Feedback mechanisms controlling Antarctic glacial cycle dynamics simulated with a coupled ice sheet&ndash;solid Earth model

Albrecht, Torsten; Bagge, Meike; Klemann, Volker

doi:https://doi.org/10.5194/egusphere-2023-2990

Preprints

https://doi.org/10.5194/egusphere-2023-2990

Preprints

21 Dec 2023

| 21 Dec 2023

Feedback mechanisms controlling Antarctic glacial cycle dynamics simulated with a coupled ice sheet–solid Earth model

Torsten Albrecht, Meike Bagge, and Volker Klemann

Abstract. The dynamics of the ice sheets on glacial-interglacial time scales are highly controlled by interactions with the solid Earth, i.e., glacial isostatic adjustment (GIA). Particularly at marine ice sheets, competing feedback mechanisms govern the migration of the ice sheet's grounding line and hence the ice sheet stability. In this study, we run coupled ice sheet–solid Earth simulations over the last two glacial cycles. For the ice sheet dynamics we apply the Parallel Ice Sheet Model PISM and for the load response of the solid Earth we use the three-dimensional viscoelastic Earth model VILMA, which, in addition, considers the gravitationally consistent redistribution of water (the sea level equation). We decided on an offline coupling between the two model components. By convergence of trajectories of the Antarctic Ice Sheet deglaciation we determine optimal coupling time step and spatial resolution and compare patterns of inferred relative sea level change since the Last Glacial Maximum with the results from previous studies. With our coupling setup we evaluate the relevance of feedback mechanisms for the glaciation and deglaciation phases in Antarctica considering different 3D Earth structures resulting in a range of load-response time scales. For rather long time scales, in a glacial climate associated with far-field sea level low stand, we find grounding line advance up to the edge of the continental shelf mainly in West Antarctica, dominated by a self-amplifying GIA feedback, which we call the `forebulge feedback'. For the much shorter time scale of deglaciation, dominated by the Marine Ice Sheet Instability, our simulations suggest that the stabilizing GIA feedback can significantly slow-down grounding line retreat in the Ross sector, which is dominated by a very weak Earth structure (i.e. low mantle viscosity and thin lithosphere). This delaying effect prevents a Holocene grounding line retreat beyond its present-day location, which is discussed in the scientific community, supported by observational evidence at the Siple Coast and by previous model simulations. The described coupled framework, PISM-VILMA, allows for defining restart states to run multiple sensitivity simulations from. It can be easily implemented in Earth System Models (ESMs) and provides the tools to gain a better understanding of ice sheet stability on glacial time scales as well as in a warmer future climate.

Received: 12 Dec 2023 – Discussion started: 21 Dec 2023

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Journal article(s) based on this preprint

19 Sep 2024

Feedback mechanisms controlling Antarctic glacial-cycle dynamics simulated with a coupled ice sheet–solid Earth model

Torsten Albrecht, Meike Bagge, and Volker Klemann

The Cryosphere, 18, 4233–4255, https://doi.org/10.5194/tc-18-4233-2024,https://doi.org/10.5194/tc-18-4233-2024, 2024

Short summary

Torsten Albrecht, Meike Bagge, and Volker Klemann

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2023-2990', Matt King, 28 Feb 2024

