the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 07 Dec 2023
Novel approach to estimate the water isotope diffusion length in deep ice cores with an application to MIS 19 in the EPICA Dome C ice core
Abstract. Accurate estimates of water isotope diffusion lengths are crucial when reconstructing and interpreting water isotope records from ice cores. This is especially true in the deepest, oldest sections of deep ice cores, where thermally enhanced diffusive processes have acted over millennia on extremely thinned ice. Previous estimation methods, used with great success in shallower, younger ice cores, falter when applied to these deep sections, as they fail to account for the statistics of the climate on millennial timescales. Here, we present a new method to estimate the diffusion length and apply it to the Marine Isotope Stage 19 (MIS 19) interglacial at the bottom of the EPICA Dome C (EDC) ice core. In contrast to the conventional estimator, our method uses other interglacial periods taken from further up in the ice core to estimate the structure of the variability before diffusion. Through use of a Bayesian framework, we are able to constrain our fit while propagating the uncertainty in our assumptions. We estimate a diffusion length of 31 ± 5 cm for the MIS 19 period, which is significantly smaller than previously estimated (40 cm–60 cm). Similar results were obtained for each interglacial used to represent the undiffused climate signal, demonstrating the robustness of our estimate. Our result suggests better preservation of the climate signal at the bottom of EDC and likely other deep ice cores, offering greater potentially recoverable temporal resolution and improved reconstructions through deconvolution.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
(624 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2023-2549', Christian Holme, 27 Feb 2024
The paper presents a novel technique that aims to solve an intrinsic challenge existent when unravelling paleo-climate data from deep ice cores. The paper is well-written and structured, the research is original, and the conclusion provides a promising outlook in the journey towards restoring paleo-climate data from the oldest ice. I therefore recommend this paper for publication in The Cryosphere after some minor revisions have been addressed.
My primary concern is that it is unclear to me why the method described in Sec. 3.1 returns the P0(f) relation that can be used in deep ice diffusion estimates. As the authors also write on line 103, P0(f) is the PSD of the isotopic profile before diffusion. They then proceed to use ice core sections with ages more than 10 kyr which at a minimum have been subjected to firn diffusion which must have altered the initial signal. They argue that the time horizon that they assess is unaffected by firn diffusion, but firn diffusion has completed its alteration of a deposited snow layer within 70-200 years (Johnsen et al., 2000). So, I recommend the authors to extend their argumentation to include why firn diffusion is negligible/irrelevant to their P0(f) estimation methodology.
It is also unclear to me whether they calculate the diffusion lengths estimate on a time or depth basis. The text and figures indicate it is on a time domain but the tables and presented values are depth-domain estimates. Moreover, if the authors take a time-domain approach, then there are some complications that they have not covered. For instance, there is an inherent uncertainty associated with an ice core chronology that is not accounted for in time scale estimates. This makes time-domain diffusion length estimates more uncertain that depth-domain estimates. This can be accounted for in the PSD estimation, and I would expect that the Bayesian framework that the authors are adopting are suitable to handle such uncertainties. So, I’d encourage the authors to (1) clarify what types of diffusion length estimates that they are calculating, and (2) consider implementing chronology uncertainties in the methodology in case they estimate time-dependent P0(f) and diffusion length estimates, and (3) that they specify the conversion factors from time-dependent diffusion length estimates to the depth-dependent estimates that are presented in the table.
Finally, I suggest that the authors define what types of diffusion lengths that they refer to throughout the paper. Are they PSD-estimated, firn diffusion lengths, ice-equivalent diffusion lengths, etc.? There are occasionally references to modelling output estimates or other studies (e.g., lines 49-51), and it will help the reader to ensure that the same metric is being used when they compare magnitudes of diffusion.
Minor Comments
- Lines 178 – 189: I’d like an extended and visual assessment of how sensitive the diffusion length outputs are to changes in priors. Given your weakly defined priors, it seems to me that it isn’t that sensitive, but I think it would be valuable to emphasize this further given this is a new methodology. This could be in an appendix. Moreover, it would be valuable with some suggestions or guidelines for prior values to select for different climate regions like East Antarctica, West Antarctica and Greenland.
