The total air content of the SPC14 ice core is displayed here at very high resolution over the last 54,000 years. It shows orbital (albeit on a short period) and variability and variability at millenial scale on some periods. By comparing this TAC record to records of other proxies and integrated insolation curves, the authors elaborate on the mechanisms which can explain the observed variations. Accumulation rate seems to be an important control on the variations but it also seems that the mechanism at play is not the same as in Greenland.

In general, the manuscript is well written and well illustrated. I recommend its publication after the following comments are taken into account.

• 105 : Replace « = » by « is »
• 153 : Can you explain how you estimate accurately the line temperature for the portion outside of the GC oven ?
• 154 : remove « is »
• 165 : the use of V1 and V2 are confusing since V1 was used and defined before (eq. 1, l. 105) and I am not sure that it refers to the same volume. Or is it the same volume ? Please clarify.
• Similarly, I am not sure that you refer to the same P1 and P2 than before (in equation 3, P1 and P2 were the pressures of first and second expansion).
• 175 – can you explain clearly what is the ratio of pressures ? Which pressures ?
• The confusions between notations noted above make it very difficult to properly understand the description of the analytical device and the way TAC is calculated. This part should be thoroughly rewritten.
• 195 and after – not enough information is given on the cut-bubble correction for this study. Can you explain in more details how the correction has been derived and how the micro-CT measurements have been used ? Is it possible to show the correction for the top 200 m since it appears that this correction is variable from sample to sample ?
• 206 : Did you try to have the TAC also on a gas age ?
• Also, as you compare it later with the d15N of N2, I imagine that d15N of N2 is on gas age and TAC on ice scale – what is the mechanistic link between the two if they are not on the same age scale ?
• 241 : change the « x » symbol
• 251 : explain what are standardized versions of « TAC" and « Vcr* »
• 290 : I know that it is explained in other places in the manuscript but it is important to document here the speed of the change. In particular, it is important to document the speed of the change because you mention that it is « abrupt ».
• 345 : why do you mention only the resemblance between TAC and accumulation rate and between TAC and d15N of N2 ?
  • First, you should explain on which timescale the different records are compared (the sentence « « are also highly correlated with d15N-N2 at all depth » is quite confusing – indeed, if TAC and d15N-N2 are correlated on a depth timescale, then I do not understand why TAC should be on an ice scale since d15N-N2 is on a gas timescale)
  • Second, why don’t you also mention the resemblance between TAC and d18O of ice ? I imagine that there is also a good correlation ? What would be the r2 for the correlation between TAC and d18Oice
  • Any link between millennial variations of TAC and millennial variations of dust concentration ? What would be the r2 ? Dust load can indeed also influences grain size and this influence has not been discussed in this manuscript. It is important to add a few sentences on this possible influence in a revised manuscript.
• It is really interesting that the TAC signal at SP can not be explained the same way as the TAC signal at NGRIP. However, it would be great to ellaborate a bit more and provide one figure showing the comparison between the two records and their relationship with accumulation rate so that the reader understands clearly the different relationships between TAC and accululation rate in the two sites.
• I am not sure to support the first sentence of section 3.5. Indeed, if the dependence of TAC on accumulation rate (or other influences) is not the same on different sites (+ this study does not provide a clear mechanism), we should be very cautious in using the finding on SP to better interpret « future TAC record » since the controls may be different.
• The multiple regression is a bit difficult to follow. Indeed, while we can assume that ISI and accumulation rate are largely independent, there is strong links between d189ice, d15N-N2, Dage and accumulation rate so that I do not really understand why the multiple regression is not simply done on ISI and accumulation rate (or ISI and d15N-N2) ? The choice of the multiple regression on 4 parameters, 3 of them being strongly linked should be much better explained.
• ISI and accumulation account for 14 and 15% of the multiple regression (l. 422). This is quite weak. Would these proportions be larger if the multiple regression is done only on ISI and accumulation rate ?
• The influence of the dDage/dt is discussed but does not help to identify the mechanism at play (l. 439 : « the reason dDage/dt helps explain TAC changes in the firn is not at first clear ») so why not exploring the influence of dAccu/dt or d(d15N-N2)/dt or … ? The choice of the parameters used in the multiple regression line should be much more discussed.
• 445 : The influence of ISI on TAC is not so obvious because the record is short. Is is possible that the effect of accumulation rate on TAC is inhibited because the ISI is on a minimum and thus inhibits the metamorphism mechanism leading to grain size modification ?
• The conclusion starting on l. 467 is surprising : why isn’t the influence of accumulation rate on Dage and d15N-N2 not mentionned ? How much can the influence of accumulation rate on both TAC and d15N-N2 (Dage) explain the strong link between TAC and d15N-N2 (Dage) ? I feel that some explanations are missing here so as not to give the impression of a circular reasoning.

