Drought severity–duration–frequency curves: a foundation for risk assessment and planning tool for ecosystem establishment in post-mining landscapes

Halwatura, D.; Lechner, A. M.; Arnold, S.

doi:https://doi.org/10.5194/hess-19-1069-2015

Articles | Volume 19, issue 2

https://doi.org/10.5194/hess-19-1069-2015

© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/hess-19-1069-2015

© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 19, issue 2

Research article

|

26 Feb 2015

Research article |

| 26 Feb 2015

Drought severity–duration–frequency curves: a foundation for risk assessment and planning tool for ecosystem establishment in post-mining landscapes

D. Halwatura, A. M. Lechner, and S. Arnold

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Final revised paper (published on 26 Feb 2015)
Preprint (discussion started on 13 May 2014)

Interactive discussion

Status: closed

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

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RC C1792: 'Design droughts as planning tool for ecosystem establishment in post-mining landscapes', Anonymous Referee #1, 09 Jun 2014
- AC C2509: 'Comments for the anonymous referee #1', Devanmini Halwatura, 16 Jul 2014
RC C2130: 'Reviewer comment', Anonymous Referee #2, 30 Jun 2014
- AC C2897: 'Responses to reviewer #2', Devanmini Halwatura, 04 Aug 2014

Peer-review completion

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

ED: Reconsider after major revisions (22 Jul 2014) by Nadia Ursino

AR by Devanmini Halwatura on behalf of the Authors (06 Aug 2014) Author's response Manuscript

ED: Reconsider after major revisions (07 Aug 2014) by Nadia Ursino

AR by Devanmini Halwatura on behalf of the Authors (11 Aug 2014) Author's response Manuscript

ED: Referee Nomination & Report Request started (11 Aug 2014) by Nadia Ursino

RR by Anonymous Referee #1 (19 Aug 2014)

RR by C Prakash Khedun (14 Oct 2014)

RR by Anonymous Referee #4 (15 Oct 2014)

Suggestions for revision or reasons for rejection

Main comments
The paper illustrates the application of Severity-Duration-Frequency (SDF) curves of droughts as a risk-based planning tool in the rehabilitation of post-mining landscapes. The topic is interesting, even if it is not particularly original, since applications of SDF curves of drought are already present in literature (Dalezios et al., 2000; Shiau and Modarres, 2009; Todisco et al., 2009, Reddy and Ganguli, 2012). For example in Shiau and Modarres (2009), SDF curves derived from copula models are obtained (based on SPI); in Todisco et al. (2013) SDF curves are derived empirically and based on an agricultural drought index. Some innovative aspects can be found in the use of indices other than SPI (RDI and SPEI), but (as acknowledged by the authors themselves), the specific aims considered in the paper would require the adoption of agricultural drought indices (able to evaluate the role played by soil characteristics).
In my opinion the paper requires a major revision for the reasons detailed in the following points.
1) The first observation is about the method used by the authors to derive the SDF curves (shown in figures 6 and 7, for the OR condition and in Appendix D for the AND condition). These curves represent joint drought duration and severity return periods (Shiau, 2006) and from a statistical viewpoint they actually link duration, severity and frequency. Moreover, we think that the information obtained from these curves could be used with proficiency for the aims of the paper (i.e. to find drought management strategies well-matched with the specific behaviour of the drought characteristics D and S).The problem is that IDF curves (for rainfall) as well as SDF curves (for drought) have to be derived from joint conditional probabilities (Singh and Zhang, 2007; Shiau and Modarres, 2009) and not from simple joint probabilities (as done by the authors in the paper). There are differences from both the statistical and practical viewpoint. For drought management purposes, the type of curves given in fig. 6 and 7 could be exhaustive, but these curves are different from those that are usually called SDF. The authors should clarify this point taking into account the references given above.
2) At line 16 of page 6 the authors indicate that in Appendix A there is a description of the equations required for the calculation of the considered drought indices (namely SPI, RDI, SPEI). Appendix A contains many inaccuracies and errors:
a. The equation provided for SPI (A1) is not related to its calculation, but to the calculation of the severity of a drought event, based on SPI. This information, in a slightly different form, is already given in the text (pag. 6 line 27). Anyway, nothing is said about SPI calculation in Appendix A.
b. For RDI two equations are provided (A2 and A3). The explanation of the terms that appear in these equations is confusing (lines 8-9) and contains some errors. There is also a reference to a term not reported in the equations (Yk).
c. For SPEI, only the final part of the index calculation is provided (eq. A4, A5) and there is a reference to a not defined D value. In the paper D stands for Duration of drought, but in SPEI calculation it should represent the difference between precipitation and reference evapotranspiration. Moreover, equations A4 and A5 are not specific for SPEI, since they are also used for SPI (it is just necessary to change the reference variable).
In practice Appendix A is completely useless in the present form.
3) In the application of copula models, the selection of both univariate distributions and copula models is critical for the reliability of the application. In the paper, the results of these selection processes can be only deduced from figure 2, but the authors do not provide any discussion. For example: what is the goodness of fit criterion used for univariate distributions? Why Frank copula is judged better than Gumbel copula?
4) In the section “future research” the authors indicate the opportunity to introduce in this type of application, some information related to soil properties (for example by using agricultural drought indices instead of meteorological drought indices). This could, actually, improve the reliability of the application. Anyway, if the objective is the minimization of the risk of failure of initial ecosystem establishment, the use of a standardized index (meteorological or agricultural) could have some weak points. Indeed, the risk of failure related to the establishment of a certain vegetation type, is more dependent on the absolute (and not relative) availability of water. For example a SPI value of -1 in winter at Sydney (table 1) should have no practical consequences on vegetation, because the normal (i.e. SPI=0) rainfall amount, can likely determine a surplus condition in terms of plant water availability. This aspect should be discussed by the authors.

