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the Creative Commons Attribution 4.0 License.
| 04 Mar 2026
Post-deposition processes affecting water stable isotope records at Little Dome C, Antarctica: new records from two firn cores and virtual firn core modelling
Abstract. The variability of water isotopes in Antarctic ice cores is of major interest for reconstructing past climate through changes in temperature and the hydrological cycle. Archived during the deposition of successive layers of snow, water molecules undergo various processes that can modify the isotopic signal initially imprinted in snowfall during the process of snow densification to ice (i.e. firn). Diffusion is a well-known effect that affects water isotope composition by smoothing the initial climate-related signal. Here, we focus on new water isotopes profiles of two firn cores from Little Dome C (LDC), dated thanks to sulphate concentration measurements, with the aim to identify the physical processes affecting the isotopic signal in the firn at the drilling site for the new Beyond Epica Oldest Ice (BELDC) deep ice core on the East Antarctic Plateau. We use a simple Virtual Firn Core model (VFC) to best fit our δ18O firn profiles. We conclude that the VFC should include a 8 cm surface mixing layer and that diffusion is overestimated below a depth of 3 meters.
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RC1: 'Comment on egusphere-2026-871', Anonymous Referee #1, 31 Mar 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-871/egusphere-2026-871-RC1-supplement.pdfCitation: https://doi.org/
10.5194/egusphere-2026-871-RC1 -
AC1: 'Reply on RC1', Emma Samin, 23 Jul 2026
Dear reviewer,
Thank you very much for your insightful comments on our article. We have taken care to revisit all the points you raised and to address them as precisely as possible. Please find our answers below, or in the attached pdf file, where we have compiled the answers with figures. The figures are also available separately in the supplements.
Major comments:
1. The abstract would benefit from further revision to improve the logical flow, as the connections between different parts currently feel somewhat disjointed. In particular, too much emphasis is placed on the objectives and significance of the study, while the description of the results remains relatively brief. Additionally, although some key conclusions are mentioned, several valuable findings—such as the influence of storage processes on ice core isotopes, as well as the potential effects of surface mixing and stratigraphic noise—do not appear to be adequately reflected. A more balanced presentation of results and conclusions would strengthen the abstract.
Many thanks for these suggestions. We will make sure that these different aspects of the results are listed in the revised version of the abstract.
2. The two ice cores were processed using different sample segmentation methods (one was directly segmented, while the other was analyzed by CFA continuous flow analysis). Could this difference introduce measurement errors for water stable isotopic profile? How did the authors consider the potential impact of such methodological differences on the model evaluation?
The two ice cores were actually processed the same way for the top 3 m, i.e. through discrete sampling. We thus do not expect any influence of the analytical methodology for the observed differences between the two ice cores which is largely performed over this depth range. Then, for deeper sections on which the ICORDA core has been analysed through CFA and the Subglacior through discrete measurements, we refer to the comparison between CFA and discrete measurements described in Petteni et al. (2025). Such a comparison was performed on the Paleo core, drilled on a site with similar surface characteristics (temperature, accumulation) than the LDC site. In the Petteni et al. (2025) study, a good agreement is shown between the discrete and CFA measurements both on high frequency variability and amplitude of the isotopic record. We will provide these explanations in the revised manuscript.
3. The description of the VFC model lacks clarity regarding how the different post‑depositional processes are specifically coupled—for example, whether these processes are linked through a particular parameter. The description remains too general to allow a thorough evaluation of the model’s operational mechanism, which in turn compromises the completeness and reproducibility of the methodological workflow. This is especially important given that the authors claim to have improved upon the original VFC model by incorporating surface mixing and the stratigraphic noise. Could the authors provide a more detailed explanation in this section, or perhaps include a detailed explanation in the appendix to ensure completeness and reproducibility?
Thank you for this question. Our study is not a process study and we do not point to a specific mechanism for explaining the mixing in the top layer. We simply invoke snow reworking and/or convective mixing of the water vapor in the top of the firn. The surface wind may be a key driver for the mixing processes but to parameterize its effect, we would need to perform the study on different sites characterized by different wind speed which is beyond the scope of our study. We thus stick to the suggestion of Ollivier et al. (in rev) that a mixing effect occurs on a few centimetres at the surface of the firn in the neighbouring Dome C site and propose to include surface mixing in a very simple way, i.e. averaging the isotopic values over a few centimetres at the surface. The next step would be to study if sites with higher surface wind speed have smoother variations in the water isotopic records to further test the process of mixing through surface wind.
L174 – 177, We will improve our description of the VFC model as:
“Stratigraphic noise has been introduced in the classical VFC model to represent in a very crude way the effect of sublimation, condensation from the atmosphere or subsurface layers, or freezing. However, such post-deposition effects alone are probably not enough for explaining the enhanced diffusion observed in the water isotopic record on the top of the firn which we think is primarily explained by mixing of the snow and/or water vapor. In this study, we thus propose a very simple way to include the effect of surface reworking caused by wind, or the ‘ventilation’ effect caused by variations in surface pressure or convection due to temperature gradient i.e. different processes which lead to the mixing of the isotopic signature over a few centimetres at the surface. According to Ollivier et al. (in review), surface layers at Dome C are indeed affected by the mixing of the water isotopic signal through water vapour circulation or snow reworking in the top few centimetres in addition to sublimation effects. To account for this mixing effect, we average the isotopic profile using a sliding window of a few centimetres, thereby applying a spatial moving average with all points evenly weighted to the isotopic profile of the uncompacted snow. The mixing that occurs at the surface is thus already propagated along the entire length of the virtual firn core.”4. Some of the model parameters used by the authors are derived from Dome C rather than from the LDC site. This choice may introduce some bias, and the authors should provide a justification for this in the discussion section.