The authors present an important development in coupling of a 3D GIA code with the PISM ice sheet model. They focus on the period LGM to present although the model is run for >200ka before present. The authors in particular investigate dynamics of ice sheet retreat and advance in the context of evolving sea level and bedrock, noting the existence of a 'forebulge feedback'.
The paper is well written and an important advance on previous work. I expect the paper to be influential in future developments and research that couple GIA to ice sheets or indeed to a full coupled climate model. THere is a wealth of well presented figures and the datasets are promised at final acceptance and the codes are available including the coupling codes.
I have two concerns with the paper, although I think adding some modest text and discussion would be sufficient for now
1. the authors explore mantle viscosities only down to about 10^19 Pa s whereas geodetic and seismic based studies have indicated viscosities for the upper mantle of as low as 10^18 Pa s in the Amundsen Sea and northern Antarctic Peninsula (Barletta et al. 2018; Nield et al 2014). Are the authors arguing implicitly these are transient viscosities and hence higher steady state? Or something else? Regardless, some discussion is required as 1-2 orders of magnitude change in viscosity could have a big impact on the results especially with the very low thicknesses of the elastic lithosphere in these regions. would you speculate what those differences would be? Much larger forebulges much closer to the ice load I guess - but what would that do?
2. building on this, presumably the time step and the horizontal resolution findings are a function of minimum viscosity.
3. the viscosity model adopted by the authors indicates low viscosity mantle in the Siple Coast region. Nield et al 2016 suggested that the upper-most mantle in this region was >10^20 Pa s. I think some discussion is required on this point.
minor remarks
L38 the phrase from the semicolon doesn't make sense to me and i think requires a full sentence
L59 I think it appropriate to reference Gomez here also
L71 this paragraph - I think the work of Coulon et al JGR 2021 is appropriate to mention here since they had lateral-varying version of ELRA
L127 ice->Ice
L190 lacks->lags
L215 the part in brackets is not sufficiently clear to reproduce this.
FIgure 6 it would be good to have 2 further panels focused on just the last 1ka or so.
Late Holocene readvance. THis is an interesting topic of present interest. I personally would like to see present-day RSL or VLM in a figure in supplementary material but I leave that to you. I am wondering if in East Antarctica coastline we have present-day uplift or subsidence in the model (see King et al. 2022 - but it is self-indulgent and not essential)?
L300 the text says that 3dmin is described in Fig 8a,d but those are ref-max.
L395 could not the interior subsidence is consistent with increase holocene accumulation as per other studies
L417 more->steeper
L419 *the* literature
L422 *The* largest...
FIgure 11. could you add the present-day GL location please?
Matt King Feb 28 2024
Fig S1a - it is not clear what the data are 'relative' to
'mio.' abbreviation is used throughout (and in Fig S2) but is not an English abbreviation
reference
Nield et al 2016 https://academic.oup.com/gji/article/205/1/1/2594800
King et al 2022 https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2021GL097232

Citation: https://doi.org/10.5194/egusphere-2023-2990-RC1
- AC1: 'Reply on RC1', Torsten Albrecht, 14 May 2024
  
  Reply to RC1: Matt King, 28 Feb 2024
  Citation: https://doi.org/10.5194/egusphere-2023-2990-RC1
  The authors present an important development in coupling of a 3D GIA code with the PISM ice sheet model. They focus on the period LGM to present although the model is run for >200ka before present. The authors in particular investigate dynamics of ice sheet retreat and advance in the context of evolving sea level and bedrock, noting the existence of a 'forebulge feedback'.
  The paper is well written and an important advance on previous work. I expect the paper to be influential in future developments and research that couple GIA to ice sheets or indeed to a full coupled climate model. There is a wealth of well presented figures and the datasets are promised at final acceptance and the codes are available including the coupling codes.
  I have two concerns with the paper, although I think adding some modest text and discussion would be sufficient for now
  We feel delighted by the positive evaluation of our study by the first reviewer and will try to address all raised points in detail (in bold black font).
  1. the authors explore mantle viscosities only down to about 10^19 Pa s whereas geodetic and seismic based studies have indicated viscosities for the upper mantle of as low as 10^18 Pa s in the Amundsen Sea and northern Antarctic Peninsula (Barletta et al. 2018; Nield et al 2014). Are the authors arguing implicitly these are transient viscosities and hence higher steady state? Or something else? Regardless, some discussion is required as 1-2 orders of magnitude change in viscosity could have a big impact on the results especially with the very low thicknesses of the elastic lithosphere in these regions. Would you speculate what those differences would be? Much larger forebulges much closer to the ice load I guess - but what would that do?
  
  2. building on this, presumably the time step and the horizontal resolution findings are a function of minimum viscosity.
  (Response ot 1 and 2): There is evidence for geodetically inferred viscosity values down to 10¹⁸ Pa s in the Amundsen Sea and northern Antarctic Peninsula (Barletta et al. 2018; Nield et al 2014), but it is under debate, if these extreme low viscosities reflect a transient response of the viscoelastic material or a steady state response allowing an efficient material transport in the mantle (Ivins et al. 2020, 2021). According to our whole-Antarctica investigation we keep a lower limit of 10¹⁹ Pa s to keep integration time manageable and also in view of the millennial time scale of the glacial cycle.
  
