Statistical Analysis of Extreme Events in Precipitation, Stream Discharge, and Groundwater Head Fluctuation: Distribution, Memory, and Correlation

Round 1

Reviewer 1 Report

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Comments for author File: Comments.docx

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

The authors present an interesting study about hydrological extremes. I believe the topic and the application presented have an interest to readers of the journal. Moreover, the kind of results that are discussed in this case study have also an interest to practitioners and researches.

But there exists a strong and solid state of the art concerning procedures, tests, methods and criteria employed in the context of statistical analysis of hydrological extremes, which apparently is ignored in many essential aspects by the authors.

Consequently, and from my point of view, some important work should be done, including major revision of the manuscript, in order to attend the mentioned issue. Some comments below might be useful in this concern:

Concerning distribution fittings, the proper way to do it should be using a convenient and justified parameter estimation procedure (maximum likelihood, moments, weighted moments, etc… ).  The authors do not report any method.

On the other hand, figures 6, 7 and 8 would be much clearer if the usual –LN [-LN F] scale is used, to visualize clearly the behavior of the different CDF used in the study. The authors can find hundreds of studies about extreme distribution functions in hydrology, using this kind of formats to present and compare results, starting with a convenient plotting position criteria.

To compare performance or goodness for the several distributions used, adequate tests for this purpose should be used, which is not the case in the manuscript.

The Gumbel distribution is a classical, well known distribution of extended use internationally. I suggest to rewrite equation (7) in some of the usual formats employed commonly in hydrological engineering applications. In any case, it is not well expressed as it is now written in the manuscript.

Is there any justification to take 6 hours as the minimum interval to separate independent rainfall events?. There are different approaches in the literature tackling this issue. See REstrepo-Posada and others. Surely, the adoption of such criteria needs some additional explanation.

The authors report a good behavior of the stretched Gaussian distribution describing storm properties for both the extreme values and also the entire data sets.

But for other variables studied, they do not find a clear best distribution. At this point, it is meaningful to test some of the most popular and most frequently used distributions in hydrology for this purposes [GEV, TCEV, GP, SQRT-ETmax, log-Pearson III, etc, …]

Due to the statistical approach of the presented research, it is clear that the introduction of this kind of distributions makes sense, and will enrich the study, probably yielding to better statistical representations.

Please, correct the following list of spelling errors:

243: precipitation

253: recordered

256: previous

259: measurement

273: precipitation

292: introduced

333: necessarily; dryer

324: Name of the parameters

337: consensus

338: variable

343: First, a?

Please, re-write the sentence:

335: Changing climate is likely the driver for these changes creating more intense.

Author Response

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Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

For my part, the manuscript can be accepted in the present form. Concerning some of the issues mentioned in my review, my opinion is that there are several ways to rigorously and adequately perform a statistical extreme value analysis, and also specific ways to clearly represent results after such an analysis. And I personally believe that authors might be interested in them, in case their research lines continue linked to these matters.

An example of one of them, that might be of interest for the authors as a typical example, can be found in the following link. See figure 1 in the following paper:

https://journals.ametsoc.org/doi/pdf/10.1175/JAM2349.1

Other commonly used alternatives can be found in the following LINK [“Frequency analysis of Extreme Events”]. Also, the authors can find interesting considerations about DISTRIBUTION FUNCTIONS, PARAMETER ESTIMATION, PROBABILITY PLOTS, and GOODNESS-OF-FIT TESTS.

https://engineering.tufts.edu/cee/people/vogel/documents/frequencyAnalysis.pdf

Author Response

We would like to thank the reviewer for their endorsement of our manuscript, and their first round of reviews which have greatly improved our manuscript. These references you sent us on extreme value plotting, and the frequency analysis chapter are helpful, and we will incorporate them into our future works.  We appreciate the time you’ve taken to read and give thoughtful comments that will improve our works.