River floods caused about 7 million fatalities in the twentieth century 1 , and their direct global average annual loss (AAL) is estimated at US$ 104 billion (2015Exposure to floods is expected to grow by a factor of three by 2050 owing to increases in population and economic assets in flood-prone areas 3 . Depending on the socio-economic scenario, human losses from flooding are projected to rise by 70-83% and direct flood damage by 160-240% relative to 1976-2005, with a temperature increase of 1.5 °C (ref. 4 ). Understanding river flooding and its associated impacts are critical to effective risk reduction.River floods occur when a river overtops its banks and inundates adjacent areas. The expected impact floods have on society and the environment, often termed flood risk, results from the superposition of three components and the associated processes, which tend to be interlinked [5][6][7] , including over large distances 8 . These components are: hazards -the processes leading to high river flood levels; exposure -the elements at risk, such as population or infrastructure; and vulnerabilitythe susceptibility of the elements at risk when they are affected by a flood 2 . These components are, in turn, the compound effects of multiple processes (fig. 1).

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

A statistical distribution is termed heavy-tailed if its tail decays slower than that of an exponential distribution, leading to a higher occurrence probability of extreme events (El Adlouni et al., 2008;. Several classes of heavy tail distributions are distinguished which characterize the degree of tail heaviness (El Adlouni et al., 2008;Wietzke et al., 2020). The Generalized Pareto (GP) and Generalized Extreme Value (GEV) distributions with positive shape parameters are two widely used heavy tail distributions for modeling precipitation and streamflow series, respectively.

Abstract. Air pollution is a pressing issue that is associated with adverse effects on human health, ecosystems, and climate. Despite many years of effort to improve air quality, nitrogen dioxide (NO2) limit values are still regularly exceeded in Europe, particularly in cities and along streets. This study explores how concentrations of nitrogen oxides (NOx = NO + NO2) in European urban areas have changed over the last decades and how this relates to changes in emissions. To do so, the incremental approach was used, comparing urban increments (i.e. urban background minus rural concentrations) to total emissions, and roadside increments (i.e. urban roadside concentrations minus urban background concentrations) to traffic emissions. In total, nine European cities were assessed. The study revealed that potentially confounding factors like the impact of urban pollution at rural monitoring sites through atmospheric transport are generally negligible for NOx. The approach proves therefore particularly useful for this pollutant. The estimated urban increments all showed downward trends, and for the majority of the cities the trends aligned well with the total emissions. However, it was found that factors like a very densely populated surrounding or local emission sources in the rural area such as shipping traffic on inland waterways restrict the application of the approach for some cities. The roadside increments showed an overall very diverse picture in their absolute values and trends and also in their relation to traffic emissions. This variability and the discrepancies between roadside increments and emissions could be attributed to a combination of local influencing factors at the street level and different aspects introducing inaccuracies to the trends of the emission inventories used, including deficient emission factors. Applying the incremental approach was evaluated as useful for long-term pan-European studies, but at the same time it was found to be restricted to certain regions and cities due to data availability issues. The results also highlight that using emission inventories for the prediction of future health impacts and compliance with limit values needs to consider the distinct variability in the concentrations not only across but also within cities.