Age, thinning and spatial origin of the Beyond EPICA ice from a 2.5D ice flow model

Chung, Ailsa; Parrenin, Frédéric; Mulvaney, Robert; Vittuari, Luca; Frezzotti, Massimo; Zanutta, Antonio; Lilien, David A.; Cavitte, Marie G. P.; Eisen, Olaf

doi:https://doi.org/10.5194/egusphere-2024-1650

Preprints

https://doi.org/10.5194/egusphere-2024-1650

Preprints

14 Jun 2024

| 14 Jun 2024

Age, thinning and spatial origin of the Beyond EPICA ice from a 2.5D ice flow model

Ailsa Chung, Frédéric Parrenin, Robert Mulvaney, Luca Vittuari, Massimo Frezzotti, Antonio Zanutta, David A. Lilien, Marie G. P. Cavitte, and Olaf Eisen

Abstract. The European Beyond EPICA – Oldest Ice consortium is currently conducting an ice core drilling project at Little Dome C (LDC) in Antarctica with the aim of retrieving a continuous ice core up to 1.5 Ma. In order to determine the age of the ice at a given depth, 1D numerical models are often employed. However, they do not take into account any effects due to horizontal flow. We present a 2.5D inverse model that determines the age–depth profile along a flow line from Dome C (DC) to LDC that is assumed to be stable in time. The model is constrained by dated radar internal reflecting horizons. Surface velocity measurements are used to determine the flow line and ascertain the flow tube width, which also allows the model to consider lateral divergence. This new model therefore improves on the results produced by 1D models previously applied to the DC area. By inferring a mechanical ice thickness, the model predicts either the thickness of a basal layer of stagnant ice or a basal melt rate.

Results show that the deepest ice at Beyond EPICA Little Dome C (BELDC) originates from around 15 km upstream. The oldest ice with useful age resolution, i.e. with an age density of 20 kyr m^-1, is predicted to be 1.12 Ma at BELDC. Over the LDC area, the 2.5D model predicts a basal layer 200–250 m thick at the base of the ice sheet. Modelled ice particle trajectories suggest that this layer could be composed of stagnant ice, accreted ice or even disturbed ice containing debris. We explore the possibilities, though this is an open question that may only be answered by analysis the Beyond EPICA ice core once it has been drilled. Finally, we discuss in detail a thinning in the basal layer which is less than predicted by the model, as observed in other ice cores. This could mean that modelled ages are significantly over-estimated in the deepest part of the ice column. Given that the age estimate from the 2.5D model is younger than previous estimates, we suggest that horizontal flow is an important factor in this region. However, our model assumes that the flow line features such as flow direction and dome location have not change over the time period considered, which might not be the case.

Received: 31 May 2024 – Discussion started: 14 Jun 2024

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Journal article(s) based on this preprint

01 Oct 2025

Age, thinning and spatial origin of the Beyond EPICA ice from a 2.5D ice flow model

Ailsa Chung, Frédéric Parrenin, Robert Mulvaney, Luca Vittuari, Massimo Frezzotti, Antonio Zanutta, David A. Lilien, Marie G. P. Cavitte, and Olaf Eisen

The Cryosphere, 19, 4125–4140, https://doi.org/10.5194/tc-19-4125-2025,https://doi.org/10.5194/tc-19-4125-2025, 2025

Short summary

Ailsa Chung, Frédéric Parrenin, Robert Mulvaney, Luca Vittuari, Massimo Frezzotti, Antonio Zanutta, David A. Lilien, Marie G. P. Cavitte, and Olaf Eisen

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-1650', Anonymous Referee #1, 06 Aug 2024

