30 Jul 2021

30 Jul 2021

Review status: a revised version of this preprint is currently under review for the journal HESS.

Flexible and Consistent Quantile Estimation for Intensity-Duration-Frequency Curves

Felix S. Fauer, Jana Ulrich, Oscar E. Jurado, and Henning W. Rust Felix S. Fauer et al.
  • Institute of Meteorology, Freie Universität Berlin, Carl-Heinrich-Becker-Weg 6-10, 12165 Berlin, Germany

Abstract. Assessing the relationship between intensity, duration and frequency (IDF) of extreme precipitation is required for the design of water management systems. However, when modeling sub-daily precipitation extremes, there are commonly only short observation time series available. This problem can be overcome by applying the duration-dependent formulation of the generalized extreme value (GEV) distribution which fits an IDF model with a range of durations simultaneously. The originally proposed duration-dependent GEV model exhibits a power-law like behaviour of the quantiles and takes care of a deviation from this scaling relation (curvature) for sub-hourly durations (Koutsoyiannis et al., 1998). We suggest that a more flexible model might be required to model a wide range of durations (1 min to 5 days). Therefore, we extend the model with two features: i) different slopes for different quantiles (multiscaling) and ii), newly introduced in this study, the deviation from the power-law for large durations (flattening). Based on the quantile skill score, we investigate the performance of the resulting flexible model with respect to the benefit of the individual features (curvature, multiscaling, flattening) with simulated and empirical data. We provide detailed information on the duration and probability ranges for which specific features or a systematic combination of features leads to improvements for stations in a case study area in the Wupper catchment (Germany). Our results show that allowing curvature or multiscaling improves the model only for very short or long durations, respectively, but leads to disadvantages in modeling the other duration ranges. In contrast, allowing flattening on average leads to an improvement for medium durations between 1 hour and 1 day without affecting other duration regimes. Overall, the new parametric form offers a flexible and performant model for consistently describing IDF relations over a wide range of durations, which has not been done before as most existing studies focus on durations longer than one hour or day and do not address the deviation from the power law for very long durations (2–5 days).

Felix S. Fauer et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2021-334', Rasmus Benestad, 10 Aug 2021
    • AC1: 'Reply on RC1', Felix Fauer, 26 Aug 2021
  • RC2: 'Comment on hess-2021-334', Anonymous Referee #2, 13 Aug 2021
    • AC2: 'Reply on RC2', Felix Fauer, 27 Aug 2021
  • RC3: 'Comment on hess-2021-334', Anonymous Referee #3, 09 Sep 2021
    • AC3: 'Reply on RC3', Felix Fauer, 21 Sep 2021
  • RC4: 'Comment on hess-2021-334', Anonymous Referee #4, 15 Sep 2021
    • AC4: 'Reply on RC4', Felix Fauer, 21 Sep 2021

Felix S. Fauer et al.

Data sets

Annual Maxima of Station-based Rainfall Data over Different Accumulation Durations Felix S. Fauer, Jana Ulrich, Oscar E. Jurado, Henning W. Rust

Model code and software

IDF: Estimation and Plotting of IDF Curves Jana Ulrich, Laura Mack, Oscar E. Jurado, Felix S. Fauer, Christoph Ritschel, Carola Detring, Sarah Joedicke

Felix S. Fauer et al.


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Short summary
Extreme rainfall events are modeled in this study for different time scales. A new parametrization of the dependence between extreme values and their time scale enables our model to estimate extremes on very short (1 minute) and long (5 days) time scales at the same time. We compare different approaches of modeling this dependence and find that our new model improves performance for time scales between 2 hours and 2 days without affecting model performance on other time scales.