the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 13 Mar 2025
Gridded Intensity-Duration-Frequency (IDF) curves: understanding precipitation extremes in a drying climate
Abstract. Traditionally, Intensity-Duration-Frequency (IDF) curves are based on rain gauge data under the assumption of stationarity. However, only limited long time series of sub-daily precipitation data are available worldwide, making it difficult to accurately estimate precipitation intensity for different durations and return periods, while climate change is challenging stationarity. This study aims to better understand how the stationary assumption and data length of hourly precipitation data influence the annual maximum intensities of precipitation events in continental Chile, a region with varying climate and topography that has been affected by an unprecedented drought since 2010. Five hourly gridded precipitation datasets (IMEGv06B, IMERGv07B, ERA5, ERA5-Land, CMORPH-CDR) and 161 quality-checked rain gauges are used to compute annual maximum intensities (Imax, mm h−1) using the stationary and non-stationary Gumbel distribution for six return periods (2–100 years) and 11 durations (1–72 h). Bias-correction factors are applied to match the gridded Imax values with the in situ ones, and the modified Mann-Kendall test is used to assess the trends in Imax. Annual maximum intensities are calculated for the 20-year period (2001–2021) for all products, while an additional 40-year period (1981–2021) is used for ERA5 and ERA5-Land to assess the impact of data length. Our results revealed significant decreasing trends across Chile for CMORPH-CDR, decreas-ing trends in Central-Southern Chile (32–43° S) for ERA5 and ERA5-Land, and isolated, divergent trends for IMERGv06B and IMERGv07B. In addition, our results show that Imax reaches its maximum values in central and southern Chile, for all durations, in contrast to the mean annual precipitation, which increases steadily towards the south. For durations of 24 hours or more, the highest intensities are primarily found in the Andes, particularly between the Maule and Araucanía region (35–40° S). While the Imax values were similar for IMERGv07B, ERA5 and ERA5-Land, they were much higher for IMERGv06B and CMORPH-CDR. The difference between stationary and non-stationary Imax values ranges from 0 to 5 mm h−1 and become smaller for durations greater than 8 h. Despite the differences observed in the Gumbel parameters for ERA5 and ERA5-Land when using 20- and 40-year records, the resulting Imax values showed differences with median values below 1 mm −1. The Imax values are available on a public and user-friendly web platform (https://curvasIDF.cl/).
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CC1: 'Comment on egusphere-2025-621', Rasmus Benestad, 21 Mar 2025
I had a quick scan of the paper, and thought that the authors may be interested in some related work from Norway where efforts have been on estimating the shape of the curves representing IDFs directly rather than individual return values. See e.g. https://doi.org/10.5194/hess-27-3719-2023 and https://doi.org/10.1088/1748-9326/abd4ab
Citation: https://doi.org/10.5194/egusphere-2025-621-CC1 -
RC1: 'Comment on egusphere-2025-621', Anonymous Referee #1, 02 May 2025
In this study, the Authors propose an IDF model for Chile by estimating the spatial maximum precipitation intensities, in varying climatic conditions and topography, through gridded (of 5 datasets) and 161 gauged hourly precipitation data by using stationary and non-stationary Gumbel distribution models. Please see several major and minor issues that I hope they ca be of help to the Authors:
1) Regarding the traditional methods in the literature, please see a recent and the most advanced stochaatic framework for the stationary IDF curves with application in the entire country of Greece by Koutsoyiannis et al. (2024; https://doi.org/10.1080/02626667.2024.2345813) and Iliopoulou et al. (2024; https://doi:10.1080/02626667.2024.2345814). In there, multiple sources have been used, like re-analysis and satellite data as well as rain-gauges, and they have been spatially combined following the regional model described in Iliopoulou et al. (2024; doi:10.3390/hydrology9050067). I would recommend the Authors to discuss these methods and to provide the differences presented in theirs as part of their literature review.
2) In the analysis, it is mentioned that the bias-correction factors are applied to match the gridded maximum intensity values with the in situ ones by implementing the modified Mann-Kendall test for the trends; however, there are also maps with high statistical significance (as 0.05 and 0.10), which may be considered quite large. I would recommend showing just the ones with significance lower than 0.05, while the rest can be showed in a supplementary material. Also, please include in the Conclusions whether there are any trends with significance 0.01 or lower, which I would consider the most important ones to report.
3) Regarding the sentence “In addition, our results show that Imax reaches its maximum values in central and southern Chile, for all durations, in contrast to the mean annual precipitation, which increases steadily towards the south.”, please separate the comparisons with extreme rainfall (I think it is better characterizing it like this instead of “maximum”, which could be confused with the empirical maximum values) and the mean rainfall, and perform comparisons for Chile for both.
