion

Status: closed

RC1:
'Review of Montelli and Kingslake', Anonymous Referee #1, 21 Jun 2022

Review of Montelli and Kingslake: “Geothermal heat flux is the dominant source of uncertainty in

englacial-temperature-based dating of ice-rise formation

Montelli and Kingslake use an inverse approach to estimate the uncertainty in determining the age of grounding at ice rises from the englacial temperature profile. They apply this technique to Crary Ice Rise – the primary location where this technique of dating the grounding of the ice shelf has been applied. The authors conclude that the uncertainty in geothermal flux is the primary source of uncertainty; given the uncertainty in geothermal flux, particularly in the Ross region, this is an important conclusion.

The technique is similar to previous work using borehole temperature profiles to infer past temperature but is instead oriented towards inferring the timing of grounding in the ice-sheet to ice rise transition. Therefore, the past histories are assumed to be defined, and the modern parameters are assumed to be unknown – essentially a reversal of the assumptions used for in the borehole thermometry work. The manuscripts does a good job of exploring many sources of uncertainty, although quite a few more remain. The work is a useful contribution and improves our understanding of the limitations of ice-rise grounding from englacial temperature profiles.

The paper is mostly well organized with clear descriptions and illustrations of the model set up. However, the choice of vertical velocity profile is not clear. For instance, what is the Dansgaard-Johnson kink-height being used? And I think a value of “n” of 3 is being used for the Lliboutry approximation, but this is often employed because different choices of “n” allow a wider range of vertical velocities than the D-J approximation (e.g. Kingslake et al., 2014). The shape of the vertical velocity likely can vary a lot for these types of scenarios – an ice shelf should have a nearly linear vertical velocity while an established divide will be highly non-linear, and typically represented with “n” significantly less than 3.

The paper also seems primarily focused on Ross-like locations. Most ice rises have accumulation rates much greater than 0.1 m/yr. I think the paper would benefit from specific discussion of how well englacial temperature profiles would constrain timing of grounding in other locations than the Ross and Filchner Ronne – where the accumulation rates are greater. This would provide guidance of where it is promising to obtain englacial temperature profiles and where it is unlikely to be useful. My guess is that higher accumulation rates shorten the timescale that regrounding can be inferred for.

The paper should also discuss the impact of horizontal advection on the temperature profile. When can the effects of the upstream flow – starting with thicker ice, colder temperatures, and different accumulation rates (West Antarctica has weird accumulation gradients so it’s not obvious that being higher and colder also means less accumulation) – be safely neglected. A few forward runs based on Mercer Ice Stream and Crary would be useful to discuss this potential uncertainty qualitatively. It would be beyond the scope of the paper to include this in the inversion. I also wonder if the forward modeling in Figures 5 and 6 could be restricted to the thinner ice sites. Are there examples of 2500m thick grounding events (L405 suggests ice rises are general much thinner).

The paper should also be clear about the thermal properties being used. Regarding Table 1: I’m a bit confused by the values the authors have chosen for ice which I think is because the heat capacity and thermal conductivity values are switched. The heat capacity is chosen as 2.3 J/kg/K yet Cuffey and Paterson (2010) give the range of values between 0 and -50C as 2097 to 1741 J/kg/K. The factor of 1000 not withstanding, the chosen value does not fall within this range. Similarly for the thermal conductivity, the authors give 2000 W/m/K yet the Cuffey and Paterson range is 2.1 to 2.76 for 0 to -50C. It seems like the authors switched the values. The heat capacity of bedrock (assuming that the thermal conductivity of bedrock is actually the heat capacity) seems too low as well. Also, the authors should at the very least discuss the uncertainty of these values and the uncertainty of not treating them as temperature-dependent. It seems like this will be an important enough source of uncertainty to include in a paper about the uncertainty of dating ice rise formation with the englacial temperature profile, but maybe it isn’t.

Overall, this manuscript is a valuable contribution that improves inferences of past ice sheet behavior. That the code for the inversions will be made publicly available is an asset that can be applied beyond this specific application (it didn’t look the like the github link was active yet, but I wouldn’t expect it to be before the paper is accepted).

Minor comments

L294: The example of accumulation is not surprising. Most analyses will use a percent change in accumulation rate rather than a fixed amount. This better reflects the variability in climate.

Figures 3 and 4 – It would be good to label all of the axes even if all of the axes in a column or row are the same.

Fig. 5 caption is long and very repetitive. It seems like this 5 scenarios text could be shared with only the differences articulated each time.

Fig. 5 C – check values. Most heat fluxes are given in W m-2, so I think you should stay consistent with that.

