Review of „Effective diffusivity of sulfuric acid in Antarctic ice cores“ submitted to Climate of the Past by Fudge et al.

The diffusion of impurities within the ice matrix is an important mechanism that can lead to post-depositional change. These changes need to be recognized and constrained for proper interpretation of the climatic signals in the ice core impurity records. Sulfuric acid peaks related to volcanic eruptions are a prime example in this regard. In their manuscript Fudge et al. investigate the effective diffusivity of sulfuric acid along the full depth range in the EPICA Dome C ice core. In doing so they extend a previous foundational approach by Barnes et al. (2003) treating the Holocene sections (in the following, like in the manuscript, referred to as B03). The authors find an average value comprised of values for glacial and interglacial period that is an order of magnitude lower than the Holocene value by B03. This would suggest that records related to sulfuric acid are preserved longer and to greater depth, which is of relevance to the interpretation of existing and future ice core records. Although the manuscript is generally well written, at some central points it needs more work and clarification. At present the main result is difficult to appreciate without in-depth knowledge on the subject or reading the B03 paper first. It is especially important for the reader to understand where the discrepancy with the previous estimate by B03 stems from.

General comments:

The difference with the previous estimate of the effective diffusion reported in B03 is a major result here, but comparatively little is said about how the authors explain this difference. Is this a result of differences in the method, the data, or lies within the range of uncertainty so the values actually agree (more regarding uncertainty below). In section 3.1 it is mentioned that the approach employed here was also tested for the Holocene considered in B03. In line 195 values for the residual concentration co are compared. The value reported by B03 is (0.54 +/- 0.04) (mM in the text and µM in the caption of Figure 4 in B03). What is the uncertainty for the new value reported here, co = 0.62? It is stated that the small difference could stem from updates in the sulfate data and thinning function but this is not shown, e.g. by using the original B03 data. If the values for the residual concentration and the peak width agree, what is the according value for the Holocene for the effective diffusion (Deff)? Is this different from B03 and if so, why? If I understand Table 1 correctly, the reported Deff is the value for the last two interglacials combined?

The more important implication of this is the following: If the values by B03 were an overestimation, it is important to understand where this is coming from. If only slightly other data and thinning functions were used as input, this would indicate that the calculations are very sensitive to such changes. The same argument holds for the case of slight differences in how Deff is calculated. I would have expected consistent values for the Holocene with B03, which would then have allowed to discuss why the values for previous interglacial and glacial periods are different by an order of magnitude, possibly indicating changes in the physical mechanism. I may have misunderstood this point, but strongly believe this issue should be addressed more clearly, thus helping the reader to appreciate the difference in Deff found in this study.

The treatment of uncertainties for Deff needs to be clarified. In section 3.1 it is mentioned that the uncertainty results from the 95% confidence intervals in a fit to the individual data points (log of scaled mean gradient), while Deff is derived from a fit to the medians. What is the difference in values if you calculate Deff as a fit to the individual datapoints? What justifies regarding the two low values (notably for a glacial and an interglacial) as outliers? The differences in the two methods indicate substantial dependency on the way these values are derived, correct? This would be easier to assess if the values for the volcanic width method also had some uncertainty estimation.

My confusion about the uncertainty treatment translates into the following important question: After having treated glacials and interglacials separately, the authors suggest a general value of (5+/-2) x 10^-9 m^2 a^-1. It is unclear to me where this uncertainty value comes from. More importantly, this value is interpreted as representative for both, glacials and interglacials – implying that within the uncertainty of the method, potential differences in Deff cannot be recognized? I am not sure if I am following, however considering the differences in climatic states, impurity concentration, grain size and temperature this seems surprising and deserves further discussion. Ultimately the physical mechanism remains unclear, and as a reader I had hoped that the results presented here would give more insight. Since the localization of sulfuric acid in the ice matrix remains unknown, it would have been beneficial for this discussion to include, at least partially, a similar analysis for sodium – like in the B03 paper. In the case of sodium growing evidence suggests that it might be predominantly located at the grain boundaries. Including at least exemplarily sodium could also provide an additional route for comparison with the results of B03. Would be very interesting if a similar discrepancy prevails.

Specific comments:

I suggest a better introduction of what the parameter Deff actually means earlier in the manuscript, as some readers may not be familiar with it. Maybe a simple sketch figure could help, also to illustrate the basics of the two methods.

The same applies to the method used in Fudge et al. (2016), a bit additional detail would help.

I am not sure if “artificial diffusion” is a good term. The point is that decreasing sampling resolution introduces additional smoothing to the data. Maybe “bias by artificial smoothing” would be better?

The results by Traversi et al. (2009) suggested that, in the deep ice, there is distinct lateral variability of sulfate, and this raises some question regarding the 1D approach used here – would we expect systematic bias in the estimation of Deff in this case? Could be worth mentioning.

Line 109: is z not the unthinned ice equivalent depth as in B03? Please clarify.

Line 117: “k is the wave number” – of what? This is a bit abrupt and is not clear until line 127.

