A Simulation Approach to Characterizing Sub-Glacial Hydrology

Pierce, Chris; Gerekos, Christopher; Skidmore, Mark; Beem, Lucas; Blankenship, Don; Lee, Won Sang; Adams, Ed; Lee, Choon-Ki; Stutz, Jamey

doi:https://doi.org/10.5194/egusphere-2023-1685

Preprints

https://doi.org/10.5194/egusphere-2023-1685

Preprints

30 Aug 2023

| 30 Aug 2023

A Simulation Approach to Characterizing Sub-Glacial Hydrology

Chris Pierce, Christopher Gerekos, Mark Skidmore, Lucas Beem, Don Blankenship, Won Sang Lee, Ed Adams, Choon-Ki Lee, and Jamey Stutz

Abstract. The structure and distribution of sub-glacial water directly influences Antarctic ice mass loss by reducing basal shear stress and enhancing grounding line retreat. A common technique for detecting sub-glacial water involves analyzing the spatial variation in reflectivity from an airborne ice penetrating radar (IPR) survey. Basic IPR analysis exploits the high dielectric contrast between water and most other substrate materials, where a reflectivity increase ≥ 15 dB is frequently correlated with the presence of sub-glacial water. There are surprisingly few additional tools to further characterize the size, shape, or extent of hydrological systems beneath large ice masses.

We adapted an existing radar backscattering simulator to model IPR reflections from sub-glacial water structures using the University of Texas Institute for Geophysics (UTIG) Multifrequency Airborne Radar Sounder with Full-phase Assessment (MARFA) instrument. Our series of hypothetical simulations modeled water structures from 5 m to 50 m wide, surrounded by bed materials of varying roughness. We compared the relative reflectivity from rounded Röthlisberger channels and specular flat canals, showing both types of channels exhibit a positive correlation between size and reflectivity. Large (> 20 m), flat canals can increase reflectivity by more than 20 dB, while equivalent Röthlisberger channels show only modest reflectivity gains of 8−13 dB. Changes in substrate roughness may also alter observed reflectivity by 3−6 dB. All of these results indicate that a sophisticated approach to IPR interpretation can be useful in constraining the size and shape of sub-glacial water, however a highly nuanced treatment of the geometric context is necessary.

Finally, we compared simulated outputs to actual reflectivity from a single IPR flight line collected over Thwaites Glacier in 2022. The flight line crosses a previously proposed Röthlisberger channel route, with an obvious bright bed reflection in the radargram. Through multiple simulations, we demonstrated the important role that topography and water geometry can play in observed IPR reflectivity. We ultimately conclude the bright reflector from our IPR flight line is more likely a broad area of wide distributed water, such as a series of flat canals or sub-glacial lake, instead of a Röthlisberger channel. The approach outlined here has broad applicability for studying the basal environment of large glaciers, and can aid in constraining the geometry and extent of sub-glacial hydrologic structures.

Received: 22 Jul 2023 – Discussion started: 30 Aug 2023

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Journal article(s) based on this preprint

04 Apr 2024

Characterizing sub-glacial hydrology using radar simulations

Chris Pierce, Christopher Gerekos, Mark Skidmore, Lucas Beem, Don Blankenship, Won Sang Lee, Ed Adams, Choon-Ki Lee, and Jamey Stutz

The Cryosphere, 18, 1495–1515, https://doi.org/10.5194/tc-18-1495-2024,https://doi.org/10.5194/tc-18-1495-2024, 2024

Short summary

Chris Pierce, Christopher Gerekos, Mark Skidmore, Lucas Beem, Don Blankenship, Won Sang Lee, Ed Adams, Choon-Ki Lee, and Jamey Stutz

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2023-1685', Anonymous Referee #1, 01 Sep 2023

The manuscript presents an interesting combination of electromagnetic modeling and radar data analysis across a modeled drainage pathway for Thwaites Glacier. The results have the potential to make an important contribution to our understanding of the glaciers subglacial hydrology, but the analysis, as written, has several issues that would need to be addressed first to reconcile the results, methods, and claims in the paper.

Major Issues:

The range of material properties for the bed and water used in the study seem too narrow given the literature cited in the paper. For example, Peters 2005 included reflectivity differences between water (including groundwater) and frozen bedrock that differ by 26 dB without invoking any change in bed roughness or geometry. If you look at Christiansen 2016 and Tulaczyk and Foley 2020 (https://doi.org/10.5194/tc-14-4495-2020) these values are also in the 25 - 27 dB range. If the manuscript seeks to diagnose the subglacial water configuration by excluding other hypotheses, then the complex permittivity for both water and the bed explored should span the full range of this literature (and reproduce that range of reflectivities).

Similarly, the range of bed roughness considered in the study is also small compared to the literature cited by the paper. Again, Peter 2005 shows roughness-based reduction in reflectivities that are as high as 20 dB. For the reasons described above, I’d expect this paper to explore roughesses losses at that scale as well.

