Review of "Stagnant ice and age modelling in the Dome C region, Antarctica" by Aildasa Chung et al.

 This paper examines the age of the ice interior of Dome C using a 1D ice flow model combined with radar imagery. Chapter 2 describes the 1D ice flow model based on Parrenin et al. (2017) with the incorporation of mechanical ice thickness and stagnant ice. A method for optimizing unknown parameters (precipitation, flow parameters, and mechanical ice thickness) using the ages from radar imagery are described. Chapter 3 describes a method for detecting basal units and age layers from radar images, and their correspondence to the age profile from the EDC ice core. In Chapter 4, the 1D model results are validated against the age and vertical velocity profiles of the LDC or EDC, and the correspondence between the stagnant ice distribution. The results of the 1D model regarding spatial distribution of stagnant ice are compared with radar images. Chapter 5 examines uncertainties from the ice flow model and radar datasets.

Overall, I think the paper is of sufficient quality to be accepted. Below are some questions and suggestions for minor revisions.

L43: I understand that "stagnant ice" refers to ice masses with a minimal flow. Meanwhile, I think it would be meaningful to describe a definition of "stagnant ice" in this study.

L80: Is r(t) exactly the same as in Figure 2 of Parrenin et al. (2017)? If so, I recommend citing the figure.

L83: "temporally-averaged" accumulation? And, is it averaged over the last 800,000 years?

L87; Actual basal melting should be determined thermodynamic, so I think this formulation is one assumption. Does this formulation come from a condition of no discontinuity in the vertical velocity at the observed bedrock?

L90: Name of the software?

Equation 5: What is the definition of σiso? And also, write out the term "reliability index" in the description of equation 5 as the term is used later (Figure 12 and Section 5) 

L110: Any introduction for MYIC?

Table 3: "DC-LDCRAID2", "DC_LDCRAID", "DC_LDC_DIVIDE", and "DC_PNV09B" are not mentioned in the text. Which panel in Figure 2 does these names correspond to?

L203: Total ice thickness at EDC?

L208: High melting area in the lower left of the figure may not be reliable, according to Figure 12. It may be hard to explain why there's considerable basal melting where the bedrock elevation is relatively high.

Figure 5: Where does this transect correspond (on the map)?

Figure 6: The caption in Figure 6b would be "p=3.6, and stagnant ice=0" based on sentences.

L272: Confused, because according to figure 6, the p=3 for LDC. Why does figure 8 have a more significant value of p? This may come from different radar/ApRES velocity measurement datasets. Please discuss this.

Figure 7: High precipitation areas in the upper left corner might be less reliable, according to Figure 12.

Table 4: What are the values of p and a in these modeling results?

L325 For this discussion, I think it's necessary to refer to Parrenin et al. (2007) (Equations 4-5), which discusses the relationship between basal deformation and the value of p

General Comments

Chung et al. present an interesting study investigating the age-depth profile around the oldest ice site Little Dome C and the potential future site North Patch using a 1-D model. They include the possibility of stagnant ice in the model as a free parameter to better match the observed isochronal scaffold and predict the oldest ice in the area. The presence of such a layer is suggested by radar data, especially by vertical velocity observations inferred from ApRES data. The study is well written and will make a valuable contribution to the oldest ice canon. What makes it especially appealing and exiting, is the fact that hopefully in a couple of drilling seasons the modelling assumptions and findings can be confirmed or rejected.

I do have some concerns which should be addressed before publication. None of these comments are major issues, but rather address the way in which the methods, results and uncertainties are presented.

1: A more detailed discussion of the uncertainties is in order. While the authors provide a section on modelling limitations it is rather general and does not really include quantitative statements. This especially pertains to the issue of the exponential age-depth profile close to the bedrock (or alternatively close to the stagnant ice boundary). The authors do provide a wide list of factors contributing to uncertainty but I suggest including these (and quantify where possible) more prominent in the results sections already.