- Line 177 - please elaborate a bit on what N(0,02,0.07) means in terms of the gamma distribution. For instance, can you specify what N refers to in this case. Is it a normal, uniform or gamma distribution? I could assume the N(0.1, 1) and N(1.5, 1) refers to the shape and scale coefficients of the gamma distribution but please state it explicitly then.
- Line 177, you write that your fit undiffused climate spectra, but are these spectra really undiffused? I agree that they have been subjected to less diffusion that MIS 19 but I think this is something that should be addressed. See main comment.
- Line 190, as this is a seminal paper on a novel approach, then I would like to see the underlying figures in an appendix such that it is clear to the reader how the model converges from the a priori guess towards the underlying distributions. This will be helpful to future users when they are deploying your framework in practice.
- Figure 2. The power-law estimates don’t seem to fit the signal within the grey-shaded area that well (particularly fig. 2c for MIS 9). Why is that? The coefficients’ standard deviations seem small relative to the visual deviation, so perhaps you could update Figure 2 with the confidence intervals from the estimated parameters?
- Figure 5. Missing reference in Figure 5 caption
Citation: https://doi.org/10.5194/egusphere-2023-2549-RC1 - AC1: 'Reply on RC1', Fyntan Shaw, 27 May 2024
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RC2: 'Comment on egusphere-2023-2549', Anonymous Referee #2, 20 Apr 2024
The authors use a novel approach to estimate the strength of the molecular diffusion in the ice dated back to MIS 19, the oldest interglacial recorded in an Antarctic ice core. The diffusion length is deduced from the analysis of the spectral properties of the isotopic time series with the use of a Bayesian approach. The only, but important, assumption is that the spectral properties of MIS 19 are similar as those of younger isotopic stages (MIS 1, MIS 5 and MIS 9).
The authors conclude that the diffusion length is 31 +/- 5 cm, which is much shorter than in the previous works (40-60 cm). It’s a very good news for the climatologists seeking for the Earth’s oldest ice, and this is one of the reasons why I like this manuscript.
I do not have major comments on the MS, only a couple of minor suggestions:
Line 61 – you have a citation of this dataset in the “Data availability” section, so it’s possible to remove it from here.
Table 1 – the depth range for MIS 1 starts from 7.755 m and the time range from 0 ka, but at the depth of 7.6 m the age a priori cannot be 0 years.
Line 87 – significantly affect?
Citation: https://doi.org/10.5194/egusphere-2023-2549-RC2 - AC2: 'Reply on RC2', Fyntan Shaw, 27 May 2024
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2023-2549', Christian Holme, 27 Feb 2024
The paper presents a novel technique that aims to solve an intrinsic challenge existent when unravelling paleo-climate data from deep ice cores. The paper is well-written and structured, the research is original, and the conclusion provides a promising outlook in the journey towards restoring paleo-climate data from the oldest ice. I therefore recommend this paper for publication in The Cryosphere after some minor revisions have been addressed.
My primary concern is that it is unclear to me why the method described in Sec. 3.1 returns the P0(f) relation that can be used in deep ice diffusion estimates. As the authors also write on line 103, P0(f) is the PSD of the isotopic profile before diffusion. They then proceed to use ice core sections with ages more than 10 kyr which at a minimum have been subjected to firn diffusion which must have altered the initial signal. They argue that the time horizon that they assess is unaffected by firn diffusion, but firn diffusion has completed its alteration of a deposited snow layer within 70-200 years (Johnsen et al., 2000). So, I recommend the authors to extend their argumentation to include why firn diffusion is negligible/irrelevant to their P0(f) estimation methodology.
