Optimal design of hydrometric station networks based on complex network analysis

Agarwal, Ankit; Marwan, Norbert; Maheswaran, Rathinasamy; Ozturk, Ugur; Kurths, Jürgen; Merz, Bruno

doi:https://doi.org/10.5194/hess-24-2235-2020

Articles | Volume 24, issue 5

https://doi.org/10.5194/hess-24-2235-2020

© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/hess-24-2235-2020

© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 24, issue 5

Research article

|

08 May 2020

Research article |

| 08 May 2020

Optimal design of hydrometric station networks based on complex network analysis

Ankit Agarwal, Norbert Marwan, Rathinasamy Maheswaran, Ugur Ozturk, Jürgen Kurths, and Bruno Merz

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Final revised paper (published on 08 May 2020)
Preprint (discussion started on 13 Mar 2018)

Interactive discussion

Status: closed

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

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RC1: 'An interesting initial idea, but failing implementation and conclusions', Anonymous Referee #1, 04 Apr 2018
- AC1: 'Response letter to Reviewer 1', Ankit Agarwal, 19 Apr 2018
  - RC2: 'Additional evaluation is needed', Anonymous Referee #1, 20 Apr 2018
    - SC1: 'Review of the manuscript ' Optimal Design of Hydrometric Station Networks Based on Complex Network Analysis', Francesco Cioffi, 31 May 2018
    - AC2: 'Response letter to reviewer 1 (Reply RC2)', Ankit Agarwal, 09 Aug 2018
RC3: 'Not ready for publication', Anonymous Referee #2, 26 Jun 2018
- AC3: 'Response letter to reviewer 2 (Reply RC3)', Ankit Agarwal, 15 Aug 2018

Peer-review completion

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

ED: Reconsider after major revisions (further review by editor and referees) (19 Sep 2018) by Roger Moussa

AR by Anna Mirena Feist-Polner on behalf of the Authors (02 Jan 2019) Author's response

ED: Referee Nomination & Report Request started (31 Jan 2019) by Roger Moussa

RR by Eric Gaume (18 Feb 2019)

Suggestions for revision or reasons for rejection

The manuscript presents a novel approach for the ranking of stations of a measuring network that may be used for instance to improve a network structure or reduce the number of stations with the minimum loss of information. The presentation and validation of the proposed approach presents nevertheless some major defaults and limitations that have not been solved in this revised version.
First, the ranking method and criterions are defined without explicitly considering the objectives of this ranking procedure: identifying the stations providing the largest or the least additional information to the network. As far as I could understand from the manuscript, the ranking is based to some kind of correlation measure – event synchronization. A priori, the stations that appear to be “synchronized” with the largest number of other stations will have the highest ranks. If it is so, the results will contradict the objectives: identify stations providing additional information. But, the proposed ranking method is more complex. The authors should at least try to analyze the characteristics of the stations with the resulting highest ranks. Figure 8 which has been added is one first, but not sufficient step into this direction.
Second, the validation procedure, based on estimated kriging error variances (or standard deviation) is not satisfactory (table 1). By the way, the definition of this kriging error is missing in the manuscript. Since the variograms do not vary with the network and location, these theoretical kriging errors do only depend on the network structure (density and distribution of inter-distances between stations) and most probably also on the variance of the measured field for the considered variable. The authors should verify what is precisely computed in the kriging software they use. Removing 10% of the stations from the network, reduces the network density, and should result in an increase of the “kriging error” with a magnitude provided by the random removal tests. An increase of the variance, as observed with the removal of the 10% lower ranked stations, is hardly possible except if the variance of the observed field is decreased. I suspect that, the 10% lower ranked stations may correspond to stations with atypical measurements contributing significantly to the variance of the observed field: i.e. stations providing important additional information. If this is confirmed, the proposed ranking methods leads to a result that is exactly the opposite of its objectives. This is the reason why I asked the authors to provide the variance of the various tested fields in table 1 and to conduct leave-one-out tests to compute real interpolation errors for the various tested networks. None of these important results have been provided in the revised version or in the responses of the authors.
To my opinion, the presented method and results may be interesting, but raise some major questions that have not been answered by the authors in the revised version of their manuscript. The method and results deserve an in-depth critical analysis before they can be published. I therefore suggest rejecting the manuscript in its present form.

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RR by Anonymous Referee #2 (26 Feb 2019)

Suggestions for revision or reasons for rejection

This is the second version of the manuscript describing how to use network analyses for optimizing the design of station networks. The manuscript has been improved, and although I am far from convinced by the application of the methodology in hydrology, I think the idea and the application still has a novelty that makes it worth publishing after another revision.

This manuscript has two parts:
- the new node ranking measure, which can be applied to any network analyses
- application of complex network analyses (and the new node ranking measure) to a precipitation network.