  3. the viscosity model adopted by the authors indicates low viscosity mantle in the Siple Coast region. Nield et al 2016 suggested that the upper-most mantle in this region was >10^20 Pa s. I think some discussion is required on this point.
  We base our study on the considered a priori 3D viscosity structure, where we did not consider readjustment due to other geodetic inferences. Furthermore, we discuss feedback mechanisms with the Antarctic Ice Sheet and do not aim on specific regional aspects. We agree with the reviewer that the Siple Coast region would be a key region to investigate in regional studies, as done recently in Lowry et al., 2024
  
  minor remarks
  L38 the phrase from the semicolon doesn't make sense to me and i think requires a full sentence
  We will start with 'This gravitational-rotational-deformational (GRD) correction is usually considered as being part of GIA.' in the revised manuscript.
  
  L59 I think it appropriate to reference Gomez here also
  Added Gomez et al., 2010.
  
  L71 this paragraph - I think the work of Coulon et al JGR 2021 is appropriate to mention here since they had lateral-varying version of ELRA
  We assume the referee is referring to Coulon et al., 2021 for a version of ELRA with basically two different relaxation times (and flexural rigidities) for WAIS and EAIS. We will add this reference with a statement on 'The local response time can be also varied laterally’ after L75. We removed the citation of Coulon et al., 2021 in L87 with respect to SGVEM models. We also added a reference to the nice overview of GIA models given in Table 1 in Swierczek-Jereczek et al., [preprint] in L72.
  
  L127 ice->Ice
  Of course
  
  L190 lacks->lags
  Of course
  
  L215 the part in brackets is not sufficiently clear to reproduce this.
  In fact there is no smoothing applied, we will omit this in the revised text. The ice sheet reconstruction ICE6G_C covers the last glacial cycle ranging from 122-0 kyr BP, subdivided into 100 steps. We prepend the same time series, where the timestep is set back by 124 kyr (246-124 kyr BP). Then the combined 246 kyr timeseries is linearly interpolated to have equidistant time steps of 0.1 kyr, which agrees with the coupling time step. We will add this to the revised manuscript: ‘... ICE-6G_C reconstruction (available for the last 122 kyr, repeated for the penultimate glacial cycle with a time shift by 124 kyr and concatenated at the Last Interglacial) similar to Han et al. (2022).’
  
  FIgure 6 it would be good to have 2 further panels focused on just the last 1ka or so.
  That is certainly a highly interesting period. We are working on a follow-on PISM-VILMA study on the historical period with comparison to satellite era GNSS data., But as our focus here is not an in-depth discussion of a Late Holocene readvance (King et al. 2022) or more common era dynamics, we do not want to overemphasize such dynamics, which cannot be completely represented in the current set-up.
  
  Late Holocene readvance. This is an interesting topic of present interest. I personally would like to see present-day RSL or VLM in a figure in supplementary material but I leave that to you. I am wondering if in East Antarctica coastline we have present-day uplift or subsidence in the model (see King et al. 2022 - but it is self-indulgent and not essential)?
  As discussed above, we would like to leave this analysis to a follow-on study.
  
  L300 the text says that 3dmin is described in Fig 8a,d but those are ref-max.
  The 3dmin and 3dref cases are very similar in LGM extent, we will mention this comparison by referring to Figs. 8. a,d and b, e in the revised manuscript.
  
  L395 could not the interior subsidence is consistent with increase holocene accumulation as per other studies
  As we use the WDC ice core temperature reconstruction for the last 67 kyr of climatic forcing (cf. Albrecht et al., 2020a), also for the scaling of the precipitation in EAIS, we can assume slightly more precipitation during the mid-Holocene than for present-day, but significantly less precipitation during LGM. Since the LGM we see a clear sign of interior bedrock uplift (RSL decrease) in our results. As the focus of this study is on deglaciation, as well as on glacial build-up, we have not discussed Holocene aspects in more detail.
  
  L417 more->steeper
  Agree.
  
  L419 *the* literature
  Agree.
  
