Mapping rainfall hazard based on rain gauge data: an objective cross-validation framework for model selection

Blanchet, Juliette; Paquet, Emmanuel; Vaittinada Ayar, Pradeebane; Penot, David

doi:https://doi.org/10.5194/hess-23-829-2019

Articles | Volume 23, issue 2

https://doi.org/10.5194/hess-23-829-2019

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

https://doi.org/10.5194/hess-23-829-2019

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

Articles | Volume 23, issue 2

Research article

|

13 Feb 2019

Research article |

| 13 Feb 2019

Mapping rainfall hazard based on rain gauge data: an objective cross-validation framework for model selection

Juliette Blanchet, Emmanuel Paquet, Pradeebane Vaittinada Ayar, and David Penot

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Final revised paper (published on 13 Feb 2019)
Preprint (discussion started on 23 Mar 2018)

Interactive discussion

Status: closed

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

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- Supplement

RC1: 'Interactive comment on "An objective cross-validation framework for mapping rainfall hazard based on rain gauge data" by J. Blanchet et al.', Richard Katz, 26 Apr 2018
- AC1: 'Reply to Reviewer #1', J. Blanchet, 03 Jul 2018
RC2: 'Review', Anonymous Referee #2, 06 Jun 2018
- AC2: 'Reply to reviewer #2', J. Blanchet, 03 Jul 2018

Peer-review completion

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

ED: Publish subject to revisions (further review by editor and referees) (12 Jul 2018) by Carlo De Michele

AR by J. Blanchet on behalf of the Authors (13 Jul 2018) Author's response Manuscript

ED: Referee Nomination & Report Request started (24 Jul 2018) by Carlo De Michele

RR by Richard Katz (24 Aug 2018)

Suggestions for revision or reasons for rejection

GENERAL COMMENTS

The revised version of the manuscript is somewhat improved, as the authors have addressed my comments at least to some extent. My main remaining reservation concerns how the results on the fitting of marginal distributions are interpreted in terms of heavy tails.

For this reason, I recommend that the manuscript be accepted for publication subject to minor revision.

SPECIFIC COMMENTS

(1) Interpretation of results concerning heavy tails

The interpretation of the results concerning the shape of the upper tail of the distribution of rainfall amounts still suffers from a lack of reliance on what is known from extreme value theory. In particular, the return level plots for the fitted mixtures of gamma distributions (Fig. 7) all appear approximately linear for high values (i.e., indicative of light-tailed, not heavy-tailed, distributions). Apparently, using a mixture of gamma distributions reduces the bias attributable to fitting the entire span of the values of rainfall rather than only fitting the upper tail (i.e., the mixture of gamma distributions does not necessarily have a heavy, or even a heavier, tail in the sense of extreme value theory).

Along the same lines, the corresponding return level plots (Fig. 9) for sub-exponential distributions with heavy tails (in either an asymptotic or sub-asymptotic extreme value theory sense) do not necessarily indicate that the fitted models have too heavy a tail. Rather, their lack of fit in the upper tail is at least partially attributable to being based on fitting the entire range of rainfall values.

For this reason, I fear that the statement in the Conclusion and discussion section "distributions showing sub-exponential tails (EGP for example) give usually unrealistic return levels" (p. 28, line 18) will be misunderstood. At best, it is only relevant to the situation in which the distribution (or mixture of distributions) is being fitted to the entire range of rainfall values. As such, it does not necessarily imply anything about how heavy the upper tail of the distribution of rainfall amounts actually is.

EDITORIAL COMMENTS

(1) Table 1

The table indicates that CDFs are listed. Yet for some distributions (i.e., gamma and lognormal) the expressions given are actually for probability density functions, not CDFs.

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RR by Anonymous Referee #3 (29 Aug 2018)

ED: Reconsider after major revisions (further review by editor and referees) (30 Aug 2018) by Carlo De Michele

AR by J. Blanchet on behalf of the Authors (10 Oct 2018) Author's response Manuscript

ED: Referee Nomination & Report Request started (15 Oct 2018) by Carlo De Michele

RR by Richard Katz (17 Nov 2018)

RR by Anonymous Referee #3 (19 Dec 2018)

Suggestions for revision or reasons for rejection

The authors have answered to all the questions of my previous review and have clarified some key-points of the manuscript.
Despite this, I still think that there is a significant open issue, that should be amended for the manuscript to be ready for publication.
I still think that the advances that the proposed framework could provide to the scientific community does not emerge clearly from the manuscript: the objective framework can be quite useful from an operational point of view, but it ends up being a concatenation of standard approaches that consider a combination of standard indices for taking the final decision.
The authors state in answer 2 to my previous report that “they are not aware of any study comparing objectively the full procedure going from point measurements to mapped distribution”. It could be true, but considering that in the literature there are plenty of methodologies for comparing different parent distribution and different mapping approaches, even separately (the authors list some of them in the manuscript (P2 LL 25-29), for stressing the relevance of their work the authors should do a better job in underling the advantages of using the kind of “unified objective framework” they propose. Is it faster compared to adopting the assessment of the marginal and of the mapping technique separately? Is it more efficient? More powerful in rank the performance of the different models?
This point is not explored at all in the manuscript. Section 4.1 and 4.2 are dedicated, as the authors state in answer 1 to my previous report, to describe the results of the application to the case study, analysing the performance of the tested models with the proposed indices. This can be used for showing the significance of the proposed indices, but can this be considered a validation of the framework on its own? As mentioned in my previous revision, if a fair comparison with analogous techniques is not feasible, at least considering the results on a different basin could provide some sort of validation. Despite the basin is considered only for demonstration purposes, showing that the framework is able to provide the best distribution-mapping tool for any considered region, could be a good test for underling the potentialities of the framework in ranking the different considered models according to the input data.

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ED: Publish subject to minor revisions (review by editor) (09 Jan 2019) by Carlo De Michele

AR by J. Blanchet on behalf of the Authors (23 Jan 2019) Author's response Manuscript

ED: Publish as is (05 Feb 2019) by Carlo De Michele

Short summary

We propose an objective framework for estimating rainfall cumulative distribution functions in a region when data are only available at rain gauges. Our methodology allows us to assess goodness-of-fit of the full distribution, but with a particular focus on its tail. It is applied to daily rainfall in the Ardèche catchment in the south of France. Results show a preference for a mixture of Gamma distribution over seasons and weather patterns, with parameters interpolated with a thin plate spline.