The paper ‘Flexible and Consistent Quantile Estimation for Intensity-Duration-Frequency Curves’ by Fauer et al. provides a timely discussion about intensity-duration-frequency (IDF) analysis of sub-daily rainfall intensities. They present and discuss a flexible method for calculating IDF curves based on a new parametric approach and evaluate three different options. 

Due to the small samples of the rainfall from clouds which rain gauges with a diameter of centimetres represent, I wonder if it's justifiable to combine data from stations with a distance below 250 m into a single station data set. It’s probably OK for the statistical properties, but maybe not so for the raw data - especially on short time intervals (too much random sampling noise?). At least, there ought to be a test of the robustness of the results to this assumption. 

Perhaps it would make the flow of the text better if there was some connection between the return value (probability) and the quantile? I thought the part on Quantile Skill Index (e.q. 13) wasn’t as easy to follow as the preceding sections (how does it link to the preceding discussion on the GEV and the estimation of the parameters?). 

The description of the bootstrapping was a bit difficult to follow - perhaps explain it more carefully or add an illustration?

Very brief catches (e.g. minutes) of rainfall with rain gauges are expected to be subject to a large degree of sampling uncertainty, aren't they? (depending on the number of rain drops falling onto the cross section representing the measurement). Maybe this also can explain some discrepancies at the extreme short end of the scale? 

One reason why annual maxima of different durations do not follow the same scaling process could be that different rain-producing meteorological phenomena have different temporal and spatial scales. If the rainfall can be considered as a ‘by-product’ of different processes and conditions (e.g. convection, weather fronts, cyclones, and derechoes), then different statistics may perhaps show the true situation? But I’m still struggling to understand what the skill estimates really say.   

A new and relevant paper DOI: 10.1088/1748-9326/abd4ab suggests a simple formula for expressing IDF curves even for sites with limited data. This formula is based on more ‘physical’ parameters (wet-day mean precipitation and wet-day frequency), rather than the stronger reliance on the statistical/mathematical theory behind GEV. It would be interesting to compare the results presented here with this formula. It also fits in the comparison of different ways to parametrize IDF curves. At least, it could be included in the introduction and the discussion of different ways of calculating IDFs.

Appendices: when describing what calculations and processing was done in this analysis, it’s more elegant to use past tense rather than present tense (my subjective opinion). But mixing past and present tense makes the text inconsistent and a ‘clumsy’ read. Also check the references therein (‘??’). 

The paper proposes a new flexible approach to derive IDF relationships enabling curvature or multiscaling features to model very short or long-duration rainfall. The paper adds value in modeling short-duration rainfall and I suggest minor revisions:

1. Line # 29: could be written as Methods
2. In lines # 65-70: A few aspects of nonstationarity could be discussed here, discuss briefly the added value of this study to address nonstationarity as compared to the methods discussed in the literature (Cheng and AghaKouchak 2014; Ganguli and Coulibaly 2017).
3. Section 2.1: Lines 90 – 95: This is not very clear - why 8 stations were merged into a single station leaving 92 overall stations out of 100 stations? Which physiographic or hydrologic similarity measures were adopted for regionalization?
4. It has been shown in the literature that the Generalized Maximum likelihood method, in general, does not provide a credible estimate of the shape parameter, yielding an abrupt estimate of shape estimate (Martins and Stedinger 2000). Have your values lie within the credible limits of shape parameter range as shown in the literature, boxplots showing the range of shape parameters for different duration could help to identify this issue
5. In skill score index in lines 190-200: what M and R represent, If R denotes empirical distribution, which empirical plotting position formula was used to estimate it? Typically Gringorten's plotting position formula is in use to characterize extremes.
6. Fig. 7: Could you please show the difference in return levels in an inset diagram with vs without flattening? How much is the percentage difference between the two statistics in order to qualify as significant?
7. Between lines 360-363: Any discussion on copula-based IDF estimation that claims to preserve the inherent non-linearity between intensity vs duration?
8. Line # 433: few outlying events correspond to higher quantile (or at the tail of the distribution) leave the confidence intervals.

References

Cheng L, AghaKouchak A (2014) Nonstationary Precipitation Intensity-Duration-Frequency Curves for Infrastructure Design in a Changing Climate. Scientific Reports 4:srep07093. https://doi.org/10.1038/srep07093

Ganguli P, Coulibaly P (2017) Does Nonstationarity in Rainfall Requires Nonstationary Intensity-Duration-Frequency Curves? Hydrol Earth Syst Sci Discuss 2017:1–31. https://doi.org/10.5194/hess-2017-325

Martins ES, Stedinger JR (2000) Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data. Water Resources Research 36:737–744

The manuscript presents a very interesting and timely discussion on development of IDF curves using duration dependent GEV distribution. The authors have investigated various formulations of duration dependent GEV distribution by considering features like flattening, multiscaling and curvature observed in IDF curves. The discussion based on the comparison of the performance of different models is well presented. 

Some minor points that need clarification are as follows:

• How was the value of z_n estimated (refer equation 13) for computing the Quantile Skill Index (QSI)? Did the authors perform any sensitivity  analysis to evaluate the effect of plotting position used on QSI? 
• The cross validation setting used needs a more clear explanation. How was the block for cross validation choosen?
• Section 2.6 on boot strapping and coverage is confusing and needs a more clear description.

The authors provided a flexible model for constructing the consistent IDF curves by revising the duration-dependent formulation. They investigated the impacts of features like curvature, multi-scaling and flattening on the performance of deviation of IDF curves, and also considers the combination of these features. Overall, I think the novelty of this study is well, and that the paper is relatively well presented. Besides, I have several comments about the manuscript. 

Comments:

1. In this study, the authors investigated the features of curvature, multi-scaling and flattening on the deviation of IDF curves under the stationary assumption. Particularly, the parameters of GEV are modelled as functions of duration. Do you consider the impacts of climate change on the IDF under a changing environment? There are studies who try to update the IDF curves considering the nonstationarity, such as Agilan and Umamahesh (2017) and Ganguli Coulibaly (2017), and Yan et al. (2021) provided a review about this topic. In a nonstationary model, the parameters are modelled as function of covariates, please make a discussion or outlook about this topic, which should be highlighted under the changing environment.

References:

Agilan, V., & Umamahesh, N. V. (2017). What are the best covariates for developing non-stationary rainfall intensity-duration-frequency relationship? Advances in Water Resources, 101, 11–22.

Ganguli, P., & Coulibaly, P. (2017). Does nonstationarity in rainfall require nonstationary intensity-duration-frequency curves? Hydrology and Earth System Sciences, 21(12), 6461–6483. 

Yan L, Xiong L, Jiang C, Zhang M, Wang D, Xu C-Y. (2021) Updating intensity–duration–frequency curves for urban infrastructure design under a changing environment. WIREs Water. 2021; e1519. 

2. In this study, the authors just consider the GEV distribution for the deviation of IDF, I think for the study area, lognormal or Gamma distribution may also exhibit comparative or better performance. It makes sense for engineering design to try other probability distributions and compare the results.

3. Make a discussion about the deviation of the copula-based IDF curves.

4. For Figure 3, the Quantile skill index is difficult to understand, please make a clearer legend for potential readers.