This study present a so called 2.5D inverse model for simulating the age–depth relationships along a flow line from Dome C to Little Dome C in Antarctica. This is an important topic in glaciology, e.g., finding a location of an old ice core, which matchs the scope of The Cryosphere. However, I find it is very difficult for me to understand this manuscript, and at some places I feel not much senses to me.
The main reason is that the authors do not even put some basic explanations of their model. I do not undertand why “a full description of the forward model will be available in a separate subsequent article” is possible if they do not make it clear in this paper? For example, Eqn 1 gives the vertical velocity profile, but what does the horizontal ice velocity (flux) look like? Both horizontal and vertical ice velocity are critical in determing the shapes of age-depth profiles. The authors also do not explain basically the inverse model, e.g., what is p_prior and why they need to use a term “mechanical ice thickess” since they have already the observed ice thickness data - this do not make much sense not using the observed data!
Actually, the age-depth modeling is not new. If the authors can dig a bit in past literatures, they can easily find some nice and important papers, like Greve et al. (2002) and Rybak and Huybrechts (2003). Based on ice flow models and the Eulerian or Lagrangian methods, we can determine the age-depth relationships in a more physical way. I do not see the authors even mention these previous work in the Introduction section. I am not sure what the “forward model” is about if they do not use a physical ice flow model. If I am not convinced the velocity field is correct, it is also hard for me to believe the inversed age-depth profiles are correct either. The inverse model is then just an optimization approach to find the numbers that match the radar chronology record, but without much physics inside.
The writings also make me confused often. For example,
L13, “the 2.5D model predicts a basal layer 200–250 m thick at the base of the ice sheet”, what is “basal layer 200-250 thick”?
L68, “There is no direct thermal representation in the forward model as we use an inferred mechanical ice thickness to determine a basal melt rate”, this sentence comes from no where, and has no references and no explanations.
L80: what is the form of “horizontal flux shape function”?
L97: no definitions for p and Hw
L110: What is delta q and delta x?
Table 1: what is the spatial locations for these 19 IRHs?
These kind of major and minor issues make me feel very difficult to read and understand this manuscript. Thus, I suggest the authors take another careful round of modifications and re-submit the manuscript after they add the necessary inputs.
References:
Ralf Greve, Yongqi Wang, and Bernd Mügge. Comparison of numerical schemes for the solution of the advective age equation in ice sheets. Annals of Glaciology, 35:487–494, 2002.
Oleg Rybak and Philippe Huybrechts. A comparison of eulerian and lagrangian methods for dating in numerical ice-sheet models. Annals of Glaciology, 37:150–158, 2003.

Citation: https://doi.org/10.5194/egusphere-2024-1650-RC1
- AC1: 'Reply on RC1', Ailsa Chung, 14 Mar 2025
  
  We would like to thank the reviewer for the helpful comments. We attatch our responses to their comments.
  
  Citation: https://doi.org/10.5194/egusphere-2024-1650-AC1
RC2:
'Comment on egusphere-2024-1650', Anonymous Referee #2, 10 Sep 2024

Chung et al. use a 2.5D flowband model and dated internal layers to estimate the age of basal ice along a flowline from Dome C to the Beyond EPICA drill site of Little Dome C. The model finds the best fit spatial pattern of accumulation rate, velocity shape function, and mechanical ice thickness, which can then be translated to either stagnant ice thickness or basal melt rate. The primary result is that the age of basal ice (for Little Dome C this is just above the layer of stagnant ice) is younger than previously suggested, which has implications for the Beyond EPICA ice core.
The modeling is novel and well described. The manuscript is clearly written with a clear and well supported conclusion. There is acknowledgement of the unknown basal process which adds to the excitement of what Beyond EPICA will find when the drilling is completed this season (assuming good fortune). The discussion of ice cores having younger ages than the model predicts is interesting and useful component. The paper is ready for publication, but I hope the authors will consider the including the points below.
The one area that I suggest more of is a discussion of the age results with Lilien et al., 2021. While Lilien et al., 2021 is mentioned in multiple places, it is not clear how this age scale differs. Lilien et al. suggested that a 1.5Ma age, rather than a 1.1Ma age, is likely to be reached, but I think this is not so much a difference in the depth-age relationship as in the definition of "interpretable ice", with this paper using a value of 20 ka/m while Lilien et al. find 14 ka/m. It is a bit difficult for people outside of Beyond EPICA to keep the differences straight, so providing discussions and summaries of the differences more clearly is quite helpful.
A few other minor comments:
- The discussion of ice fabric is appreciated and not including ice fabric in your model is understandable. However, it seems like the effects of fabric could be parameterized through constraints on the shape of the velocity, i.e. the p value. This is obviously future work, but I think considerable progress could be made without trying to model fabric evolution.
- The last sentence of the abstract is frustrating. Why end on such a sour note? Can you finish instead with a concluding note about the progress you have made?

Citation: https://doi.org/10.5194/egusphere-2024-1650-RC2
- AC2: 'Reply on RC2', Ailsa Chung, 14 Mar 2025
  
  We would like to thank the reviewer for the helpful comments. We attatch our responses to their comments.
  
