Satellite Magnetics Suggest a Complex Geothermal Heat Flux Pattern beneath the Greenland Ice Sheet
Round 1
Reviewer 1 Report
The manuscript by Kolster et al. presents a probabilistic inversion of Curie isotherm depth and geothermal heat flow for Greenland. While I generally like the approach, the results should be presented a bit clearer as parts of the necessary details to comprehend the study are hidden in the supplementary material. For example, no input data and fit to data is shown. At least a map of the magnetic anomaly used should be shown and the fit to the field. But here I would also like to see the magnetization map, which belongs to the Curie depth estimates.
Most essential for the inversion is the figure “hidden” in Figure A1. How confident are you that there are no internal variations within the C Greenland domain? You do allow for some variation in magnetization as much as I understand, but these model results have to be shown as well. And did you try to vary the tectonic definition, e.g. allowing the inversion to randomly select a tectonic origin. As the map is largely based on assumptions, this is otherwise a very hard constraint.
The same holds for the assumption of two-layered magnetization and especially allowing for high magnetization in the lower crust. That is certainly not what is generally observed with magnetic inversion, especially as the distinction between upper and lower crustal sources is very difficult to achieve. For me it is also not clear how you incorporated the prior information on the layers in your inversion.
And how did you high-pass the data and forward model? I assume you selected a certain spectral range. But if you limit yourself to spherical harmonic degree 160, your models should look coarser as they do at the moment? I guess some interpolation was involved in producing Figures 3 and 4?
These things have to be clarified to fully comprehend the analysis and in generally, I would have liked amore thorough discussion on alternative GFH models, less focus on the plume-track.
I have a few more comments to the text directly:
Line 40-48: This statement is a bit harsh wrt. earlier studies. I agree that not always all details are documented, which makes evaluation of earlier studies difficult. However, this relates as well to the fact, that in the past publishing of codes and data was difficult. Hence, I recommend to tone this statement as bit down.
Line57ff: “We find that the uncertainties 58 associated with Geothermal Heat flux raise serious questions regarding their use to predict, e.g., plume traces, and seek to challenge the current modelling meta through an interdisciplinary, uncertainty-based modelling method.”
Yes, but the question remains whether a plume track should still have s signature in GHF? For example, Heyn & Conrad (https://doi.org/10.1029/2022GL098003) recently showed that only younger continental and cratonic plume tracks can be identified by observed lithosphere thinning, and maybe older tracks by an increased surface heat flux. Hence, the underlying assumptions that GHF in Greenland reflects a plume track might not be met and the lithospheric structure has larger importance. However, GHF as discussed here has large bearing for ice-sheet dynamics and the manuscript would be more just, if this is discussed in more detail, also in relation with the existing new GHF database for Greenland (Colgan et al. 2022, https://doi.org/10.5194/essd-14-2209-2022).
Line 124: Moho depths, not MOHO depths. It’s not an abbreviation.
Line 233: All the names have to be annotated on a map.
Line 246ff “All models predict heightened geothermal heat flux beneath the North East Green
land Ice Stream (NEGIS), with a large peak immediately beneath its origin.“
Not shown on map, but just from inspection of Figure 4, I am not sure that I would agree with this statement. However, here a valuable contribution could be made to the GHF at NGRIP, where largely different values have been proposed. It seems like, that from your study, only moderately higher GHF is likely, pointing to a local effect on the published measurements.
Table D2: This table was cut-off in my documents for review.
Line 661ff: After all the probabilistic inversion, you suddenly adopt constant values. This is certainly not justified as you cover different tectonic domain. So, maybe there is value in studies like Martos et al., or Artemieva et al. 2021 where they choose these values in order to fit GHF observation.
Author Response
Thanks a lot for these comments and suggestions. It is always refreshing to get an outside view on these things. I have provided a point-by-point walkthrough of your review below, with both answers and a summary of specific actions taken.
Comment 1:The manuscript by Kolster et al. presents a probabilistic inversion of Curie isotherm depth and geothermal heat flow for Greenland. While I generally like the approach, the results should be presented a bit clearer as parts of the necessary details to comprehend the study are hidden in the supplementary material. For example, no input data and fit to data is shown. At least a map of the magnetic anomaly used should be shown and the fit to the field. But here I would also like to see the magnetization map, which belongs to the Curie depth estimates.Answer 1:I completely agree with the lack of presentation regarding data and data misfit, and have now included magnetic maps corresponding to both the data, the model, and the corresponding fit.
