the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 31 Jul 2025
Transport behavior displayed by water isotopes and potential implications for assessment of catchment properties
Abstract. Measurements of water isotopes are used routinely to estimate water transit time distributions and aquifer storage thickness in catchments. Water isotopes (e.g., D2O/H218O) are generally considered to behave identically to water molecules (H2O); they are thus often considered fully representative of water movement and preferred over inert chemical tracers for catchment assessment purposes. However, laboratory-scale measurements presented here show that water isotopes exhibit transport behavior that is essentially identical to that of inert chemical tracers. The resulting measurements are then interpreted quantitatively, focusing on a comparative assessment of apparent mean water and mean tracer velocities, and the applicability of Fickian and non-Fickian (anomalous) transport models. For both water isotopes and inert chemical tracers, the measured mean tracer velocity is not necessarily equal to the apparent mean water velocity. It is thus critical to recognize this inequality when estimating catchment properties. For example, accounting for anomalous transport of water isotopes can significantly reduce overall estimates of aquifer storage thickness over an entire watershed.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Hydrology and Earth System Sciences.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: open (until 11 Sep 2025)
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RC1: 'Comment on egusphere-2025-3365', Brandi Gaertner, 31 Jul 2025
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Thank you for giving me the opportunity to read your manuscript. It is well written and interesting. Your results provide novel and important information to the scientific community.
You did a great job describing the rather complex methods in a way that is easily understood by the readers. Your discussion on the implication of the findings to catchment water movement is well described, and provides direct, actionable, and targeted advice to hydrologic planners.
Overall, I was very impressed and I only have minor revision requests:
Line 79 Introduction: I recommend breaking the last paragraph of the introduction into two paragraphs. The first should provide more literature on chemical tracers (namely Br and D2O/H2O, used in your study) and any other literature that has studied on water transport as it relates to chemical tracer behavior. Additionally, this should include the literature of Fickian and non-Fickian (anomalous) transport models and how they apply to water behavior, as you have mentioned in your abstract.
The second paragraph should describe your objectives and include the more specific explanation of your methods shown in lines 79 – 85.
Line 258: Explain Fickian and non-Fickian transport in 1-2 sentences.
Conclusion: I recommend providing one more paragraph summarizing the findings that your results may indicate smaller aquifer thickness requirements. I also recommend providing a sentence or paragraph on the applicability of this research to global aquifers/catchments to provide a global perspective/conclusion to this research.
Citation: https://doi.org/10.5194/egusphere-2025-3365-RC1 -
AC1: 'Reply on RC1', Brian Berkowitz, 12 Aug 2025
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The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-3365/egusphere-2025-3365-AC1-supplement.pdf
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AC1: 'Reply on RC1', Brian Berkowitz, 12 Aug 2025
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RC2: 'Comment on egusphere-2025-3365: the map is not the territory', Anonymous Referee #2, 04 Aug 2025
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The title of this paper "Transport behavior displayed by water isotopes and potential implications for assessment of catchment properties" is misleading, as it suggests the paper has something to say about water isotopes and their use in assessing catchment properties. I see no evidence of this whatsoever.
The core claims of the paper rest on two points:
1. stable water isotopes behave similarly to inert tracers like Br-
2. The v_T parameter of a CTRW model fit to breakthrough curves showing non-fickian behavior is not the same as the value of v_W calculated from v_W=Q/(nA).
I have no major issue with either of these points, per se. However the authors then argue that there is some issue with using isotopes to understand water movement through catchments -- as though the movement of water molecules were somehow different from the movement of "water" itself.
To me the issue seems to rest entirely on the assumption that the v_T parameter that arises in CTRW theory is the 'true' mean velocity of the tracer, and that this ought to correspond with the value of v_W calculated as mentioned. Tf there is a mismatch between theory and observation then the issue is not with reality, it is with the theory.