  L422 *The* largest...
  Agree, we apologize, as non native speakers tend to use not enough articles.
  
  FIgure 11. could you add the present-day GL location please?
  In this transect, the present-day grounding line location is located far in the interior at around 1200 km distance from the edge of the continental shelf and therefore outside of the original frame. Here, we plotted a larger frame with the grey dashed lines delineating the present-day (observed) shape (see Fig. AC1). Accordingly we will replace the figure and adjust the figure caption in the revised manuscript.
  
  Fig. AC1: Analogous to Fig. 11b in manuscript, but with larger frame. In dark grey the present-day observed ice sheet and (initial) bedrock elevation.
  
  Fig S1a - it is not clear what the data are 'relative' to
  The data is relative to the present-day observation from Bedmap2 (Fretwell et al., 2013), i.e. 57.7 m SLE.
  
  'mio.' abbreviation is used throughout (and in Fig S2) but is not an English abbreviation
  This is used as German abbreviation, we will use ‘million’ (or 10⁶) instead throughout the revised text and figure labels.
  
  References:
  Nield et al 2016 https://academic.oup.com/gji/article/205/1/1/2594800
  King et al 2022 https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2021GL097232
  
  References, which were not already listed in the original manuscript:
  Ivins et al. 2020 https://doi.org/10.1088/1361-6633/aba346
  Ivins et al. 2021 https://doi.org/10.1093/gji/ggab452
  Lowry et al., 2024 https://doi.org/10.1038/s41467-024-47369-3
  Nield et al 2014 https://doi.org/10.1016/j.epsl.2014.04.019
  Swierczek-Jereczek et al. [preprint] https://doi.org/10.5194/egusphere-2023-2869
  
  Citation: https://doi.org/10.5194/egusphere-2023-2990-AC1
RC2:
'Comment on egusphere-2023-2990', Holly Han, 29 Feb 2024

Growth or retreat of grounded ice sheets barystatically contributes to global sea level by exchanging mass between cryosphere and hydrosphere. In addition, it changes local relative sea level by causing deformation of the solid Earth and perturbing the Earth’s gravitational field and rotation vectors, imprinting spatially varying sea-level changes.
In a little over the past decade, numerous modeling studies have shown the presence and significant impact of the feedback mechanisms between ice sheets, sea level and the solid Earth on ice-sheet modeling, highlighting the importance of coupled ice sheet – solid Earth/sea level modeling, particularly for the marine-based West Antarctic Ice Sheet (WAIS), which is situated upon reverse-sloped bedrock and under threat by MICI, and thus its stability is closely linked to the ocean depth at the grounding line and configuration of bed topography underneath. Moreover, the structure of the Earth across Antarctica is laterally heterogenous; it is characterized by thinner lithosphere and lower mantle viscosity in West Antarctica (WA), which causes faster viscous response of the solid Earth to ice loading/unloading, requiring a rather short coupling interval between the ice sheet model and solid Earth/sea-level model. Thus, capturing the interactions between ice sheets, solid Earth and sea level, as well as considering the 3D structure of the Earth and having a “short” coupling interval in the coupled modeling are warranted for accurate modeling of the Antarctic Ice Sheet.
In their paper, Albrecht and colleagues develop a newly coupled ice sheet-solid Earth/sea level model using the PISM and VILMA, which are a published ice-sheet model and viscoelastic solid Earth model, respectively. They explore Antarctic Ice Sheet dynamics over the last two glacial cycles in simulation experiments with varying Earth structure profiles, number of topographic corrections for the initial topography, coupling interval, and spatial resolution of the solid Earth model. They find a combination of these parameters according to the convergence of the AIS volume configuration and explore sensitivity of AIS to different 3D Earth Structure profiles. In addition to observing the negative sea-level feedback mechanism on grounding line retreat that has been seen by other modeling groups, the authors also observe what they call the “forebulge feedback”, which helps the grounding line to advance by reducing the local ocean depth during the glacial buildup phase. The authors also explore and confirm the effect of far-field sea-level forcing from melting of the Northern Hemispheric Ice Sheet during the last deglaciation on the AIS dynamics, which has been previously verified by other studies.
The model development, simulation experiments and analysis done in this manuscript represent lots of hard work by the authors, and undoubtingly an important contribution to the ice sheet and GIA community. It is great to see independent groups around the world building the capability of modeling coupled ice sheet - solid Earth/sea level dynamics; together which will push for better representation of ice-sheet physics and better prediction of future sea level. While I support this topic material is suitable for publication in the journal The Cryosphere, I anticipate major revision needs to be done regarding several aspects including more thorough literature review and correct citation, more exhaustive discussion on outcomes and justifications on experimental choices, which might incur additional simulations.