The manuscript presents new total air content (TAC) data from south pole core SPC14. The data covers 54kyr in quite high resolution and although measured in two laboratories in consistent quality. The manuscript is well structured and well written starting out with a comprehensive introduction lining out the problems with total air content (TAC). The manuscript makes it clear that it is not solving the riddle but adding another piece to the puzzle. It is a step forward in our understanding of TAC offering some hypothesis that are however not consistent with all features seen in TAC data from the northern hemisphere. I have a few questions and suggestions below and suggest publication with minor revisions.

Minor comments:

Page 4: Given that each flask will be slightly different and the amount of ice too, the volume of the setup is changing. How are you taking this into account? 

Line 201: Clathrates close to the surface are probably opening when evacuated. A correction for this effect may be appropriate. I suggest to add a statement that the correction should probably be a constant in the clathrate zone and at most 1.9%.

Line 278: see comment to figure 4

Line 320-340: Hard to follow and some repetitions, please revise this section. A more straight forward argumentation seem to me to plot the ice sheet elevation from where the ice originates versus age. 

Line 363: delete “when”

Line 365-376: I seem to understand that low accumulation leads to denser firn therefore lower TAC. What about d15N? 

Line 377-385: If the orbital and millennial effects were the same you should also see an orbital signal in d15N. Do you?

Figure 1: Please add a depth scale to that graph so that the location of the bubble-clathrate transition can be identified.

Figure 3: Should refer to section 3.2. Please explain how the standardization is constructed, although it is explained in the referenced papers. What is the purpose of the standardization?

Figure 4: I don’t understand how the minima and maxima from the insolation and the and from TAC from linear regression can be shifted. Please explain.

The manuscript contributes to deeper understanding of the complicated nature of the variability of the total air content of polar ice by providing and interpreting the high-resolution air content record from the South Pole ice core covering the last 54 ka. The local insolation effect on TAC is confirmed for the site without a diurnal cycle in solar insolation and with an accumulation rate that is 3 times higher than at the Antarctic sites where this effect was first discovered (Dome C and Vostok), thus further promoting TAC as a useful tool for orbital dating of the ice cores. The high resolution of the obtained record made it possible to study millennial-scale variations in TAC and to relate them to changes in the snow accumulation rate. This relationship appears to be different from that earlier observed in and explained for the NGRIP ice core, even though the amplitude of the millennial variations of TAC is similar in both cores. The authors propose a rather plausible mechanism by which pore volume at the close-off can be affected by changes in accumulation through accompanying changes in grain size in the near-surface snow. I would only suggest that the authors develop the description of this mechanism a little in order to make it clearer and more consistent with what has already been published on this topic. They also attempt to explain the difference in mechanisms linking TAC to accumulation at the cold and relatively dry sites in Antarctica and at the warmer sites with higher accumulation in Greenland, and this explanation also sounds quite plausible.

In general it is a good paper, but it needs a number of minor improvements and corrections (see my comments below).

L39-40. ‘For temperature, Martiniere et al. (1992) demonstrated a spatial correlation between site temperature and pore volume at close-off, using data from late Holocene ice core samples’. 

Since this spatial correlation is mentioned for the first time in the manuscript, it is more correct here to refer to the 1979 paper by Reynaud and Lebel in which it was initially presented.

L45-48 ‘The proposed mechanism for this relationship requires that

higher local summer insolation increases the size of snow grains in the first few meters of firn, which then decreases the pore volume in these same layers as they reach bubble close-off (Raynaud et al., 1997, Arnaud, 2000).’

Replace Raynaud et al., 1997 with Raynaud et al., 2007.

2.1 Total air content measurements.

The description of the measuring technique, though it is detailed in many technical aspects, lacks important information about absolute accuracy of the TAC measurements and their reproducibility. The latter is important for evaluating the contribution of experimental uncertainties to the total variance of the experimental TAC record.

Caption for Fig 1: ‘Measurements are averaged duplicate measurements’. 

Does it mean that for each depth two parallel samples were measured and the average value is shown in the figure? If so, please provide the discrepancy between the individual measurements. If not, please explain what you meant to say.

There is no information about the mass and shape of the ice samples used (important for estimating the cut bubble effect since this effect depends on the specific surface area of the samples).

L183-186. The amount of air trapped in refrozen ice (I wouldn't call it "solubility") depends, in addition to the air pressure in the flasks, on the number and size of air bubbles formed in this ice. These values can vary considerably from one experiment to another and are difficult to predict.

L193-202 Cut bubble correction.

1. One could understand from this text that cut bubble correction depends on the number and size of the bubbles. In fact (see Saltykov, 1976; Martienerie et al., 1990) this correction depends only on the size of the bubbles (or more precisely, on the bubble-size distribution) and on the specific surface area of the sample. How did you estimate the latter? 

2. Bubbles efficiently expand during ice storage at a relatively elevated temperature (e.g. at -20 ºC), so, with other things being equal, the correction increases with the time of storage and therefore bubble measurements should be done at the same time as TAC measurements.

3. The correction for gas loss for bubble-free ice (i.e. ice containing only hydrates) is needed in the same way as it is needed for bubbly ice, because the ice sample loses its gas from cut hydrates as it does from the cut bubbles. In addition, if the temperature of storage was not low enough (say, above -40…-30 ºC) many hydrates in ice can dissociate with formation of air cavities whose size also needs to be measured.

