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