The LDC site is not much documented while many studies of surface snow and firn were performed at the Dome C site, 35 km away. Moreover, altitude, temperature and accumulation rate are very similar on both sites. DC and LDC sites are also located within the same grid cell of the LMDZ6-iso grid. As a consequence, in the absence of any better alternative, we derive the parameters for LDC from DC. We agree that we need to provide these explanations in the revised manuscript.
5. When generating synthetic monthly data of precipitation δ18O, the origin and applicability of the temperature‑isotope conversion coefficient are questionable. The gradient of 0.5‰·°C⁻¹ may only be derived from the results at Dome C over the past decade. Whether this coefficient is applicable to the LDC region and to the past two thousand years remains unclear and should be addressed
You are right to raise this point. There are no published studies on the exact slope to use for LDC, neither for short or long scales. For this reason, we have chosen to use the commonly accepted value of 0.5‰·°C⁻¹. However, we can carry out a sensitivity test on our synthetic data generator by varying this slope. We compared the spectra and the profile obtained for synthetic data with a slope of 0.5‰·°C⁻¹ and with a slope of 0.755‰·°C⁻¹ (Figure R1). The spectra are very similar at low frequencies and differ slightly at high frequencies; however, this difference does not affect our conclusion when comparing the VFC results over 84 m with the observations (ICORDA-LDC). The reconstructed profiles are also very similar. We therefore conclude that we can use the slope published for Dome C, pending better values for LDC, and for long timescales, without this affecting our conclusions. We propose to add this figure in the Appendix (you can find the figure in the supplementary material).
6. The identification of sulfate peaks should be described in more detail. The identification of significant peaks would normally require an iterative method, but in this study, the description only states that sulfate peaks were determined based on Dome C results, without providing a detailed explanation. Additionally, differences in sulfate peaks between the two ice cores are observed, but no detailed explanation is given. A more thorough description would improve the reliability of the dating results.
Indeed, in Gauthier et al. (2016), an iterative method has been proposed for the peak detection. As an answer to this comment, we also tried the same algorithm as in Gauthier which confirms the position of the peak as identified in the first version. This will be explained better in the new version of the manuscript as:
Section 2.3, L 156:
“To identify the sulphates peaks in the record, we use the peak detection method described in Gautier et al. (2016), based on an iterative method. The algorithm works by detecting high sulphate concentrations relative to a baseline noise level. To determine this baseline level, that could have varied in time, the algorithm scans the ice core in 1-metre sections and calculates the mean concentration (m) and standard deviation (σ). Values above m + 2σ are subtracted at each iteration, and m and σ values are recalculated, until the background noise level is isolated. The details of the algorithm are described in Gautier et al. (2016).”About the presence/absence of some peaks according to the core, we agree that we lack an explanation for this in the text. We will comment it as:
Section 3.2, L 252:
“As in the study conducted at Dome C by Gautier et al. (2016), it is noticeable that some peaks appear in one of the cores but are absent from the other, despite the cores proximity. Gautier et al. (2016) suggest that snow drift and surface roughness may explain the absence of certain peaks in firn cores that are, nevertheless, very close to one another. “7. The calculation of the RMS score is based only on the differences in PSD at two specific frequency points (the inflection point A and the high‑frequency upper limit point B), rather than on the entire spectrum or the whole depth profile. This approach provides very limited information and may not adequately reflect how well the model matches the observations across the full frequency spectrum or the entire depth range. Additionally, is it reasonable to use average weighting in this calculation? Could the authors provide a detailed explanation of the considerations behind this formula?
Several reviewers noted this inconsistency for the RMS score calculation. We thus modified our method for calculating the RMS score. We now calculate the RMSD score across a wide continuous range of the spectrum, i.e. between the start of the frequency’s PSD drop and the very high frequencies, stopping at twice the resolution of the widest samples to ensure that at least two points are included in the spectrum calculation. We will change this criterion in the text as:
Section 3.3.1, L 313 – 315:
“We then define the spectral slope as the attenuation slope of the high frequencies between the inflection point and a high frequency upper limit set at twice the resolution of the widest discrete sample for the top part of both cores. For the top of ICORDA-LDC, the widest samples are between 3 and 4 cm, so we decide to set the upper limit at frequency = 15 m-1 (corresponding to ~7 cm). For the top of Subglacior-LDC, the samples minimal resolution is between 4 and 5 cm, then we set the limit at Frequency = 10 m-1 (corresponding to 10 cm).”We will change the values and the figures according to the new spectral limit on the right.
We also carried out around a hundred simulations for each combination, in order to derive the average spectrum and eliminate the random component in the noise implementation, as it became apparent to us that 10 cores were insufficient to eliminate random variability in the VFC spectrum due to the addition of noise.
The section 4.2 will be updated by adding the following elements in the revised version:New figure (N1) in Section 4.2: (see supplement)
“With ICORDA-LDC, this score reveals two main findings:
(1) At least 7 cm of surface mixing is required to achieve RMS scores < 0.5 and thus bring the model closer to the observations. Above 6 cm, the RMSD score drops to reach its minimum values whatever the noise level. It appears that the mixing is the main parameter controlling the model convergence towards the observations.
(2) Above 50% noise, the peak observed around 18 cm in ICORDA-LDC is no longer visible. See Fig (N2) for a mixing scale of 7 cm.”
New figure (N2) in Section 4.2 for a mixing scale of 7 cm: (see supplement)
“We conclude that to make the model match the observations (and thus, in practice, bring the two spectra closer together), we must add a mixing layer of at least 7 cm at the surface and limit the addition of stratigraphic noise to below 50 per cent. This allows to preserve the presence of the frequency peak at 18 cm, which has been documented in several Antarctic ice cores (Laepple et al., 2018).