Update Neuhaus reference

L 388-390 – It might be worth mentioning here that in addition to cooling effects from groundwater, you might also expect heating effects from friction during the regrounding. There is likely to be a very complicated and stressful (pun intended, sorry) time period when grounding occurs.

L412-416 – ApRES vertical velocity constraints were used at Dome C to improve inferences of past temperature change. It’s pretty buried in a complicated paper, but it highlights the point being made: Buizert et al., 2021, Science, “Antarctic surface temperature and elevation during

the Last Glacial Maximum”

L445 – delete “comprehensive” or modify it with “most comprehensive yet

Citation: https://doi.org/10.5194/egusphere-2022-236-RC1
- AC1: 'Reply on RC1', Aleksandr Montelli, 03 Aug 2022
  
  Thank you for a detailed and helpful review. Your suggestions will improve this manuscript.
  
  Citation: https://doi.org/10.5194/egusphere-2022-236-AC1
- AC2: 'Reply on RC1', Aleksandr Montelli, 03 Aug 2022
  
  Thank you for a detailed and helpful review. Your suggestions will certainly help improve this manuscript.
  
  Citation: https://doi.org/10.5194/egusphere-2022-236-AC2
- AC4: 'Reply on RC1', Aleksandr Montelli, 05 Aug 2022
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-236/egusphere-2022-236-AC4-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2022-236-AC4
RC2:
'Comment on egusphere-2022-236', Anonymous Referee #2, 26 Jun 2022

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-236/egusphere-2022-236-RC2-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2022-236-RC2
- AC3: 'Reply on RC2', Aleksandr Montelli, 03 Aug 2022
  
  Thank you for a detailed and helpful review. Your suggestions will certainly help improve this manuscript.
  
  Citation: https://doi.org/10.5194/egusphere-2022-236-AC3
- AC5: 'Reply on RC2', Aleksandr Montelli, 05 Aug 2022
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-236/egusphere-2022-236-AC5-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2022-236-AC5

Interactive discussion

Status: closed

RC1:
'Review of Montelli and Kingslake', Anonymous Referee #1, 21 Jun 2022

Review of Montelli and Kingslake: “Geothermal heat flux is the dominant source of uncertainty in

englacial-temperature-based dating of ice-rise formation

Montelli and Kingslake use an inverse approach to estimate the uncertainty in determining the age of grounding at ice rises from the englacial temperature profile. They apply this technique to Crary Ice Rise – the primary location where this technique of dating the grounding of the ice shelf has been applied. The authors conclude that the uncertainty in geothermal flux is the primary source of uncertainty; given the uncertainty in geothermal flux, particularly in the Ross region, this is an important conclusion.

The technique is similar to previous work using borehole temperature profiles to infer past temperature but is instead oriented towards inferring the timing of grounding in the ice-sheet to ice rise transition. Therefore, the past histories are assumed to be defined, and the modern parameters are assumed to be unknown – essentially a reversal of the assumptions used for in the borehole thermometry work. The manuscripts does a good job of exploring many sources of uncertainty, although quite a few more remain. The work is a useful contribution and improves our understanding of the limitations of ice-rise grounding from englacial temperature profiles.

The paper is mostly well organized with clear descriptions and illustrations of the model set up. However, the choice of vertical velocity profile is not clear. For instance, what is the Dansgaard-Johnson kink-height being used? And I think a value of “n” of 3 is being used for the Lliboutry approximation, but this is often employed because different choices of “n” allow a wider range of vertical velocities than the D-J approximation (e.g. Kingslake et al., 2014). The shape of the vertical velocity likely can vary a lot for these types of scenarios – an ice shelf should have a nearly linear vertical velocity while an established divide will be highly non-linear, and typically represented with “n” significantly less than 3.

The paper also seems primarily focused on Ross-like locations. Most ice rises have accumulation rates much greater than 0.1 m/yr. I think the paper would benefit from specific discussion of how well englacial temperature profiles would constrain timing of grounding in other locations than the Ross and Filchner Ronne – where the accumulation rates are greater. This would provide guidance of where it is promising to obtain englacial temperature profiles and where it is unlikely to be useful. My guess is that higher accumulation rates shorten the timescale that regrounding can be inferred for.

The paper should also discuss the impact of horizontal advection on the temperature profile. When can the effects of the upstream flow – starting with thicker ice, colder temperatures, and different accumulation rates (West Antarctica has weird accumulation gradients so it’s not obvious that being higher and colder also means less accumulation) – be safely neglected. A few forward runs based on Mercer Ice Stream and Crary would be useful to discuss this potential uncertainty qualitatively. It would be beyond the scope of the paper to include this in the inversion. I also wonder if the forward modeling in Figures 5 and 6 could be restricted to the thinner ice sites. Are there examples of 2500m thick grounding events (L405 suggests ice rises are general much thinner).