The authors present a simulation that is focusable (and focused) which should allow them to probe the specularity of bed echoes for each of the hypothesized configurations. Since, as the paper mentions, this was the key observable in classifying the downstream water system of Thwaites as concentrated rather than distributed, it would seem incumbent on the authors to address whether their interpretations of the (inherently more ambiguous) reflectivity signal would also explain that larger catchment-wide specularity signature.

Line 180: The authors state that they “confine” themselves to Röthlisberger channels and flat canals for this study. That is a fine choice to support the claim (if it survives addressing the issues raised above) that the bright spot (and downstream water network) is likely not a canonical Röthlisberger channel. However, in order to claim (as the authors do in their abstract and conclusion) that the wanted body is “distributed” (which has a specific subglacial hydrological meaning and implication for modeling) they would need to also address other “concentrated” water geometries and exclude them as well. These include Nye Channels, Creytes & Schoof water sheets (https://doi.org/10.1029/2008JF001215) an other concentrated/efficient water configurations (https://doi.org/10.1098/rspa.2014.0907). Otherwise the authors should limit themselves to falsifying the hypothesis that the bright echo on THW2/UBH0c/X243a is a canonical Röthlisberger channel and remove language like “We ultimately conclude the bright reflector from our IPR flight line is more likely a broad area
20 of wide distributed water, such as a series of flat canals or sub-glacial lake” which cannot be supported by a study that does not consider other “concentrated " water geometries.

Minor Issues:

Abstract Line 1: Depending on its configuration water can either enhance or reduce sliding and/or retreat.

Abstract Line 3: Given the recent paper by Schlegel et al. ( https://doi.org/10.1017/aog.2023.2) you may want to consider the use of IPR here.

Table 1: 1.71 MW seems like an extremely high value. It’s unusual to report a post-processing number for transmit power and presenting it in this way could confuse readers significantly.

Citation: https://doi.org/10.5194/egusphere-2023-1685-RC1
- AC1:
  'Reply on RC1', Christopher Pierce, 22 Nov 2023
  We appreciate this reviewer's insightful comments on our manuscript "A Simulation Approach to Characterizing Sub-Glacial Hydrology". These will be very helpful in improving the final product.
  In response to the Major Issues raised by the reviewer, we submit the following responses:
  Regarding the range of material properties used in the study:
  As the reviewer correctly points out, we did not explore many possible combinations of bed materials. This was intentional, as the scope of this work was to introduce the conceptual framework for using such a simulation technique in the study of sub-glacial hydrology, then demonstrate its potential usefulness in constraining hypotheses for a single feature seen in a recent IPR survey.
  
  The emphasis of the work and most important conclusions involve the water geometries considered in the study. Altering the substrate dielectric constant will merely scale power. We acknowledge that definitive diagnosis of the subglacial environment beneath Thwaites may require additional assessment with a broader combination of materials. The nature of this technique may never eliminate all possible combinations of materials and geometry. However, it can be a valuable tool for narrowing the range of likely sub-glacial configurations.
  
  We propose revisions to acknowledge the range of unexplored material properties more explicitly. This will include stating that we have not completely excluded all other possible hypotheses. Instead, we have found at least one possible match between the observed reflectivity and a hypothetical water structure.
  
  Regarding the range of bed roughness explored:
  Peters 2005 presented a calculation for theoretical scattering loss due to sub-glacial roughness. In their calculations, small scale RMS roughness up to sigma_bed / lambda = 0.5 was considered, based on observations of RMS roughness calculated from IPR data over Ice Stream C. As the reviewer points out, Peters calculated a scattering loss of 21 dB if sigma_bed / lambda = 0.5.
  
  However, the Peters paper may have ignored the length scales over which roughness is measured, which is an important consideration. The theoretical scattering loss calculated in Peters assumes correlation length is very small compared to the first Fresnel zone (~100m in our case). However, the range of actual IPR derived roughness observed in Peters beneath Ice Stream C were compiled over a 1km distance, obviously violating this assumption. Peters appears to assume the range of RMS roughness seen with this 1km correlation length translates directly to their calculated theoretical roughness / scattering curve. This logic will result in incorrect understanding of the relationship between scattering and roughness.
  
  Our method attempts to improve upon this by considering roughness at a meaningful length scale for scattering (correlation length <<100m). We explored a range of roughness up to sigma_bed / lambda = 0.2, with correlation length as small as possible relative to the 1^st Fresnel zone. Actual roughness at this length scale is not directly observable by conventional IPR, and therefore the true range of realistic values is unknown. Previous studies such as Peters 2005 or Bingham and Siegert 2009 measure roughness over longer distances, which may be relevant for modeling applications but is insufficient for our purposes. Our range may be smaller than the theoretical range explored in Peters 2005, however we attempt to justify our choice through direct observations of glacier bed roughness matched to our smallest possible correlation length.
  
  Further, we note that in our real-world IPR simulations, roughness on long length scales (>~10²m) is captured explicitly through our simulation methods. We build a digital elevation model (DEM) derived from IPR ice geometry observations with approximately 5-8m spacing.
  
