15 Sep 2021
15 Sep 2021
Analysis of high streamflow extremes in climate change studies: How do we calibrate hydrological models?
 ^{1}Department of Civil, Environmental and Mechanical Engineering, University of Trento, Trento, I38123, Italy
 ^{2}Department of Engineering, Roma Tre University, Roma, I 00154, Italy
 ^{1}Department of Civil, Environmental and Mechanical Engineering, University of Trento, Trento, I38123, Italy
 ^{2}Department of Engineering, Roma Tre University, Roma, I 00154, Italy
Abstract. Climate change impact studies on hydrological extremes often rely on the use of hydrological models with parameters inferred by using observational data of daily streamflow. In this work we show that this is an error prone procedure when the interest is to develop reliable Empirical Cumulative Distribution Function curves of annual streamflow maximum. As an alternative approach we introduce a methodology, coined Hydrological Calibration of eXtremes (HyCoX), in which the calibration of the hydrological model is carried out by directly targeting the probability distribution of high flow extremes. In particular, hydrological simulations conducted during a reference period, as driven by climate models’ outputs, are constrained to maximize the probability that the modeled and observed high flow extremes belong to the same population. The application to the Adige river catchment (southeastern Alps, Italy) by means of HYPERstreamHS, a distributed hydrological model, showed that this procedure preserves statistical coherence and produce reliable quantiles of the annual maximum streamflow to be used in assessment studies.
Bruno Majone et al.
Status: final response (author comments only)

RC1: 'Comment on hess2021467', Anonymous Referee #1, 22 Oct 2021
The manuscript investigates different settings for calibration of hydrological models. Specifically, the authors focus on the reliability in representing streamflow extremes and analyze two major issues that arise when climate model forcing are used as input of hydrological models to assess possible change of discharge maxima, namely:
 Unreliable distribution of simulated streamflow maxima when hydrological models are calibrated by optimizing metrics designed to reliably reproduce ordinary streamflow
 Errors and biases attributable to the use of climate model forcing are used as input of hydrological models (when previously calibrated using ground data).
Although both the above issues are not new, they are often neglected in climate change studies. Here the authors present a tailored calibration approach to tackle both issues, i.e. providing a good and reliable representation of streamflow maxima when using climate model forcing as input of hydrological models.
The proposed approach is applied to a set of climate model outputs, as well as to ground data, to emphasize with exhaustive examples the magnitude of errors related to two issues.
In light of the above considerations, it is my opinion that the material and methods presented in the paper can be useful and of interest for HESS readers and, more in general, scientists interested in the field.
However, despite I recognize the potential interest of the paper, I have a major concern related to writing, since there are some parts of the manuscript that are unclear, sometimes there is unnecessary information or excessive repetition of information. Moreover, the text can also be better organized. For these reasons, I cannot recommend the publication of the actual manuscript, but I am confident that the material and results can be presented in an effective and informative exposition, if ALL the authors dedicate the due amount of time to proofread and revise the manuscript.
In the following I will provide some (not exhaustive examples related to my concerns.
 In Line 108 I read “where i is the position of Qs … and Qo… in the ranked samples of the simulated (s) and observed (o) annual streamflow maxima, respectively, ....” and a few lines below (lines 110112), the same information is repeated “As customary in statistics ðs … indicates the ranked time series of the annual maxima ðs … of simulated streamflow. A similar definition has been introduced for observed streamflow.” As a reviewer, I guess that authors assumed: i) that the reader knows what is a ranked variable, ii) that the reader know how to extract annual maxima from continuous time series (see my comment 5). Moreover, I notice also that no comment is provided on the rank ordering (i.e. decreasing or increasing), so I guess that the authors do not provide this in formation since this does not affect the result of eq. (1), and this is reasonable.
 Then I continue my reading and in lines 113119 I find an explanation of the pvalue (e.g. “The pvalue is the probability of rejecting the null hypothesis when it is true. It can also be defined as the smallest significance level ð¼ at which the null hypothesis would be rejected”). So the reader should know the meaning of ranked variables, but he should probably ignore the meaning of pvalue???? Maybe that a statement that pvalues associated to the KolmogorovSmirnov statistic is used as a metric of coherence between observed and simulated maxima would suffice.
 Eq. (2) in Line 124 provides the Weibull plotting position formula that is introduced in line 121 by the sentence “The daily average annual streamflow maxima are extracted from the chronological daily time series ….”, but authors forgot to state that this formula is not valid for chronological maxima, but for ranked records with increasing order.
 Line 143144 (just above eq.4) “simulated, ðs … and observed, ðo, flow duration curves (i.e., the ranked streamflow values this time in descending order)” and just after eq. 4 a repetition in line 146 “(ranked from the larger to the smaller value)”
 Lines 160163. Here it is explained with a confusing and wrong notation how annual maxima are extracted from a time series. Why this information is provided here and not before (see my comment 1)? Does the reader need this information?
 Lines 253254 and line 257 provide the same information (line 257 report a reference to eqs. 4 and 5). The two text can be merged (or reference to equation should be provided first).
 Section 4.2 provide much more details (e.g. on calibration process and confidence bands) than previous Section 4.1. …. Again: usually the due information should be provide that first time is needed.
 Maybe my previus comment n.7 on the way of writing can be skipped. Indeed I do not understand the choice to present first in Section 4.1 the calibration with CM and then in Section 4.2 the calibration with ground data (with more details). I would suggest to exchange the order of the two sections to show first the drawback when using CM forcing on hydrological models calibrated with ground data (i.e. the actual content of Section 4.2) and then the improvement when calibrating the hydrological model with the same forcing used for simulation (i.e. the actual content of Section 4.1).