The paper should also be clear about the thermal properties being used. Regarding Table 1: I’m a bit confused by the values the authors have chosen for ice which I think is because the heat capacity and thermal conductivity values are switched. The heat capacity is chosen as 2.3 J/kg/K yet Cuffey and Paterson (2010) give the range of values between 0 and -50C as 2097 to 1741 J/kg/K. The factor of 1000 not withstanding, the chosen value does not fall within this range. Similarly for the thermal conductivity, the authors give 2000 W/m/K yet the Cuffey and Paterson range is 2.1 to 2.76 for 0 to -50C. It seems like the authors switched the values. The heat capacity of bedrock (assuming that the thermal conductivity of bedrock is actually the heat capacity) seems too low as well. Also, the authors should at the very least discuss the uncertainty of these values and the uncertainty of not treating them as temperature-dependent. It seems like this will be an important enough source of uncertainty to include in a paper about the uncertainty of dating ice rise formation with the englacial temperature profile, but maybe it isn’t.

Overall, this manuscript is a valuable contribution that improves inferences of past ice sheet behavior. That the code for the inversions will be made publicly available is an asset that can be applied beyond this specific application (it didn’t look the like the github link was active yet, but I wouldn’t expect it to be before the paper is accepted).

Minor comments

L294: The example of accumulation is not surprising. Most analyses will use a percent change in accumulation rate rather than a fixed amount. This better reflects the variability in climate.

Figures 3 and 4 – It would be good to label all of the axes even if all of the axes in a column or row are the same.

Fig. 5 caption is long and very repetitive. It seems like this 5 scenarios text could be shared with only the differences articulated each time.

Fig. 5 C – check values. Most heat fluxes are given in W m-2, so I think you should stay consistent with that.

Update Neuhaus reference

L 388-390 – It might be worth mentioning here that in addition to cooling effects from groundwater, you might also expect heating effects from friction during the regrounding. There is likely to be a very complicated and stressful (pun intended, sorry) time period when grounding occurs.

L412-416 – ApRES vertical velocity constraints were used at Dome C to improve inferences of past temperature change. It’s pretty buried in a complicated paper, but it highlights the point being made: Buizert et al., 2021, Science, “Antarctic surface temperature and elevation during

the Last Glacial Maximum”

L445 – delete “comprehensive” or modify it with “most comprehensive yet

Citation: https://doi.org/10.5194/egusphere-2022-236-RC1
- AC1: 'Reply on RC1', Aleksandr Montelli, 03 Aug 2022
  
  Thank you for a detailed and helpful review. Your suggestions will improve this manuscript.
  
  Citation: https://doi.org/10.5194/egusphere-2022-236-AC1
- AC2: 'Reply on RC1', Aleksandr Montelli, 03 Aug 2022
  
  Thank you for a detailed and helpful review. Your suggestions will certainly help improve this manuscript.
  
  Citation: https://doi.org/10.5194/egusphere-2022-236-AC2
- AC4: 'Reply on RC1', Aleksandr Montelli, 05 Aug 2022
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-236/egusphere-2022-236-AC4-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2022-236-AC4
RC2:
'Comment on egusphere-2022-236', Anonymous Referee #2, 26 Jun 2022

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-236/egusphere-2022-236-RC2-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2022-236-RC2
- AC3: 'Reply on RC2', Aleksandr Montelli, 03 Aug 2022
  
  Thank you for a detailed and helpful review. Your suggestions will certainly help improve this manuscript.
  
  Citation: https://doi.org/10.5194/egusphere-2022-236-AC3
- AC5: 'Reply on RC2', Aleksandr Montelli, 05 Aug 2022
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-236/egusphere-2022-236-AC5-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2022-236-AC5

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

ED: Publish subject to revisions (further review by editor and referees) (16 Aug 2022) by Nanna Bjørnholt Karlsson

AR by Aleksandr Montelli on behalf of the Authors (27 Sep 2022) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (07 Oct 2022) by Nanna Bjørnholt Karlsson

RR by Anonymous Referee #1 (22 Oct 2022)

Suggestions for revision or reasons for rejection

Second review of Montelli and Kingslake, Geotheral heat flux is the dominant source of uncertainty in the englacal-temperature-based dating of ice-rise formation

The revised paper is a significant improvement and will be a useful contribution to the field. The method and application to Crary Ice Rise is thoughtful and compelling.