Line 149: Why do you choose the largest 25 events? How sensitive are your results regarding changing this value? What if you use the largest 50, 100 or all?

Line 278: Would the neutralization not affect also sulfuric acid?

Line 295: “The scaled mean gradients have not been corrected for artificial smoothing” – why not?

I am not sure how Climate of the Past is handling data availability and if “available upon request” is accepted.

Technical comments:

Line 95: “is uses”

Line 240: “increses”

Line 403: “B03)”

Review of manuscript egusphere-2022-1219 by Fudge et al.

General comments:

The manuscript presents estimates of sulfate diffusivity mostly centred on the EPICA Dome C ice core. Two mathematical methods are used and lead to fairly consistent results. Such diffusivity estimates are important to better understand and constrain long term signal preservation in ice cores.

In my opinion, some implicit assumptions should be clarified and better discussed, especially the chemical interactions of sulfate (or sulfuric acid) with other impurities and possible role of non diffusive processes on the apparent effective diffusivity. It should help building a more in-depth discussion of uncertainties, the effects of temperature and differences between ice formed during interglacial or glacial periods, and differences between ice cores. Suggestions are provided below.

The manuscript title and most parts of the discussion assume that all sulfate is in the form of sulfuric acid. Although the fact that part of the sulfate could be in the form of salt micro-inclusions is briefly mentioned lines 57-58, it is re-formulated immediately after in terms of where sulfuric acid is located. The chemical form of sulfate and its relation with sulfate mobility in ice should be better introduced (as for example in Ng et al. 2021 and references cited) and discussed.

The manuscript uses a method by Barnes et al., 2003 on the same ice core but different time periods. Diffusivity values one order of magnitude lower than in Barnes et al. (2003) are obtained but no clear explanation is provided, although an attempt to replicate the calculation by Barnes et al. (2003) could be performed.

Barnes et al. (2003) restricted their study to the top 350m of the core which has undergone only weak temperature variations after the dampening of the seasonal variability (in the top ~20m), weak progressive thinning due to ice flow and weak background (non volcanic) chemical composition change. The implicit assumptions made by extending the Barnes et al. (2003) calculation to much longer periods should be better introduced and discussed. Numerical tests performed with the diffusion model presented in Section 2.3 could be helpful. For example, the manuscript analyses ice deposited during several glacial and interglacial periods which have experienced ice temperatures progressively rising from -55°C (or less in glacial periods) to -10°C or more. Diffusion speed and diffusivity are generally very sensitive to temperature, as could be estimated for example by the equation below Figure 4 in Fudge et al. (2016), and the much higher diffusivity inferred from the WAISD ice core (2.2 x 10^-8) by Fudge et al. (2016) than from EDC or Dome Fuji in the manuscript (about 5 x 10^-9). The role of temperature and temperature gradients on diffusive and non diffusive processes should be better introduced and discussed. Analysing the diffusivity values obtained for each of the five investigated glacial cycles (which could be provided in Appendix A) could also help improving the discussion of uncertainties as well as the roles of temperature, chemical composition of the ice etc.

Specific comments:

Lines 46-47: the implicit assumption that all sulfate is under the form of sulfuric acid should be clarified and discussed.

Lines 66-71: the reason why the diffusivity value of 4.7 x 10-⁸ for EDC (Barnes et al. 2003) is viewed as considerably higher than the WAISD value of 2.2 x 10^-8 and the expected effect of temperature should be clarified.

Lines 80-85, 196 and 493: a reference (or references) should be provided for the EDC sulfate record, not only the analytical method. Is it the same as Traversi et al. (2009)? Updates in the sulfate data set are briefly mentioned at line 196 without a reference. I was surprised to find only part of the EDC sulfate record in a public database (down to 2094m, doi:10.25921/kgv8-cn35) and strongly encourage the authors of the manuscript to document and place the full record in a public database.

Line 86: references should be provided for the data plotted on Figure 1.

Lines 100-104: several aspects of the replication and extension to longer periods of the calculation by Barnes et al. (2003) should be further discussed (see also general comments). Is the same diffusivity estimate obtained when replicating the calculation for the same period (Holocene)? Barnes et al. (2003) indicate some assumptions made in their calculation that are not valid on longer time scales (e.g. in their paragraph [16]: constant in time downward velocity in ice and effective diffusivity). They also discuss the scaling parameters in relation with the origins of sulfate (biogenic versus volcanic) in their paragraph [14].

Lines 123-127: this simplistic correction for the final thinning ignores the strong variation with time of the annual layer thickness. A step by step approach is used with the diffusion model (line 151 of the manuscript). The effect of neglecting the progressive thinning could be estimated with the diffusion model, such tests may improve the estimation of the uncertainty.