  An entire study could be dedicated to sub-glacial roughness and the impact on radar returns. Ideally this will incorporate a range of RMS roughness and correlation lengths on radar scattering. However, such a study is well beyond the scope of this paper.
  
  We acknowledge that more work should be performed in this realm, which we are willing state explicitly in the manuscript. We will alter language in the introduction, conclusion, and abstract to be clear about scope of the investigation, so it is clear why a more detailed roughness analysis is left to future work.
  
  Regarding the omission of simulated specularity content:
  The reviewer is correct in their observation that a focused simulation product could, in theory, be used to generate and analyze specularity in the same manner as we have demonstrated for reflectivity. Unfortunately, we acknowledge this as a current limitation of the methodology as presented. Schroeder 2015 suggested aperture lengths of up to 2km to generate specularity content for IPR data from Thwaites Glacier. This is reasonable when focusing real IPR data products, however it is unrealistic when focusing our simulated radargrams.
  
  As we discuss in the Methodology section, the simulator is bound by a simulation radius “R”, which limits the domain of facets from which to consider transmitted and reflected waves. Increasing R exponentially raises computational cost. Conversely, R must be greater than the aperture length to generate a valid focused product. Even with access to high performance computing resources, simulations with R>2km are unrealistic.
  
  Due to the above, analysis was necessarily limited to reflectivity. The study seeks to remove some of the ambiguity the reviewer expresses around interpreting this metric. We further limit our interpretation of the reflectivity signal to the transect in question, as a proof of concept for the simulation method. Any attempt to extrapolate our findings to catchment-wide conclusions based on a single transect would be erroneous at this time. Although well outside the scope of this study, it is absolutely an area of future interest.
  
  We suggest a revision to the discussion section, addressing the above concern and why the study is currently confined to reflectivity alone.
  
  Regarding limiting the study's scope to Röthlisberger channels and flat canals, coupled with conclusion language such as “We ultimately conclude the bright reflector from our IPR flight line is more likely a broad area of wide distributed water, such as a series of flat canals or sub-glacial lake”
  We concur with the reviewer’s assessment on this point. Similar to this reviewer’s feedback regarding material properties, we have not explored and eliminated all possible geometries. We can be more precise with language regarding what hypotheses our work has excluded, what hypotheses may be compatible with the data, and what remains unexplored.
  
  As such, our language concluding the structure of the water may be too strongly worded. We will soften this language as the reviewer suggests, stating that the bright echo a) is not consistent with a Röthlisberger channel, b) is consistent with a broad specular water body as we have suggested, and c) other configurations (such as Nye channels, etc) and bed materials (tills, frozen bedrock, clays) remain unexplored. Therefore, it is possible other combinations also match the reflectivity profile in THW2/UBH0c/X243a.
  
  In response to the Minor Issues raised, we submit the following responses:
  Abstract Line 1: Depending on its configuration water can either enhance or reduce sliding and/or retreat.
  Thank you. We agree with this suggested change.
  
  Abstract Line 3: Given the recent paper by Schlegel et al. ( https://doi.org/10.1017/aog.2023.2) you may want to consider the use of IPR here.
  We thank the reviewer for bringing this to our attention. We will change our nomenclature from IPR to airborne RES, consistent with Schlegel et al.
  
  Table 1: 1.71 MW seems like an extremely high value. It’s unusual to report a post-processing number for transmit power and presenting it in this way could confuse readers significantly.
  The reviewer’s concern on this point is reasonable. We have coherently pre-summed the radar power for simulation expediency. Therefore, the power in our simulations is significantly higher than MARFA’s 8kW native power. We want to be clear this is NOT the same as post-processing, which may sum power incoherently. Summation happens during data processing after an actual survey.
  
  For additional clarity, we suggest putting native MARFA values in parentheses next to the simulator parameters. In the table description, we can state that native instrument values are in parentheses where they deviate from the simulation parameters, and the reason for this difference is because the simulator approximates pre-summed power and PRF for computational efficiency.
  
  Citation: https://doi.org/10.5194/egusphere-2023-1685-AC1
RC2:
'Comment on egusphere-2023-1685', Anonymous Referee #2, 03 Nov 2023
The manuscript offers a compelling blend of electromagnetic modelling and radar data analysis in the context of Thwaites Glacier's subglacial drainage pathway. While the results hold promise for enhancing our knowledge of glacier subglacial hydrology, however it needs to be improved considering the suggestions below.
Some of the Major issues to be addressed, they are.
If the manuscript aims to identify the subglacial water arrangement by eliminating alternative hypotheses, it is imperative that the comprehensive permittivity values for both water and the glacier bed cover the entire spectrum found in existing literature, thus reproducing the full range of reflectivity associated with these parameters.

The paper primarily focused on the regional scale of Thwaites' downstream water system. However, it is imperative to acknowledge the broader applicability of the model for a more extensive catchment when considering its practical utility.

