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River floods are generated by various processes that, if disregarded, may induce errors in flood hazard assessment. This is particularly relevant where events extraordinarily larger than the typical floods have been observed, that is, for rivers with a flood divide in their flood‐frequency curves. We identify 11 such cases in a large set of German catchments and test a statistical approach that accounts for different runoff‐generation processes to predict the magnitude and frequency of extraordinarily high floods. We observe that in catchments with a flood divide, ordinary peaks are generated by different runoff‐generation processes and the distribution of at least one process is heavy‐tailed. By accounting for the different tail behaviors of multiple processes, we can reproduce flood‐frequency curves in these catchments. Our findings shed light on the origin of flood divides and set a method to improve the estimation of high flood quantiles in these high‐risk cases. Plain Language Summary: River floods can be caused by many different processes. Neglecting this fact may impair our capability to predict the probability of occurrence of the most extreme floods. In this study, we combine knowledge of runoff‐generation mechanisms across different events with a statistical method which uses information on these ordinary events to infer the magnitude and frequency of floods. We apply the method to 11 rivers in Germany where extraordinarily high floods have been observed. By accounting for ordinary runoff events and their diverse runoff‐generation processes we obtain accurate estimates of the magnitude of rare and extreme floods, substantially improving results provided by traditional methods. Key Points: We develop a statistical model to predict extraordinarily high floods occurring in river basins with variable flood extremesThe approach leverages knowledge of various hydrologic processes generating runoff events to estimate the magnitude of extreme floodsBy accounting for multiple processes in flood magnitude‐frequency analysis, we improve the estimation of extraordinarily high floods [ABSTRACT FROM AUTHOR]

The accurate estimation of hydrologic extremes is central to planning and engineering mitigation and adaptation measures. The traditional extreme value theory is based on often overlooked assumptions that preclude the use of all available observations and negatively affect estimation uncertainty. The Metastatistical Extreme Value Distribution (MEVD) was introduced to make full use of available data and was shown to significantly improve estimation uncertainty for large extremes. However, no systematic understanding existed as to how to optimally apply the MEVD depending on the statistical properties of the observed variables. With reference to daily rainfall, we identify here the local climatic factors that define the optimal MEVD formulation. We analyze a large set of long daily rainfall records, as well as synthetic time series with prescribed statistical characteristics, and find that (1) in most climates the MEVD should be based on yearly estimates of the ordinary rainfall distributions, and only in climates with less than n¯= 20–25 year the estimation of distributional/year the estimation of distributional parameters requires samples longer than 1 year; (2) the interannual variability in the distributions of rainfall should be explicitly resolved when n¯> 20–25 rainy days/year. Finally, we use the optimized MEVD to study the variability of daily rainfall extremes over 294 years in Padova (Italy) and compare it to traditional extreme value estimates. We find that, through its improved accuracy for short observations, MEVD better resolves high‐quantile fluctuations and allows the emergence of long‐term trends over estimation noise. Plain Language Summary: In a world that is experiencing more and more frequent episodes of extreme weather, accurate methods to estimate "rare events" is crucial in many fields, such as engineering design, insurance and reinsurance purposes, and policy making. Here, we refine the Metastatistical Extreme Value Distribution (MEVD) to minimize uncertainty in the estimation of large extremes in daily rainfall on the basis of short observational records. When applied to a 294‐year record, the MEVD is found to be a significant improvement over traditional approaches in resolving fluctuations of extremes on short time scales and in unveiling long‐term trends that would be partially masked by estimation noise. Key Points: We identify the optimal formulation of the Metastatistical Extreme Value Distribution applying it to daily rainfallInterannual variability should be resolved to better define the probability distribution of daily rainfall extremesThe MEVD provides clear advantages over traditional extreme value theory in trend detection [ABSTRACT FROM AUTHOR]

Tropical cyclones (TCs) generate extreme precipitation with severe impacts across large coastal and inland areas, calling for accurate frequency estimation methods. Statistical approaches that take into account the physical mechanisms responsible for these extremes can help reduce the estimation uncertainty. Here we formulate a mixed‐population Metastatistical Extreme Value Distribution explicitly incorporating non‐TC and TC‐induced rainfall and evaluate its implications on long series of daily rainfall for six major U.S. urban areas impacted by these storms. We find statistically significant differences between the distributions of TC‐ and non‐TC‐related precipitation; moreover, including mixtures of distributions improves the estimation of the probability of extreme precipitation where TCs occur more frequently. These improvements are greater when rainfall aggregated over durations longer than one day are considered. Plain Language Summary: The accurate estimation of the frequency of extreme rainfall has broad implications in designing mitigation measures, policy making, risk management, geology/geomorphology, insurance and reinsurance, and water‐borne disease prevention and management. In many parts of the world tropical cyclones play a significant role in generating heavy rainfall, but the evaluation of their contribution to the frequency of extremes is problematic, due to the low number of tropical cyclones in the measured historical record. Here, we introduce a new statistical tool that explicitly includes tropical cyclone rainfall together with rainfall generated by other physical mechanisms and provides a way to maximize the information that can be extracted from available observations. When applied to locations on the U.S. eastern seaboard, we find that this method significantly improves estimates of extreme rainfall. Key Points: We study rainfall extremes from tropical cyclone (TC) and non‐TC rainfall mixtures at six U.S. locationsThe Metastatistical Extreme Value Distribution based on mixed populations outperforms single population formulationsThe advantage of considering different rainfall sources is greater for 3‐day cumulative rainfall [ABSTRACT FROM AUTHOR]