2: A more detailed description of the 1d model and assumption flowing into it would be in order. I know that it has been described extensively in previous publications but a little more detail would be nice. Especially given the fact, that the 1d modelling including a stagnant ice layer is the major focus of this study. Currently, there is much more emphasis on the description of the radar systems and field seasons, which is nice but they have been discussed in the original publications. You could save some space there and in turn expand the model description/physical reasoning behind a stagnant ice layer.

3:For the reader to appreciate the advance represented in introducing a stagnant ice column H_m it would be nice to have a comparison to 1d modelling where this column is not assumed. I can see that adding a free parameter which you can optimize leads to a better fit with the traced and dated internals. However, I am missing

• a physical explanation of why there should be a stagnant ice column. I see that in section 5.3 you discuss the nature of the stagnant ice, but this is almost at the end of the paper. I suggest to introduce this in a concise manner earlier
• a quantification how this assumption improves the fit over the previous version of the 1d model.

I don’t know how expensive it is to run the previous version over the transects. You could also select a few points for a comparison. How much do we gain by assuming a stagnant ice column, how does the age profile look like, if you don’t assume it. Your current Figure 11 could be also done with no inclusion of a basal unit (either in an additional figure or included in the same figure).

Structure: there is a lot of information especially in figures with maximum age/age density etc along the radar transects. As a reader I think the central figures are figure 6 (ApRES derived velocity which motivates the assumption of stagnant ice) and figure 11 (the actual age depth profile at BELDC). Figure 6 could follow right after Figure 1 actually as it provides the physical data supporting the assumption of stagnant ice. Some streamlining of the sections would further improve accessibility.

Minor comments:

Very verbose abstract with technical details

e.g. :… here defined as the age at a maximum age density of 20 kyr m-1

What do you mean by ‘seem’? Is this uncertain due to measurement uncertainties? If not I’d suggest to drop ‘seem’

Suggest to make this the first sentence and then motivate why:

The European Beyond EPICA project aims to extract a continuous ice core of up to 1.5 Ma, with a maximum age density of 20 kyr m−1 at this site called Beyond EPICA Little Dome C (BELDC).

l27 … is whether the deepest ice lying just above the bedrock proves useful for paleoclimate reconstructions?

L30 submeter?

L31 is this published? If there is a theory behind why I suggest to quickly mention it here.

L33 what do you mean by ‘uncertain’? suggestion : interpreting these results remains challenging

L34 no continuous record?

L35 is it not called echo-free zone anymore, should it be called differently? Sorry for my ignorance, I am no radar expert.

I have the feeling the introduction could be rearranged somewhat. As of now, it jumps from topic to topic making it a bit strenuous to follow.

be caused by a backscatter power that is sufficiently far below the noise level and therefore …

L50 :

So Lilien et al. used a 1d model (different approach?) already. I would thus rephrase the subsequent sentence, simply stating that your objective is now to expand this analysis to the whole Dome C region (with a different, more robust?, method)  and not stating that this would give a better idea (this sort of diminishes Lilien et al.’s work).

Suggestion: Lilien et al. (2021) accessed the age-depth profile at the BELDIC site, inverting the optimal value of the thickness of a layer of stagnant ice, which was found to be close to the observed thickness of the basal unit. Here, we expand on their work investigating the whole Dome C region presenting (is this the first time this approach is presented? If not, use e.g. ‘employing‘ and cite) a 1D numerical model which uses inverse methods to infer a layer of stagnant ice from the isochronal information. This approach will elucidate the spatial extent of this inferred stagnant ice layer and its impact on the age profile in the region.

I assume that you don’t capture ice-dynamic behaviour in a 1d model?

Parrenin et al use the assumption of covariance between melting and surface accumulation to use a analytical expression of the thinning function and state that this only leads to an error of <6% in the thinning function. How would this error propagate in the method applied here, what does it mean for the age uncertainty? Generally, I would suggest to expand the discussion of uncertainties due to the assumptions made in this study.