Citation: https://doi.org/10.5194/egusphere-2023-2990-RC2
- AC2: 'Reply on RC2', Torsten Albrecht, 14 May 2024
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-2990/egusphere-2023-2990-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2023-2990-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2023-2990', Matt King, 28 Feb 2024

The authors present an important development in coupling of a 3D GIA code with the PISM ice sheet model. They focus on the period LGM to present although the model is run for >200ka before present. The authors in particular investigate dynamics of ice sheet retreat and advance in the context of evolving sea level and bedrock, noting the existence of a 'forebulge feedback'.
The paper is well written and an important advance on previous work. I expect the paper to be influential in future developments and research that couple GIA to ice sheets or indeed to a full coupled climate model. THere is a wealth of well presented figures and the datasets are promised at final acceptance and the codes are available including the coupling codes.
I have two concerns with the paper, although I think adding some modest text and discussion would be sufficient for now
1. the authors explore mantle viscosities only down to about 10^19 Pa s whereas geodetic and seismic based studies have indicated viscosities for the upper mantle of as low as 10^18 Pa s in the Amundsen Sea and northern Antarctic Peninsula (Barletta et al. 2018; Nield et al 2014). Are the authors arguing implicitly these are transient viscosities and hence higher steady state? Or something else? Regardless, some discussion is required as 1-2 orders of magnitude change in viscosity could have a big impact on the results especially with the very low thicknesses of the elastic lithosphere in these regions. would you speculate what those differences would be? Much larger forebulges much closer to the ice load I guess - but what would that do?
2. building on this, presumably the time step and the horizontal resolution findings are a function of minimum viscosity.
3. the viscosity model adopted by the authors indicates low viscosity mantle in the Siple Coast region. Nield et al 2016 suggested that the upper-most mantle in this region was >10^20 Pa s. I think some discussion is required on this point.
minor remarks
L38 the phrase from the semicolon doesn't make sense to me and i think requires a full sentence
L59 I think it appropriate to reference Gomez here also
L71 this paragraph - I think the work of Coulon et al JGR 2021 is appropriate to mention here since they had lateral-varying version of ELRA
L127 ice->Ice
L190 lacks->lags
L215 the part in brackets is not sufficiently clear to reproduce this.
FIgure 6 it would be good to have 2 further panels focused on just the last 1ka or so.
Late Holocene readvance. THis is an interesting topic of present interest. I personally would like to see present-day RSL or VLM in a figure in supplementary material but I leave that to you. I am wondering if in East Antarctica coastline we have present-day uplift or subsidence in the model (see King et al. 2022 - but it is self-indulgent and not essential)?
L300 the text says that 3dmin is described in Fig 8a,d but those are ref-max.
L395 could not the interior subsidence is consistent with increase holocene accumulation as per other studies
L417 more->steeper
L419 *the* literature
L422 *The* largest...
FIgure 11. could you add the present-day GL location please?
Matt King Feb 28 2024
Fig S1a - it is not clear what the data are 'relative' to
'mio.' abbreviation is used throughout (and in Fig S2) but is not an English abbreviation
reference
Nield et al 2016 https://academic.oup.com/gji/article/205/1/1/2594800
King et al 2022 https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2021GL097232

Citation: https://doi.org/10.5194/egusphere-2023-2990-RC1
- AC1: 'Reply on RC1', Torsten Albrecht, 14 May 2024
  