For the first part, it seems the authors have introduced a new and improved measure, and although not a network expert myself, I think they have documented well the usefulness.
For the second part, I am still not convinced by the usefulness of the methodology for meteorological networks. However, I think the idea of using it here is interesting enough to merit publication anyway. I have a few suggestions below for analyses and figures that could convince me more, but some of them might fit better in a follow-up paper.

Figs 3 and 4 appears to show a spatial network. However, the networks analysed here are made from correlations, therefore it would be interesting to see this transformation, and how spatial patterns of station proximity are kept or distorted. The authors have also added Fig 9, which is very useful, but I still think a more local map, showing all stations and their connections, would be useful.

The authors mention the threshold effect in the answers, but I don’t think it is enough just to mention that threshold effects also exist in other fields. I think this is an issue that should be added to the discussion of the manuscript.

The methodology is presented as an alternative method for network optimization. But there is little discussion about the alternatives, and what advantages this particular method could provide. An alternative method is to optimize based on the kriging error. My guess is that the proposed method might be better for observations which are not only connected by spatial proximity, or where the effect of spatial proximity differs in different part of the study domain, but this would have to be properly described/discussed/analysed.

Measurement uncertainty seems not to be mentioned at all. This would most likely have an effect of the results. I can understand that this might be too complex to address properly in this manuscript, but at least the assumption about no measurement errors should be added to the text somewhere.

I think Fig 2 is somewhat unclear. If I understand it right, the temporal distance between events in the two figures in the middle should reflect the first figure, but I don’t see that this is the case.

In 2.3, it is somewhat unclear which of the measures that are part of the methodology, and which are the measures that are used for comparison. Maybe Fig 3 could be used for explaining some of the concepts here?

The wording seems to be based on the concept of network analyses. For example on P8, L17, it is referred to flow of information. What is really the flow of information in this case? Contrary to computer networks or social networks, the correlation of a variable between two observation locations is independent of the “flow” through a station between them. I think the authors should really consider the wording when they describe a network that is based on correlation rather than physical nodes with direct links.

I’m still puzzled by the reduction in kriging error when removing stations, even if these are practically redundant. Regarding the kriging error, it is only written that that this is estimated “across the entire study area”. I would expect “across the study area” to mean a grid covering Germany, but the authors should add some more details about how many and how they selected the evaluation locations.

P17L10-11 I had a quick look at the cited paper, and I don’t see that they describe how M out of N stations can reduce the uncertainty.

Minor edits
P3L14 “This interactionS is” - remove S or change This is.
P4L5 remove space after Bullmore and Sporns, 2012) ,
P7L4 hybrid nodes are poorly defined, maybe make a reference to Fig 3 here?
P9L4 I’m sure there is a fairly good English translation for Grosswetterlage.
Fig 3 caption Most of this is a description that belongs (and mostly already is) in the main text.
Many places: I’d say that the “relative kriging error” should rather be referred to as something like the “relative increase of kriging error”.
P17L9 “in the region,.”
P17 Caption Fig 8 “showing on Germany” – should be rephrased
P19L5-6 This sentence is first of all unclear. Additionally, many variogram models have a range parameter that is not equal to a distance where the correlation is zero.

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ED: Reconsider after major revisions (further review by editor and referees) (13 Mar 2019) by Roger Moussa

Dear Authors,

This is the second version of the manuscript describing how to use network analyses for optimizing the design of station networks. This is a novel approach for the ranking of stations of a measuring network that may be used for instance to improve a network structure or reduce the number of stations. Two reviewers have evaluated this revised version. Reviewer #1 mentioned that the presentation and validation of the proposed approach presents major defaults and limitations that have not been solved in this revised version, and asked to reject the manuscript. Reviewer #2 mentioned that the manuscript has been improved, but still asked for major revisions.

The method and results deserve an in-depth critical analysis before they can be published. I therefore would like to give a third and last chance for the authors to make substantial corrections in order to give responses to all points raised by both reviewers, especially:
- More detailed analysis and discussion on the ranking method and criterions, such as the characteristics of the stations with the resulting highest ranks (see Reviewer #1).
- Detailed analysis of the validation procedure (see Reviewer #1).
- Application of complex network analyses to a precipitation network (see Reviewer #2): further analysis on threshold effects, the methodology for network optimization and the added-value in comparison to other methods, uncertainty analysis, etc.

The paper will be reconsidered after “Major revisions”. In the revised version, authors are invited to respond point by point to each comment of each referee, giving convincing proofs to all questions raised by referees. Please highlight clearly what you changed in the revised manuscript, so the referees are able to assess your changes. The paper will be send again through the review process.

