Technical note: Uncertainty in multi-source partitioning using large tracer data sets

Correa, Alicia; Ochoa-Tocachi, Diego; Birkel, Christian

doi:https://doi.org/10.5194/hess-23-5059-2019

Articles | Volume 23, issue 12

https://doi.org/10.5194/hess-23-5059-2019

© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/hess-23-5059-2019

© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 23, issue 12

Technical note

|

16 Dec 2019

Technical note |

| 16 Dec 2019

Technical note: Uncertainty in multi-source partitioning using large tracer data sets

Alicia Correa, Diego Ochoa-Tocachi, and Christian Birkel

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Final revised paper (published on 16 Dec 2019)
Preprint (discussion started on 21 May 2019)

Interactive discussion

Status: closed

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

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SC1: 'Short comment on form and content', Bettina Schaefli, 28 May 2019
- AC1: 'Response to Bettina Schaefli's comment', Alicia Correa, 21 Jun 2019
RC1: 'referee comment', Anonymous Referee #1, 29 Jun 2019
- AC2: 'Response to comments from the Referee 1', Alicia Correa, 16 Sep 2019
- AC5: 'Manuscript track_changes', Alicia Correa, 16 Sep 2019
RC2: 'referee comment', Anonymous Referee #2, 02 Jul 2019
- AC3: 'Response to comments from the Referee 2', Alicia Correa, 16 Sep 2019
- AC4: 'Manuscript track_changes', Alicia Correa, 16 Sep 2019

Peer-review completion

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

ED: Reconsider after major revisions (further review by editor and referees) (17 Sep 2019) by Markus Hrachowitz

AR by Alicia Correa on behalf of the Authors (18 Sep 2019) Author's response Manuscript

ED: Referee Nomination & Report Request started (18 Sep 2019) by Markus Hrachowitz

RR by Anonymous Referee #2 (27 Sep 2019)

RR by Anonymous Referee #1 (11 Oct 2019)

Suggestions for revision or reasons for rejection

Dear authors,

I am pleased to read an updated and improved version of you manuscript entitled “Technical note: Uncertainty in multi-source partitioning using large tracer data sets”. Overall, I consider that you have successfully implemented most of the changes suggested by both reviewers during the first round of revisions. I only have one major comment and few minor concerns/technical suggestions that could help improve the manuscript.

Major comment:

- I understand the decision of the authors to present this work in the format of a technical note. Yet, their statements along the manuscript should be aligned to the proposed method and the presented analyses only. Thus, even when I agree that their methods is very valuable for the proposed purpose, a formal evaluation of the robustness of the method in comparison to other methodologies is not presented. In the new version of the manuscript the authors claim the robustness of their method based on the analysis of the effect of different data inputs on the resulting source uncertainties (P.10 , L.172-174). However, this analysis does not provide more information than the sensitivity of the estimated uncertainties to input data with different conditions. Thus, I strongly suggest the authors to avoid any misleading conclusion about the supposed robustness of their method throughout the manuscript, particularly in section 4 and P.2, L.53.

Minor comments:

P.1,L.12-13: This sentence is still difficult to understand. Do you mean “However, the source contributions may be uncertain and to date only Bayesian approaches to estimate the uncertainty of two and three sources exist.” Or something along those lines. Revise sentence for clarity.

P1,L13: replace “expand this methods developing an” by “introduce an alternative”.

P1,L16: delete “particularly”.

P1,L18: delete “were used”

P2,L30-31: Avoid double parenthesis.

P2,L33: “tracer mass balance”

P2,L34: sources and dynamics of what? Specify for clarity.

P2,L39: “mixing space”

P2,L47: “and their individual uncertainty”

P2,L53: replace “a novel and robust” by “an alternative”

P2.,L54: perhaps good be good to give examples of what sources and mixture refer to. For instance “end members or sources (e.g., precipitation, soil water, snowmelt) to a mixture (e.g., streamflow)”

P2,L55-60: These 2 long sentences could be split at least into 4-5 shorter ones to make it easier to read. Also, I think that mentioning the “application of a final equation” is not the best way to mention that the methodology has already been a applied without a formal description of the method. Please re-phrase for clarity.

P2,L58: Noting was mentioned about the method in the rest of the introduction, so this sentence comes as a complete surprise. I suggest mentioning something about the proposed Taylor series approximation around P1,L54 so here you relate it directly to “the calculation of partial derivatives, degrees of freedom and confidence interval limits”.

P3,L62-70: It would be helpful to specify if each of the variables correspond to vectors and matrices and what is the specific data related to these variables.

P3,L69-70: unclear, please split into 2 sentences for clarity. Also, I do not see the need to use a footnote. Foot note 1 could easily be included in this short paragraph.

P5,L76: add symbol of variance

P5,L76: define cA

P5,Eq. 11: define n

P6,L85: crossreference Eq6

P7,L99: the IUSS reference is the general classification of soils, not the proportions of each of them at your study site as stated. Suggest deleting this reference and use one specific for the study area.

P7,L107-108: suggest moving these results from the cited references to L.115, so it is clear what the end members of the system are and easier to relate them to the rest of this section.

P7,L120-124 & P8,L125: This is basically a repetition of the methods section. Why not simply mention that A,B,C, and D now are represented by end member RF,AN,HS, and SW in the corresponding equations to shorten the text?

P8,L125: Suggest to keep using the same notation than in the methods across the whole manuscript (i.e., A,B,C,D instead of EM1,E2,EM3,EM4). After all, that is the same notation used in tables 1-4. However, whatever your decision, everything needs to be consistent, i.e., correct in tables 5-8.

P8,L127-128: “U1, U2 and U3 represent the principal components PC1,PC2 AND PC3, respectively”

P9,L129: “… procedure was applied to all…”

P9,L140-155: perhaps would be best to include this description using an additional section to the paper eg.: 3. Sensitivity of source uncertainty to input data. Then, a subsection with the same suggested name could be added to section 3. Application to describe the results of this analysis. For now, this part appears as a surprise to the reader.

P9,L143-144: delete, repeated in the next sentence.

P9,L145: report how the 50% of data in set 1 was selected.

P9,L148: the second “example”

P9,L160-162: rewrite sentence for clarity.

P10,L172: delete “been” and consider my major comment with regards to the “robustness” of the method.

P10,L79: “… a larger number of source contributions (>3) and the…”

Tables 5-8: to keep consistency throughout the manuscript I suggest you use the notation A,B,C,D instead of the EMx notation.

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ED: Publish subject to minor revisions (review by editor) (21 Oct 2019) by Markus Hrachowitz

AR by Anna Wenzel on behalf of the Authors (29 Oct 2019) Author's response Manuscript

ED: Publish as is (30 Oct 2019) by Markus Hrachowitz

Short summary

The applications and availability of large tracer data sets have vastly increased in recent years leading to research into the contributions of multiple sources to a mixture. We introduce a method based on Taylor series approximation to estimate the uncertainties of such sources' contributions. The method is illustrated with examples of hydrology (14 tracers) and a MATLAB code is provided for reproducibility. This method can be generalized to any number of tracers across a range of disciplines.