Based on surface and sub-surface water isotope data (top 6 cm), Ollivier et al. (in review) proposed a preferred mixing layer of 4 cm at DC and imputed it to changes in wind strength and snow properties. Our study suggests that 4 cm is not sufficient to explain the observed water isotopes variability over the top 3 m at LDC. However, the authors suggest that a mixing layer of 7 cm is also possible (Section 3.1) which agrees with our result.
Neither any of the combinations of noise and mixing can reproduce well the profile and spectra of Subglacior-LDC, as shows by the RMSD score (Fig. N3 a, b). In contrast to ICORDA-LDC, Subglacior-LDC displays a particularly flat signal from 0 to 1.5 m depth.”New Figure (N3) in Secion 4.2: (see supplement)
“Taking storage diffusion into account clearly improves the RMSD score (Fig. 13 c, d), with values below 0.5, although it does not perform as well as the best scores for the ICORDA-LDC reconstruction when mixing is included. It should be noted that, with the addition of this storage diffusion, the effect of mixing and noise is no longer visible in the RMS score. Moreover, the peak corresponding to a 19 cm periodicity disappears from the VFC spectrum (Fig 14), in agreement with the observations in Subglacior-LDC. When a firn core is stored for too long before being analysed, diffusion caused by storage erases the isotopic signal in the upper part whatever its origin (deposition or post-deposition effect).”
New figure (N4) in Section 4.2 for a mixing scale of 7 cm: (see supplement)
“Adding the storage diffusion brings the spectrum of the model closer to that of the observations, but cuts off the high frequencies too sharply (Fig. 14). The storage effect as modelled in Dallmayr et al. (2025) cannot fully reconcile the model with the observations, but still clearly improve the RMSD score and the VFC spectrum, as observation match over the top part. We note that Dallmayr et al. (2025) estimated σstorage at a depth between 2.40 and 3.40 m, i.e., shifted slightly deeper than our 0-3 m depth interval. Because open porosity is larger close to the surface, we probably underestimate the diffusion due to storage effect in the Subglacior-LDC core. This storage effect is minimized for the ICORDA-LDC core due to the short storage time (a few months) prior to isotopic measurements.”
8. The authors explain that even when incorporating storage effects, the influence on ice core isotopes still cannot effectively reconcile the differences between the VFC model simulations and the Subglacior‑LDC observations in terms of power spectral density. They suggest that adding storage effects would improve the agreement. However, as shown in Figure 13, at high frequencies, the VFC model simulations already fall below the actual observations, while at low frequencies, the simulations remain higher than the observations. This pattern suggests that simply increasing the storage effects may not necessarily lead to a better match between the model and the observations. Other factors might be at play. In this regard, the authors should provide further explanation and clarification.
We should reformulate this indeed. We agree with the reviewer that our conclusion is that the storage effect as modelled in Dallmayr et al. (2025) cannot fully reconcile the model with the observations. Still, it was worth trying it since it improves the VFC - observation match over the top 1.5 m and also improves the RMSE when comparing the VFC spectrum and the spectrum of observations. We propose to include this discussion as written in the suggestion of modified text in the answer to the previous comment.
9. The conclusions might be better restricted to the LDC site rather than being generalized to broader contexts. Limiting the scope of the conclusions to the specific study site would help avoid overextrapolation.
We will modify the conclusion accordingly.
Minor comments:
1. The writing in the main text and the abstract is sometimes too casual, and some sentences are hard to follow, especially in the Discussion. To improve overall clarity and readability, it might be helpful to have the manuscript carefully checked and revised by a native English speaker.We will perform a careful check of the revised manuscript to improve clarity and readability.
2. Multiple references are separated by commas; these should be changed to semicolons.
Thank you for pointing that out. We will separate the references with semicolons in the revised version.
3. Section 2.1: Please state the depths of the two ice cores in this section
The total depths of the two firn cores is given just before, at the beginning of section 2 (L 94-95: 120 m for Subglacior-LDC, 130 m for ICORDA-LDC).
4. Section 2.2, second paragraph: The tense is inconsistent. Please revise.
Thank you for pointing that out. We will revise the tense in the revised version.
5. Section 2.3: The description of the sulfate measurement method using the Subglacior-LDC is missing. Please provide the method and a reference citation.
Thank you for pointing that out. We will add this sentence in the revised version: “Subglacior-LDC sulphate profile was analysed with a resolution of 2 cm, following Gautier et al. (2016).”
6. Section 2.3: Can the dating accuracy or error be provided?
Thank you for this question, it is indeed interesting to consider the uncertainty in the dating. In our calculation of ages from tie points, the only uncertainty relates to accumulation. In Ooms et al. (2026), the accumulation rate at Dome C over the last decade is estimated at 24 ± 6 mm.w.e/year, corresponding to an uncertainty σaccu of 0.25 years over 1 year. We apply this uncertainty to the LDC site, as we have no better estimate. By incrementing over several years and referring to the nearest tie point (Δtnearest), we calculate the age uncertainty σaccu,age as (Eq. R1):
σaccu,age= √(∆tnearest*σaccu ²) (Eq.R1)
The Figure R2 shows the evolution of the uncertainty over the age in between the tie points: (see supplement)
We will provide the age error in the revised version.
7. Section 2.5, Line 183: Does the calculation of diffusion length require the atmospheric pressure parameter? Please clarify.
