A wide variety of processes controls the time of occurrence, duration, extent, and severity of river floods. Classifying flood events by their causative processes may assist in enhancing the accuracy of local and regional flood frequency estimates and support the detection and interpretation of any changes in flood occurrence and magnitudes. This paper provides a critical review of existing causative classifications of instrumental and preinstrumental series of flood events, discusses their validity and applications, and identifies opportunities for moving toward more comprehensive approaches. So far no unified definition of causative mechanisms of flood events exists. Existing frameworks for classification of instrumental and preinstrumental series of flood events adopt different perspectives: hydroclimatic (large‐scale circulation patterns and atmospheric state at the time of the event), hydrological (catchment scale precipitation patterns and antecedent catchment state), and hydrograph‐based (indirectly considering generating mechanisms through their effects on hydrograph characteristics). All of these approaches intend to capture the flood generating mechanisms and are useful for characterizing the flood processes at various spatial and temporal scales. However, uncertainty analyses with respect to indicators, classification methods, and data to assess the robustness of the classification are rarely performed which limits the transferability across different geographic regions. It is argued that more rigorous testing is needed. There are opportunities for extending classification methods to include indicators of space–time dynamics of rainfall, antecedent wetness, and routing effects, which will make the classification schemes even more useful for understanding and estimating floods. This article is categorized under: Science of Water > Water Extremes Science of Water > Hydrological Processes Science of Water > Methods

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This paper proposes a method from Scan statistics for identifying flood‐rich and flood‐poor periods (i.e., anomalies) in flood discharge records. Exceedances of quantiles with 2‐, 5‐, and 10‐year return periods are used to identify periods with unusually many (or few) threshold exceedances with respect to the reference condition of independent and identically distributed random variables. For the case of flood‐rich periods, multiple window lengths are used in the identification process. The method is applied to 2,201 annual flood peak series in Europe between 1960 and 2010. Results indicate evidence for the existence of flood‐rich and flood‐poor periods, as about 2 to 3 times more anomalies are detected than what would be expected by chance. The frequency of the anomalies tends to decrease with an increasing threshold return period which is consistent with previous studies, but this may be partly related to the method and the record length of about 50 years. In the northwest of Europe, the frequency of stations with flood‐rich periods tends to increase over time and the frequency of stations with flood‐poor periods tends to decrease. In the east and south of Europe, the opposite is the case. There appears to exist a turning point around 1970 when the frequencies of anomalies start to change most clearly. This turning point occurs at the same time as a turning point of the North Atlantic Oscillation index. The method is also suitable for peak‐over‐threshold series and can be generalized to higher dimensions, such as space and space‐time.

Floods often come as a surprise. Examples of extreme floods that have occurred unexpectedly and have led to disastrous socio-economic consequences abound in the literature (Merz et al., 2015). Figure 1 shows one example time series with such a surprising flood. The 2002 flood peak of the River Kamp, Austria, was about three times larger than the highest flood in the 100-year observational period before and has indeed caused enormous damage triggering desperate emergency measures in the region (Blöschl et al., 2006). From a statistical perspective, the occurrence of such an event is very unlikely if the extreme value behavior conforms to an asymptotically exponential (light-tailed) distribution. However, if the underlying probability distribution has a heavy tail, its occurrence is less unlikely. A heavy upper tail implies that the extreme values are more likely to occur than would be predicted by distributions with exponential asymptotic behavior, such as Exponential, Gamma, and Gumbel distributions (El Adlouni et al., 2008). Because human intuition tends to expect light tail behavior, processes that show heavy tail behavior often lead to surprise (Taleb, 2007).Heavy-tailed behavior of flood peak distributions is of the highest relevance for flood design and risk management. Neglecting heavy tail behavior, if it exists, results in underestimating the probability of occurrence of extremes. This underestimation may result in biased flood management measures, such as underestimated dike

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Generalized linear (GL-) statistics are defined as functionals of an U -quantile process and unify different classes of statistics such as U -statistics and Lstatistics. We derive a central limit theorem for GL-statistics of strongly mixing sequences and arbitrary dimension of the underlying kernel. For this purpose we establish a limit theorem for U -statistics and an invariance principle for U -processes together with a convergence rate for the remaining term of the Bahadur representation. An application is given by the generalized median estimator for the tailparameter of the Pareto distribution, which is commonly used to model exceedances of high thresholds. We use subsampling to calculate confidence intervals and investigate its behaviour under independence and strong mixing in simulations.

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