the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 23 Apr 2024
The grain-scale signature of isotopic diffusion in ice
Abstract. Diffusion limits the survival of climate signals on ice-core isotopic records. Diffusive smoothing acts not only on annual signals near the surface, but also on long time-scale signals at depth as they shorten to decimetres or centimetres. Short-circuiting of the slow diffusion in crystal grains by fast diffusion along liquid veins can explain the “excess diffusion” found on some records. But direct experimental evidence is lacking whether this mechanism operates as theorised; current theories of the short-circuiting also under-explore the role of diffusion along grain boundaries. The nonuniform patterns of isotope concentration across crystal grains induced by the short-circuiting offer a testable prediction of these theories. Here, we extend the modelling for grain boundaries (as well as veins) and calculate these patterns for different grain-boundary diffusivities and thicknesses, temperatures, and vein-water flow velocities. Two isotopic patterns are shown to prevail in ice of millimetre grain size: (i) an axisymmetric “pole” pattern with excursions in δ centred on triple junctions, in the case of thin, low-diffusivity grain boundaries; (ii) a “spoke” pattern with excursions around triple junctions showing the impression of grain boundaries, when these are thick and highly diffusive. The excursions have widths ~ 0.1–0.5 of the grain radius and variations in δ ~ 10–2 to 10–1 of the bulk isotopic signal, which set the minimum required measurement capability for laser-ablation mapping to detect them. We examine how the predicted patterns vary with depth through a bulk-signal wavelength to suggest an experimental procedure of testing ice-core samples for these signatures of isotopic short-circuiting. Because our model accounts for veins and grain boundaries, its predicted enhancement factor (quantifying the level of excess diffusion) characterises the bulk isotopic diffusivity more comprehensively than past studies.
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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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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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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Referee report on egusphere-2024-1012', Anonymous Referee #1, 30 May 2024
This manuscript is a pure modelling study (following a recent study of the same type by the same author) of the diffusion through vein and grain boundary in addition to slow diffusion in ice. Initially, larger than expected diffusion (excess diffusion) has been observed in several cases ; those cited in this study are GRIP Holocene, WAIS deglaciation and EPICA Dome over Marine Isotopic Stage 9. Studies of grain boundaries and vein contributions to the diffusion were already performed, e.g. in the book chapter of Johnsen et al. (2000) cited in the present study. The present study wants to go one step further compared to Johnsen et al. (2000) and following his recent paper to show the expected isotopic patterns to be observed at the grain scales for a range of parameters.
The main problem is that no observation is provided and even if laser ablation techniques are progressing, we are still far to the point where such observation can be done and it is also not clear that observations will actually be possible in a near future (see following comments). As it stands now, this study is focused on the resolution of the differential equations for diffusion through ice, grain boundary and vein in cylindrical coordinates. This is a serious calculation work giving the expected changes of patterns with changing parameters. I do not see how it can really be used by others as long as no observation is provided and there are no clear other scientific perspectives for this work. But the study is seriously conducted and well detailed.
I concentrate below on comments along the text.
- Introduction : the introduction is well written and summarizes previous findings on diffusion. It is interesting that the author mention the 3 cases where excess diffusion has been identified but I am wondering if the origin of the excess diffusion is the same for all three cases. Indeed in the case of EPICA Dome C, the ice is very deep and old, with relatively large ice crystals and the origin of the excess diffusion may be different than for WAIS and GRIP Holocene. It would be nice to have a discussion on these differences and perhaps discuss the possible mechanisms in each cases.
- 2.1- the system is clearly described
- 2.2- Figure 2 is complicated to understand and it was only much later during the reading of the manuscript that I could really understand what « high », « medium-high », …, « low » mean. It should be explained in this section as well as in the caption of figure 2.
Also, in some places the description is not accurate, e.g. « departures from the formulas by a few times », « Pre-melting occurs at high temperature », « ice-core samples can be very variable in these », … and should be precised.
