The probability distribution of daily precipitation at the point  and catchment scales in the United States

Ye, Lei; Hanson, Lars S.; Ding, Pengqi; Wang, Dingbao; Vogel, Richard M.

doi:https://doi.org/10.5194/hess-22-6519-2018

Articles | Volume 22, issue 12

https://doi.org/10.5194/hess-22-6519-2018

© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/hess-22-6519-2018

© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 22, issue 12

Research article

|

17 Dec 2018

Research article |

| 17 Dec 2018

The probability distribution of daily precipitation at the point and catchment scales in the United States

Lei Ye, Lars S. Hanson, Pengqi Ding, Dingbao Wang, and Richard M. Vogel

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Final revised paper (published on 17 Dec 2018)
Preprint (discussion started on 01 Mar 2018)

Interactive discussion

Status: closed

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

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- Supplement

RC1: 'Data from processes with mixed-type marginals cannot be treated using continuous marginals', Simon Michael Papalexiou, 28 Mar 2018
- AC1: ''Response to RC1', Lei Ye, 21 Jun 2018', Lei Ye, 21 Jun 2018
RC2: 'Review of paper by Ye et al.', Anonymous Referee #2, 26 Apr 2018
- AC2: 'Response to RC2', Lei Ye, 21 Jun 2018
RC3: 'Review of submitted paper from Ye et al.', Anonymous Referee #3, 26 Apr 2018
- AC3: ''Response to RC3', Lei Ye, 21 Jun 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) (21 Jun 2018) by Louise Slater

AR by Lei Ye on behalf of the Authors (26 Sep 2018) Author's response Manuscript

ED: Referee Nomination & Report Request started (30 Sep 2018) by Louise Slater

RR by Simon Michael Papalexiou (28 Oct 2018)

Suggestions for revision or reasons for rejection

The authors have put a significant effort to improve the manuscript and corrected its major flaw. As in my first review, I believe the paper adds to the literature of statistical hydrology as its one of the few (maybe the only one) studying the distribution of precipitation at the catchment level. There are several minor points that need corrections; I would also like to propose a couple of minor suggestions to improve the paper, and provide an explanation to a point related to one of my previous works. My recommendation is publication after the following corrections:
Abstract: Personally, I would avoid a direct comparison of two- (G2) and three-parameter distributions (P3). Especially, since P3 is a generalization of G2 with an additional location parameter then “by definition” always will perform better. So maybe the authors wish to reform these statements.
Heading: In some heading authors are using “:” in the end that is not necessary.
Section 1.1: The GG was also used in stochastic modelling of precipitation, see Fig.5 for hourly and Fig.6 for daily in Papalexiou (2018). Actually any distribution that describes well wet-day precipitation (or at any other scale) can be used as this stochastic modelling scheme makes feasible to use any probability distribution and any correlation structure. Additionally, the GG was also used to generate gridded daily precipitation that is consistent with monthly observations (see Fig. 11 in Papalexiou et al., 2018).
L147: Here is mentioned that there is a consensus in using GEV, G, or GPA, for annual maxima. I would agree for G and GEV but the GPA is mainly used for peak above threshold values. Most of annual maxima samples have a bell-shaped density while the GPA is always J-shaped and of course its origin is from the Pickands–Balkema–de Haan theorem which refers to POT values.
L160. Please delete the “generalized” before the “Burr type XII”. Also just to explain the point made by the authors in in the following lines regarding L-skew/L-kurt diagrams for the GG and BrXII(of course they do not have to add this in the manuscript). The truth is that they exist and I had formed the theoretical spaces similar to L-CV/L-skew but the problem was that the space was not “one-to-one”, I mean that for different shape-parameters points the same point in the L-skew/L-kurt emerged. So, it was not possible to depict the theoretical space without avoiding overlapping.
L217: Since the authors are not including zeros in the analysis (and that is correct) there is no point to mention zeros a possible explanation of the skewness. So, the distribution of daily totals (of wet days of course) is highly skewed due to small nonzero values and high variance, i.e., since its bounded at zero and there is a high frequency of close-to-zero values and the variance is high then inevitable this creates the positive skewness.
L265: use italics for p, n and i, to display the equation properly.
Section 4.1.2: I think the explanation why points shift towards the G2 or P3 curve is due to the areal averaging process which lowers the variance and the kurtosis. I am a bit surprised though that I do not see lower values of skewness.
L321: At least in the title (4.2) I would suggest not using the abbreviation PPCC
L388: I am sure that the statement “the KAP is required to capture the tail behavior…” is a bit risky. I stress again that the Kappa distribution is a four parameter distribution and therefore has a huge flexibility and can fit to anything. Yet this does not imply that it can capture the behavior of the tail; the extrapolations could be very risky especially if estimation is based on small samples.
Table 2: An optional suggestion: there is a huge mess in the literature regarding the parameter symbols used in distribution which creates confusion. For example, here η, ω, ξ, μ, σ ,p, d, λ, β, b, φ, κ etc are used. There are only 3 type of parameters, location, scale and shape. I personally follow a clear and simple convention, i.e., α for location, β for scale, and γ for shape; if more than one parameter of the same type exist I use indices (γ_1, γ_2). This allows the reader to know the function of the parameters. Of course there are classical cases like the normal distribution where is standard to μ and σ due to the link with mean an sd. Please check the equations: the P3 authors show is something between Weibull and Gamma. To simplify reading authors can use exp instead of e. Check how equation are depicted, probably authors introduced eqs as pictures that creates distortion and unequal font size. Authors are not showing the Kappa distribution as it forms a space, but for completeness I would suggest to provide its formula.
Table 3: The Generalized Pareto is not the GP2, either correct the name or the equation. Please, correct the formula of the Weibull distribution, you are using exp and then superscript; no need for {} or [].
Figure 2: X-axis maybe days? The same holds for Fig.3
Fig 5. I mentioned that before. The theoretical lines of G2 = P3, GP2 = GPA, LN2 = LN3 for Lskew-Lkurt diagrams. Authors can mention that if they wish.
Sincerely,
Simon Michael Papalexiou
References
Papalexiou, S.M., 2018. Unified theory for stochastic modelling of hydroclimatic processes: Preserving marginal distributions, correlation structures, and intermittency. Advances in Water Resources 115, 234–252. https://doi.org/10.1016/j.advwatres.2018.02.013
Papalexiou, S.M., Markonis, Y., Lombardo, F., AghaKouchak, A., Foufoula‐Georgiou, E., 2018. Precise Temporal Disaggregation Preserving Marginals and Correlations (DiPMaC) for Stationary and Nonstationary Processes. Water Resources Research. https://doi.org/10.1029/2018WR022726

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RR by Anonymous Referee #3 (10 Nov 2018)

ED: Publish subject to technical corrections (11 Nov 2018) by Louise Slater

AR by Lei Ye on behalf of the Authors (19 Nov 2018) Author's response Manuscript