To reply to this question and clarify our calculation following your comment below, we propose to add this text to better explain our calculation of the diffusion length:
“In the VFC model, firn diffusion represents the progressive smoothing of the original water-isotope signal after snow deposition. In the upper firn, the snow is still porous, so water vapour can move through the air-filled pore space and exchange isotopes with surrounding snow grains. This process gradually reduces small-scale variations in δ¹⁸O, in the same way that a moving average or low-pass filter removes the shortest wavelengths from a signal. We describe this smoothing using the classical firn-diffusion approach of Johnsen (1977), Johnsen et al. (2000), and Gkinis et al. (2014), in which the strength of diffusion is expressed by the diffusion length, σ. The diffusion length can be understood as the typical depth scale over which the isotope signal has been blurred: the larger σ is, the more strongly short-scale variability is attenuated. In the model, σ is calculated as a function of depth because diffusion evolves as the firn becomes denser and less porous. It also depends on local temperature, accumulation rate and atmospheric pressure, which control how efficiently water vapour can move through the firn. More details on how this parameter is calculated can be found in Gkinis et al. (2021).”
8. Appendix B: The content is too brief, only showing results. Appropriate text and necessary formulas should be provided to explain the calculation process.
We replied to this comment above (question 7).
9. Section 3.1: After removing the top 3 m, the standard deviations of the isotope data in both two cores become larger. This is unreasonable because diffusion should reduce high frequency isotopic fluctuations with increasing depth (as stated in the introduction). Such an effect will decrease the standard deviation. So, please check the accuracy of the data and provide a reasonable explanation for this result.
We provide below some explanations for this apparent mismatch.
For Subglacior-LDC, the low standard deviation at the surface corresponds to the surprising flat isotopic profile measured in the upper part of the core. We suggest that the disappearance of the isotopic variability is at least partly linked to strong storage diffusion in this section of very low density (very high porosity).
For ICORDA-LDC, the lower standard deviation on the top 0-3 m is due to differences in resolution between the upper part (analysed as discrete samples) and the rest of the core (analysed using CFA). This is the reason why we have distinguished between the [0–3 m] and [3–30 m] lines in the table. If we reduce the resolution of the entire core to that of the widest sample (4 cm), we obtain std [0 – 84 m] = 1.217; std [0–3 m] = 1.314; std [3–84 m] = 1.212, which is consistent with the diffusion increase with depth. We will insist on these differences of resolution for the different series of measurements and implication for the presented values of the standard deviation. We thus confirm the consistency of the data with these explanations.10. Table 1: Units are missing, and the necessity of this table is not clear. Please revise or justify.
Thank you for pointing the lack of unit, we will correct it in our table. As our data will be published on Pangaea, you are right to point out that this table is not necessary in the appendix; we therefore propose to remove it.
11. Figure 3: The y‑axis mark in the second subplot is incomplete, and the label for sulfate lacks the ion symbol (SO₄²⁻).
Thank you for pointing that out. We will revise the figure.
12. Section 4.2: The authors state that a 6–8 cm mixed layer is "consistent with Ollivier et al.". However, Ollivier et al. reportedly proposed a 4 cm mixed layer. Unless Ollivier et al. also considered 6 – 8 cm as possible or within their uncertainty range, this is a logical contradiction. It seems the intended meaning might be that the 6–8 cm mixed layer is consistent with Ollivier et al.'s interpretation that the mixed layer is driven by wind and snow properties, rather than consistent with the numerical value of 4 cm. However, the current wording is misleading. Please clarify explicitly what "consistent" refers to.
Thank you for your comment. We propose to qualified this statement as:
“Based on surface and sub-surface water isotope data (top 6 cm), Ollivier et al. (in review) proposed a preferred mixing layer of 4 to 8 cm at DC depending on the parameterization of the fractionation during sublimation. Our study is in better agreement with a 8 cm mixing layer.”13. Numerous spelling errors and inappropriate word usages are found throughout the text. The following list provides only some of the visible problems, but these are by no means exhaustive. The authors should carefully check and revise all language issues in the manuscript.
Thank you very much for listing these spelling errors, we will be careful to correct all of them in the revised version.
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AC1: 'Reply on RC1', Emma Samin, 23 Jul 2026
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RC2: 'Comment on egusphere-2026-871', Anonymous Referee #2, 10 Jun 2026
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AC2: 'Reply on RC2', Emma Samin, 23 Jul 2026
Dear reviewer,
Thank you very much for your insightful comments on our article. We have taken care to revisit all the points you raised and to address them as precisely as possible. Please find our answers below, or in the attached pdf file.
Major comments:
1. Implementing a surface mixing is a great contribution to the discussion on the signal formation; however, the manuscript lacks any substantive discussion of other post depositional modifications, particularly sublimation, wind-driven erosion and snow redistribution. These processes are known to affect isotopic records in low accumulation regions such as Little Dome C. The authors mention these processes in the introduction and the title also suggests that these processes are addressed in the study. These processes should be at least discussed regarding their potential influence on the presented records (if not modelled). Furthermore, I am not an expert in simulating long time scales; therefore, I am unable to assess whether the assumption regarding the input climate for the 80m simulation is accurate, and I hope that another reviewer will be able to address this issue.
We agree that we did not detail enough the other post-deposition studies. These processes are not explicitly represented in the VFC model. Actually, they are represented through the noise term but as we show in this paper, using intermittency of the precipitation and noise does not match properly the observations at LDC so that an improved representation of the processes is needed. We propose here to add the mixing in the top which is a simplified way to represent the forced exchange of water vapor through pressure or temperature gradients and mechanical snow reworking.