Comment 2:Most essential for the inversion is the figure “hidden” in Figure A1. How confident are you that there are no internal variations within the C Greenland domain? You do allow for some variation in magnetization as much as I understand, but these model results have to be shown as well. And did you try to vary the tectonic definition, e.g. allowing the inversion to randomly select a tectonic origin. As the map is largely based on assumptions, this is otherwise a very hard constraint.
Answer 2:I considered varying the bounds as you suggest, but decided against this when I realized that the computation time required would be astronomical using the currently available computing power and supporting software (mainly due to the requirement of doing both the current modelling and the variable extents simultaneously). It could be interesting to conduct a seperate study on the extents themselves, however, purely VIS information could be used to reduce the amount of model parameters. However, this would still require some form of information on the potential variance of the extent to be available.Going back to your comment, I have now added a note in the discussion highlighting the added uncertainties that the currently employed domains (and especially the C. Greenland domain) could pose. I also note that this is indeed a hard constraint in the Introduction to Appendix B.Comment 3:The same holds for the assumption of two-layered magnetization and especially allowing for high magnetization in the lower crust. That is certainly not what is generally observed with magnetic inversion, especially as the distinction between upper and lower crustal sources is very difficult to achieve. For me it is also not clear how you incorporated the prior information on the layers in your inversion.
Answer 3:Thanks, I can see now that I have failed to explain how we used this! Somehow I must have managed to leave it out when I wrote Appendix B - I have now added it there.
As stated in Appendix B, we chose to base our assumptions primarily on the scarce results and suggestions available from studies of what is expected to have been deeper crust. When we had any such information or gist of information on lower crust, we simply averaged the two values to get a single scalar to use as the mean in the prior distribution for the main runs (but we still performed additional test runs where deeper susceptibility estimates were completely omitted, as shown in the prior parameters in in Appendix D / table D.1. I would like to stress here that since we always this parameter vary, the initial value is not a hard constraint.
Comment 4:And how did you high-pass the data and forward model? I assume you selected a certain spectral range. But if you limit yourself to spherical harmonic degree 160, your models should look coarser as they do at the moment? I guess some interpolation was involved in producing Figures 3 and 4?
These things have to be clarified to fully comprehend the analysis and in generally, I would have liked amore thorough discussion on alternative GFH models, less focus on the plume-track.Answer 4:Great catch. I have actually already described the spherical harmonic range for the data in the Method section, but see now that I have neglected to do the same for the model (we of course use the same approach and spherical harmonic span in both places). Any contribution outside the spherical harmonic range of the model was similarly disregarded. I have now changed the original statement to hopefully be a bit clearer, and further stated the same for the model output.
We did indeed interpolate the model results to ease interpretation (it proved quite hard to visually compare the data when plotted as scattered points on such small images (as you can probably also see from the data and model response/fit figures). I already state that the data has been interpolated directly in the figure text, so I have not added any further text/statements in this specific regard.We have also tried to shift the focus a bit towards GTHF throughout the text, as you propose.
Please note that I have also removed the model using spherical harmonic degree up to 160, as I discovered it to be problematic due to the low amount of realizations we were able to compute for a model of such a scale (since it required an exponential & disproportional increase in computational time, while only encompassing a minor increase in power contained at the altitude of evaluation).Comment 5:Line 40-48: This statement is a bit harsh wrt. earlier studies. I agree that not always all details are documented, which makes evaluation of earlier studies difficult. However, this relates as well to the fact, that in the past publishing of codes and data was difficult. Hence, I recommend to tone this statement as bit down.
Answer 5:I have tried to rewrite this section a bit, putting emphasis on the fact that typical shortcomings have little to do with the research effort and everything to do with the impracticality/impossibility of obtaining the required data. The intention is not to make harsh statements, but to clarify for the reader how certain uncertainties and assumptions are unavoidable in the modelling process.
In other words, the intention is simply to highlight the unknowns and uncertainties that make this field of study so challenging. I hope that the statement reflects this better now.
Comment 6:
Line57ff: “We find that the uncertainties 58 associated with Geothermal Heat flux raise serious questions regarding their use to predict, e.g., plume traces, and seek to challenge the current modelling meta through an interdisciplinary, uncertainty-based modelling method.”