Minor comments:
Line 25: Better to add more recent citations.

Line 32: Missing citations

In the introduction section where the objectives are outlined, it is important to include the potential applications of the model to other catchments, thereby emphasising its versatility beyond the specific case of Thwaites Glacier.

Providing a dedicated "Study Area" section, rather than including it in the introduction, would offer a more comprehensive understanding of the research area.

Additionally, separating the "Results" and "Discussion" sections would enhance the clarity and structure of the paper. It would improve the presentation if all figures and tables were enclosed by borders for a more organized and visually clear layout.

In the conclusion section, it would be beneficial to provide an overview of future work, offering the potential research directions and developments to be pursued.
Citation: https://doi.org/10.5194/egusphere-2023-1685-RC2
- AC2:
  'Reply on RC2', Christopher Pierce, 22 Nov 2023
  We would like to thank this reviewer for their comments on our manuscript "A Simulation Approach to Sub-Glacial Hydrology". Their insight will be very helpful in improving the final product.
  In response to the reviewer's "Major Issues", we submit the following responses:
  Regarding the range of permittivity values for the bed material used in the study:
  As the reviewer correctly points out, we did not explore many possible combinations of bed materials. This was intentional, as the scope of this work was to introduce the conceptual framework for using such a simulation technique in the study of sub-glacial hydrology, then demonstrate its potential usefulness in constraining hypotheses for a single feature seen in a recent IPR survey.
  
  The emphasis of the work and most important conclusions involve the water geometries considered in the study. Altering the substrate dielectric constant will merely scale power. We acknowledge that definitive diagnosis of the subglacial environment beneath Thwaites may require additional assessment with a broader combination of materials. The nature of this technique may never eliminate all possible combinations of materials and geometry. However, it can be a valuable tool for narrowing the range of likely sub-glacial configurations.
  
  We propose revisions to acknowledge the range of unexplored material properties more explicitly. This will include stating that we have not completely excluded all other possible hypotheses. Instead, we have found at least one possible match between the observed reflectivity and a hypothetical water structure.
  
  Regarding the broader applicability of the model beyond the Thwaites water system:
  We appreciate and agree with the reviewer on this point. The choice of the Thwaites water system was a convenient example of how this method can be used, but of course the method could be applied more broadly to examine other regions and hypotheses. We propose additional language in the abstract, introduction and conclusions discussing the broader applicability of the technique, and also clarify that our Thwaites use case is just one example.
  
  Regarding the minor comments raised by this reviewer:
  Line 25: Better to add more recent citations.
  We agree to add updated citations for the relationship between hydrology, shear stress, and ice rheology as suggested.
  
  Line 32: Missing citations
  We agree to add citations establishing IPR as a technique in the study of hydrology, as the reviewer suggests.
  
  In the introduction section where the objectives are outlined, it is important to include the potential applications of the model to other catchments, thereby emphasising its versatility beyond the specific case of Thwaites Glacier.
  This comment appears similar to the reviewer’s second concern under “Major Issues”. We believe our proposed resolution addresses both points.
  
  On providing a dedicated "Study Area" section:
  We appreciate this comment and agree to create a dedicated “Study Area” section to describe the target region of Thwaites glacier.
  
  On separating "Results" and "Discussion" to improve clarity:
  We will address the reviewer’s concern by separating the Results and Discussion for clarity.
  
  On adding table and figure borders:
  We acknowledge that authors and readers have differing stylistic preferences. However, we believe our figures are well aligned with the Cryosphere style guidance and prefer to keep them as is.
  
  With respect to adding a discussion of future research directions in the Conclusions:
  We agree to add language as suggested by the reviewer.
  
  Citation: https://doi.org/10.5194/egusphere-2023-1685-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2023-1685', Anonymous Referee #1, 01 Sep 2023

The manuscript presents an interesting combination of electromagnetic modeling and radar data analysis across a modeled drainage pathway for Thwaites Glacier. The results have the potential to make an important contribution to our understanding of the glaciers subglacial hydrology, but the analysis, as written, has several issues that would need to be addressed first to reconcile the results, methods, and claims in the paper.

Major Issues:

The range of material properties for the bed and water used in the study seem too narrow given the literature cited in the paper. For example, Peters 2005 included reflectivity differences between water (including groundwater) and frozen bedrock that differ by 26 dB without invoking any change in bed roughness or geometry. If you look at Christiansen 2016 and Tulaczyk and Foley 2020 (https://doi.org/10.5194/tc-14-4495-2020) these values are also in the 25 - 27 dB range. If the manuscript seeks to diagnose the subglacial water configuration by excluding other hypotheses, then the complex permittivity for both water and the bed explored should span the full range of this literature (and reproduce that range of reflectivities).

Similarly, the range of bed roughness considered in the study is also small compared to the literature cited by the paper. Again, Peter 2005 shows roughness-based reduction in reflectivities that are as high as 20 dB. For the reasons described above, I’d expect this paper to explore roughesses losses at that scale as well.