We will explain this strategy better in the new version of the manuscript:
“The mixing of the isotopic signature of the surface layer – whether due to wind or to the ventilation of the firn caused by barometric pumping or to convective mixing due to temperature gradients – is not the only post-depositional process affects the water isotopes in the snow surface. Vapour exchange between the snow surface and the atmosphere (Ritter et al., 2016; Wahl et al., 2022; Dietrich et al., 2023) has an impact on the isotopic composition of snow (Casado et al., 2021, Ollivier et al., 2025). The effect of surface sublimation is currently being investigated and may bias the mean isotopic composition of the profile (Ollivier et al., in revision). It will be considered in a future optimisation of the VFC model. Condensation of water vapor from the atmosphere on surface or subsurface cold snow and surface freezing can also affect the isotopic signature of the surface layers (Craig and Gordon, 1965; Merlivat and Jouzel, 1979; Cappa et al., 2003; Casado et al., 2021). In the present VFC model, these effects are all included in the noise term but future developments may include a more physical representation of these post-deposition processes.”
2. It remains unclear whether the implemented surface mixing is an analogue to diffusion and the manuscript does not sufficiently explain how mixing is calculated. In line 176 it is written that the mixing is a “spatial moving average”, but it is not mentioned if this is, for instance, a weighted average, and during which step of the modelling this mixing is applied. A more explicit description of the underlying assumptions and of the parameterisation would strengthen the methodological transparency of the study.
Thank you for this comment. The simplest way to include the surface mixing is to average the isotopic values over a few centimetres at the surface. We will extend our description of the VFC model as:
L174 – 177:
“Stratigraphic noise has been introduced in the classical VFC model to represent in a very crude way the effect of sublimation, condensation from the atmosphere or subsurface layers, or freezing. However, such post-deposition effects alone are probably not enough for explaining the enhanced diffusion observed in the water isotopic record on the top of the firn which we think is primarily explained by mixing of the snow and/or water vapor. In this study, we thus propose a very simple way to include the effect of surface reworking caused by wind, or the ‘ventilation’ effect caused by variations in surface pressure or convection due to temperature gradient i.e. different processes which lead to the mixing of the isotopic signature over a few centimetres at the surface. According to Ollivier et al. (in review), surface layers at Dome C are indeed affected by the mixing of the water isotopic signal through water vapour circulation or snow reworking in the top few centimetres in addition to sublimation effects. To account for this mixing effect, we average the isotopic profile using a sliding window of a few centimetres, thereby applying a spatial moving average with all points evenly weighted to the isotopic profile of the uncompacted snow. The mixing that occurs at the surface is thus already propagated along the entire length of the virtual firn core.”3. The authors acknowledge that one core was stored for some years and that Dallmayr et al. (2025) reported isotopic changes associated with storage. Given this, a direct comparison of both cores without applying a correction is not well justified. If storage effects are analogous to diffusion, back-diffusion algorithms may offer a viable correction approach and should at least be considered and discussed.
We do not feel that back-diffusion is useful in this study in which we do not aim to reconstruct the initial signal and prefer to stick with forward diffusion within the VFC model following the general flow of the manuscript. Moreover, the diffusion length estimated by Dallmayr et al. (2025) for storage diffusion was performed for firn densities significantly higher than for the surface firn (2.40 to 3.40 m depth in Dallmayr et al., 2025) so that any back-diffused reconstructed signal will be associated with large uncertainties. We will however add this comment in the revised manuscript for the future uses of these records for paleoclimatic reconstructions.
4. The manuscript relies on SO₄ concentrations alone for core dating. The authors might consider calculating non-sea-salt sulphate (nss-SO₄) concentrations and using a robust threshold criterion. This would yield more reliable stratigraphic tie points and improve comparability with other records and studies.
Following a comment of reviewer 1, we have improved the detection of sulphate peaks using the iterative method described in Gautier et al. (2016) for the peak detection. We use now the same algorithm than in Gautier et al. (2016) and describe the new version of the method as:
Section 2.3, L 156:
“To identify the sulphates peaks in the record, we use the peak detection method described in Gautier et al. (2016), based on an iterative method. The algorithm works by detecting high sulphate concentrations relative to a baseline noise level. To determine this baseline level, that could have varied in time, the algorithm scans the ice core in 1-metre sections and calculates the mean concentration (m) and standard deviation (σ). Values above m + 2σ are subtracted at each iteration, and m and σ values are recalculated, until the background noise level is isolated. The details of the algorithm are described in Gautier et al. (2016).”Following your suggestion, we have also tested the use of nss-SO₄. We compared our raw sulphate data with the data obtained by applying
[SO42-]nss = [SO42-]total – k * [Na+] (from Ishino et al., 2019)
with k = 0.16 +/- 0.09 for Dome C (Legrand et al., 2012), the [SO42-]/[Na+] mass ratio in sea salt particles.The results are very comparable when looking at the SO42- or nss-SO42- records; we observe only very slight differences in the intensity of the peaks, which are not significant. Furthermore, in his thesis manuscript, Gautier argues that the use of nss-SO42- has no impact on the detection of volcanic peaks at distant sites such as Dome C (and therefore also Little Dome C).
(Reference: Section I.1.3.3, Contribution du bruit de fond, in Elsa Gautier. Empreinte isotopique et histoire du volcanisme stratosphérique des 2600 dernières années enregistrées à Dôme C, Antarctique. Sciences de la Terre. Université Grenoble Alpes, 2015. Français.)5. The study by Ollivier et al. is often cited, especially in the discussion. Yet, since this paper is not published, it is in parts difficult to follow the line of argument. The authors should briefly summarise the key findings of Ollivier et al. where relevant. Additionally, it remains unclear whether the results presented here (and those of Ollivier et al.) are specific to the Dome C region or whether they can be generalised to the broader East Antarctic Plateau. A discussion on the question of spatial applicability would strengthen the manuscript.