- 160 : the author refers to the hypothesis of liquid diffusion at -32°C for Db and say that this estimate will be ruled out but they do not give the value for Db in this case and we can not really see it in Table 1.
In general, it would be nice to make a more clear link between the hypotheses listed in p. 7 and the values for Db explored in this manuscript and listed in Table 1. Perhaps the authors could take in Table 1 the values of Db from the litterature (or explain how the range of chosen values are linked to previous estimates) and refer to the different papers in Table 1 so that we can make the link between the present study and the previous studies.
- The fractionation explanation is not very clear from l. 162. Which fractionation does the author refer to ? No data for fractionation is given nor its dependency to temperature.
- 2.3 – The formulation and resolution follow a classical mathematical approach. Still, because many parameters and variables are involved in this resolution, it would help to have somewhere a table gathering the different parameters and variables, explaining their meaning and giving their values. As it is now, it is difficult to read. It is also certainly possible to have the details on the resolution (e.g. the sections 2.4, 2.5 and 2.6) in an appendix and go directly to the results once the problem and the way to solve it has been defined.
3-
-l. 369 : no reference nor explanation for the choice of the fractionation coefficients are given
- l. 373 : I do not see why studying signal wavelength of 5 mm ? Such signal is not detectable in ice core, even in CFA because of mixing in the system – at best the resolution could be 1 cm which will not enable capturing such signal. Also the following discussion (section 3.1) and display of the results (figure 4 and all figures after figures 4) with a wavelength of 2 cm is not very realistic. Also because firn diffusion occurs with a diffusion length of several cm, it would be more realistic to discuss signals of wavelength 10 cm at least. This is a major limitation of this study and it is important to address it for more realism and potential use of this study for ice core people. Some figures are shown in the supplement (showing much less excess diffusion) but not really discussed in the main text.
- l. 376 : intermediate
- l. 408 and after : some terms need to be better explained : « vertical stretches », « stretch transition », « transitions » (from what to what ?), « hole type», « spoke type»
- l. 447 : The sentence lacks a word.
- l. 464 : when should we have vein-water flow – please explain this case a little bit
- when discussing enhancement factors in this study (e.g. figure 6), it should be compared to what has been measured (if possible on signals with similar wavelength in the data and modeling approach).
- When showing isotopic patterns in the figure, the unit should be provided
- l. 634 : I do not really see how a signal of 2 cm wavelength can be well determined by CFA, see comment above.
- l. 670 and below: the author correctly notes that it is really difficult to find ice to test this effect since the isotopic signal usually measured has a wavelength much higher than 2 cm and for short wavelength, the amplitude of the signal is accordingly small.
- l. 729 : a sensitivity of 0.1 per mill is required but for which isotopic delta ? d18O or dD ?
Citation: https://doi.org/10.5194/egusphere-2024-1012-RC1 - AC1: 'Reply on RC1', Felix Ng, 13 Jun 2024
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RC2: 'Comment on egusphere-2024-1012', Anonymous Referee #2, 03 Jun 2024
Dear Author and Editor,
Please find attached my review for the manuscript.
- AC2: 'Reply on RC2', Felix Ng, 13 Jun 2024
-
EC1: 'Editor's recommendation', Florent Dominé, 05 Jun 2024
Dear Author,
Both reviews are in general positive but do make constructive suggestions that will help you prepare an improved revised version. In particular:
- Please ensure that all hypotheses and simplifications that you use are explicitly stated. You may also briefly discuss their limitations.
- Please ensure that all your equation developments are reasonably easy to follow and to reproduce by scientists in the field. Your choice of parameter values must be justified. Reviewer 2 makes a number of remarks on this aspect that deserve your attention. Among these, your choice of grain size, and the impact of choosing other grain sizes, should be discussed.
- The relationship to ice core measurement must be improved, as recommended by Reviewer 1.