The authors present a simulation that is focusable (and focused) which should allow them to probe the specularity of bed echoes for each of the hypothesized configurations. Since, as the paper mentions, this was the key observable in classifying the downstream water system of Thwaites as concentrated rather than distributed, it would seem incumbent on the authors to address whether their interpretations of the (inherently more ambiguous) reflectivity signal would also explain that larger catchment-wide specularity signature.

Line 180: The authors state that they “confine” themselves to Röthlisberger channels and flat canals for this study. That is a fine choice to support the claim (if it survives addressing the issues raised above) that the bright spot (and downstream water network) is likely not a canonical Röthlisberger channel. However, in order to claim (as the authors do in their abstract and conclusion) that the wanted body is “distributed” (which has a specific subglacial hydrological meaning and implication for modeling) they would need to also address other “concentrated” water geometries and exclude them as well. These include Nye Channels, Creytes & Schoof water sheets (https://doi.org/10.1029/2008JF001215) an other concentrated/efficient water configurations (https://doi.org/10.1098/rspa.2014.0907). Otherwise the authors should limit themselves to falsifying the hypothesis that the bright echo on THW2/UBH0c/X243a is a canonical Röthlisberger channel and remove language like “We ultimately conclude the bright reflector from our IPR flight line is more likely a broad area
20 of wide distributed water, such as a series of flat canals or sub-glacial lake” which cannot be supported by a study that does not consider other “concentrated " water geometries.

Minor Issues:

Abstract Line 1: Depending on its configuration water can either enhance or reduce sliding and/or retreat.

Abstract Line 3: Given the recent paper by Schlegel et al. ( https://doi.org/10.1017/aog.2023.2) you may want to consider the use of IPR here.

Table 1: 1.71 MW seems like an extremely high value. It’s unusual to report a post-processing number for transmit power and presenting it in this way could confuse readers significantly.

Citation: https://doi.org/10.5194/egusphere-2023-1685-RC1
- AC1:
  'Reply on RC1', Christopher Pierce, 22 Nov 2023
  We appreciate this reviewer's insightful comments on our manuscript "A Simulation Approach to Characterizing Sub-Glacial Hydrology". These will be very helpful in improving the final product.
  In response to the Major Issues raised by the reviewer, we submit the following responses:
  Regarding the range of material properties used in the study:
  As the reviewer correctly points out, we did not explore many possible combinations of bed materials. This was intentional, as the scope of this work was to introduce the conceptual framework for using such a simulation technique in the study of sub-glacial hydrology, then demonstrate its potential usefulness in constraining hypotheses for a single feature seen in a recent IPR survey.
  
  The emphasis of the work and most important conclusions involve the water geometries considered in the study. Altering the substrate dielectric constant will merely scale power. We acknowledge that definitive diagnosis of the subglacial environment beneath Thwaites may require additional assessment with a broader combination of materials. The nature of this technique may never eliminate all possible combinations of materials and geometry. However, it can be a valuable tool for narrowing the range of likely sub-glacial configurations.
  
  We propose revisions to acknowledge the range of unexplored material properties more explicitly. This will include stating that we have not completely excluded all other possible hypotheses. Instead, we have found at least one possible match between the observed reflectivity and a hypothetical water structure.
  
  Regarding the range of bed roughness explored:
  Peters 2005 presented a calculation for theoretical scattering loss due to sub-glacial roughness. In their calculations, small scale RMS roughness up to sigma_bed / lambda = 0.5 was considered, based on observations of RMS roughness calculated from IPR data over Ice Stream C. As the reviewer points out, Peters calculated a scattering loss of 21 dB if sigma_bed / lambda = 0.5.
  
  However, the Peters paper may have ignored the length scales over which roughness is measured, which is an important consideration. The theoretical scattering loss calculated in Peters assumes correlation length is very small compared to the first Fresnel zone (~100m in our case). However, the range of actual IPR derived roughness observed in Peters beneath Ice Stream C were compiled over a 1km distance, obviously violating this assumption. Peters appears to assume the range of RMS roughness seen with this 1km correlation length translates directly to their calculated theoretical roughness / scattering curve. This logic will result in incorrect understanding of the relationship between scattering and roughness.
  
  Our method attempts to improve upon this by considering roughness at a meaningful length scale for scattering (correlation length <<100m). We explored a range of roughness up to sigma_bed / lambda = 0.2, with correlation length as small as possible relative to the 1^st Fresnel zone. Actual roughness at this length scale is not directly observable by conventional IPR, and therefore the true range of realistic values is unknown. Previous studies such as Peters 2005 or Bingham and Siegert 2009 measure roughness over longer distances, which may be relevant for modeling applications but is insufficient for our purposes. Our range may be smaller than the theoretical range explored in Peters 2005, however we attempt to justify our choice through direct observations of glacier bed roughness matched to our smallest possible correlation length.
  