Lines 139-145: the references cited here for the identification of volcanic peaks cover a much shorter time period than the five glacial cycles considered in the manuscript. On the other hand, Fujita et al. (2015) stopped the volcanic synchronization of EDC and DF at 216kyr BP due to the smoothing of the peaks. Traversi et al. (2009) find artefacts of non volcanic origin below 2800m depth in the EDC core, and the recent study by Wolff et al. (2023) found evidence of this behaviour at shallower depths: 2500m (300ka, see their Data Section and Figure 3). Here and in other part of the manuscript, a discussion of possible artefacts due to sulfate variability of non volcanic origin should be included.

Lines 254-258: Figure 4 seems to suggest that a single diffusivity cannot explain both the smallest observed increase in event durations and the largest observed increase in event durations. The range of event durations should be discussed in terms of uncertainty on the diffusivity, possible role of non diffusive mechanisms and/or change in the nature of detectable events.

Lines 267-272: A better evaluation and discussion of the uncertainty could be made by analysing all individual estimates (for each glacial cycle) of the diffusivity. These values could be provided in Appendix A. I found interesting that the most reliable diffusivity estimates, for the last cycle, all lead to lower values in glacial ice than interglacial ice. This should be further commented in the manuscript (see also next comment on lines 275-278).

Lines 275-278: the analysis of the Dome Fuji ice core ECM profile deserves more attention in my view. The increased reduction of the diffusivity in glacial ice compared to interglacial ice is attributed to the neutralization of acids where dust is in higher concentration. This process should have been introduced much earlier in the manuscript as it should affect the mobility of sulfate if it does not remain in the form of sulfuric acid (see also general comment and specific comment on lines 46-47). The ECM profile of the EDC ice core is publicly available with 1 cm resolution:

https://www.ncei.noaa.gov/pub/data/paleo/icecore/antarctica/epica_domec/

It would be very interesting to check if it confirms the lower diffusivity in glacial ice than interglacial ice and increased difference inferred from ECM than from sulfate.

Lines 282-287 (and 321-323): this section is unclear. Does it just mean that the reduced and more variable diffusivity values obtained for the past 5 cycles are simply attributed to the correction of artificial smoothing without considering other sources of uncertainty? The uncertainty estimate should be clarified.

Lines 295-296: I do not understand why the scaled mean gradients are not corrected for artificial smoothing for the oldest ice, which should be the most affected due to its high thinning rate. The corrected values should be also provided, possibly on an additional panel of Figure 5.

lines 317-319: some test results should illustrate this important statement.

Lines 329-330: this should be further discussed in relation with the findings of Wolff et al. (2023) (see comment on lines 139-145) and the neutralization of acids in glacial ice considered at line 278.

Lines 337-338: the diffusivity contrast between interglacial and glacial ice deserves a more detailed analysis (se also comments on lines 267-272 and 275-278).

Lines 338-339: the absence of temperature effect in the range -55°C to -10°C is a very strong conclusion in apparent contradiction with the physics of diffusion and the diffusivity calculated for the WAISD ice and should be further discussed (see also general comments).

Line 364: Figure 6 - it would be interesting to plot the expected diffusivity variations with temperature together with the EDC borehole temperature (see next comment).

Lines 393-421: this section comparing WAISD and EDC diffusivities is difficult to follow, the typing error in the WAISD diffusivity (2.2 x 10^-9 whereas it should be 2.2 x 10^-8) adds to the confusion (see also comment on lines 66-71). A diffusivity of 2.2 x 10^-8 is much higher than any value inferred from the EDC or DF records but the authors conclude that it neither supports nor refutes the lack of temperature dependence of the effective diffusivity below -10°C. I checked the orders of magnitudes with the temperature dependent diffusivity formulation below Figure 4 in Fudge et al. (2016) and found 2 10^-8 at -30°C, 5.6 10^-9 at -40°C and 1.4 10^-9 at -50°C. The argument of a higher thinning rate at WAISD holds only for the last glacial cycle but not the previous ones at EDC. The effect of accumulation rate is considered in terms of grain growth but also affects the impurity concentrations in ice and possible neutralization of acids (see line 278). The consistency of a lower diffusivity at WAISD (about 5. 10^-9) with an absence of sulfate peaks at ages older than 52 ka should be evaluated. Overall, the absence of temperature dependence of the diffusivity below -10°C may be an oversimplification.

Lines 424-425: the absence of diffusion during the Holocene disagrees with the conclusion of Barnes et al. (2003) using the same methodology. The reasons for this disagreement should be discussed.

Lines 429-430: the recent study by Lin et al. (2022) could be mentioned here.

Lines 476-477: this sentence should be reformulated in a less affirmative way (see comment on lines 393-421).

Technical corrections:

Line 43: Kahle et al., 2021?

Line 95: variability uses

Line 215: Figure 3 is difficult to read, the two panels should be enlarged and symbols representing all gradients made more visible

Line 240: increases

Line 402: 2.2 x 10^-8 instead of 2.2 x 10^-9

References not cited in the manuscript:

Lin et al., Clim. Past, 2022. https://doi.org/10.5194/cp-18-485-2022

Wolff et al., Clim. Past, 2023. https://doi.org/10.5194/cp-19-23-2023