Minor points
1) Line 24 pag. 6: the reference to rainfall deficit is not completely correct since RDI and SPEI are based not only on rainfall.
2) Line 30 pag. 6: a brief description of the methods and criteria used to assess the goodness of fit of D and S marginal distribution should be provided.
3) Lines 28-30 pag.7 and lines1-4 pag.8: The authors probably want to describe the procedures adopted for the copula model selection (Frank or Gumbel) not for parameters selection (the parameter fitting is obtained by the IFM method as already explained by the authors).
4) Lines 3-4 pag.8: Section 2 is for the description of the methods. The information that the best distribution for S and D are respectively the gamma and the logistic, should be reported(and possibly discussed) in the result section.
5) Line 18 pag. 8: Appendix C instead of D
6) Lines 23-24 pag.8 and fig.4. In our opinion a comparison of two different indices (RDI and SPEI) at two different time scales (3 and 12 months) makes not sense. And the observation at lines 25-26 is a logical consequence of the fact that the shorter the time scale, the higher is the oscillation frequency of the index time series, so shorter duration and severities are expected (but more drought events).
References
Dalezios NR, Loukas A, Vasiliades L, Liiakopoulos E (2000) Severity–duration–frequency analysis of droughts and wet periods in Greece. Hydrol Sci J 45(5):751–770.
Reddy, MJ Ganguli P, Application of copulas for derivation of drought severity–duration–frequency curves, Hydrological Processes, 26, 1672-1685
Shiau JT, Modarres R (2009) Copula-based drought severity–duration–frequency analysis in Iran. Meteorol Appl 16:481–489.
Shiau JT (2006) Fitting drought duration and severity with two-dimensional copulas, water resources management, 20: 795-815.
Singh VP, Zhang L. (2007), IDF curves using Frank Archimedean copula, J Hydrologic engineering, 12(6) 651-662
F. Todisco, F. Mannocchi , L. Vergni, (2013) Severity–duration–frequency curves in the mitigation of drought impact: an agricultural case study, Nat Hazards (2013) 65:1863–1881 .

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ED: Reconsider after major revisions (22 Oct 2014) by Nadia Ursino

AR by Devanmini Halwatura on behalf of the Authors (02 Dec 2014) Author's response Manuscript

ED: Referee Nomination & Report Request started (02 Dec 2014) by Nadia Ursino

RR by Anonymous Referee #5 (14 Dec 2014)

RR by Anonymous Referee #6 (18 Dec 2014)

ED: Reconsider after major revisions (18 Dec 2014) by Nadia Ursino

AR by Devanmini Halwatura on behalf of the Authors (28 Jan 2015) Author's response Manuscript

ED: Publish as is (30 Jan 2015) by Nadia Ursino

AR by Devanmini Halwatura on behalf of the Authors (04 Feb 2015)