Flexible and Consistent Quantile Estimation for Intensity-Duration-Frequency Curves
Felix Fauer, Jana Ulrich, Oscar E. Jurado, Henning W. Rust
Abstract
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).