Yes, but the question remains whether a plume track should still have s signature in GHF? For example, Heyn & Conrad (https://doi.org/10.1029/2022GL098003) recently showed that only younger continental and cratonic plume tracks can be identified by observed lithosphere thinning, and maybe older tracks by an increased surface heat flux. Hence, the underlying assumptions that GHF in Greenland reflects a plume track might not be met and the lithospheric structure has larger importance. However, GHF as discussed here has large bearing for ice-sheet dynamics and the manuscript would be more just, if this is discussed in more detail, also in relation with the existing new GHF database for Greenland (Colgan et al. 2022, https://doi.org/10.5194/essd-14-2209-2022).
Answer 6:Essentially everything about the plume trace mentioned here will be circumstantial (as is also true for many other studies). The time scales mentioned in the Heyn & Conrad paper are interesting, suggesting that our assumptions regarding the plume trace could be are probably less solidly founded in South/South-East Greenland, as opposed to other regions. The models also show a larger variation in this region, which is interesting. I have now included these considerations (including the reference) in the discussion.
With regard to the database (Colgan et al.), I feel that we have already covered the troubles with the spatial dispersion of available heat flux measurements, (almost no heat flow measurements inside Greenland, as they are essentially limited to the borehole projects), but I am very happy to include the reference as it serves to prove exactly this point. The reference is now included in both the introduction and the discussion.Comment 7:Line 124: Moho depths, not MOHO depths. It’s not an abbreviation.
Answer 7:Good catch, thanks! I found two occurrences of this, which have both been corrected.
Comment 8:Line 233: All the names have to be annotated on a map.
Answer 8:Agreed. Labels for Kong Christian IX Land and Kong Frederik IX land is have now been included in Figure 1, which has also been referred to in the text accordingly.
Comment 9:Line 246ff “All models predict heightened geothermal heat flux beneath the North East Greenland Ice Stream (NEGIS), with a large peak immediately beneath its origin.“
Not shown on map, but just from inspection of Figure 4, I am not sure that I would agree with this statement. However, here a valuable contribution could be made to the GHF at NGRIP, where largely different values have been proposed. It seems like, that from your study, only moderately higher GHF is likely, pointing to a local effect on the published measurements.
Answer 9:
When evaluating Figure 4 it is important to remember that we let the model go quite "wild", so the MCT and GTHF baselines may not be accurate (I also state this quite explicitly in the discussion). Mainly the relative spatial variations should be used for evaluation. With this in mind (i.e., disregarding the absolute value and solely Looking at the variations), the models consistently predict that the highest / one of the highest positive GTHF peaks in the interior of Greenland lies beneath NEGIS. I therefore don't think that I can reasonably denote it as "moderate" based on Figure 4 (essentially for the same reason that I discontinued using "large").
I have therefore instead changed "large peak" to "significant positive peak", so that it will be more in line with the relative spatial variations being robustly predicted (while the baseline may vary a bit more, especially in Figure 4). Given the relative variation perspective, the models consistently predict the area with highest / one of the highest GTHF in the interior of Greenland.
Comment 10:Table D2: This table was cut-off in my documents for review.
Answer 10:Thanks. This should be fixed now.
Comment 11:Line 661ff: After all the probabilistic inversion, you suddenly adopt constant values. This is certainly not justified as you cover different tectonic domain. So, maybe there is value in studies like Martos et al., or Artemieva et al. 2021 where they choose these values in order to fit GHF observation.
Answer 11:I completely agree that it is not justified. The conversion from the well-resolved, robust MCT estimates is still difficult to convert to GTHF without coarse assumptions. I do this for lack of a better option, as also stated in the text, but I will be publishing both the MCT model, resultant GTHF model, and some code for a basic 1-layer thermal model alongside the paper, so that anyone can plug in whichever thermal parameters of the crust they wish, or even use the MCT directly in their own models.
This is also the exact reason that we explicitly state that "the underlying MCT maps are considered the primary result of this study" at the end of the method section.I am still not convinced by the method of constraining / fitting the model to agree with existing GTHF measurements. Due to the scarcity of data, if just a single of the existing GTHF measurements is an outlier, or in any other way does not provide a fair estimate for the relatively huge area it represents, the entire model will be skewed due to such a constraint. Since GTHF can vary quite a lot across even small distances, I found it important to demonstrate a model without those constraints.
Perhaps the data is indeed representative, and won't skew the models. Obviously, I do not know the answer, but I think that my concerns here are pretty fair, at least from a mathematical standpoint. This is also why I find it so important to publish the MCT results as well, so that others may decide for themselves how best they want to fit them / constrain them to other existing information, should they wish to do so.
Obviously and ultimately, we are all just doing the best we can with the information available to us. I just hope that someone comes along in the future with more information than I have now, and can use these results as a stepping stone.