  Further, we note that in our real-world IPR simulations, roughness on long length scales (>~10²m) is captured explicitly through our simulation methods. We build a digital elevation model (DEM) derived from IPR ice geometry observations with approximately 5-8m spacing.
  
  An entire study could be dedicated to sub-glacial roughness and the impact on radar returns. Ideally this will incorporate a range of RMS roughness and correlation lengths on radar scattering. However, such a study is well beyond the scope of this paper.
  
  We acknowledge that more work should be performed in this realm, which we are willing state explicitly in the manuscript. We will alter language in the introduction, conclusion, and abstract to be clear about scope of the investigation, so it is clear why a more detailed roughness analysis is left to future work.
  
  Regarding the omission of simulated specularity content:
  The reviewer is correct in their observation that a focused simulation product could, in theory, be used to generate and analyze specularity in the same manner as we have demonstrated for reflectivity. Unfortunately, we acknowledge this as a current limitation of the methodology as presented. Schroeder 2015 suggested aperture lengths of up to 2km to generate specularity content for IPR data from Thwaites Glacier. This is reasonable when focusing real IPR data products, however it is unrealistic when focusing our simulated radargrams.
  
  As we discuss in the Methodology section, the simulator is bound by a simulation radius “R”, which limits the domain of facets from which to consider transmitted and reflected waves. Increasing R exponentially raises computational cost. Conversely, R must be greater than the aperture length to generate a valid focused product. Even with access to high performance computing resources, simulations with R>2km are unrealistic.
  
  Due to the above, analysis was necessarily limited to reflectivity. The study seeks to remove some of the ambiguity the reviewer expresses around interpreting this metric. We further limit our interpretation of the reflectivity signal to the transect in question, as a proof of concept for the simulation method. Any attempt to extrapolate our findings to catchment-wide conclusions based on a single transect would be erroneous at this time. Although well outside the scope of this study, it is absolutely an area of future interest.
  
  We suggest a revision to the discussion section, addressing the above concern and why the study is currently confined to reflectivity alone.
  
  Regarding limiting the study's scope to Röthlisberger channels and flat canals, coupled with conclusion language such as “We ultimately conclude the bright reflector from our IPR flight line is more likely a broad area of wide distributed water, such as a series of flat canals or sub-glacial lake”
  We concur with the reviewer’s assessment on this point. Similar to this reviewer’s feedback regarding material properties, we have not explored and eliminated all possible geometries. We can be more precise with language regarding what hypotheses our work has excluded, what hypotheses may be compatible with the data, and what remains unexplored.
  
  As such, our language concluding the structure of the water may be too strongly worded. We will soften this language as the reviewer suggests, stating that the bright echo a) is not consistent with a Röthlisberger channel, b) is consistent with a broad specular water body as we have suggested, and c) other configurations (such as Nye channels, etc) and bed materials (tills, frozen bedrock, clays) remain unexplored. Therefore, it is possible other combinations also match the reflectivity profile in THW2/UBH0c/X243a.
  
  In response to the Minor Issues raised, we submit the following responses:
  Abstract Line 1: Depending on its configuration water can either enhance or reduce sliding and/or retreat.
  Thank you. We agree with this suggested change.
  
  Abstract Line 3: Given the recent paper by Schlegel et al. ( https://doi.org/10.1017/aog.2023.2) you may want to consider the use of IPR here.
  We thank the reviewer for bringing this to our attention. We will change our nomenclature from IPR to airborne RES, consistent with Schlegel et al.
  
  Table 1: 1.71 MW seems like an extremely high value. It’s unusual to report a post-processing number for transmit power and presenting it in this way could confuse readers significantly.
  The reviewer’s concern on this point is reasonable. We have coherently pre-summed the radar power for simulation expediency. Therefore, the power in our simulations is significantly higher than MARFA’s 8kW native power. We want to be clear this is NOT the same as post-processing, which may sum power incoherently. Summation happens during data processing after an actual survey.
  
  For additional clarity, we suggest putting native MARFA values in parentheses next to the simulator parameters. In the table description, we can state that native instrument values are in parentheses where they deviate from the simulation parameters, and the reason for this difference is because the simulator approximates pre-summed power and PRF for computational efficiency.
  
  Citation: https://doi.org/10.5194/egusphere-2023-1685-AC1
RC2:
'Comment on egusphere-2023-1685', Anonymous Referee #2, 03 Nov 2023
The manuscript offers a compelling blend of electromagnetic modelling and radar data analysis in the context of Thwaites Glacier's subglacial drainage pathway. While the results hold promise for enhancing our knowledge of glacier subglacial hydrology, however it needs to be improved considering the suggestions below.
Some of the Major issues to be addressed, they are.
If the manuscript aims to identify the subglacial water arrangement by eliminating alternative hypotheses, it is imperative that the comprehensive permittivity values for both water and the glacier bed cover the entire spectrum found in existing literature, thus reproducing the full range of reflectivity associated with these parameters.