Kind regards,

Roger Moussa

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AR by Ankit Agarwal on behalf of the Authors (14 May 2019) Author's response Manuscript

ED: Referee Nomination & Report Request started (31 May 2019) by Roger Moussa

RR by Jon Olav Skøien (01 Aug 2019)

Suggestions for revision or reasons for rejection

This is the third version of a manuscript describing how to use network analyses for optimizing the design of station networks. The manuscript has been further improved, but there are still a few open issues. I’m still not completely convinced by the methodology, but as also mentioned in my previous reviews, I like the novelty of the approach and the attempt to think out-of-the-box, and think the authors should get a last chance to convince us that it deserves publication. I have some suggestions below on how the authors can make this publishable, even though we are not convinced by the usefulness. I think the authors should present the current state of the methodology and the analysis as less mature than what they now try to conclude, as I think follow-up studies are necessary before the methodology can be considered a trustworthy optimization tool for measurement networks.

As mentioned before, I would like to see an example of the transition from observations of a very reduced measurement network to a complex network, and how the nodes will be ranked in this network. Ideally, this should show the locations of (maybe) 6-10 stations with a table indicating their cross-correlations, and the resulting network. If this adds too much to the paper, it should be added to the appendix. Figure 8 is interesting, but it does not answer the question I have asked previously. Such a figure would also be an answer to the first comments of Reviewer #1, who also seems to find it difficult to visualize how the methodology will identify redundant stations or stations that provide additional information. The analysis of 1229 stations is nice to see the overall effect, but it does not help us to understand the method.

There is still no information about the evaluation locations for finding the kriging error. The author response refers to section 4.4, but no, it is not there. And the fact that there is still a decrease in kriging error for case II indicates that something in the setup does not follow the standard procedures for estimating the effect of removing stations on kriging error, even if the authors have now removed the emphasize on this in the text.

I see that the authors still use phrases as “global bridge nodes are able to control the flow of information” (P20). Being a measurement network, a node does not control anything. Nodes that are identified as bridge nodes might be particularly important also in a measurement network, but the authors should manage to describe the particular usefulness of these nodes in the context of measuring, process identification or interpolation of measurements, not use the terminology of a physical network. The authors mentions “Information flow, or in our context, transferability of precipitation measurement across locations, would be restricted in their absence” on P9L15-17. This is a start, but should probably be better emphasized, and not only on this location.

The discussion and conclusions are mainly a summary of the results, with some very positive interpretations of the results and the usability for measurement networks. Whereas I understand why this is done, and I know that this is a rather typical end of a manuscript, I think the authors need to reflect a bit more about advantages and disadvantages of testing this methodology within measurement networks. I don’t think the suggested figures above would completely convince me, so it would be much easier to accept a manuscript that also includes some doubts and constructive self-criticism. We are two reviewers who have presented the authors with many uncertainties and doubts. I think the authors would strengthen the manuscript by trying to further address some of these in the discussion, not necessarily giving a good answer to all, but accept that the methodology still has its uncertainties in this context. A considerable amount of work would still be necessary to convince me that this is really the way forward, but I’m happy if the conclusions just prepare the ground for these in forthcoming work.

Seeing Figure 4 again, I wonder if the authors could comment on the following assumption that would be somewhat intuitive for a geoscientist, although it might not be correct:
Node 7 is correlated with four other stations, and its value could most likely be replaced by the interpolated value without much loss of information. Stations 5, 10 and 11 are each correlated with one station only, and might have more unique information than station 7. Maybe the implicit assumption of the complex network is that station 7 will be representative for a larger area than station 10? But again, it is challenging to understand the choices and consequences of using this new methodology for measurement networks without a figure as the one mentioned under 1. further up.

I find it hard to visually compare the values of the measures in Figs 3-4. I think it would be easier if the numbers were ordered in a column instead of a row. Alternatives would be more space between the commas and next number, or different colour for each measure.

Edits
P1L14 though -> although?
P1L26 rain GAUGE stations?
P2L31 “We use complex network which” -> something seems to be missing
P3L5 Check grammar: An example … are …
P3L8 comma before respectively
P8L2-3 the term “except node 3” is ambiguous, it could also mean that Bri != 0 for Node 3. Rephrase?
P19L4 high degree or betweenness stations -> doesn’t read well, something missing?
P19L6-7 two times “or”
P19L14 Fig. 8 IS also …?
P19L15-19 It is not clear how the citation relates to what comes after. Something missing? Is this referring to two different areas in the same modelling region that, despite different local variance, will have the same modelled kriging error (function of the variogram model and configuration of neighbouring observations), or is it about two modelling regions with different variograms and different error structure?