Thanks a lot for this review. I really appreciate the time you have taken to give such thorough considerations, and I feel that the manuscript has been improved based on your comments.
Reviewer 2 Report
This is a case study of Greenland geothermal flux, mantle plume and lithosphere. The data collection and calculation methods of this study are relatively common, but due to the hotspot and importance of this research area, the achievements are exciting. The study points out that it is important to determine areas of interior Greenland that may have had direct interaction with the Iceland plume is critical to model the impact of a potential plume-related heat anomaly on the past and future evolution of the Greenland Ice Sheet. The results show that there is a high heat flow near the beginning of the ice flow in northeastern Greenland. Such discovery can effectively promote the research on the mass balance of Greenland ice sheet. Such research ideas also provide new ideas for AIS research. Because of the above views, I believed that this article should be published, and the editorial department is recommended to accept it.
Author Response
Thank you very much for this review - it is much appreciated. I also completely agree with the future prospects mentioned. I hope that this method and modelling results can help contribute to future ice sheet / mass balance studies in the future.
Reviewer 3 Report
Dear Authors, I have just completed the review of your manuscript.
The article is well written with a robust methodological section. The inversion approach seems well constrained. The intriguing results indicate once again the importance of the study of the magnetic field for the tectonic interpretation of remote regions such as the polar ones.
In my opinion the paper is suitable for publication but I have two major remarks that should be accounted before the publication .
1)I am little bit confusing because your results are not clearly indicating which is the best recovery model for MCT. You have explored and discussed more of ten different parametizations (which resulted in different MCT results), without any clear indication which was the best. As you stated, the magnetic inversion suffers of a not unique solution that means (in part that) if you provide thousands of parametizations you will obtain thousands of different inverse models. You should to indicate the best model on the base of statistical parameters (i.e RMS or X-square of solutions).
Without this information I am not able to understand and evaluate your final conclusions. How did you based your final interpretation? At row 232 you stated “Comparison with the results of [15] reveal similarities in the two satellite data-based models…..”. How did you do this comparison ? What of the ten inverse MCT model did you used for the comparison?
I am suggesting to identified the best MCT (and GTHF) model and provide a more robust interpretation.
2) D.2 Estimating the geothermal heat flux
The GTHF is based on the localization of the depth of Curie isotherm. Your model assumed a curie temperature equal to the curie temperature (CT)of magnetite (580°). This is true in case of magnetite S.S. The TC of ironoxides s.l varying in terms of % amount of Ti and Fe. The Curie Temperature of titano-magnetites (which is more abundant that the magnetite S.S) is about 350° (but also lower!, see. Kent, D. V., and J. Gee (1996), Magnetic alteration of zero-age oceanic basalt, Geology, 24, 703–706). So I well constrained model of heat flux should be based on accurate evaluation of the mineral chemistry of the main rock forming the MCT. In addition you can add an additional evaluation of GTHF models distinguished using CT for magnetite s.s and Titano-magnetites.
minor remarks
-A figure of magnetic field of study area is needed
-Table D.1 Can explain why you used the same parameter for runs Ia, Ib, mean and II2?
-What is the difference between Ia and Ib and mean?
-Table D.2 is partially truncated. Probably issue in the pdf generation.
Author Response
Thank you for this review; it has been helpful to get fresh eyes on our paper.
I have reproduced your comments below, alongside my response.
Comment 1:
I am little bit confusing because your results are not clearly indicating which is the best recovery model for MCT. You have explored and discussed more of ten different parametizations (which resulted in different MCT results), without any clear indication which was the best. As you stated, the magnetic inversion suffers of a not unique solution that means (in part that) if you provide thousands of parametizations you will obtain thousands of different inverse models. You should to indicate the best model on the base of statistical parameters (i.e RMS or X-square of solutions).
Without this information I am not able to understand and evaluate your final conclusions. How did you based your final interpretation? At row 232 you stated “Comparison with the results of [15] reveal similarities in the two satellite data-based models…..”. How did you do this comparison ? What of the ten inverse MCT model did you used for the comparison?
I am suggesting to identified the best MCT (and GTHF) model and provide a more robust interpretation.
Response 1:
I see now that I have made this somewhat vague. I have now tried to clarify this better in the text as per your comment. The model 1b can be regarded as the "main" model. The parametrization remain the same across models - but the models are free to vary under the parameters given in the appendix. The primary result here is that while the absolute values of each model do not necessarily agree (mainly due to the non-linearity), the general variation is similar across almost all models (i.e feature robustness).