The paper primarily focused on the regional scale of Thwaites' downstream water system. However, it is imperative to acknowledge the broader applicability of the model for a more extensive catchment when considering its practical utility.

Minor comments:
Line 25: Better to add more recent citations.

Line 32: Missing citations

In the introduction section where the objectives are outlined, it is important to include the potential applications of the model to other catchments, thereby emphasising its versatility beyond the specific case of Thwaites Glacier.

Providing a dedicated "Study Area" section, rather than including it in the introduction, would offer a more comprehensive understanding of the research area.

Additionally, separating the "Results" and "Discussion" sections would enhance the clarity and structure of the paper. It would improve the presentation if all figures and tables were enclosed by borders for a more organized and visually clear layout.

In the conclusion section, it would be beneficial to provide an overview of future work, offering the potential research directions and developments to be pursued.
Citation: https://doi.org/10.5194/egusphere-2023-1685-RC2
- AC2:
  'Reply on RC2', Christopher Pierce, 22 Nov 2023
  We would like to thank this reviewer for their comments on our manuscript "A Simulation Approach to Sub-Glacial Hydrology". Their insight will be very helpful in improving the final product.
  In response to the reviewer's "Major Issues", we submit the following responses:
  Regarding the range of permittivity values for the bed material used in the study:
  As the reviewer correctly points out, we did not explore many possible combinations of bed materials. This was intentional, as the scope of this work was to introduce the conceptual framework for using such a simulation technique in the study of sub-glacial hydrology, then demonstrate its potential usefulness in constraining hypotheses for a single feature seen in a recent IPR survey.
  
  The emphasis of the work and most important conclusions involve the water geometries considered in the study. Altering the substrate dielectric constant will merely scale power. We acknowledge that definitive diagnosis of the subglacial environment beneath Thwaites may require additional assessment with a broader combination of materials. The nature of this technique may never eliminate all possible combinations of materials and geometry. However, it can be a valuable tool for narrowing the range of likely sub-glacial configurations.
  
  We propose revisions to acknowledge the range of unexplored material properties more explicitly. This will include stating that we have not completely excluded all other possible hypotheses. Instead, we have found at least one possible match between the observed reflectivity and a hypothetical water structure.
  
  Regarding the broader applicability of the model beyond the Thwaites water system:
  We appreciate and agree with the reviewer on this point. The choice of the Thwaites water system was a convenient example of how this method can be used, but of course the method could be applied more broadly to examine other regions and hypotheses. We propose additional language in the abstract, introduction and conclusions discussing the broader applicability of the technique, and also clarify that our Thwaites use case is just one example.
  
  Regarding the minor comments raised by this reviewer:
  Line 25: Better to add more recent citations.
  We agree to add updated citations for the relationship between hydrology, shear stress, and ice rheology as suggested.
  
  Line 32: Missing citations
  We agree to add citations establishing IPR as a technique in the study of hydrology, as the reviewer suggests.
  
  In the introduction section where the objectives are outlined, it is important to include the potential applications of the model to other catchments, thereby emphasising its versatility beyond the specific case of Thwaites Glacier.
  This comment appears similar to the reviewer’s second concern under “Major Issues”. We believe our proposed resolution addresses both points.
  
  On providing a dedicated "Study Area" section:
  We appreciate this comment and agree to create a dedicated “Study Area” section to describe the target region of Thwaites glacier.
  
  On separating "Results" and "Discussion" to improve clarity:
  We will address the reviewer’s concern by separating the Results and Discussion for clarity.
  
  On adding table and figure borders:
  We acknowledge that authors and readers have differing stylistic preferences. However, we believe our figures are well aligned with the Cryosphere style guidance and prefer to keep them as is.
  
  With respect to adding a discussion of future research directions in the Conclusions:
  We agree to add language as suggested by the reviewer.
  
  Citation: https://doi.org/10.5194/egusphere-2023-1685-AC2

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) (01 Dec 2023) by Vishnu Nandan

AR by Chris Pierce on behalf of the Authors (05 Jan 2024) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (08 Jan 2024) by Vishnu Nandan

RR by Anonymous Referee #1 (09 Jan 2024)

Suggestions for revision or reasons for rejection

For the most part, I agree with the revisions. However an issue remains with the following response:

The range of material properties for the bed and water used in the study seem too
narrow given the literature cited in the paper. For example, Peters 2005 included
reflectivity differences between water (including groundwater) and frozen bedrock that
differ by 26 dB without invoking any change in bed roughness or geometry. If you look
at Christiansen 2016 and Tulaczyk and Foley 2020 (https://doi.org/10.5194/tc-14-4495-
2020) these values are also in the 25 - 27 dB range. If the manuscript seeks to diagnose
the subglacial water configuration by excluding other hypotheses, then the complex
permittivity for both water and the bed explored should span the full range of this
literature (and reproduce that range of reflectivities).
o In the Discussion, we have added a figure and text addressing the range of
possible dielectric constants that were not explored in this study. We provide
justification as to why much of this range is unlikely due to the observed
reflectivity profile and physical environment. We have also adjusted the language
in our Results, Discussion, and Conclusions to indicate that we have eliminated a
Röthlisberger channel as the possible source of the bright echo on
THW2/UBH0c/X243a. We state that the echo is consistent with canals or a sub-
glacial lake, while acknowledging that we have not explored all possible
alternatives required to make a conclusive diagnosis.”