- I mentioned in my initial evaluation that the possible impact of small angle boundaries may also deserve consideration as diffusion short-circuits. Their presence is likely because of ice deformation. Please consider addressing this topic. How would considering these defects affect your equations and conclusions?
Please explain how you plan to respond to these suggestions, as well as the other Reviewers’ comments.
I look forward to reading your responses.
Best regards,
Florent Domine
Editor
Citation: https://doi.org/10.5194/egusphere-2024-1012-EC1 - AC3: 'Reply on EC1', Felix Ng, 14 Jun 2024
Interactive discussion
Status: closed
-
RC1: 'Referee report on egusphere-2024-1012', Anonymous Referee #1, 30 May 2024
This manuscript is a pure modelling study (following a recent study of the same type by the same author) of the diffusion through vein and grain boundary in addition to slow diffusion in ice. Initially, larger than expected diffusion (excess diffusion) has been observed in several cases ; those cited in this study are GRIP Holocene, WAIS deglaciation and EPICA Dome over Marine Isotopic Stage 9. Studies of grain boundaries and vein contributions to the diffusion were already performed, e.g. in the book chapter of Johnsen et al. (2000) cited in the present study. The present study wants to go one step further compared to Johnsen et al. (2000) and following his recent paper to show the expected isotopic patterns to be observed at the grain scales for a range of parameters.
The main problem is that no observation is provided and even if laser ablation techniques are progressing, we are still far to the point where such observation can be done and it is also not clear that observations will actually be possible in a near future (see following comments). As it stands now, this study is focused on the resolution of the differential equations for diffusion through ice, grain boundary and vein in cylindrical coordinates. This is a serious calculation work giving the expected changes of patterns with changing parameters. I do not see how it can really be used by others as long as no observation is provided and there are no clear other scientific perspectives for this work. But the study is seriously conducted and well detailed.
I concentrate below on comments along the text.
- Introduction : the introduction is well written and summarizes previous findings on diffusion. It is interesting that the author mention the 3 cases where excess diffusion has been identified but I am wondering if the origin of the excess diffusion is the same for all three cases. Indeed in the case of EPICA Dome C, the ice is very deep and old, with relatively large ice crystals and the origin of the excess diffusion may be different than for WAIS and GRIP Holocene. It would be nice to have a discussion on these differences and perhaps discuss the possible mechanisms in each cases.
- 2.1- the system is clearly described
- 2.2- Figure 2 is complicated to understand and it was only much later during the reading of the manuscript that I could really understand what « high », « medium-high », …, « low » mean. It should be explained in this section as well as in the caption of figure 2.
Also, in some places the description is not accurate, e.g. « departures from the formulas by a few times », « Pre-melting occurs at high temperature », « ice-core samples can be very variable in these », … and should be precised.
- 160 : the author refers to the hypothesis of liquid diffusion at -32°C for Db and say that this estimate will be ruled out but they do not give the value for Db in this case and we can not really see it in Table 1.
In general, it would be nice to make a more clear link between the hypotheses listed in p. 7 and the values for Db explored in this manuscript and listed in Table 1. Perhaps the authors could take in Table 1 the values of Db from the litterature (or explain how the range of chosen values are linked to previous estimates) and refer to the different papers in Table 1 so that we can make the link between the present study and the previous studies.
- The fractionation explanation is not very clear from l. 162. Which fractionation does the author refer to ? No data for fractionation is given nor its dependency to temperature.
- 2.3 – The formulation and resolution follow a classical mathematical approach. Still, because many parameters and variables are involved in this resolution, it would help to have somewhere a table gathering the different parameters and variables, explaining their meaning and giving their values. As it is now, it is difficult to read. It is also certainly possible to have the details on the resolution (e.g. the sections 2.4, 2.5 and 2.6) in an appendix and go directly to the results once the problem and the way to solve it has been defined.