L105 which were taken during the period … and informed the selection …

L113 …assuming an electromagnetic wave velocity in ice of … as in Winter et al. … [I assume this is not a universal number, but a deliberate choice]

L114-116 maybe mention here shortly why you briefly describe this.

While I appreciate the description of the different radar setups and campaigns including uncertainty assessments, I have the feeling that they are quiet extensive compared to the description of the 1d model, the assumptions flowing into it and the corresponding uncertainties. I would therefore extend the discussion of the 1d model a little (which barely covers a single page) and trim down the radar setup description (right now 4 pages!).

I recommend this especially considering that in the introduction you note that you present a 1d model. So the reader would assume the modelling is the focus here and not the field work/equipment/technical aspects which have been described in detail elsewhere.

Many of the things you list in your radar/fieldwork description could be neatly summarized in a table (number of IRHs, depths, ages, coverage, no of transects etc.). This would make it much more accessible.

Confused by the section header: Inferred ages for EDC

What you discuss here are modelled ages in closest vicinity to the EDC-site (closest point on transect)? Maybe the header should reflect this (likewise for tables 1 and 2 which say age at EDC, should prob read closest point to EDC as in Table 3). I assume this is to give an idea for the estimated age variation around EDC I was not sure what to take away from this rather compact subsection. You propose to evaluate the accuracy of the model. To me this section suggests that there are high age variations (~200 ka) around the EDC site. Or are they assumed to be uniform and thus the 200 ka variations are a measure of uncertainty of the model? Also, how do I interpret ages at 3189 m depth if the the total ice thickness at the respective locations is <3189 m (as is the case for DC_PNV09B)? Maybe I misunderstand?

Section 4.2

Here the model results for the stagnant ice column are discussed. As the assumption of a stagnant ice column is the main focus of this paper I would suggest you expand a little on that and remind the reader of the implications of the modelling/inversion/optimisation exercise. It is otherwise really easy to miss the main focus of the paper.

L204 age uncertainty for the oldest ice at dome c of pm 96 ka? Typo I assume. 9.6ka (see figure 6 Bazin et al. 2013 and supplements)?

L219 colormaps are inconsistent with the colorbars (see comments on Figure 3 below). I assume the red and blue colormaps are combined in the figure.

In 4.2 and figure 3 you discuss/show the modelled stagnant ice/melting but then you discuss the radar derived stagnant ice column. Easy for the reader to confuse modelled and observed numbers here, as figure 3 only shows modelled quantities.

L221 I suggest you mention the melt rate uncertainty here.

L234: To the naked eye panel a and b are quasi identical, maybe consider plotting the mismatch between the modelled and radar inferred H_m (observations in panel a, delta in panel b).

L235 Figure 5a shows the modelled age of a single …

L237 This is probably the strongest modelling case for a stagnant ice unit shown in the paper. It would be very nice to have a comparison for Dome C, where we have a very good age-model. What happens if you apply your 1d model including the mechanical ice thickness as an optimization parameter. Does your model suggest a stagnant layer for EDC, EDML, Dome Fuji etc.? This goes back to my general point, that a comparison to model output without the inclusion of mechanical ice thickness would very much strengthen the message of this study.

L243 maybe replace ‘described’ by ‘constrained‘ but maybe I am not completely clear what you mean here.

L244 this is a key sentence, but I am missing the underlying data. Where is the comparison between the fit with and without the option of a stagnant base layer? I am writing this as I am reading, so maybe this will pop up further below. Looking at Fig. 11 it seems to me that the fit in Lilien et al. 2021 which does not include H_m is very good already. Surely the standard deviation becomes smaller with an additional tuning parameter, but I would argue that this alone is not yet a convincing statement without a physical explanation as to why such a layer would be present.

[…]

Having looked at Figure 6 now, I guess the comparison of the ApRES and modelled velocities is the main argument for the presence of a stagnant ice layer. Maybe it makes sense to show this right at the beginning? For me it is difficult how big the difference in vertical deformation is between p=3.04 and p=3.6 is. How big is p for EDC and LDC if you use the old version of the 1d model (without optimising for H_m)? For the readers not familiar with the peculiarities of the model it is difficult to assess the significance here.

