Estimation and calibration of the water isotope differential diffusion length in ice core records

van der Wel, G.; Fischer, H.; Oerter, H.; Meyer, H.; Meijer, H. A. J.

doi:https://doi.org/10.5194/tc-9-1601-2015

Articles | Volume 9, issue 4

https://doi.org/10.5194/tc-9-1601-2015

© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/tc-9-1601-2015

© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 9, issue 4

Research article

|

20 Aug 2015

Research article |

| 20 Aug 2015

Estimation and calibration of the water isotope differential diffusion length in ice core records

G. van der Wel, H. Fischer, H. Oerter, H. Meyer, and H. A. J. Meijer

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Final revised paper (published on 20 Aug 2015)
Preprint (discussion started on 13 Feb 2015)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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RC C246: 'Estimation and calibration of the water isotope differential diffusion length in ice core records', Anonymous Referee #1, 18 Mar 2015
- AC C730: 'Author response to the review of Anonymous Referee #1', Gerko van der Wel, 09 May 2015
RC C255: 'good progress on the isotope-diffusion-paleothermometer', Eric Steig, 23 Mar 2015
- AC C731: 'Author response to the review of Eric Steig, Referee #2', Gerko van der Wel, 09 May 2015

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Gerko van der Wel on behalf of the Authors (06 Jun 2015) Author's response Manuscript

ED: Referee Nomination & Report Request started (11 Jun 2015) by Martin Schneebeli

RR by Eric Steig (26 Jun 2015)

Suggestions for revision or reasons for rejection

I am very happy with the revised manuscript, and the thorough response to my concerns. Thank you!

I am particularly pleased by the now very clear discussion of the theory -- this will be helpful to others who may with to adopt these methods in their own work.

This paper should be published following very minor changes.

I congratulate the authors on their work.

I do have a few suggestions for further improvement.

Most important, I do not think the manuscript states one very important fact, which is critical to the novel correlation method

It is shown that one can numerically diffuse the deltaD data, and use correlation to determine the point at which the diffusion lengths of the deltaD and delta18O are equal. Since the differential diffusion is given by:

\Delta\sigma^2 = \sigma_{18}^2 - \sigma_D^2

and since

\sigma_D^2 + \sigma_{Dadd}^2 = \sigma_{18}^2

then clearly:

\Delta\sigma^2 = \sigma_{Dadd}^2

In other words, the additional diffusion necessary to reach the maximum correlation point is equivalent to the differential diffusion value that is sought. This is elegant. But I don't think this is ever stated clearly.

I suggest that a statement be added page 943, lines 1-3, as follows.

"Thus a maximum in correlation coefficient occurs when the total diffusion length (firn diffusion and numerical diffusion) of dD equals the firn diffusion length of d18O. The additional diffusion necessary to reach the maximum correlation point is equivalent to the differential diffusion value that is sought. That is:

\sigma_{Dadd}^2 = \Delta\sigma^2 (Eq. #)

Reviewer 1 raised this point in the original, but I think it can still be made clearer with this addition.

Some other corrections:

In the abstract: "The correlation based method proofs …." should be "The correlation-based method prooves"

Also in the abstract, I still think it is unfair to the pioneering work of Gkinis et al. to say that:
"...the estimation of the diffusion length using Power Spectral Densities (PSD) of the record of a single isotope species can be biased due to the lack of knowledge about the isotope signal before diffusion." I am concerned that casual readers will use this new paper as evidence that that previous work is invalid, which is certainly not the case. This would also affect the Buizert, Gkinis et al. paper from Science (2014), which should also be cited here. A fairer statement and also more informative statement would be something like this: "We show that the estimation of the diffusion length using Power Spectral Densities (PSD) of the record of a single isotope species can be biased by uncertainties in spectral properties the isotope signal prior to diffusion."

Page 6-7 it states that "Diffusion in the ice matrix will cause the length to increase, but this process is much slower than the dissusion in firn and only becomes significant for very old or warm ice (near the bedrock)." This isn't quite true. For example, we find that in the WAIS Divide ice core, it is clear that the ice is warm enough (-30°C) that measureable diffusion is occurring in the ice itself, and this constitutes and important correction. I suppose it is a matter of opinion whether -30°C is "warm" but I would suggest saying something like this:

"Diffusion in the ice matrix will cause the length to increase, but this process is much slower than the dissusion in firn and generally becomes significant only for very old or relatively warm ice (e.g., near the bedrock)."

Page 16: "This also implies that seasonal d-excess variations in real firn and ice cores are at least partly created by diffusion." Johnsen et al., 2000 were the first to explain this, I think, and should be cited here.

Page 16, "while (diffusion-created) seasonal variation in d-excess can still be counted." An example of a paper in which this was done should be cited here. I think there is a nice paper by Oerter et al. for example, on alpine cores. The authors no doubt can come up with other examples.

Often, "deuterium" and "oxygen-18" are used, when what is really mean is the concentration of the isotopologues H-18O-H and H-16O-D relative to H-16O-H. In practice, what is really being done is treating the parameters \deltaD and \delta^{18}O as proxies for those concentrations. This is fine, because they are linearly proportional. I think for most of the paper it would be better to just say \deltaD and \delta^{18}O, rather than "dueterium" or "oxygen-18".

Finally, throughout the paper, Deuterium, Nitrogen, Oxygen, etcl. should not be capitalized.

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ED: Publish subject to technical corrections (01 Jul 2015) by Martin Schneebeli

AR by Gerko van der Wel on behalf of the Authors (12 Jul 2015) Manuscript

Short summary

The diffusion of the stable water isotope signal during firnification of snow is a temperature-dependent process. Therefore, past local temperatures can be derived from the differential diffusion length. In this paper we develop a new method for determining this quantity and compare it with the existing method. Both methods are applied to a large number of synthetic data sets to assess the precision and accuracy of the reconstruction and to a section of the Antarctic EDML ice core record.