There are three aspects which deserve a little last attention.
1) The supplemental figure should have some text accompanying it and explaining the important results.
2) The supplemental figure addresses uncertainty in bulk values for the thermal conductivity for rock and ice. However, the thermal conductivity for ice is temperature dependent. The modeling uses a fixed value and simply shifting what that value is does not encompass the full uncertainty of allowing it to vary with temperature. The conclusion of a paper by one of our grad students was fundamentally changed by including the temperature dependent thermal conductivity. The modeling does not need to be redone with a temperature dependent thermal conductivity, but the limitation and appropriateness of including in future models does need a paragraph (or at least multiple sentences). The primary way the temperature-dependent conductivity has the potential to change the result is that it changes the slope of the englacial temperatures in a way that is different than if the value is different but still constant.
3) Section 3.2 “Englacial temperature profile sensitivity” lacks a clear message. I think this section would be improved if it was framed around identifying which parameters are most important for ice-rise dating. A new intro paragraph should explain this, and then a new conclusion paragraph should summarize what was learned. For instance, the vertical velocity profile is relatively unimportant for shallow ice rises, which is an interesting result because the onset of divide flow is then unlikely to change the answer significantly. I also think that the main value of the 2000m thick results is showing the difference for what is important for borehole thermometry compared to that for ice rise dating - a poitn that should be made in the new introductory paragraph.

A few other minor comments:
- What is the unit ‘m/ky’ or ‘m k.y.-1’. I found this very confusing. I think this is mostly used (inaccurately) as the accumulation rate (m/yr) but in some instances it may be a change in accumulation rate per time for the accumulation history? This needs to be made clear.

- I also suggest an additional figure, like a new figure 1, which is a large image of Antarctica with locations mentioned in the text. The location of Crary Ice Rise is pretty subtle in Fig. 1a. And then I have no idea where the Lazarev and Riiser-Larsen seas are. It would be great to have a figure which shows where this method can be best applied.

Hide

ED: Publish subject to minor revisions (review by editor) (28 Oct 2022) by Nanna Bjørnholt Karlsson

AR by Aleksandr Montelli on behalf of the Authors (11 Nov 2022) Author's response Author's tracked changes Manuscript

ED: Publish subject to technical corrections (21 Nov 2022) by Nanna Bjørnholt Karlsson

Dear A. Montelli and J. Kingslake,

Thank you for submitting a revised version of your manuscript and for responding to the comments from the referee so thoroughly.
I am now happy to recommend your manuscript for publication pending a few technical corrections pertaining to the figures.

Fig. 1: The maps a-e are now tiny and even zoomed in using a large screen, I struggle to see the details. For example, in Fig. 1a a circle denotes ice rises but I can't see any circles. Since there are no page limitations in TC, there should be no reason for these figures to be small. You could also consider splitting the figure so that Fig 1f,g and h are separate.

Fig. 8: I like the addition of this figure but the quality of the figure could be increased by making a few changes. Firstly, I find the use of a diverging colour map for the geothermal flux confusing. Readers typically associate a diverging colour map with values going from some negative to some positive values. Further, the blue colours of the high-end values make it difficult to see the blue circles along the margin. I suggest you change the colour map to a non-diverging colour scheme. To keep it simple, it could just be black-white. Secondly, the use of a rainbow colour map for ice rise thickness is problematic here as green and red dots are now located next to each other. TC guidelines request that authors try to avoid using red-green colour schemes (https://www.the-cryosphere.net/submission.html#figurestables). Please use a different colour scheme.

Once these few changes have been implemented, your manuscript is ready to be published. Thank you for submitting your work to The Cryosphere.
Best,
Nanna B Karlsson

Hide

AR by Aleksandr Montelli on behalf of the Authors (25 Nov 2022) Manuscript

Journal article(s) based on this preprint

16 Jan 2023

Geothermal heat flux is the dominant source of uncertainty in englacial-temperature-based dating of ice rise formation

Aleksandr Montelli and Jonathan Kingslake

The Cryosphere, 17, 195–210, https://doi.org/10.5194/tc-17-195-2023,https://doi.org/10.5194/tc-17-195-2023, 2023

Short summary

Aleksandr Montelli and Jonathan Kingslake

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Short summary

Thermal modelling and Bayesian inversion techniques are used to evaluate the uncertainties inherent in inferences of ice-sheet evolution from borehole temperature measurements. We show that the same temperature profiles may result from a range of parameters, of which geothermal heat flux through underlying bedrock plays a key role. Careful model parametrization and evaluation of heat flux are essential for inferring past ice-sheet evolution from englacial borehole thermometry.


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