Given that long time series for temporally highly resolved precipitation observations are rarely available, it is necessary to pool information to obtain reliable estimates of the distribution of extreme precipitation, especially for short durations. In this study, we use a duration-dependent generalized extreme value distribution (d-GEV) with orthogonal polynomials of longitude and latitude as spatial covariates, allowing us to pool information between durations and stations. We determine the polynomial orders with step-wise forward regression and cross-validated likelihood as a model selection criterion. The Wupper River catchment in the West of Germany serves as a case study area. It allows us to estimate return level maps for arbitrary durations, as well as intensity-duration-frequency curves at any location—also ungauged—in the research area. The main focus of the study is evaluating the model performance in detail using the Quantile Skill Index, a measure derived from the popular Quantile Skill Score. We find that the d-GEV with spatial covariates is an improvement for the modeling of rare events. However, the model shows limitations concerning the modeling of short durations d≤30min. For ungauged sites, the model performs on average as good as a generalized extreme value distribution with parameters estimated individually at the gauged stations with observation time series of 30–35 years available.

Abstract. 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 duration-dependent 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).

To explicitly account for asymptotic dependence between rainfall intensity maxima of different accumulation duration, a recent development for estimating Intensity-Duration-Frequency (IDF) curves involves the use of a max-stable process. In our study, we aimed to estimate the impact on the performance of the return levels resulting from an IDF model that accounts for such asymptotical dependence. To investigate this impact, we compared the performance of the return level estimates of two IDF models using the quantile skill index (QSI). One IDF model is based on a max-stable process assuming asymptotic dependence; the other is a simplified (or reduced) duration-dependent GEV model assuming asymptotic independence. The resulting QSI shows that the overall performance of the two models is very similar, with the max-stable model slightly outperforming the other model for short durations (d≤10h). From a simulation study, we conclude that max-stable processes are worth considering for IDF curve estimation when focusing on short durations if the model’s asymptotic dependence can be assumed to be properly captured.

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).

Abstract. Ozone pollution and high temperatures have adverse health impacts that can be amplified by the combined effects of ozone and temperature. Moreover, changes in weather patterns are expected to alter ozone pollution episodes and temperature extremes. In particular, atmospheric blocking is a high-impact, large-scale phenomenon at mid-high latitudes that has been associated with temperature extremes. This study examines the impact of atmospheric blocking on the ozone and temperature dependence among measurement stations over Europe during the period 1999–2015. We use a copula-based method to model the dependence between the two variables under blocking and non-blocking conditions. This approach allows us to examine the impact of blocks on the joint probability distribution. Our results showed that blocks lead to increasing strength in the upper tail dependence of ozone and temperature extremes (> 95th percentile) in north-west and central Europe (e.g. the UK, Belgium, Netherlands, Luxembourg, Germany and the north-west of France). The analysis of the probability hazard scenarios revealed that blocks generally enhance the probability of compound ozone and temperature events by 20 % in a large number of stations over central Europe. The probability of ozone or temperature exceedances increases 30 % (on average) under the presence of atmospheric blocking. Furthermore, we found that, in a number of stations over north-western Europe, atmospheric blocking increases the probability of ozone exceedances by 30 % given high temperatures. Our results point out the strong influence of atmospheric blocking on the compounding effect of ozone and temperature events, suggesting that blocks might be considered a relevant predicting factor when assessing the risks of ozone-heat-related health effects.