Many thanks for this comment. Indeed, we should better explain the main finding of the Ollivier et al. (in revision). The authors used a model for post deposition processes at the surface of the firn on the Dome C site taking into account the sublimation effect. This model was already developed for Greenland (Dietrich et al., 2023) and applied by Ollivier et al. (in revision) for the first time to the surface of Dome C. Ollivier et al. found that to get the best agreement between model outputs and isotopic measurements of the surface (0-3 cm) and subsurface snow (3-6 cm), a mixing length of 4 to 8 cm should be introduced in the model. Because this paper is still in revision, we will better describe the model and the results in the new version of the manuscript.
Reviewer 1 also pointed out the possible differences between DC and LDC and associated limitations when using results from Dome C to LDC. However, the LDC site is not much documented while many studies of surface snow and firn were performed at the Dome C site, 35 km away. Moreover, altitude, temperature and accumulation rates are very similar on both sites. DC and LDC sites are also located within the same grid cell of the LMDZ6-iso grid. As a consequence, in the absence of any better alternative, we derive the parameters for LDC from DC. We agree that we need to provide these explanations in the revised manuscript.
We agree that we have to be more specific in our conclusions. We propose to add the following comment in the revised version:
“The firn cores from LDC are characteristic of a site with very low accumulation, typical of the East Antarctic Plateau. Among the sites investigated on the East Antarctic Plateau, Dome C has a particularly low accumulation rate, and Little Dome C is estimated to have an accumulation rate that is even slightly lower. The raw result of our study in terms of combination of level of noise and surface mixing scale applies first to Little Dome C on which we have firn isotopic profiles, but the model with the mixing addition can be used for other Antarctic sites, to identifying the best range of noise level and mixing scale for different sites.”
6. I am missing a data availability statement, links to a data repository to access the data and a link to the code of the model. I would only accept this study for publication if these links were included.
Your request is perfectly justified. Data are ready to be published to Pangaea, at the same time as the study publication, under the following references that will be added in a “Data availability” section in the final version of the manuscript:
Samin, Emma; Landais, Amaëlle; Fourré, Elise; Combacal, Thomas; Minster, Bénédicte; Gautier, Elsa; Jossoud, Olivier; Jacob, Roxanne; Orsi, Anaïs; Possenti, Philippe; Alemany, Olivier (2026): Field density profile of ICORDA-LDC firn core from Little Dome C, Antarctica [dataset]. PANGAEA, https://doi.org/10.1594/PANGAEA.993899
Samin, Emma; Landais, Amaëlle; Fourré, Elise; Combacal, Thomas; Minster, Bénédicte; Gautier, Elsa; Jossoud, Olivier; Jacob, Roxanne; Orsi, Anaïs; Possenti, Philippe; Alemany, Olivier (2026): Sulphates record from ICORDA-LDC firn core from Little Dome C, Antarctica [dataset]. PANGAEA, https://doi.org/10.1594/PANGAEA.993900
Samin, Emma; Landais, Amaëlle; Fourré, Elise; Combacal, Thomas; Minster, Bénédicte; Gautier, Elsa; Jossoud, Olivier; Jacob, Roxanne; Orsi, Anaïs; Possenti, Philippe; Alemany, Olivier (2026): Water isotopes record from ICORDA-LDC firn core from Little Dome C, Antarctica [dataset]. PANGAEA, https://doi.org/10.1594/PANGAEA.993901
Samin, Emma; Landais, Amaëlle; Fourré, Elise; Combacal, Thomas; Minster, Bénédicte; Gautier, Elsa; Jossoud, Olivier; Jacob, Roxanne; Orsi, Anaïs; Possenti, Philippe; Alemany, Olivier (2026): Water isotopes record from Subglacior-LDC firn core from Little Dome C, Antarctica [dataset]. PANGAEA, https://doi.org/10.1594/PANGAEA.993902
The code of the model is still under development to implement new surface processes, such as sublimation, and will be available in its final version in the coming months. We would prefer to keep only a single version of the model online, but we propose making our version available on request, by adding this note to the revised version.
Minor comments:
• L. 26: It is mentioned that the deposited snow preserves an imprint of local and global climatic conditions. I am a bit puzzled with this statement and am also missing the respective references to both, the local and the global signal.
With this sentence, we actually had in mind the fact that water isotopic composition archives a climatic signal which can be representative of a large spatial scale (when it comes to large changes such as deglaciations) but it also affected by local variations in deposition rate for example. Still, we agree that the sentence is not so easy to understand with much context and we propose to replace it by:
“The successive layers of snow accumulated in polar regions preserves an information on past climatic conditions. As an example, the isotopic composition of the snow is largely used as a proxy for temperature at the time of precipitation (Jouzel et al., 2013).
• L. 169: Using 1 cm, are you just following Laepple et al. (2018) or did you also perform a sensitivity test to figure out what the best noise scale is (for your specific data)?
We carried out tests at the beginning of our study modifying the noise scale (between 1 and 3 cm), but none of these runs improved the agreement between VFC outputs and observations. The model - observations mismatch could only be improved through implementation of the mixing parameters. Moreover, the 1 cm noise scale proposed by Laepple et al. (2018) seems well justified and we thus kept this value for the manuscript. We will however make clear in the new manuscript that we ran tests with different noise scale without being able to improve the data - model comparison.
• L. 186: Are you applying the MTM method in depth or time dimension?
We apply it in depth. We will include this clarification in the revised version.
• L. 228: The unit “m” following “0.48 ‰2” is unclear.