  Reply to RC1: Matt King, 28 Feb 2024
  Citation: https://doi.org/10.5194/egusphere-2023-2990-RC1
  The authors present an important development in coupling of a 3D GIA code with the PISM ice sheet model. They focus on the period LGM to present although the model is run for >200ka before present. The authors in particular investigate dynamics of ice sheet retreat and advance in the context of evolving sea level and bedrock, noting the existence of a 'forebulge feedback'.
  The paper is well written and an important advance on previous work. I expect the paper to be influential in future developments and research that couple GIA to ice sheets or indeed to a full coupled climate model. There is a wealth of well presented figures and the datasets are promised at final acceptance and the codes are available including the coupling codes.
  I have two concerns with the paper, although I think adding some modest text and discussion would be sufficient for now
  We feel delighted by the positive evaluation of our study by the first reviewer and will try to address all raised points in detail (in bold black font).
  1. the authors explore mantle viscosities only down to about 10^19 Pa s whereas geodetic and seismic based studies have indicated viscosities for the upper mantle of as low as 10^18 Pa s in the Amundsen Sea and northern Antarctic Peninsula (Barletta et al. 2018; Nield et al 2014). Are the authors arguing implicitly these are transient viscosities and hence higher steady state? Or something else? Regardless, some discussion is required as 1-2 orders of magnitude change in viscosity could have a big impact on the results especially with the very low thicknesses of the elastic lithosphere in these regions. Would you speculate what those differences would be? Much larger forebulges much closer to the ice load I guess - but what would that do?
  
  2. building on this, presumably the time step and the horizontal resolution findings are a function of minimum viscosity.
  (Response ot 1 and 2): There is evidence for geodetically inferred viscosity values down to 10¹⁸ Pa s in the Amundsen Sea and northern Antarctic Peninsula (Barletta et al. 2018; Nield et al 2014), but it is under debate, if these extreme low viscosities reflect a transient response of the viscoelastic material or a steady state response allowing an efficient material transport in the mantle (Ivins et al. 2020, 2021). According to our whole-Antarctica investigation we keep a lower limit of 10¹⁹ Pa s to keep integration time manageable and also in view of the millennial time scale of the glacial cycle.
  
  3. the viscosity model adopted by the authors indicates low viscosity mantle in the Siple Coast region. Nield et al 2016 suggested that the upper-most mantle in this region was >10^20 Pa s. I think some discussion is required on this point.
  We base our study on the considered a priori 3D viscosity structure, where we did not consider readjustment due to other geodetic inferences. Furthermore, we discuss feedback mechanisms with the Antarctic Ice Sheet and do not aim on specific regional aspects. We agree with the reviewer that the Siple Coast region would be a key region to investigate in regional studies, as done recently in Lowry et al., 2024
  
  minor remarks
  L38 the phrase from the semicolon doesn't make sense to me and i think requires a full sentence
  We will start with 'This gravitational-rotational-deformational (GRD) correction is usually considered as being part of GIA.' in the revised manuscript.
  
  L59 I think it appropriate to reference Gomez here also
  Added Gomez et al., 2010.
  
  L71 this paragraph - I think the work of Coulon et al JGR 2021 is appropriate to mention here since they had lateral-varying version of ELRA
  We assume the referee is referring to Coulon et al., 2021 for a version of ELRA with basically two different relaxation times (and flexural rigidities) for WAIS and EAIS. We will add this reference with a statement on 'The local response time can be also varied laterally’ after L75. We removed the citation of Coulon et al., 2021 in L87 with respect to SGVEM models. We also added a reference to the nice overview of GIA models given in Table 1 in Swierczek-Jereczek et al., [preprint] in L72.
  
  L127 ice->Ice
  Of course
  
  L190 lacks->lags
  Of course
  
  L215 the part in brackets is not sufficiently clear to reproduce this.
  In fact there is no smoothing applied, we will omit this in the revised text. The ice sheet reconstruction ICE6G_C covers the last glacial cycle ranging from 122-0 kyr BP, subdivided into 100 steps. We prepend the same time series, where the timestep is set back by 124 kyr (246-124 kyr BP). Then the combined 246 kyr timeseries is linearly interpolated to have equidistant time steps of 0.1 kyr, which agrees with the coupling time step. We will add this to the revised manuscript: ‘... ICE-6G_C reconstruction (available for the last 122 kyr, repeated for the penultimate glacial cycle with a time shift by 124 kyr and concatenated at the Last Interglacial) similar to Han et al. (2022).’
  
