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Statistical distributions of flood peak discharge often show heavy tail behavior, that is, extreme floods are more likely to occur than would be predicted by commonly used distributions that have exponential asymptotic behavior.
This heavy tail behavior may surprise flood managers and citizens, as human intuition tends to expect light tail behavior, and the heaviness of the tails is very difficult to predict, which may lead to unnecessarily high flood damage.
Despite its high importance, the literature on the heavy tail behavior of flood distributions is rather fragmented.
In this review, we provide a coherent overview of the processes causing heavy flood tails and the implications for science and practice.
Specifically, we propose nine hypotheses on the mechanisms causing heavy tails in flood peak distributions related to processes in the atmosphere, the catchment, and the river system.
We then discuss to which extent the current knowledge supports or contradicts these hypotheses.
We also discuss the statistical conditions for the emergence of heavy tail behavior based on derived distribution theory and relate them to the hypotheses and flood generation mechanisms.
We review the degree to which the heaviness of the tails can be predicted from process knowledge and data. Finally, we recommend further research toward testing the hypotheses and improving the prediction of heavy tails.
We investigate whether the distribution of maximum seasonal streamflow is significantly affected by catchment or climate state of the season/month ahead. We fit the Generalized Extreme Value (GEV) distribution to extreme seasonal streamflow for around 600 stations across Europe by conditioning the GEV location and scale parameters on 14 indices, which represent the season-ahead climate or catchment state. The comparison of these climate-informed models with the classical GEV distribution, with time-constant parameters, suggests that there is a substantial potential for seasonal forecasting of flood probabilities. The potential varies between seasons and regions. Overall, the season-ahead catchment wetness shows the highest potential, although climate indices based on large-scale atmospheric circulation, sea surface temperature or sea ice concentration also show some skill for certain regions and seasons. Spatially coherent patterns and a substantial fraction of climate-informed models are promising signs towards early alerts to increase flood preparedness already a season ahead.
Hydrodynamic interactions, i.e. the floodplain storage effects caused by inundations upstream on flood wave propagation, inundation areas, and flood damage downstream, are important but often ignored in large-scale flood risk assessments. Although new methods considering these effects sometimes emerge, they are often limited to a small or meso scale. In this study, we investigate the role of hydrodynamic interactions and floodplain storage on flood hazard and risk in the German part of the Rhine basin. To do so, we compare a new continuous 1D routing scheme within a flood risk model chain to the piece-wise routing scheme, which largely neglects floodplain storage. The results show that floodplain storage is significant, lowers water levels and discharges, and reduces risks by over 50%. Therefore, for accurate risk assessments, a system approach must be adopted, and floodplain storage and hydrodynamic interactions must carefully be considered.
In some catchments, the distribution of annual maximum streamflow shows heavy tail behavior, meaning the occurrence probability of extreme events is higher than if the upper tail decayed exponentially. Neglecting heavy tail behavior can lead to an underestimation of the likelihood of extreme floods and the associated risk. Partly contradictory results regarding the controls of heavy tail behavior exist in the literature and the knowledge is still very dispersed and limited. To better understand the drivers, we analyze the upper tail behavior and its controls for 480 catchments in Germany and Austria over a period of more than 50 years. The catchments span from quickly reacting mountain catchments to large lowland catchments, allowing for general conclusions. We compile a wide range of event and catchment characteristics and investigate their association with an indicator of the tail heaviness of flood distributions, namely the shape parameter of the GEV distribution. Following univariate analyses of these characteristics, along with an evaluation of different aggregations of event characteristics, multiple linear regression models, as well as random forests, are constructed. A novel slope indicator, which represents the relation between the return period of flood peaks and event characteristics, captures the controls of heavy tails best. Variables describing the catchment response are found to dominate the heavy tail behavior, followed by event precipitation, flood seasonality, and catchment size. The pre-event moisture state in a catchment has no relevant impact on the tail heaviness even though it does influence flood magnitudes.
Floods affect more people than any other natural hazard; thus flood warning and disaster management are of utmost importance.
However, the operational hydrological forecasts do not provide information about affected areas and impact but only discharge and water levels at gauges.
We show that a simple hydrodynamic model operating with readily available data is able to provide highly localized information on the expected flood extent and impacts, with simulation times enabling operational flood warning.
We demonstrate that such an impact forecast would have indicated the deadly potential of the 2021 flood in western Germany with sufficient lead time.