  Citation: https://doi.org/10.5194/egusphere-2024-1650-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-1650', Anonymous Referee #1, 06 Aug 2024

This study present a so called 2.5D inverse model for simulating the age–depth relationships along a flow line from Dome C to Little Dome C in Antarctica. This is an important topic in glaciology, e.g., finding a location of an old ice core, which matchs the scope of The Cryosphere. However, I find it is very difficult for me to understand this manuscript, and at some places I feel not much senses to me.
The main reason is that the authors do not even put some basic explanations of their model. I do not undertand why “a full description of the forward model will be available in a separate subsequent article” is possible if they do not make it clear in this paper? For example, Eqn 1 gives the vertical velocity profile, but what does the horizontal ice velocity (flux) look like? Both horizontal and vertical ice velocity are critical in determing the shapes of age-depth profiles. The authors also do not explain basically the inverse model, e.g., what is p_prior and why they need to use a term “mechanical ice thickess” since they have already the observed ice thickness data - this do not make much sense not using the observed data!
Actually, the age-depth modeling is not new. If the authors can dig a bit in past literatures, they can easily find some nice and important papers, like Greve et al. (2002) and Rybak and Huybrechts (2003). Based on ice flow models and the Eulerian or Lagrangian methods, we can determine the age-depth relationships in a more physical way. I do not see the authors even mention these previous work in the Introduction section. I am not sure what the “forward model” is about if they do not use a physical ice flow model. If I am not convinced the velocity field is correct, it is also hard for me to believe the inversed age-depth profiles are correct either. The inverse model is then just an optimization approach to find the numbers that match the radar chronology record, but without much physics inside.
The writings also make me confused often. For example,
L13, “the 2.5D model predicts a basal layer 200–250 m thick at the base of the ice sheet”, what is “basal layer 200-250 thick”?
L68, “There is no direct thermal representation in the forward model as we use an inferred mechanical ice thickness to determine a basal melt rate”, this sentence comes from no where, and has no references and no explanations.
L80: what is the form of “horizontal flux shape function”?
L97: no definitions for p and Hw
L110: What is delta q and delta x?
Table 1: what is the spatial locations for these 19 IRHs?
These kind of major and minor issues make me feel very difficult to read and understand this manuscript. Thus, I suggest the authors take another careful round of modifications and re-submit the manuscript after they add the necessary inputs.
References:
Ralf Greve, Yongqi Wang, and Bernd Mügge. Comparison of numerical schemes for the solution of the advective age equation in ice sheets. Annals of Glaciology, 35:487–494, 2002.
Oleg Rybak and Philippe Huybrechts. A comparison of eulerian and lagrangian methods for dating in numerical ice-sheet models. Annals of Glaciology, 37:150–158, 2003.

Citation: https://doi.org/10.5194/egusphere-2024-1650-RC1
- AC1: 'Reply on RC1', Ailsa Chung, 14 Mar 2025
  
  We would like to thank the reviewer for the helpful comments. We attatch our responses to their comments.
  
  Citation: https://doi.org/10.5194/egusphere-2024-1650-AC1
RC2:
'Comment on egusphere-2024-1650', Anonymous Referee #2, 10 Sep 2024

Chung et al. use a 2.5D flowband model and dated internal layers to estimate the age of basal ice along a flowline from Dome C to the Beyond EPICA drill site of Little Dome C. The model finds the best fit spatial pattern of accumulation rate, velocity shape function, and mechanical ice thickness, which can then be translated to either stagnant ice thickness or basal melt rate. The primary result is that the age of basal ice (for Little Dome C this is just above the layer of stagnant ice) is younger than previously suggested, which has implications for the Beyond EPICA ice core.
The modeling is novel and well described. The manuscript is clearly written with a clear and well supported conclusion. There is acknowledgement of the unknown basal process which adds to the excitement of what Beyond EPICA will find when the drilling is completed this season (assuming good fortune). The discussion of ice cores having younger ages than the model predicts is interesting and useful component. The paper is ready for publication, but I hope the authors will consider the including the points below.
The one area that I suggest more of is a discussion of the age results with Lilien et al., 2021. While Lilien et al., 2021 is mentioned in multiple places, it is not clear how this age scale differs. Lilien et al. suggested that a 1.5Ma age, rather than a 1.1Ma age, is likely to be reached, but I think this is not so much a difference in the depth-age relationship as in the definition of "interpretable ice", with this paper using a value of 20 ka/m while Lilien et al. find 14 ka/m. It is a bit difficult for people outside of Beyond EPICA to keep the differences straight, so providing discussions and summaries of the differences more clearly is quite helpful.
A few other minor comments:
- The discussion of ice fabric is appreciated and not including ice fabric in your model is understandable. However, it seems like the effects of fabric could be parameterized through constraints on the shape of the velocity, i.e. the p value. This is obviously future work, but I think considerable progress could be made without trying to model fabric evolution.
- The last sentence of the abstract is frustrating. Why end on such a sour note? Can you finish instead with a concluding note about the progress you have made?