3-
-l. 369 : no reference nor explanation for the choice of the fractionation coefficients are given
- l. 373 : I do not see why studying signal wavelength of 5 mm ? Such signal is not detectable in ice core, even in CFA because of mixing in the system – at best the resolution could be 1 cm which will not enable capturing such signal. Also the following discussion (section 3.1) and display of the results (figure 4 and all figures after figures 4) with a wavelength of 2 cm is not very realistic. Also because firn diffusion occurs with a diffusion length of several cm, it would be more realistic to discuss signals of wavelength 10 cm at least. This is a major limitation of this study and it is important to address it for more realism and potential use of this study for ice core people. Some figures are shown in the supplement (showing much less excess diffusion) but not really discussed in the main text.
- l. 376 : intermediate
- l. 408 and after : some terms need to be better explained : « vertical stretches », « stretch transition », « transitions » (from what to what ?), « hole type», « spoke type»
- l. 447 : The sentence lacks a word.
- l. 464 : when should we have vein-water flow – please explain this case a little bit
- when discussing enhancement factors in this study (e.g. figure 6), it should be compared to what has been measured (if possible on signals with similar wavelength in the data and modeling approach).
- When showing isotopic patterns in the figure, the unit should be provided
- l. 634 : I do not really see how a signal of 2 cm wavelength can be well determined by CFA, see comment above.
- l. 670 and below: the author correctly notes that it is really difficult to find ice to test this effect since the isotopic signal usually measured has a wavelength much higher than 2 cm and for short wavelength, the amplitude of the signal is accordingly small.
- l. 729 : a sensitivity of 0.1 per mill is required but for which isotopic delta ? d18O or dD ?
Citation: https://doi.org/10.5194/egusphere-2024-1012-RC1 - AC1: 'Reply on RC1', Felix Ng, 13 Jun 2024
-
RC2: 'Comment on egusphere-2024-1012', Anonymous Referee #2, 03 Jun 2024
Dear Author and Editor,
Please find attached my review for the manuscript.
- AC2: 'Reply on RC2', Felix Ng, 13 Jun 2024
-
EC1: 'Editor's recommendation', Florent Dominé, 05 Jun 2024
Dear Author,
Both reviews are in general positive but do make constructive suggestions that will help you prepare an improved revised version. In particular:
- Please ensure that all hypotheses and simplifications that you use are explicitly stated. You may also briefly discuss their limitations.
- Please ensure that all your equation developments are reasonably easy to follow and to reproduce by scientists in the field. Your choice of parameter values must be justified. Reviewer 2 makes a number of remarks on this aspect that deserve your attention. Among these, your choice of grain size, and the impact of choosing other grain sizes, should be discussed.
- The relationship to ice core measurement must be improved, as recommended by Reviewer 1.
- I mentioned in my initial evaluation that the possible impact of small angle boundaries may also deserve consideration as diffusion short-circuits. Their presence is likely because of ice deformation. Please consider addressing this topic. How would considering these defects affect your equations and conclusions?
Please explain how you plan to respond to these suggestions, as well as the other Reviewers’ comments.
I look forward to reading your responses.
Best regards,
Florent Domine
Editor
Citation: https://doi.org/10.5194/egusphere-2024-1012-EC1 - AC3: 'Reply on EC1', Felix Ng, 14 Jun 2024
Peer review completion
Journal article(s) based on this preprint
Data sets
Numerical code of the study "The grain-scale signature of isotopic diffusion in ice" Felix Ng https://figshare.com/s/e42a421e53b02efdaa0f
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Numerical code of the study "The grain-scale signature of isotopic diffusion in ice" Felix Ng https://figshare.com/s/e42a421e53b02efdaa0f
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Supplement of the study "The grain-scale signature of isotopic diffusion in ice" Felix Ng https://figshare.com/s/37cfa936be37610f24e8
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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.
- Preprint
(2114 KB) - Metadata XML
-
Supplement
(972 KB) - BibTeX
- EndNote
- Final revised paper