It is also unclear to me whether they calculate the diffusion lengths estimate on a time or depth basis. The text and figures indicate it is on a time domain but the tables and presented values are depth-domain estimates. Moreover, if the authors take a time-domain approach, then there are some complications that they have not covered. For instance, there is an inherent uncertainty associated with an ice core chronology that is not accounted for in time scale estimates. This makes time-domain diffusion length estimates more uncertain that depth-domain estimates. This can be accounted for in the PSD estimation, and I would expect that the Bayesian framework that the authors are adopting are suitable to handle such uncertainties. So, I’d encourage the authors to (1) clarify what types of diffusion length estimates that they are calculating, and (2) consider implementing chronology uncertainties in the methodology in case they estimate time-dependent P0(f) and diffusion length estimates, and (3) that they specify the conversion factors from time-dependent diffusion length estimates to the depth-dependent estimates that are presented in the table.
Finally, I suggest that the authors define what types of diffusion lengths that they refer to throughout the paper. Are they PSD-estimated, firn diffusion lengths, ice-equivalent diffusion lengths, etc.? There are occasionally references to modelling output estimates or other studies (e.g., lines 49-51), and it will help the reader to ensure that the same metric is being used when they compare magnitudes of diffusion.
Minor Comments
- Lines 178 – 189: I’d like an extended and visual assessment of how sensitive the diffusion length outputs are to changes in priors. Given your weakly defined priors, it seems to me that it isn’t that sensitive, but I think it would be valuable to emphasize this further given this is a new methodology. This could be in an appendix. Moreover, it would be valuable with some suggestions or guidelines for prior values to select for different climate regions like East Antarctica, West Antarctica and Greenland.
- Line 177 - please elaborate a bit on what N(0,02,0.07) means in terms of the gamma distribution. For instance, can you specify what N refers to in this case. Is it a normal, uniform or gamma distribution? I could assume the N(0.1, 1) and N(1.5, 1) refers to the shape and scale coefficients of the gamma distribution but please state it explicitly then.
- Line 177, you write that your fit undiffused climate spectra, but are these spectra really undiffused? I agree that they have been subjected to less diffusion that MIS 19 but I think this is something that should be addressed. See main comment.
- Line 190, as this is a seminal paper on a novel approach, then I would like to see the underlying figures in an appendix such that it is clear to the reader how the model converges from the a priori guess towards the underlying distributions. This will be helpful to future users when they are deploying your framework in practice.
- Figure 2. The power-law estimates don’t seem to fit the signal within the grey-shaded area that well (particularly fig. 2c for MIS 9). Why is that? The coefficients’ standard deviations seem small relative to the visual deviation, so perhaps you could update Figure 2 with the confidence intervals from the estimated parameters?
- Figure 5. Missing reference in Figure 5 caption
Citation: https://doi.org/10.5194/egusphere-2023-2549-RC1 - AC1: 'Reply on RC1', Fyntan Shaw, 27 May 2024
-
RC2: 'Comment on egusphere-2023-2549', Anonymous Referee #2, 20 Apr 2024
The authors use a novel approach to estimate the strength of the molecular diffusion in the ice dated back to MIS 19, the oldest interglacial recorded in an Antarctic ice core. The diffusion length is deduced from the analysis of the spectral properties of the isotopic time series with the use of a Bayesian approach. The only, but important, assumption is that the spectral properties of MIS 19 are similar as those of younger isotopic stages (MIS 1, MIS 5 and MIS 9).
The authors conclude that the diffusion length is 31 +/- 5 cm, which is much shorter than in the previous works (40-60 cm). It’s a very good news for the climatologists seeking for the Earth’s oldest ice, and this is one of the reasons why I like this manuscript.
I do not have major comments on the MS, only a couple of minor suggestions:
Line 61 – you have a citation of this dataset in the “Data availability” section, so it’s possible to remove it from here.
Table 1 – the depth range for MIS 1 starts from 7.755 m and the time range from 0 ka, but at the depth of 7.6 m the age a priori cannot be 0 years.
Line 87 – significantly affect?
Citation: https://doi.org/10.5194/egusphere-2023-2549-RC2 - AC2: 'Reply on RC2', Fyntan Shaw, 27 May 2024
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Andrew Mark Dolman
Torben Kunz
Vasileios Gkinis
Thomas Laepple
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(624 KB) - Metadata XML