Since the authors have not simulated other “concentrated” water bodies, such as those mentioned in the review, their claim that the signatures are consistent with lakes or canals are too strong. This is especially true in the absence of specularity simulations. The results, as presented, only falsify the hypothesis of Röthlisberger channels and do not support a broader claim than that. Therefore the paper should be revise to remove the claims about distributed water bodies like canals or lakes. Unless the additional analyses mentioned in the review can be added and support such a claim.

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ED: Reconsider after major revisions (further review by editor and referees) (09 Jan 2024) by Vishnu Nandan

AR by Chris Pierce on behalf of the Authors (26 Jan 2024) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (30 Jan 2024) by Vishnu Nandan

RR by Anonymous Referee #1 (30 Jan 2024)

Suggestions for revision or reasons for rejection

I appreciate that the authors have softened their language on the strength of their conclusion, but fear that they have not addressed the fundamental issue of reconciling their results with the larger body of observations of radar observations of subglacial hydrology in this region. Indeed most of those observations were made using the same set of data with some of the same co-authors as this work. As a result, it seems reasonable to expect some reconciliation of the results presented here and the results in that other work.

Here is my understanding of the evidence produced by this study:

- The pattern of relative reflectivity along the profile matches the strength reflections of flat water bodies - specifically canals and lakes - rather than R channels using the model presented by the authors.

Here is my understanding of the evidence produced in other studies:

- In the upstream region, there are bright, highly specular, anisotropically specular returns from subglacial water bodies

- In the downstream region there are diffuse, bright water bodies.

Here is my understanding of the mapping of brightness and specularity to the three categories/geometries of water bodies discussed in the paper:

- Lakes will be the brightest, will be highly specular, and will be isotropically specular

- Canals will be the next brightest, will be highly specular, but will be anisotropically specular

- R-channels will be dimmer, will not specular

I believe that the excellent modeling work done in this paper highlights that R-channels will be dimmer than previously appreciated an that is evidence against that geometry (with its curved interface on the base of the ice) for the water system in that region. To me this is a significant contribution to our understanding of the glacier and is supported by the results in this paper and the body of observations.

However, the authors go on to propose two alternatives (based only on the relative reflectivity evidence) which would both produce specular returns. Because this region has low specularity echoes (as observed using this same data set in publications with some of the same authors of this paper) it would seem that this conflict in interpretation should be resolved as part of this manuscript.

Some options to do so would include:

- Making a case for why the proposed geometry did not produce specular echoes (either through modeling specularity, analyzing the data, or making a physical argument based on scattering or processing effects)

- Dropping the claim that the observations are consistent with lakes or canals and instead proposing other/additional geometries that would produce the reflectivity pattern as modeled by the authors but would also not produce specular echoes.

- Keeping the interpretation of R-channels an invoking another process (e.g. reduced local englacial attenuation due to enhanced basal melting and the vertical advection of cold ice above the channels).

I'm sure there are other ways to reconcile these observations and looking forward to learning more about the glacier through the authors' analysis, evidence and reasoning to do so.

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ED: Publish subject to revisions (further review by editor and referees) (31 Jan 2024) by Vishnu Nandan

AR by Chris Pierce on behalf of the Authors (15 Feb 2024) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (18 Feb 2024) by Vishnu Nandan

RR by Anonymous Referee #1 (19 Feb 2024)

ED: Publish as is (19 Feb 2024) by Vishnu Nandan

AR by Chris Pierce on behalf of the Authors (20 Feb 2024) Manuscript

Journal article(s) based on this preprint

04 Apr 2024

Characterizing sub-glacial hydrology using radar simulations

Chris Pierce, Christopher Gerekos, Mark Skidmore, Lucas Beem, Don Blankenship, Won Sang Lee, Ed Adams, Choon-Ki Lee, and Jamey Stutz

The Cryosphere, 18, 1495–1515, https://doi.org/10.5194/tc-18-1495-2024,https://doi.org/10.5194/tc-18-1495-2024, 2024

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Chris Pierce, Christopher Gerekos, Mark Skidmore, Lucas Beem, Don Blankenship, Won Sang Lee, Ed Adams, Choon-Ki Lee, and Jamey Stutz

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Short summary

Water beneath glaciers in Antarctica can influence how the ice slides or melts. Airborne radar can detect this water, which looks bright in radar images. Unfortunately, common techniques cannot identify the water’s size or shape. We used a simulator to show how the radar image changes based on the bed material, size and shape of the water body. This technique was used to assess a suspected water body beneath Thwaite's Glacier. We found it is most likely a series of wide, flat canals or a lake.


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