The unit of the PSD is the square of the unit of the variable (‰ in this case), divided by the frequency, thus ‰²/m-1, or ‰²m.
• Figure 5: what are the cycles than are mentioned here? I am missing the description and usage of them in the text.
Thank you for your comment, we will extend the description of these cycles in the revised version.
• L. 309: removes
Thank you for pointing that out. It will be corrected in the revised version of the manuscript.
• L. 342: Please clarify what physical process or quantity is represented by the surface mixing term.
Thank you for your comment. We are aware that our study is not a process study and we cannot point to a specific mechanism for explaining the mixing in the top layer. The surface wind may be a key driver for the mixing process but to parameterize this effect, we would need to perform the study on different sites characterized by different wind speed which is beyond the scope of our study. We thus stick to the suggestion of Ollivier et al. (in rev) that a mixing effect occurs on a few centimetres at the surface of the firn in the neighbouring Dome C site and propose the simplest way to include surface mixing, i.e. averaging the isotopic values over a few centimetres at the surface. The next step would be to study if sites with higher surface wind speed have smoother variations in the water isotopic records to further test the process of mixing through surface wind. We will better explain this point it in the revised version.
• L. 421: “visual comparison” – can you try to quantify it or at least show the comparison (not only in the appendix)?
Following a major comment of Reviewer 1, we decided to revised our computation method for the RMS score. We now calculate the RMSD score across a wide continuous range of the spectrum, i.e. between the start of the frequency’s PSD drop and the very high frequencies, stopping at twice the resolution of the widest samples to ensure that at least two points are included in the spectrum calculation. The integration of the score along a wider range of the spectrum allows a better picture of the model performance.
We also carried out around a hundred simulations for each combination, in order to derive the average spectrum and eliminate the random component in the noise implementation, as it became apparent to us that 10 cores were insufficient to eliminate random variability in the VFC spectrum due to the addition of noise.
Both improvements improved the robustness of the comparison between the model and the observations spectra. The new figures and results will be discussed in Section 4.2 of the revised version.
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AC2: 'Reply on RC2', Emma Samin, 23 Jul 2026
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RC3: 'Comment on egusphere-2026-871', Anonymous Referee #3, 12 Jun 2026
The manuscript presents an important new dataset from Little Dome C and provides a useful attempt to reconcile observed firn isotope variability with a virtual firn core framework. The data are valuable and the comparison between observations and simulations is generally convincing. However, I have several concerns regarding the interpretation of the model results and the robustness of some conclusions.
My primary concern relates to the optimization strategy used to infer the preferred combinations of noise and mixing parameters. The model-observation agreement is quantified using an RMS score calculated from only two points in the power spectrum, namely the inflection point and the high-frequency limit. While this approach is computationally simple, it does not fully exploit the information contained in the observed spectra. Different parameter combinations may produce similar values at these two frequencies while exhibiting substantially different behaviour elsewhere in the spectrum. Because the inferred 8 cm mixing scale is one of the central conclusions of the manuscript, I encourage the authors to demonstrate that this result remains robust when alternative metrics based on the full spectrum, spectral slope, or integrated spectral differences are considered.
A second concern relates to the interpretation of the Subglacior-LDC record. The manuscript attributes much of the discrepancy between observations and simulations to storage diffusion occurring during the five years between drilling and analysis. While this explanation is plausible and supported by previous work, the additional storage-diffusion experiment still fails to reproduce the observed profile and spectral characteristics. The discussion subsequently suggests that even stronger storage diffusion may be required. At present, this argument remains somewhat speculative because storage diffusion is invoked to explain residual discrepancies that are not directly quantified. The authors should clarify which aspects of the mismatch can be explained by storage effects and which remain unexplained.
The interpretation of the inferred surface mixing process would also benefit from further clarification. The manuscript demonstrates that introducing a mixing parameter improves agreement between simulations and observations, but the physical meaning of this parameter remains somewhat ambiguous. Throughout the discussion, the mixing term is interpreted as representing barometric pumping, firn ventilation, wind-driven snow reworking, and surface redistribution. These processes operate on different spatial and temporal scales and may not necessarily be represented by a single effective parameter. The limitations of this interpretation should therefore be discussed more explicitly.
Finally, I encourage the authors to moderate several statements that imply a direct physical estimate of an 8 cm mixing layer. The analysis demonstrates that an effective mixing scale of approximately 8 cm provides the best agreement within the current modelling framework. However, given the uncertainties associated with model structure, forcing data, chronology, and optimization criteria, it would be more appropriate to describe this value as a model-derived effective parameter rather than a uniquely constrained physical property of the firn.
Citation: https://doi.org/10.5194/egusphere-2026-871-RC3 -
AC3: 'Reply on RC3', Emma Samin, 23 Jul 2026
Dear reviewer,
Thank you very much for your insightful comments on our article. We have taken care to revisit all the points you raised and to address them as precisely as possible. Please find our answers below, or in the attached pdf file, where we have compiled the answers with figures. The figures are also available separately in the supplements.Comments:
1. My primary concern relates to the optimization strategy used to infer the preferred combinations of noise and mixing parameters. The model-observation agreement is quantified using an RMS score calculated from only two points in the power spectrum, namely the inflection point and the high-frequency limit. While this approach is computationally simple, it does not fully exploit the information contained in the observed spectra. Different parameter combinations may produce similar values at these two frequencies while exhibiting substantially different behaviour elsewhere in the spectrum. Because the inferred 8 cm mixing scale is one of the central conclusions of the manuscript, I encourage the authors to demonstrate that this result remains robust when alternative metrics based on the full spectrum, spectral slope, or integrated spectral differences are considered.