As all models fit the data equally well, a statistical analysis of the proposed type is unfortunately not straightforward. Instead, I base the choice of "primary" model on the amount of realizations gathered (700 for runs Ia and Ib, and of these two we suspect Ia to have overfitted slightly, so Ib is the best candidate). The rest of the modelling runs purely serve for robustness/stress testing.
For the comparison I looked at the general traits of the models (for example, essentially all of the models show a significant heightening of heat flux near NEGIS).
Please note that I have also removed the model using spherical harmonic degree up to 160, as I discovered it to be problematic due to the low amount of realizations we were able to compute for a model of such a scale (essentially it required exponentially more computational time, while only encompassing a minor increase in power contained at the evaluation altitude.
Comment 2:
D.2 Estimating the geothermal heat flux
The GTHF is based on the localization of the depth of Curie isotherm. Your model assumed a curie temperature equal to the curie temperature (CT)of magnetite (580°). This is true in case of magnetite S.S. The TC of ironoxides s.l varying in terms of % amount of Ti and Fe. The Curie Temperature of titano-magnetites (which is more abundant that the magnetite S.S) is about 350° (but also lower!, see. Kent, D. V., and J. Gee (1996), Magnetic alteration of zero-age oceanic basalt, Geology, 24, 703–706). So I well constrained model of heat flux should be based on accurate evaluation of the mineral chemistry of the main rock forming the MCT. In addition you can add an additional evaluation of GTHF models distinguished using CT for magnetite s.s and Titano-magnetites.
Response 2:
I absolutely agree. Unfortunately the MCT estimates are still difficult to convert to GTHF without coarse assumptions. Since the uncertainties with the other required thermal/crustal parameters most likely outweigh the impact the proposed change will have, I have elected not to include them directly in the paper (It is also a but removed from my own area of expertise) . Instead, I will be publishing both the MCT model, resultant GTHF model, and some code for a basic 1-layer thermal model alongside the paper, so that anyone can plug in whichever crustal thermal parameters and Curie temperature cut-offs they wish, or alternatively even use the MCT directly in their own models. I think this is the best way forward.
Minor remarks:
-A figure of magnetic field of study area is needed
This has now been added.
-Table D.1 Can explain why you used the same parameter for runs Ia, Ib, mean and II2?
D.1 contains the prior information, and for the main runs we use the values obtained which most closely match the existing data available, while retaining a a significant uncertainty. For this reason they are the same - but it should be noted that they do not constitute a hard constraint.
-What is the difference between Ia and Ib and mean?
The uncertainty used for the data in Ia is suspected of having been too low, which may have resulted in a bit of overfitting (this is also stated somewhere in the text). Ib is the "corrected" version of Ia. I have since removed the last of the three models, as mentioned previously.
-Table D.2 is partially truncated. Probably issue in the pdf generation.
Thank you, this should now have been corrected.
And once again thank you for taking the time to review this paper and raise your concerns.
Round 2
Reviewer 1 Report
You did a fine job in revising the manuscript and I appreciate your reply to my comments, as one has not often such a positive feedback.
My rating of "Significance of Content" and "Interest to the readers" as average is not based on the lack of technical merit, but only wrt. usefulness of the new GHF model. You nicely outlined the pitfalls and hopefully this work can be refined in the future to address in more detail the role of GHF on the ice sheet evolution in Greenland.
I have only some minor suggestions:
Line 3: "Similarly, it can provide insight into the paleo-trace of the Icelandic mantle plume, which in turn is..."
I would write "could" not can
Line 72: Maybe better to use ambigous, not dubious
Figure 2: Still a MOHO in the flowchart.
Figure 5: Here, it would be good to mention the height of calculation in the figure caption. And I would personally have clipped this to Greenland and omitted the surrounding.
Regards
Author Response
Thank you very much. I have really enjoyed this review process, which I certainly feel has improved the manuscript for the better.
I have adhered to all of your comments, but elected to leave the data fit surrounding Greenland in, as I feel this fits better with the method overview figure in the Appendix.
Thank you again for taking your time to review this.
Kind regards,
Mick
Reviewer 3 Report
Dear authors, many thanks for your effort in the review. All my previous comments have been taken into account. There are no other comments from my side.
Thank you for this very interesting article
Best regards,
Luke Cocchi
Author Response
Thank you Luke, and once again thank you for taking the time to review this, it is much appreciated.
kind regards,
Mick