L209-211. I understand that for each depth two samples were measured with the OSU vacuum line using the method described in section 2.1. Can you estimate the repeatability of the measurements and present it in the paper?

L214-217 It is not clear from the text how the data from OSU and PSU were combined (and averaged?). Were the PSU measurements made at the same depths with the same resolution as in the OSU? Might it be useful to show the OSU and PSU data (after correction for the offset) in figure 1 with a different color? Please explain and comment.

L245-248. About the Vcr.

1. The temperature used in eq. 12 (Ts) and the one in the ‘gas law’(Tc in eq. 11) are different temperatures. The first one refers to the time when snow was deposited at the ice sheet surface (corresponds to the age of the ice), the second one – to the time of pore closure (⁓gas age). Did you distinguish these temperatures when calculating Vcr using temperature reconstruction from Kahle et al (2021)? And if so, please explain how you did this, especially for the transient climatic conditions.

It seems something is missing in the sentence ‘For the temperature at bubble close-off (Ts), a temperature reconstruction from Kahle et al (2021)’. Also, please replace Ts with Tc in this sentence.

2. Eq. 12 shows the present-day (late Holocene) spatial relationship between pore volume at close-off and mean annual surface temperature. It is very unlikely that this relationship was the same in the past, especially during periods with different from today’s insolation. So strictly speaking one cannot use eq. 12 to calculate Vcr.

L253-256. ‘…Vcr is a quantity that essentially describes TAC in the absence of

temperature effects…’

Even if we assume that eq. 12 is valid for the past, the Vcr calculated from eq. 13 will contain a significant summer-temperature signal, because the impact of changing insolation on the Vc is transmitted through corresponding changes in summer temperature and temperature gradients that affect the snow metamorphism near the ice-sheet surface (Raynaud et al., 2007; Lipenkov et al., 2011). 

L260-261. Correct references here: Raynaud et al., 2007; Lipenkov et al., 2011; Eicher et al., 2016.

L317-319: I cannot understand this sentence.

L336-337. Please provide a reference for this hypothesis or justify it.

The need for Figure 6 doesn't seem obvious for me, but if you decide to keep it in the paper, it should come before Figure 5.

L367-369: ‘The size of the firn grains at the surface seems to predict at which density bubble close-off occurs, with larger grained firn closing off at a higher density (Gregory et al, 2014)’.

In fairness, it should be noted that the mechanism by which the porosity of firn at close-off is linked to the snow grain size at the surface was first proposed by L. Arnaud (1997). Later on his model was used to qualitatively describe a possible mechanism by which summer temperature and surface temperature gradients controlled by local insolation can influence pore volume at close-off, assuming a homogenous firn column and neglecting the sealing effect on the total amount of air trapped in ice (Raynaud et al., 2007; Lipenkov et al., 2011).

L373-374: ‘Low accumulation rates create more homogeneous, spherically shaped grains which

force more air to escape the ice core, leading to lower TAC’.

Please provide a reference for this statement or justify it using your own observations.

L374-376: ‘We propose that a mechanism of grain size and shape affecting pore volume leads to a positive correlation between accumulation and TAC, which we observe in the SPC14 ice core’.

L460-461: ‘We propose that a common mechanism, grain size metamorphism in the top few meters of the firn, can explain both orbital and millennial-scale times scale of TAC variations in the SPC14 ice core’.

Since this proposed mechanism is considered by the authors as one of the main merits of their work (along with the obtained high-resolution TAC record), I would advise them to pay a little more attention to its clear and consistent description, and correct alignment with what has already been published on this mechanism in connection with orbital variations in TAC. In the present manuscript, the entire description of this mechanism is confined to a single paragraph (L365-376) and seems neither clear nor complete.

3.5 Multiple regression

I don't see much point in multiple regression analysis involving non-independent variables that correlate with each other. The latter could be one of the reasons why the authors obtained such a weak contribution of the ISI to the total variance of TAC. 

Surprisingly, the authors don’t even mention the so-called ‘wind effect’ (Martinerie et al., 1994), which could account for a significant fraction of the non-orbital variability of the air content.

Technical comments

In general, the manuscript requires additional proofreading, as it still contains many minor technical errors. I will cite those which I managed to notice and remember.

L331-333 and L334-336: two identical sentences in a row.

L348, L357, L427, L560: please check and correct the table numbers you refer to here.

L371-373: the first and the second parts of the sentence seem to be poorly connected.

L420: table 2 is mentioned here for the first time, while table 3 has already been mentioned above (as table 4, I suppose).

Please check units for ISI in Fig. 4. Should it be GJ/m2?

Additional reference:

Arnaud, L., 1997. Modélisation de la Transformation de la Neige en Glace à la Surface des Calottes Polaires; étude du Transport des gaz dans ces Milieux Poreux, PhD. Université Joseph Fourier.