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).

Abstract. Recent studies have revealed evidence of trends in the median or mean flood discharge in Europe over the last 5 decades, with clear and coherent regional patterns. The aim of this study is to assess whether trends in flood discharges also occurred for larger return periods, accounting for the effect of catchment scale. We analyse 2370 flood discharge records, selected from a newly available pan-European flood database, with record length of at least 40 years over the period 1960–2010 and with contributing catchment area ranging from 5 to 100 000 km2. To estimate regional flood trends, we use a non-stationary regional flood frequency approach consisting of a regional Gumbel distribution, whose median and growth factor can vary in time with different strengths for different catchment sizes. A Bayesian Markov chain Monte Carlo (MCMC) approach is used for parameter estimation. We quantify regional trends (and the related sample uncertainties), for floods of selected return periods and for selected catchment areas, across Europe and for three regions where coherent flood trends have been identified in previous studies. Results show that in northwestern Europe the trends in flood magnitude are generally positive. In small catchments (up to 100 km2), the 100-year flood increases more than the median flood, while the opposite is observed in medium and large catchments, where even some negative trends appear, especially in northwestern France. In southern Europe flood trends are generally negative. The 100-year flood decreases less than the median flood, and, in the small catchments, the median flood decreases less compared to the large catchments. In eastern Europe the regional trends are negative and do not depend on the return period, but catchment area plays a substantial role: the larger the catchment, the more negative the trend.

This paper proposes a method to easily quantify the attenuation due to a reservoir on downstream flood peak discharges, that is, to the downstream flood frequency curve. Using a parsimonious Instantaneous Unit Hydrograph‐based model, we show that the flood peak attenuation is mainly controlled by three system characteristics: (1) the reservoir position along the river channel, (2) the spillway dimensions, quantified by the reservoir storage coefficient; and (3) the storage capacity. These three system characteristics are quantified by three dimensionless numbers, which are derived analytically for an idealized catchment. The degree of flood peak attenuation increases for increasing storage capacity and spillway dimensions, in different ways depending on the reservoir position along the river channel. An optimal position exists, which maximizes the degree of flood peak attenuation, and is in general different from the outlet of the catchment. Interestingly, for large reservoirs with relatively small spillways, a range of quasi‐optimal positions exists. With the Instantaneous Unit Hydrograph‐based model, we also investigate how the duration of extreme rainfall relevant for determining the maximum flood peaks at the catchment outlet changes depending on the three system characteristics. Some of the assumptions of the method (i.e., catchment simple morphology and linearity of reservoir response) are relaxed in a real‐world example, which demonstrates that the synthetic results approximate well what would be obtained by a more realistic model.

Flood changes may be attributed to drivers of change that belong to three main classes: atmospheric, catchment and river system drivers. In this work, we propose a data-based attribution approach for selecting which driver best relates to variations in time of the flood frequency curve. The flood peaks are assumed to follow a Gumbel distribution, whose location parameter changes in time as a function of the decadal variations of one of the following alternative covariates: annual and extreme precipitation for different durations, an agricultural land-use intensification index, and reservoir construction in the catchment, quantified by an index. The parameters of this attribution model are estimated by Bayesian inference. Prior information on one of these parameters, the elasticity of flood peaks to the respective driver, is taken from the existing literature to increase the robustness of the method to spurious correlations between flood and covariate time series. Therefore, the attribu- tion model is informed in two ways: by the use of covariates, representing the drivers of change, and by the priors, representing the hydrological understanding of how these covariates influence floods. The Watanabe-Akaike information criterion is used to compare models involving alternative covariates. We apply the approach to 96 catchments in Upper Austria, where positive flood peak trends have been observed in the past 50 years. Results show that, in Upper Austria, one or seven day extreme precipitation is usually a better covariate for variations of the flood frequency curve than precipitation at longer time scales. Agricultural land-use intensification rarely is the best covariate, and the reservoir index never is, suggesting that catchment and river drivers are less important than atmospheric ones. Not all the positive flood trends correspond to a significant correlation between floods and the covariates, suggesting that other drivers or other flood-driver relations should be considered to attribute flood trends in Upper Austria.

Abstract. Recent studies have shown evidence of increasing and decreasing trends for average floods and flood quantiles across Europe. Studies attributing observed changes in flood peaks to their drivers have mostly focused on the average flood behaviour, without distinguishing small and large floods. This paper proposes a new framework for attributing flood changes to potential drivers, as a function of return period (T), in a regional context. We assume flood peaks to follow a non-stationary regional Gumbel distribution, where the median flood and the 100-year growth factor are used as parameters. They are allowed to vary in time and between catchments as a function of the drivers quantified by covariates. The elasticities of floods with respect to the drivers and the contributions of the drivers to flood changes are estimated by Bayesian inference. The prior distributions of the elasticities of flood quantiles to the drivers are estimated by hydrological reasoning and from the literature. The attribution model is applied to European flood and covariate data and aims at attributing the observed flood trend patterns to specific drivers for different return periods at the regional scale. We analyse flood discharge records from 2370 hydrometric stations in Europe over the period 1960–2010. Extreme precipitation, antecedent soil moisture and snowmelt are the potential drivers of flood change considered in this study. Results show that, in northwestern Europe, extreme precipitation mainly contributes to changes in both the median (q2) and 100-year flood (q100), while the contributions of antecedent soil moisture are of secondary importance. In southern Europe, both antecedent soil moisture and extreme precipitation contribute to flood changes, and their relative importance depends on the return period. Antecedent soil moisture is the main contributor to changes in q2, while the contributions of the two drivers to changes in larger floods (T>10 years) are comparable. In eastern Europe, snowmelt drives changes in both q2 and q100.