  FIgure 6 it would be good to have 2 further panels focused on just the last 1ka or so.
  That is certainly a highly interesting period. We are working on a follow-on PISM-VILMA study on the historical period with comparison to satellite era GNSS data., But as our focus here is not an in-depth discussion of a Late Holocene readvance (King et al. 2022) or more common era dynamics, we do not want to overemphasize such dynamics, which cannot be completely represented in the current set-up.
  
  Late Holocene readvance. This is an interesting topic of present interest. I personally would like to see present-day RSL or VLM in a figure in supplementary material but I leave that to you. I am wondering if in East Antarctica coastline we have present-day uplift or subsidence in the model (see King et al. 2022 - but it is self-indulgent and not essential)?
  As discussed above, we would like to leave this analysis to a follow-on study.
  
  L300 the text says that 3dmin is described in Fig 8a,d but those are ref-max.
  The 3dmin and 3dref cases are very similar in LGM extent, we will mention this comparison by referring to Figs. 8. a,d and b, e in the revised manuscript.
  
  L395 could not the interior subsidence is consistent with increase holocene accumulation as per other studies
  As we use the WDC ice core temperature reconstruction for the last 67 kyr of climatic forcing (cf. Albrecht et al., 2020a), also for the scaling of the precipitation in EAIS, we can assume slightly more precipitation during the mid-Holocene than for present-day, but significantly less precipitation during LGM. Since the LGM we see a clear sign of interior bedrock uplift (RSL decrease) in our results. As the focus of this study is on deglaciation, as well as on glacial build-up, we have not discussed Holocene aspects in more detail.
  
  L417 more->steeper
  Agree.
  
  L419 *the* literature
  Agree.
  
  L422 *The* largest...
  Agree, we apologize, as non native speakers tend to use not enough articles.
  
  FIgure 11. could you add the present-day GL location please?
  In this transect, the present-day grounding line location is located far in the interior at around 1200 km distance from the edge of the continental shelf and therefore outside of the original frame. Here, we plotted a larger frame with the grey dashed lines delineating the present-day (observed) shape (see Fig. AC1). Accordingly we will replace the figure and adjust the figure caption in the revised manuscript.
  
  Fig. AC1: Analogous to Fig. 11b in manuscript, but with larger frame. In dark grey the present-day observed ice sheet and (initial) bedrock elevation.
  
  Fig S1a - it is not clear what the data are 'relative' to
  The data is relative to the present-day observation from Bedmap2 (Fretwell et al., 2013), i.e. 57.7 m SLE.
  
  'mio.' abbreviation is used throughout (and in Fig S2) but is not an English abbreviation
  This is used as German abbreviation, we will use ‘million’ (or 10⁶) instead throughout the revised text and figure labels.
  
  References:
  Nield et al 2016 https://academic.oup.com/gji/article/205/1/1/2594800
  King et al 2022 https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2021GL097232
  
  References, which were not already listed in the original manuscript:
  Ivins et al. 2020 https://doi.org/10.1088/1361-6633/aba346
  Ivins et al. 2021 https://doi.org/10.1093/gji/ggab452
  Lowry et al., 2024 https://doi.org/10.1038/s41467-024-47369-3
  Nield et al 2014 https://doi.org/10.1016/j.epsl.2014.04.019
  Swierczek-Jereczek et al. [preprint] https://doi.org/10.5194/egusphere-2023-2869
  
  Citation: https://doi.org/10.5194/egusphere-2023-2990-AC1
RC2:
'Comment on egusphere-2023-2990', Holly Han, 29 Feb 2024