• We propose a method to select ex ante the ordinary distribution in the MEV approach. • The approach identifies the optimal distribution in the majority of case studies. • The proposed methodology is robust to changes of the dataset. • Flood appraisal improves by reducing estimation bias and decreasing uncertainty. Recent advances in the study of extreme values, namely the Metastatistical extreme value (MEV) framework, showed good performances for the estimation of extremes in several fields. Here we adopt MEV for flood frequency analysis and leverage its intrinsic property of allowing for the choice of the distribution which best describes ordinary peaks to improve flood estimation. To this end, we develop a non-parametric approach to select ex ante the most suitable distribution of ordinary peaks between Gamma and Log-Normal. The method relies on the tail ratio, which we define as the ratio between the empirical 99th and 95th percentile of the ordinary peaks, and is tested by using daily streamflow time series from 182 gauges in Germany. Based on the value of the tail ratio index, we choose either the Gamma or the Log-Normal distributions to represent the ordinary peaks in each gauge. The approach correctly identifies the most suitable distribution of ordinary peaks in a large majority of the analyzed basins, and is robust to changes of the considered dataset. The preliminary selection of the ordinary distribution based on the tail ratio index improves the estimation of frequent and rare floods with respect to MEV applied with a single distribution not tailored on the specific statistical properties of the ordinary peaks. Finally, by comparing the developed methodology with the standard Generalized Extreme Value (GEV) distribution, we show that we are able to reduce the estimation uncertainty of high flood quantiles. [ABSTRACT FROM AUTHOR]

• We develop a Metastatistical Extreme Value Distribution (MEVD) tailored for floods. • We compare the MEVD with the GEV and LP3 distributions. • MEVD outperforms the GEV and LP3 in the analyzed USGS stations (76 and 86% of the cases). • We propose a mixed MEVD approach to account for El Niño Southern Oscillation. This study analyzes daily mean streamflow records from 5,311 U.S. Geological Survey stream gages in the continental United States and develops a Metastatistical Extreme Value Distribution (MEVD) tailored for flood frequency analysis. We compare the new tool with the Generalized Extreme Value (GEV) and Log-Pearson Type III (LP3) distributions and investigate the role of El Niño Southern Oscillation (ENSO) in the generation of floods. Hence, we formulate the MEVD in terms of mixture of distributions to describe the occurrence of flood peaks generated under different ENSO phases. We find that the MEVD outperforms GEV and LP3 distributions respectively in about 76% and 86% of the stations, with a significant improvement in the accuracy of quantiles corresponding to return periods much larger than the calibration sample size. The ENSO signature detected in the distributions of the daily peak flows does not necessarily improve the estimation of high return period flow values. [ABSTRACT FROM AUTHOR]

Reliable flood frequency estimates, robust with respect to small samples and to possible inter-annual variability, are key to many different sectors and applications, from the design of hydraulic structures to flood insurance, to the quantification of economic and societal impacts in general. Traditional flood frequency analysis has often become a mere mathematical, statistical fitting exercise, with little attention for the possibly different flood-generating phenomena at play. Here we apply, for the first time to flood frequency analysis, the Metastatistical Extreme Value Distribution (MEVD), a recently-developed extreme value theory that was shown to significantly improve estimation uncertainty with respect to the traditional approach hinging on the Generalized Extreme Value distribution (GEV) in rainfall applications. We then use the MEVD formulation, which can explicitly include mixed distributions of the "ordinary" floods, to investigate the role of El Niño Southern Oscillation (ENSO), a major mode of climate variability involving changes in sea surface temperature and atmospheric circulations, in the generation of extreme floods. We analyze ~3000 U.S. Geological Survey stream gauge time series across the continental United States with at least 50 years of daily observations and that do not present abrupt or gradual changes. Compared to the observations, we find that flood frequency estimates based on MEVD perform better than those estimated using the GEV at ~72% of the analyzed sites. This improvement is even more marked when the sample size used for the estimation of the parameters is limited. In terms of the role of ENSO, we find that only a small number of data records show statistical evidence that accounting for ENSO phases is beneficial in terms of extreme flood estimation accuracy. [ABSTRACT FROM AUTHOR]