Flexible and consistent quantile estimation for intensity-duration-frequency curves

Assessing the relationship between the 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 durationdependent GEV model exhibits a power-law-like behavior 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 d). Therefore, we extend the model with the following two features: (i) different slopes for different quantiles (multiscaling) and (ii) the deviation from the power law for large durations (flattening), which is newly introduced in this study. 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, and 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 h and 1 d, without affecting other duration regimes. Overall, the new parametric form offers a flexible and enhanced performance 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 1 h or day and do not address the deviation from the power law for very long durations (2-5 d).