 Lines 415420. It is not clear how calibration is performed. I guess that parameters are randomly selected according to uniform distributions (in a 12dimensional parameter space) bounded by the ranges in Table 3, but it is only my guess. The sampling rule should be clarified. It should be better clarified that 40000 have been consequently run and the best 200 ones retained (as I guess). What does “we considered the 100% confidence bands resulting from the retained solutions” means? I guess the maximum and minimum value of each parameter in the 200 retained simulations … is it?
The above points are not exhaustive, but I am confident that if the authors devote the due time, they can properly revise the whole manuscript to effectively convey their results.
 AC1: 'Reply on RC1', BRUNO MAJONE, 06 Dec 2021

RC2: 'Comment on hess2021467', Anonymous Referee #2, 21 Nov 2021
This paper calibrates a 12parameter conceptual hydrologic model (HYPERStreamHS) for the 9850km2 upper Adage River Basin (Italy), using observed data and biascorrected data of three regional climate models (EUROCORDEX), for the 19822010 reference period. The model is parameterized for the climate model data using (i) the Kolmogorov Smirnov (KS) statistic for the empirical distribution functions of annual extremes and (ii) flow duration curves. The KS test is subsequently used to test if the observed and simulated extremes are drawn from the same probability distribution. The paper also plots the parameter ranges of the 200 best solutions and models future streamflow extremes.
General comments
(1) The first key weakness of the research is that the authors calibrate 12 parameters of a conceptual hydrologic model using just 29 annual daily stream flow extremes. This is, of course, a terrible overparameterization. The effect of overparameterization on the streamflow simulations needs to be quantified.
(2) The second key weakness is that there is no evaluation (validation) of the parameterized models with an independent data series. How can we call this reliable and accurate? (Highlights, l.1819)
(3) Why not present the characteristics (figure, table) of the rainfall extremes of the observations and the climate models?
(4) It is not surprising that the KS test for comparing the empirical distributions of observed and modeled annual flow extremes will give a better result for the model optimized for these extremes with the KS statistic than for the models optimized with the flow duration curves or with the NSE. However, we can also understand that the KS test has its limitations (see Figure 3), so please present in this light.
(5) The paper is written in a wild wild way. We find Methods in the Introduction, Methods in the Results and Discussion, Introduction in the Results and Discussion, no specific research objectives in the Introduction, inexact language, superfluous text and many repetitions.
(6) In summary, the paper needs to be completely restructured and rewritten in a concise and quantitative manner. Uncertainties stemming from the two key weaknesses (1 and 2 above) need to be quantitatively addressed, metrics and pvalues of section 4.1 and 4.2 should be summarized together in one clear table. Expressions such as statistical coherence, forward simulations, extrapolations, 100% confidence bands (!?) need to be defined in the Methods and possibly reworded.
Specific comments (non exhaustive)
l.8: error prone
RC: Please quantify. The majority of your models are accepted, according to your KS pvalue.
l.39 Much less ?
l.57: iii) due to the impossibility of obtaining totally unbiased climate simulations there is no apriori guarantee that simulations fed by climate models produce samples (e.g. time series of simulated annual streamflow maximum) that are statistically coherent with observations.
RC: Your approach cannot address this problem either.
l.61: by directly targeting
RC: nonscientific language
l.6473: These are Methods
l.66: are constrained to maximize the chances ?
l.67: Statistical coherence
RC: Please define statistical coherence or use another expression.
l.75: Do we really need six references for “goaloriented”?
l.102: Section 2.2
RC: It would make more sense to present this after Section 2.4
l.111: A similar definition has been introduced for observed streamflow.
RC What writing style is this?!
l.113119: State your null hypothesis and condense this text.
l.120125: Does this need a numbered Section?
l.121: daily average
RC: average daily
l.135158: The efficiency criteria are without the max and min.
l.138: sensitive ?
l.146: repetition
l.162166: RC: Please condense.
l.171: adaptation ?
l.172: for comparison purposes in order to extrapolate
RC: Now what is it?
l.181: portion ?
l.288: parametric errors,
RC: Without comma and what do you mean? All models are simplifications of reality.
l.233: provide an assessment ?
l.244: the correction used in the reference period 19892010 is extended to the period 19802010
RC: This is not clear. Is this done by you and if so how?
l.253257: RC: Methods
l.260: On the other hand
RC: Which other?
l.278: cast ?
l.279284: RC: Introduction
l.311: coined here as Hydrological Calibration on Extremes (HyCoX)
RC: Repetition
l.326335: RC: Methods and Introduction
l.370: Fig 3
RC: It will be easier to follow if all metrics and pvalues are presented together in Table 2.
l.373: Forward ?
l.377: the 90% confidence interval of the observed ECDF
RC: of the fitted extreme value distribution function?
l.407: Extrapolation ?
l.418: 100% confidence bands ?!
l.429: Furthermore, we verified aposteriori that the optimal parameters are inside the range of variation.
RC: The methods are unclear. Is this “range of variation” (please use a better expression) for the 40,000 simulations? How can the optimal parameter fall outside the range?
l.440: The differences observed in the optimal value of model parameters are due to structural errors in the GCMs and RCMs
RC: Really? And now we use these errors to make an erroneous hydrologic model, without any independent model validation. One can understand that there are two modelling approaches each with assumptions and uncertainties. So please stick to quantitative evidence.
l.446: Furthermore, our approach provides an answer to the need of reducing uncertainty in climate change impact assessments
RC: Please quantify your uncertainty reduction.
l.452: Marked dashes ?
l.490594: RC: Please be concise. Answer your research objectives, which you should have stated in the Introduction.
 AC2: 'Reply on RC2', BRUNO MAJONE, 06 Dec 2021
Bruno Majone et al.
Bruno Majone et al.
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