4) I am confused with the comparison between “stationary and non-stationary” extreme rainfall; I think it is better to express it as “stationary and non-stationary model of extreme rainfall” since the data cannot be stationary or non-stationary but rather the model can be selected to be either stationary or non-stationary (see extended discussion and literature review in Koutsoyiannis 2024, http:// doi:10.57713/kallipos-1; and application to extreme rainfall in Iliopoulou and Koutsoyiannis, 2020, https://doi:10.1016/j.jhydrol.2020.125005).
5) The Authors present that a main drawback of a stationary model is that “simplifies the construction of IDF curves, it may not adequately capture climate change impacts or long-term variability in precipitation intensities.”, and that a non-stationary model “consider the time-dependent nature of distribution parameters and can capture existing trends in precipitation intensity.”. Although I would not argue that a non-stationary model is more flexible, since it contains additional parameters than a stationary one, please consider discussing that if the long-term dependence is inserted in the stationary model then it can also capture several observed trends and clustering (see for example in Figures 8 and 11 in in Dimitriadis et al., 2021; https://doi:10.3390/hydrology8020059, how an observed trend can be actually well simulated with a stationary model but with a more flexible probability distribution than the Gumbel one, which there was selected the Pareto-Burr-Feller one, and with acquiring for the long-term persistence of rainfall). Therefore, I would recommend to check other distributions and correlation stationary structures than the Gumbel and uncorrelated ones, to check whether there is need for non-stationary ones.
6) Please see recent research by Koutsoyiannis et al. (2023; https://doi:10.3390/w15091711) for Greece rainfall trends and about how the IMERG satellite data underestimate the rainfall extremes, which is something also observed by the Authors, if I am not mistaken.
7) Regarding the 4th questions made by the Authors, i.e. “4. What is the impact of the typical data length of P products used for estimating stationary and non-stationary IDF curves?”, please note that due to the long-term persistence observed in regular rainfall or even rainfall extremes (see the work on this subject by Iliopoulou and Koutsoyiannis, 2019; https://doi:10.1080/02626667.2019.1657578), the impact of the length of the rainfall timeseries could be highly significant even when using a stationary model.
9) Please include Tables about the rainfall gauges and gridded data that the Authors use in the analysis, and particularly, with primary information (e.g., length, zero values percentage, missing values, etc.), marginal statistics (e.g., mean, variance, skewness, kurtosis), and (cross-)correlation statistics (e.g., lag-1, 10, annual and 10 years of autocorrelation, cross-correlation among stations, etc.).
10) Please explain what the differences between the ERA5 and ERA5-Land datasets are, since I would expect to be similar for low elevation, since they are both coming from the same source.
11) About the “bias correction discussed” in Figure 3 and “presenting such a large number of figures in a single document”, I think pool graphs with all similar data on the same Figure could tackle these limitations of this study.
12) I think the strongest part of this research is the comparison among many satellite datasets and rain-gauges, and I think this should be the main point in the title and conclusions, and not so much the construction of the IDF curves, where, as discussed above, other stationary models or distributions could perform better.
13) Regarding the conclusion “Given the convergence between Imax obtained from ERA5, ERA5-Land and IMERGv07B, we recommend using the highest value among them for designing climate-resilient infrastructure.”, please mention by how much is the under/over-estimation.
14) Similarly, please mention by how much “All gridded datasets – except CMORPH-CDR – show smaller biases for longer durations.” and by how much “Both IMERG products overestimate Imax at shorter durations, while ERA5 and ERA5-Land underestimate it.”, and compare these results with the ones indicated by other studies on IMERG (for example, the one in Greece).
15) Regarding the conclusion that “Bias variability is greater in the extreme Far North and Far South, as compared to the more central macroclimatic zones.”, please check whether this is due to other factors like the number of stations, or different climatic conditions, altitude, etc.
Citation: https://doi.org/10.5194/egusphere-2025-621-RC1 -
RC2: 'Comment on egusphere-2025-621', Anonymous Referee #2, 18 Jun 2025
- Currently, much of the relevant material is included only in the supplementary section. As a suggestion, rather than presenting the full set of figures (i.e., stationary Imax, non-stationary Imax, and their differences) for every dataset, it may be more effective to focus on the most representative or significant datasets. For these selected cases, a single composite figure showing the stationary, non-stationary, and difference plots side by side could be included in the main manuscript. This approach would enhance clarity, reduce redundancy, and allow for the inclusion of more illustrative results in the main document without overwhelming the reader.
- Regarding the sections 4.6 the details currently provided in the supplementary material could be incorporated into the main text, at least one example per case, to enhance clarity and support interpretation.