Citation: https://doi.org/10.5194/egusphere-2024-1650-RC2
- AC2: 'Reply on RC2', Ailsa Chung, 14 Mar 2025
  
  We would like to thank the reviewer for the helpful comments. We attatch our responses to their comments.
  
  Citation: https://doi.org/10.5194/egusphere-2024-1650-AC2

Peer review completion

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

ED: Reconsider after major revisions (further review by editor and referees) (06 Apr 2025) by Lei Geng

AR by Ailsa Chung on behalf of the Authors (18 Apr 2025) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (25 Apr 2025) by Lei Geng

RR by Anonymous Referee #3 (28 May 2025)

Suggestions for revision or reasons for rejection

This paper presents a 2.5D inverse ice flow model to reconstruct age–depth profiles along the Dome C (DC) to Little Dome C (LDC) flow line in Antarctica, addressing limitations of conventional 1D models by incorporating horizontal ice flow dynamics. The model integrates radar-derived internal reflecting horizons (IRHs) and surface velocity data to constrain ice particle trajectories and basal conditions. Key findings include the identification of a 200–250 m thick basal layer at LDC, likely composed of stagnant, accreted, or disturbed ice, and an estimated maximum ice age of 1.12 million years (Ma) with an age resolution of 20 kyr m⁻¹. The model highlights the significance of horizontal advection, even in low-flow regions, and provides critical insights for the Beyond EPICA project’s ice core drilling efforts.The 2.5D approach represents a significant improvement over traditional 1D models by accounting for lateral ice flow divergence and vertical strain，Although it's hard to say that this model is new. This enables more accurate age–depth predictions, particularly in regions with subtle horizontal dynamics.The identification of a thick basal layer at LDC offers a plausible explanation for ice sheet behavior, including potential stagnant ice or basal melt. This aligns with previous studies while introducing new hypotheses about ice accretion or debris entrainment.The framework is adaptable to other Antarctic regions with sufficient radar and velocity data, enhancing its utility for broader ice core projects.Thus，I believe that this paper is worthy of publication after addressing some of the concerns below.
Major concerns
The model assumes steady-state flow conditions and static flow line geometry over 1.5 Ma, which may oversimplify glacial dynamics. Paleoclimatic shifts or ice sheet reorganization could alter flow patterns, introducing age uncertainties.Perhaps, a three-dimensional coupled thermomechanical ice flow model (such as Elmer/Ice) could more realistically simulate the ice flow conditions in the flux tube area. Moreover,Radar IRHs were mapped to the flow line with deviations up to 1.9 km, potentially introducing local artifacts. Shallow isochrones (<1000 m) were excluded due to radar resolution trade-offs, limiting constraints on accumulation rates. Surface velocity uncertainties persist due to low ice flow rates (~mm/yr), comparable to tectonic movements, necessitating some detailed discussion.
Minor Concerns:
In Section 2. Methods, it would be preferable to provide formulas or definitions related to the steady accumulation rate, Lliboutry velocity profile parameter p, and mechanical ice thickness Hm. Otherwise, readers may find it challenging to comprehend the relationships between these parameters.
Line 85: The explanation of how variations in parameter p affect simulation results appears somewhat vague. It would be beneficial to either present a parameterized sensitivity analysis or cite relevant references to support this discussions
Section 4.1 "Model limitations" (starting at line 220) should consider addressing the influence of bedrock uplift or subsidence caused by tectonic movements on ice thickness evolution. Assuming the basal ice indeed has an age of 1.2 million years, over such prolonged timescales, the bedrock elevation would typically have undergone complex vertical changes. These tectonic adjustments would likely exert non-negligible impacts on ice dynamics and thinning processes.
Other minor comments:
Line 8: While the study claims this is a new model, it appears to combine elements from Waddington et al. (2007) and F. Parrenin (2007; or 2011;2017). To substantiate its novelty, please provide specific technical details differentiating this model from previous methods, particularly in terms of equations, boundary conditions, or validation methods.
Line 12: The statement regarding "age density of 20 kyr m−1" requires clarification. Please specify whether this metric applies to the entire ice column or specifically to basal ice layers. Additionally, provide a brief technical definition of "age density" for readers unfamiliar with this particular terminology.
Line 14: The interpretation of ice composition ("stagnant ice, accreted ice or disturbed ice containing debris") appears speculative. We recommend either (a) presenting quantitative evidence from particle trajectory modeling to support these hypotheses, or (b) tempering the language to more explicitly acknowledge the interpretive nature of these conclusions.
Lines 33-40: The basal unit description contains ambiguous terminology. ·
Whether the radar signature describes a stagnant ice layer with particular englacial characteristics? Or, the interpretation refers specifically to melt-refreeze processes as described by Bell et al. (2011),in which those radar imaging differ from/directly support previous interpretations of basal ice.
Lines 101-102: It could be missing key references for the EDC ice core chronology. Please add citation.
Lines 126-133: The ice flow velocity description lacks critical details. ·
Figure 1 should ideally include a schematic diagram indicating the specific location of LDC within the East Antarctic Ice Sheet. Unless readers are highly familiar with this region, it would be difficult for general audiences to easily discern its geographical position and spatial relationship relative to deep ice core sites such as Dome C and Vostok.

