Geostatistical interpolation by quantile kriging

Lebrenz, Henning; Bárdossy, András

doi:https://doi.org/10.5194/hess-23-1633-2019

Articles | Volume 23, issue 3

https://doi.org/10.5194/hess-23-1633-2019

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

https://doi.org/10.5194/hess-23-1633-2019

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

Articles | Volume 23, issue 3

Research article

| Highlight paper

|

20 Mar 2019

Research article | Highlight paper |

| 20 Mar 2019

Geostatistical interpolation by quantile kriging

Henning Lebrenz and András Bárdossy

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Final revised paper (published on 20 Mar 2019)
Preprint (discussion started on 30 May 2018)

Interactive discussion

Status: closed

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

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RC1: 'The proposed technique is a step further in overcoming kriging limitations in rainfall interpolation', Anonymous Referee #1, 18 Jun 2018
- AC1: 'Responses on the Referees 1 comments on the submitted manuscript hess-2018-276', Henning Lebrenz, 14 Aug 2018
RC2: 'Intriguing, but lacks statistical rigor', Anonymous Referee #2, 27 Jun 2018
- AC3: 'Responses on the Referees 2 comments on the submitted manuscript hess-2018-276', Henning Lebrenz, 14 Aug 2018
- AC4: '2nd Response to Reviewer 2', Henning Lebrenz, 02 Oct 2018
RC3: 'Interesting approach to kriging with skewed variables and to non-stationarity', Anonymous Referee #3, 02 Jul 2018
- AC2: 'Responses on the Referees 3 comments on the submitted manuscript hess-2018-276', Henning Lebrenz, 14 Aug 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) (27 Aug 2018) by Sally Thompson

AR by Henning Lebrenz on behalf of the Authors (16 Nov 2018) Author's response Manuscript

ED: Publish subject to revisions (further review by editor and referees) (21 Nov 2018) by Sally Thompson

ED: Referee Nomination & Report Request started (02 Jan 2019) by Sally Thompson

RR by Marc F. Muller (07 Feb 2019)

Suggestions for revision or reasons for rejection

The authors have satisfactorily addressed my concerns from the last submission. I particularly appreciate your effort to explain the intuition behind the approach and the assumed underlying stochastic processes (now in Section 2.2). This makes the whole paper much clearer (and, I believe, more enjoyable to read), and allows the reader to better appreciate the depth of this paper's contribution. This is now a very nice paper and I am looking forward to seeing it published in HESS. I have a few minor suggestions that I think would improve the clarity of the paper:

1. The approach proposed is complex with numerous steps and intermediate variables. Perhaps a flow chart would be useful in (i) identifying the letter-variables (e.g., so we immediately know that u refers to the gaussian quantiles when referred to in the text) and (ii) providing a map of what transformation applies to which variable. I have attached a rough sketch of what I have in mind.

2. In the introduction, you rightly point out that temporal variations are a key feature of hydrologic variables, as opposed to the much more static geology context in which kriging was originally developed. However, when I think "hydrology", I immediately think streamflow. Of course, I realize that your paper is about rainfall, not streamflow, but I think it would be worth mentioning (here or perhaps in the conclusion) that the approach you propose is limited to spatially distributed variables. This includes rainfall, but not streamflow, which is a spatially aggregated variable that is distributed along a stream network. For this, other geostatistical approaches that account for river network topologies can be referred to (e.g., Skoien et al 2006, Muller and Thompson 2015 and Cressie et al 2006). Perhaps an interesting avenue for further research would be to extend you approach, which accounts for temporal variations, to stream networks (?).

References:
Skøien, J. O., Merz, R., and Blöschl, G.: Top-kriging - geostatistics on stream networks, Hydrol. Earth Syst. Sci., 10, 277-287, https://doi.org/10.5194/hess-10-277-2006, 2006.

Müller, M. F. and Thompson, S. E.: TopREML: a topological restricted maximum likelihood approach to regionalize trended runoff signatures in stream networks, Hydrol. Earth Syst. Sci., 19, 2925-2942, https://doi.org/10.5194/hess-19-2925-2015, 2015.

Cressie, N., Frey, J., Harch, B., and Smith, M.: Spatial prediction on a river network, J. Agr. Biol. Environ. Stat., 11, 127–150, 2006

Referee Report: PDF

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ED: Publish subject to minor revisions (review by editor) (20 Feb 2019) by Sally Thompson

AR by Henning Lebrenz on behalf of the Authors (01 Mar 2019) Manuscript

ED: Publish as is (05 Mar 2019) by Sally Thompson

AR by Henning Lebrenz on behalf of the Authors (05 Mar 2019)

Short summary

Many variables, e.g., in hydrology, geology, and social sciences, are only observed at a few distinct measurement locations, and their actual distribution in the entire space remains unknown. We introduce the new geostatistical interpolation method of quantile kriging, providing an improved estimator and associated uncertainty. It can also host variables, which would not fulfill the implicit presumptions of the traditional geostatistical interpolation methods.