Growth or retreat of grounded ice sheets barystatically contributes to global sea level by exchanging mass between cryosphere and hydrosphere. In addition, it changes local relative sea level by causing deformation of the solid Earth and perturbing the Earth’s gravitational field and rotation vectors, imprinting spatially varying sea-level changes.
In a little over the past decade, numerous modeling studies have shown the presence and significant impact of the feedback mechanisms between ice sheets, sea level and the solid Earth on ice-sheet modeling, highlighting the importance of coupled ice sheet – solid Earth/sea level modeling, particularly for the marine-based West Antarctic Ice Sheet (WAIS), which is situated upon reverse-sloped bedrock and under threat by MICI, and thus its stability is closely linked to the ocean depth at the grounding line and configuration of bed topography underneath. Moreover, the structure of the Earth across Antarctica is laterally heterogenous; it is characterized by thinner lithosphere and lower mantle viscosity in West Antarctica (WA), which causes faster viscous response of the solid Earth to ice loading/unloading, requiring a rather short coupling interval between the ice sheet model and solid Earth/sea-level model. Thus, capturing the interactions between ice sheets, solid Earth and sea level, as well as considering the 3D structure of the Earth and having a “short” coupling interval in the coupled modeling are warranted for accurate modeling of the Antarctic Ice Sheet.
In their paper, Albrecht and colleagues develop a newly coupled ice sheet-solid Earth/sea level model using the PISM and VILMA, which are a published ice-sheet model and viscoelastic solid Earth model, respectively. They explore Antarctic Ice Sheet dynamics over the last two glacial cycles in simulation experiments with varying Earth structure profiles, number of topographic corrections for the initial topography, coupling interval, and spatial resolution of the solid Earth model. They find a combination of these parameters according to the convergence of the AIS volume configuration and explore sensitivity of AIS to different 3D Earth Structure profiles. In addition to observing the negative sea-level feedback mechanism on grounding line retreat that has been seen by other modeling groups, the authors also observe what they call the “forebulge feedback”, which helps the grounding line to advance by reducing the local ocean depth during the glacial buildup phase. The authors also explore and confirm the effect of far-field sea-level forcing from melting of the Northern Hemispheric Ice Sheet during the last deglaciation on the AIS dynamics, which has been previously verified by other studies.
The model development, simulation experiments and analysis done in this manuscript represent lots of hard work by the authors, and undoubtingly an important contribution to the ice sheet and GIA community. It is great to see independent groups around the world building the capability of modeling coupled ice sheet - solid Earth/sea level dynamics; together which will push for better representation of ice-sheet physics and better prediction of future sea level. While I support this topic material is suitable for publication in the journal The Cryosphere, I anticipate major revision needs to be done regarding several aspects including more thorough literature review and correct citation, more exhaustive discussion on outcomes and justifications on experimental choices, which might incur additional simulations.

Citation: https://doi.org/10.5194/egusphere-2023-2990-RC2
- AC2: 'Reply on RC2', Torsten Albrecht, 14 May 2024
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-2990/egusphere-2023-2990-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2023-2990-AC2

Peer review completion

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

ED: Publish subject to minor revisions (review by editor) (15 May 2024) by Alexander Robinson

AR by Torsten Albrecht on behalf of the Authors (06 Jun 2024) Author's response Author's tracked changes Manuscript

ED: Publish subject to technical corrections (05 Jul 2024) by Alexander Robinson

AR by Torsten Albrecht on behalf of the Authors (11 Jul 2024) Manuscript

Journal article(s) based on this preprint

19 Sep 2024

Feedback mechanisms controlling Antarctic glacial-cycle dynamics simulated with a coupled ice sheet–solid Earth model

Torsten Albrecht, Meike Bagge, and Volker Klemann

The Cryosphere, 18, 4233–4255, https://doi.org/10.5194/tc-18-4233-2024,https://doi.org/10.5194/tc-18-4233-2024, 2024

Short summary

Torsten Albrecht, Meike Bagge, and Volker Klemann

Supplement

https://doi.org/10.5194/egusphere-2023-2990-supplement

Video supplement

Simulation of the relative sea level change rate around Antarctica with PISM-VILMA over the last 25 kyr Torsten Albrecht https://doi.org/10.5446/65479

Torsten Albrecht, Meike Bagge, and Volker Klemann

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We performed coupled ice sheet – solid Earth simulations and discovered a positive (forebulge) feedback mechanisms for advancing grounding lines, supporting a comparably larger West Antarctic Ice Sheet at Last Glacial Maximum. During deglaciation we found the stabilizing GIA feedback to dominate grounding line retreat in the Ross Sea, where a weak Earth structure is prevalent. This may have consequences for the contemporary and future ice sheet stability and potential rates of sea level rise.


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