References::
Parrenin, F. and Hindmarsh, R.: Influence of a non-uniform velocity field on isochrone geometry along a steady flowline of an ice sheet, Journal of Glaciology, 53, 612–622, https://doi.org/10.3189/002214307784409298, 2007.
Parrenin, F., Cavitte, M. G., Blankenship, D. D., Chappellaz, J., Fischer, H., Gagliardini, O., Masson-Delmotte, V., Passalacqua, O., Ritz, C., Roberts, J., Siegert, M. J., and Young, D. A.: Is there 1.5-million-year-old ice near Dome C, Antarctica?, Cryosphere, 11, 2427–2437,
https://doi.org/10.5194/tc-11-2427-2017, 2017.
Waddington, E. D., Neumann, T. A., Koutnik, M. R., Marshall, H.-P., and Morse, D. L.: Inference of accumulation-rate patterns from deep layers in glaciers and ice sheets, Journal of Glaciology, 53, 694–712, https://doi.org/10.3189/002214307784409351, 2007

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RR by Anonymous Referee #4 (29 May 2025)

ED: Publish subject to minor revisions (review by editor) (30 May 2025) by Lei Geng

AR by Ailsa Chung on behalf of the Authors (11 Jun 2025) Author's response Author's tracked changes Manuscript

ED: Publish as is (16 Jun 2025) by Lei Geng

AR by Ailsa Chung on behalf of the Authors (17 Jun 2025) Author's response Manuscript

Journal article(s) based on this preprint

01 Oct 2025

Age, thinning and spatial origin of the Beyond EPICA ice from a 2.5D ice flow model

Ailsa Chung, Frédéric Parrenin, Robert Mulvaney, Luca Vittuari, Massimo Frezzotti, Antonio Zanutta, David A. Lilien, Marie G. P. Cavitte, and Olaf Eisen

The Cryosphere, 19, 4125–4140, https://doi.org/10.5194/tc-19-4125-2025,https://doi.org/10.5194/tc-19-4125-2025, 2025

Short summary

Ailsa Chung, Frédéric Parrenin, Robert Mulvaney, Luca Vittuari, Massimo Frezzotti, Antonio Zanutta, David A. Lilien, Marie G. P. Cavitte, and Olaf Eisen

Supplement

https://doi.org/10.5194/egusphere-2024-1650-supplement

Ailsa Chung, Frédéric Parrenin, Robert Mulvaney, Luca Vittuari, Massimo Frezzotti, Antonio Zanutta, David A. Lilien, Marie G. P. Cavitte, and Olaf Eisen

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We applied an ice flow model to a flow line from the summit of Dome C to the Beyond EPICA ice core drill site on Little Dome C in Antarctica. Results show that the oldest ice at the drill site may be 1.12 Ma (at age density of 20 kyr/m) and originate from around 15 km upstream. We also discuss the nature of the 200–250 m thick basal layer which could be composed of accreted ice, stagnant ice, or even disturbed ice containing debris.


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