If the discrepancy between the two 'velocities' arises regardless of which tracer is used (which they themselves say their results support) then the use of isotopes as a tracer is not at issue. Rather it seems to me it highlights a theoretical confusion about what v_T and v_W actually mean in relation to one another. Does CTRW theory assert that they ought to be the same? Are the observations in agreement with the theory, or at odds with it? Where exactly does this difference come from? It certainly seems like a paper that disentangles that issue would be useful to the CTRW community.
Meanwhile, the community that uses isotopes to study catchment properties is moving on from the notion of 'mean travel time'. The leading-edge approaches do not require it, and it is reported less often in favor of other more reliable metrics, like those based on storage selection.
I would note in passing that the authors do not seem familiar with the storage selection approach. They seem to be under the impression that it is based on the collapse of the system to one spatial dimension (Line 331). This is not the case -- in storage selection theory the system is collapsed to zero spatial dimensions.
Citation: https://doi.org/10.5194/egusphere-2025-3365-RC2 -
AC2: 'Reply on RC2', Brian Berkowitz, 12 Aug 2025
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The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-3365/egusphere-2025-3365-AC2-supplement.pdf
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RC3: 'Reply on AC2', Anonymous Referee #2, 12 Aug 2025
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I strongly urge the authors to reconsider their statement: "We thus show that v_T, the mean travel time of the isotope and the tracer, is distinct from the mean travel time of the “water” itself, as determined from Darcy’s law." On first reading this appears to be saying "the mean travel time of the water is distinct from the mean travel time of the water". I understand this isn't their intended meaning, but this framing is at best obscure and might in fact be read as deliberately provocative.
First of all, Darcy's Law (as I have always understood it) is a statement about the relationship between a pressure gradient and bulk water flux (volume per area per time). The present paper never reports, calculates, or relies on a pressure gradient, and so they don't appear to be making use of Darcy's Law in a way that I can recognize. Consider: the quantity v_W obtained from v_W=Q/(nA) can be calculated regardless of whether the flow in the porous media is laminar (and so Darcy's law would be expected to hold) or turbulent (in which case it would not). v_W is therefore quite independent of Darcy's Law.
Second, the authors seem to want to have their cake and eat it too, when it comes to the relationship between v_T and v_W. Consider these two statements:
"In particular, we emphasize that the fundamental formulation of the ADE *requires* that the velocity term in the equation correspond to – i.e., be identical to – v_W. Every textbook development of the ADE immediately invokes the mean linear water velocity, v_W, based on Darcy’s law."
-- fine, so when the ADE applies we would expect v_W=v_T. Deviations from that would indeed be surprising, but that is not what was observed here (since the ADE does not apply to the data presented)."In fact, we do not invoke v_W in the CTRW, and thus there is no “mismatch”or inconsistency between these two parameters in the CTRW framework" and "the continuous time random walk framework (CTRW) formulation discussed below is essentially founded on v_T"
-- fine, so when the ADE does not apply and we have to use CTRW, we would not expect v_W=v_T, as their meaning diverges. v_T is a parameter of the CTRW conceptual framework, and within that framework it is conceptually distinct from v_W. They coincide only when the CTRW reduces to the ADE.In the present dataset the ADE does not apply ("the ADE cannot match the measurements, particularly the long tailing behavior") and so (by the author's logic) we should not expect v_W=v_T, and **indeed this is the case**.
So where is the mystery here?
It seems like the primary issue point being made in this paper is about how in porous media sufficiently heterogeneous as to be non-fickian the quantity v_W=Q/(nA) cannot be naively interpreted as the 'mean velocity' of the water. Instead, the presence of long tails adds some important nuance and complexity to the very notion of "mean velocity".
That might be a useful point to make, but the weird distinction the authors draw between the "velocity of the water" and the "velocity of the water isotopes" rather obscures it. Also, I would note again that the phenomenon at issue appears to be the case *regardless of what tracer is used*, so I'm still not sure why isotopes are being singled out.
Citation: https://doi.org/10.5194/egusphere-2025-3365-RC3
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RC3: 'Reply on AC2', Anonymous Referee #2, 12 Aug 2025
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AC2: 'Reply on RC2', Brian Berkowitz, 12 Aug 2025
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