L260 in Figure 6b it looks like the vertical velocity uncertainty (top 2000m) is smaller at the EDC site and not at LDC??

Figure 6b I assume there is a mistake in the numbers for p as in the caption you mention that p=3.6 and no stagnant ice for EDC.

L262 comparing the vertical velocities at LDC and EDC at around 2000m the difference seems to be very small (maybe 0.1-0.2 m/a?). I don’t know much about ApRES derived velocity uncertainties, but this seems to be somewhat narrow margins? Again, a more expansive discussion of uncertainties and potential alternative explanations would help a lot here.

L263-264 what about less-simple explanations/alternative avenues?

Fig9. It seems there are spots where the model suggests age jumps from around 1Ma to 2 Ma basically within one radar data point (e.g. at 75.5S and 125.3E). Is this an artefact or what is leading to these drastic differences?

Fig10 how is an age density at 1.2 Ma defined so close to EDC where there is no ice which is 1.2 Ma old (I am comparing to oldest ice near EDC in table III)?

L321 would be overestimated by how much? Is it possible to give rough estimates for reasonable potential SMB increases (e.g. surmised from existing modelling pre-MPT time slices)?

L323 by how much would that few percent change in the thinning function translate into age changes?

L325 “There are a few possible explanations for this” this sentence is not necessary. Suggest to provide possible explanations right away. -> ‘this could be due to …’

L327 if sliding would occur at the boundary between stagnant ice and above is there a way to detect this in the ApRES data? I am aware that ApRES is used for vertical velocities and not horizontal and I am not a radar expert, so please forgive this somewhat naïve question. There is a publication by Summers et al., 2021 which seems to suggest the extraction of horizontal velocities from ApRES.   

L341 again, I don’t think the age uncertainty is that high for the oldest ice in the EDC ice core. See comment earlier, maybe a typo which reoccurred here.

In the supplements of Bazin et al. 2013 std is given (801.5ka pm 9.6ka).

L345 check formatting of citation.

L349 To me this seems to be a considerable limitation. How do you choose the cutoff depth where you don’t trust the exponential age-depth profile anymore? If I look ~300 m above bedrock in your figure 11 true age could be anything between ca. 700 ka and 1200 ka depending on your cutoff depth. I think this should be discussed in more depth to give an idea how you quantify your uncertainties.

L355 unclear what you mean by “seem to be well adapted”?

L415-417 this is a very interesting notion. Right now basal drag in large scale 3D modelling exercises is either formulated by heuristics or established via inversion. However, if these methods overestimate basal drag they would have to be re-tuned to match present day observations and proxy reconstructions (i.e. ice would have to deform/flow less easily). So, I am not sure whether this would necessarily lead to increased sea level rise in the future. I suggest thus to rephrase the sentence into something more cautious.  

L425 as per your paragraph further above, you don’t know at which depth you cannot trust the exponential age-depth profile anymore and therefore ice could be much younger. I suggest you include this cautionary statement again here.

L437 I suggest to drop the ‘etc.’ here.

Some suggesions for the figures:

Figure 3. I am confused by the colormaps. Panel a and d show RdBu cmaps but only uniform blue, grey and red cmaps are shown in the colorbar. I assume the red and blue are combined in the figures. Please consider merging the colorbars to avoid confusion (you can e.g. define the melt rate as negative, colorbar would go from -3 – 250 m with a zero intercept in white).

You could also consider a diverging cmap for bedrock topography which makes it easier to identify mountains and valleys, but that’s a question of taste. However, you could reduce the range for the greyscale colormap so bedrock features pop up more prominently, otherwise this is basically just a light gray background in the zoomed-in panels.

Also the contour lines are somewhat busy/distracting. Maybe use fewer or skip completely.

Figure 6. x-axis should be unitless I assume.