Several reviewers noted this inconsistency for the RMS score calculation. We thus modified our method for calculating the RMS score. We now calculate the RMSD score across a wide continuous range of the spectrum, i.e. between the start of the frequency’s PSD drop and the very high frequencies, stopping at twice the resolution of the widest samples to ensure that at least two points are included in the spectrum calculation.
Over this frequency range, we calculate the log-RMSD score using the following formula:
log RMSD = √(1/N ∑ (log(OBSi)-log(MODELi))²)
We also carried out around a hundred simulations for each combination, in order to derive the average spectrum and eliminate the random component in the noise implementation, as it became apparent to us that 10 cores were insufficient to eliminate random variability in the VFC spectrum due to the addition of noise.
Both improvements improved the robustness of the comparison between the model and the observations spectra. The new figures and results will be discussed in Section 4.2 of the revised version.
This new method reveals two main findings (Figure R1): (you can find the figure in the supplementary material)
“(1) At least 7 cm of surface mixing is required to achieve RMS scores < 0.5 and thus bring the model closer to the observations. Above 6 cm, the RMSD score drops to reach its minimum values whatever the noise level. It appears that the mixing is the main parameter controlling the model convergence towards the observations.
(2) Above 50% noise, the peak observed around 18 cm in ICORDA-LDC is no longer visible. See Fig (N2) for a mixing scale of 7 cm.”
2. A second concern relates to the interpretation of the Subglacior-LDC record. The manuscript attributes much of the discrepancy between observations and simulations to storage diffusion occurring during the five years between drilling and analysis. While this explanation is plausible and supported by previous work, the additional storage-diffusion experiment still fails to reproduce the observed profile and spectral characteristics. The discussion subsequently suggests that even stronger storage diffusion may be required. At present, this argument remains somewhat speculative because storage diffusion is invoked to explain residual discrepancies that are not directly quantified. The authors should clarify which aspects of the mismatch can be explained by storage effects and which remain unexplained.
Many thanks for your comment. We applied the new-RMSD-score method to Subglacior-LDC firn core, that better highlights how the storage diffusion improve VFC representation of Subglacior-LDC. We propose new results and figures (Figures R2, R3) and to modify the description of VFC/Subglacior-LDC results in Section 4.2 as:
“Taking storage diffusion into account clearly improves the RMS score (Figures [R2, R3], see supplement), with values below 0.5, although it does not perform as well as the best scores for the ICORDA-LDC reconstruction when mixing is included. It should be noted that, with the addition of this storage diffusion, the effect of mixing and noise is no longer visible in the RMS score. Moreover, the peak corresponding to a 19 cm periodicity disappears from the VFC spectrum, in agreement with the observations in Subglacior-LDC. When a firn core is stored for too long before being analysed, diffusion caused by storage erases the isotopic signal in the upper part whatever its origin (deposition or post-deposition effect).”
“Adding the storage diffusion brings the spectrum of the model closer to that of the observations, but cuts off the high frequencies too sharply (Fig. 14). The storage effect as modelled in Dallmayr et al. (2025) cannot fully reconcile the model with the observations, but still clearly improve the RMSD score and the VFC spectrum, as observation match over the top part. We note that Dallmayr et al. (2025) estimated σstorage at a depth between 2.40 and 3.40 m, i.e., shifted slightly deeper than our 0-3 m depth interval. Because open porosity is larger close to the surface, we probably underestimate the diffusion due to storage effect in the Subglacior-LDC core.
This storage effect is minimized for the ICORDA-LDC core due to the short storage time (a few months) prior to isotopic measurements.”3. The interpretation of the inferred surface mixing process would also benefit from further clarification. The manuscript demonstrates that introducing a mixing parameter improves agreement between simulations and observations, but the physical meaning of this parameter remains somewhat ambiguous. Throughout the discussion, the mixing term is interpreted as representing barometric pumping, firn ventilation, wind-driven snow reworking, and surface redistribution. These processes operate on different spatial and temporal scales and may not necessarily be represented by a single effective parameter. The limitations of this interpretation should therefore be discussed more explicitly.
We agree with the reviewer that we used a simple representation for complex processes. This follows the general strategy when using the VFC approach in which post-deposition effects such as sublimation, wind redistribution and surface relief variations in local accumulation rate is classically represented by stratigraphic noise. We show here that the noise component is not enough to represent all the post-deposition processes (except diffusion which is explicitly calculated). We thus propose to add a mixing term which is easy to implement and which actually agrees with the recent study of Ollivier et al. (2025). Adding this term improves the model - observations agreement. We also show that introducing this mixing term makes sense with respect to several mechanisms already observed in the upper firn such as the snow reworking (under the wind influence) and the wind or temperature induced mixing of water vapor. We keep the philosophy of the VFC approach and do not introduce a mechanistical description which may be seen indeed as a limitation and justifies the need of more mechanistical models in complement to the simple VFC approach. We will explain better in the revised text the limitations of the simple VFC approach and the choice of the simple representation of the post-deposition processes in the noise and mixing components.
4. Finally, I encourage the authors to moderate several statements that imply a direct physical estimate of an 8 cm mixing layer. The analysis demonstrates that an effective mixing scale of approximately 8 cm provides the best agreement within the current modelling framework. However, given the uncertainties associated with model structure, forcing data, chronology, and optimization criteria, it would be more appropriate to describe this value as a model-derived effective parameter rather than a uniquely constrained physical property of the firn.
Many thanks for this comment which is very sound. We will modify the discussion and conclusion accordingly to clearly state the limitations of our approach with the simple model approach chosen here. This approach should ideally be combined with more process-based models.
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AC3: 'Reply on RC3', Emma Samin, 23 Jul 2026
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