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The content and purpose of Figure 7 are not entirely clear, as there is an apparent inconsistency between the figure caption and the explanation provided in the main text. A clearer alignment between the figure, its caption, and the accompanying discussion is recommended to improve reader comprehension
- Title of Figure 9: Could you please revise this in English to make it more polite?
- Page 18 - Trends in Imax:
It is unclear which specific results from the Mann-Kendall trend test are being referred to; clarifying this would strengthen the interpretation.
To better support the statement that the results of the trend analysis were similar, it would be helpful to include representative Kendall's tau values in the text. This would also aid in clarifying the patterns shown in the subsequent figures.
- Figure 3: To enhance clarity, the distinction between the red and black lines in the boxplots should be clarified in both the text and the figure caption.
- Page 13 - Stationary Max : While the GEV location parameter μ is often informally linked to central tendency measures such as the mean or mode, it is more precisely interpreted as a proxy for the mode.
Citation: https://doi.org/10.5194/egusphere-2025-621-RC2 -
RC3: 'Comment on egusphere-2025-621', Anonymous Referee #3, 23 Jun 2025
Review
The authors describe a study focused on IDF curves for the climate of Chili, researching whether the assumption of stationarity is valid for IDF parameter estimation in a changing climate.
I found it an interesting, detailed paper with a thorough methodology to research assumptions that may have implications for extreme value analysis. In that level of detail is at the same time the weak part of the paper: sometimes there is too much detail (e.g. Figure 1 is so extremely high resolution that it crashed my printer), but at other parts some more information is needed or there is quite some repetition. I find the lack of a dedicated Discussion Section also rather limiting since it makes the Results section less straightforward. The work is sound overall, but the structuring and writing could use some extra work – I’m recommending Major Revisions because of that reason.
My Major points:
- Please be careful with the overabundance of abbreviations and acronyms – and at least be consistent when using them. Especially the shortening of Precipitation to P, and then later on using a parameter p in the Gumbell distribution in equation 6 and accompanying text can get quite confusing (also because the word precipitation is fully written out in other sentences). Given the heavy statistical nature of this text, I’d suggest to keep the abbreviations in that field and the product names (GEV, IMERG etc) as they are normally shortened like that, but keep the use of abbreviating regular words to a minimum.
- In 4.1, and the definition of the bias correction factor S, the authors implicitly assume the rain gauges to be the absolute truth, without discussing the measurement accuracy of rain gauges. This needs some further discussion in my opinion: the type of rain gauge also isn’t mentioned, whereas the technique of measuring precipitation has a direct relation with the inherent error in the resulting measurement. For instance, tipping bucket gauges tend to underestimate large rainfall intensities. To this end, section 2.2.1 could be more expanded with more metadata about the rain gauges, but also the selection criteria: the authors remove over 400 stations due to “anomalously large precipitation values” , which seems strange to me if the research is about IDF curves which try to predict extremes. Why discard the whole station and not just filter instead? From figure 3 it seems like for some climatic regions the data density is very sparse as a result which would make me question the validity of the found relations. Please include selection criteria, what exactly qualifies as an anomaly versus an actual extreme event, and some discussion on the effect of rain gauge quality on the work in this paper.
- Section 2.2.2 could be more concise, it feels like a lot of repetition. Especially the IMERG7 section, which includes a massive summation of changes that feels like it could be copy-pasted from the technical documentation. That level of detail is unnecessary, same as the mention of a sixth dataset that wasn’t used – a discussion point at best, not it distracts from the actual methodology.
- Figure 3 (as well as 8) has 25 subplots which makes it nearly impossible to digest. Consider which panels need to be included to support the main text, and move the rest or the full image to the supplementary material. In general, given the comparison between stationary and non-stationary Imax distributions, it would be interesting to see some more in-depth analysis and scatterplots of comparing the distribution statistics, rather than just showing spatial maps which mainly seem to be dominated by Chile’s climatological gradient (at first glance at least)
- Section 4.6 draws heavily on the supporting material figures which is not ideal, and also has several references to other work in it already – perhaps this is better suited for a Discussion section (which is lacking at the moment, and interspersed with the Results), since this particular section uses only the ERA dataset and is therefore rather limited compared to the other Results
Citation: https://doi.org/10.5194/egusphere-2025-621-RC3
Data sets
Supplementary material for manuscript egusphere-2025-621 "Gridded Intensity-Duration-Frequency (IDF) curves: understanding precipitation extremes in a drying climate" by Soto-Escobar, Zambrano-Bigiarini, Tolorza and Garreaud Cristóbal Soto-Escobar et al. https://doi.org/10.5281/zenodo.14984455
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