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ED: Reconsider after major revisions (further review by editor and referees) (11 Sep 2019) by Roger Moussa

AR by Anna Wenzel on behalf of the Authors (24 Jan 2020) Author's response Manuscript

ED: Referee Nomination & Report Request started (04 Feb 2020) by Roger Moussa

RR by Jon Olav Skøien (03 Mar 2020)

Suggestions for revision or reasons for rejection

This is definitely an improved version of the manuscript describing how it could be possible to use complex network analyses for designing a hydrometric station network. I think this can be published with a few minor corrections. Some copy-editing is necessary, particularly of the newly added text.

I’m happy to see the appendix A, but some modifications are needed.
1. There are no references to the appendix (neither A or B) in the text, please add.
2. The actual threshold used (0.5?) could be mentioned explicitly, e.g. on P21L11.
3. The text should be edited; there are many errors and imprecise phrases. (stationS 3, comma before which, “this node particularly very important”?, …)
4. It seems coordinates in the table are missing, and the correlation matrix has been shifted.
5. I think “Autocorrelation …” in the caption can be removed, seems quite obvious.
For Appendix B:
1. “Kriging variogram modelling” is not a correct phrase.
2. P23L7 There is a comma too much before i
3. P23L9 The variogram function does not provide a unique solution for weights, there are steps in between.
4. P23L23 remove “auto-“
5. Could the tick marks in the y-scale in fig A2 be changed to nicer numbers (0.1, 0.2, 0.5, …)? Are the exponents of the y-axes correct? Mean does not have -1, as the rest. Why not use the real numbers? And is it correct with y*10^-6 for the wet days (e)?
6. “precipitation” in the caption is at the wrong place

Looking at Figs 2 and 3, I don’t see that the degree in Eq 6 is actually divided by N-1.

Check all references carefully. For example I noticed that almost all citations on P12 are missing, the same for some citations on P18. Maybe there are also more? Villarini et al. (2008) is never mentioned in the text, maybe there are more extra references as well?

Please check all new text carefully, that it grammatically correct and flows well. It is not as well written as the other parts of the manuscript. Some examples are found in the minor edits below.

A small detail on Fig 4 – are the stations in France really stations? This seems more like a gridded product to me, either interpolated from observations or a reanalysis product like ERA-INTERIM or ERA5.

P18L29-P19L8. What is referred to as intuitive is actually not necessarily correct. The kriging variance is independent of the local variability, as it is model based. It is dependent on the variogram (which is based on all the data) and the distance and direction to other observations. Hence, the sentence and the relationship to the figures is confusing. Then Heuvelink and Pebesma (2002) is not in the bibliography. I understand what is meant with the rest of the paragraph but it is not well written. It is wordy and incoherent. Please rephrase.

Minor edits
P1L16 Remove comma after although. Then maybe add one after attention in next line, or revise word order.
P1L18 defined as A collection of nodes
P3L17 This addition to the sentence seems somewhat lost, as the first part of the sentence refers to importance of nodes, not use in hydrology (or meteorological observations). Should probably also be “in ITS infancy”?
P5L6-7 Threshold alpha percentile -> The alpha percentile threshold?
P5L20&P6L2 Maybe “stations” instead of “grid sites”
P7L7 Maybe add reference to figure: “in the networks N1 and N2 IN FIG 1, all nodes…”
P8L21-22 Kurths et al. (2019) – move comma! Next line it should probably be timescaleS
P9L4-8 The last part is an assumption. Additionally, the sentence is hard to read as it is. Spatially large variations -> large spatial variability? Across locations or between locations? And is “restricted” the right word here?
P10L7-8 “and among others” – what is meant here? Something missing?
P10L11-12 I think the sentence would be more correct by adding for: FOR process identification, FOR interpolation of measurements and FOR transferability … Across stations?
P13L10 comma before “which”. Next line: whereas -> where?
P14L17-19. Sentence is not well written, please rephrase. (particularly: “for certain threshold range 90-99” and “robust for comparatively high threshold”)
P16L9 “are removed terms as Knew” – something missing?
P16L10 remove comma after similarly
P16L14 we run THE model
P16L15 R is not defined.
P18L11-12. This sentence is incomprehensible. I don’t understand what weighted kriging could do, “strengthen” should be “strengthened” and what does the last part mean?
P20L22 “out of the scope of the study domain”??

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ED: Publish subject to minor revisions (review by editor) (11 Mar 2020) by Roger Moussa

AR by Ankit Agarwal on behalf of the Authors (24 Mar 2020) Author's response

ED: Publish as is (11 Apr 2020) by Roger Moussa

Short summary

In the climate/hydrology network, each node represents a geographical location of climatological data, and links between nodes are set up based on their interaction or similar variability. Here, using network theory, we first generate a node-ranking measure and then prioritize the rain gauges to identify influential and expandable stations across Germany. To show the applicability of the proposed approach, we also compared the results with existing traditional and contemporary network measures.