the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 30 Jun 2026
Brief communication: Estimating diffusion length from low resolution data
Abstract. Data-derived estimates of water isotope diffusion lengths in ice cores enable corrections for diffusion-induced signal attenuation and are also used to infer past firn temperatures, but rely on fitting the correct spectral model to the observed power spectrum. Established approaches do not account for additional smoothing and aliasing introduced by discrete sampling, which can bias diffusion length estimates. We show that this bias increases with coarser sampling and exceeds 10 % when the sampling interval is greater than approximately twice the diffusion length. By explicitly incorporating sampling effects into the spectral model, we derive an unbiased estimator that improves diffusion length estimates from coarse, on-line measurements and from ice core sections with small diffusion lengths.
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Status: open (extended)
- RC1: 'Comment on egusphere-2026-3558', Anonymous Referee #1, 14 Aug 2026 reply
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- 1
The general model and math underpinning the updated calculations for diffusion length estimates for low-resolution, discrete data make sense as presented. However, I do have a major concern that needs to be addressed before this paper could be published. Hopefully, this concern can be addressed with only minor revisions.
My concern is centered on the white-noise power spectra that are used in the modeling. As a common example, the power spectra of ice-core water-isotope data typically exhibit white noise at periodicities less than multi-decadal scales (excluding the effects of diffusion, which results in a pseudo-red spectrum), but at periodicities greater than multi-decadal scales the spectrum is red. (This is a very general summary of the shape of the spectra, but good enough to make my point). The authors need to address this red noise at periodicities greater than multi-decadal scales. If an ice core site has a significantly large diffusion length in deep ice, is the model still valid? Is it valid to fit a white noise spectrum in the model for deep ice with diffusion lengths of 30 cm? I think there are instances where a white noise consideration would not be valid, and that large amounts of diffusion would not only alter the white noise part of the spectrum but also the red noise at periodicities > multi-decadal scales. The red noise portion of the spectrum is not the same across ice cores, thus the fitting of spectra to estimate diffusion lengths would have to account for these differences, otherwise an additional aliasing could occur. Similarly, if diffusion has significantly affected the red noise portion of the spectra, there is no way to know what the original red noise was (i.e., the power law to describe it). I would like the authors to produce a number of examples using varying ice core sites with varying outlier characteristics (low accumulation, significant thinning at depth, and significant solid-ice diffusion) to demonstrate that this method is generally valid for deep ice. As of now, the authors are not clear for what cases this model may be valid or not valid. If the method is not valid for certain sites, please explain why. If the method is valid for all sites, explain how. If there should be certain considerations to determine if the model is valid for a particular ice-core site, explain what those considerations would be. If I have misunderstood something about the model or the approach, please explain.
The authors do appear to partly address my concerns in Figure 3 by using a power-law deep-ice record. There is not much said about how this particular case was chosen (PX0(f) = 0.15f^−2.2‰2m and σ = 30 cm). Please explain why you chose this particular case.
Once this matter is addressed and explained more in depth, the paper would be suitable for publication. I do not have any concerns with the writing or grammar. It is worth mentioning again, I may have misunderstood something about the model or approach, and if so, please explain the misconception.
Thank you for the nice paper for considering these changes.