EURO-CORDEX historical climate scenarios and future projections with RCP8.5 were used in this study to produce river streamflow simulations in Europe over the period 1970–2100 under a high-end global warming scenario. These projections consist of high-resolution downscaling of GCMs from the CMIP5 and can be downloaded from different data nodes of the Earth System Grid Federation (e.g. http://http://esgf-data.dkrz.de) or from the Climate4Impact portal (http://climate4impact.eu). The seven models were chosen among those available in mid 2014, giving priority to models with driving GCMs with high ranking in the performance evaluation of CMIP5 models carried out by Perez et al. (2014). Daily historical simulations from 1970 to 2005 and climate projections with RCP8.5 from 2006 to 2100 at 0.11∘ horizontal resolution (∼ 12 km) were extracted for seven EURO-CORDEX scenarios. Overall, the seven climate scenarios are combinations of three different GCMs which were then downscaled with four RCMs as shown in Table 1. Meteorological fields used in this work are average (tas), minimum (tasmin) and maximum (tasmax) surface air temperature, total precipitation (pr), surface air pressure (ps), 2 m specific humidity (huss), 10 m wind speed (sfcWind) and surface downwelling shortwave radiation (rsds).

The Lisflood model is used in this work to perform hydrological simulations using gridded meteorological variables extracted from the climate scenarios. Lisflood (Burek et al., 2013b; van der Knijff et al., 2010) is a distributed semi-physically based rainfall–runoff model combined with a routing module for river channels. Processes simulated include canopy and surface processes, snow accumulation and melting, soil and groundwater processes, streamflow and water abstraction in the river network. Lisflood was originally designed for large river basins (De Roo et al., 2001; Thiemig et al., 2013), though it has shown skilful performance in applications to a wide range of basin sizes (e.g. Alfieri et al., 2012; Thirel et al., 2012; Wanders et al., 2014; Younis et al., 2008). Lisflood is the operational model adopted by the European Flood Awareness System (Thielen et al., 2009) and thanks to this the European setup is subject to periodical parameter calibration exercises, to include new discharge observations and update existing time series with recent data. In the current model setup, Lisflood is calibrated with the standard particle swarm 2011 algorithm (Zambrano-Bigiarini and Rojas, 2014) at 693 stations across Europe (see Fig. 1). The model calibration is based on up to 8 years of daily data using the EFAS-Meteo data set (Ntegeka et al., 2013) as meteorological input data and a network of observed discharge time series at the calibrated stations. The latest developments on the European setup include the simulation of 182 lakes and 34 large reservoirs, and the implementation of monthly maps of water use from the SCENES project (Kamari et al., 2008), which for this work are assumed constant throughout the current century.

The first part of the study focuses on the analysis of precipitation patterns of the seven climate scenarios. Considered variables are annual precipitation (prYear) and annual maximum daily precipitation (prMAX). The average change between the three future time slices and the baseline is evaluated on a spatial basis, by assessing the agreement of the ensemble projections with the above described coefficient of variation of the relative change.

In a subsequent step, the two precipitation-related variables are aggregated over 22 European river basins with upstream area at the outlet larger than 50 000 km2. The trend of annual values of basin-aggregated prYear and prMAX is then investigated by means of linear regression analysis, to estimate the sign and the average rate of the trend. In addition, the Mann–Kendall test (Kendall, 1975; Mann, 1945) is performed on the time series of the ensemble mean of prYear and prMAX, to evaluate the statistical significance of the monotonic trend, independently of its linear or non-linear behaviour.

Meteorological variables of the seven climate scenarios are regridded at 5 km × 5 km on the simulation domain shown in Fig. 1. For each time step, potential evapotranspiration maps are computed with the module Lisvap (Burek et al., 2013a), using the Penman–Monteith formulation with minimum temperature, maximum temperature, incoming solar radiation, actual vapour pressure and wind speed as input. Actual vapour pressure maps were previously calculated from surface air pressure and specific humidity using the ideal gas formula. The hydrological model Lisflood is then run for the period 1970–2005 and for the future climate scenarios 2006–2100 forced by RCP8.5, using daily precipitation, average temperature and potential evapotranspiration maps generated by Lisvap. A Gumbel extreme value distribution fitting is performed on 30 raster maps of annual maximum discharge of the baseline window (1976–2005), using the L-moments approach (Hosking, 1990). The analytical functions thus derived are used to estimate extreme discharge peaks with chosen return period Q(RP), by inverting the formulation of the Gumbel distribution: Q(RP)=ξ-αln⁡-ln⁡1-1RP, where α and ξ are the scale and location parameters of the analytical Gumbel distributions.

The peak discharge corresponding to the 2-year return period is commonly considered representative of river bank-full conditions (e.g. Carpenter et al., 1999). Hence, discharge peaks exceeding Q(RP = 2) and their corresponding time of occurrence were extracted from the hydrological simulations of baseline and climate scenarios using the peak over threshold (POT) approach described in Sect. 3.4.

The quantitative analysis of simulated streamflow is performed in a similar way as that for precipitation, by comparing the three future time slices against the baseline. The analysis focuses on three variables: the average streamflow Q‾, the mean annual daily peak flow Q‾MAX and the 100-year daily peak flow Q100. Both Q‾ and Q‾MAX are extracted directly from the model output, and are robust estimators used as benchmark values for water resources management and peak discharge analysis, respectively. The Q100 is instead estimated from the analytical extreme value distribution fitted on the series of annual maxima and is therefore affected by an additional error component. However it is commonly used in flood hazard estimation (Alfieri et al., 2014b; Di Baldassarre et al., 2010; Hall et al., 2005; Merz et al., 2008) as it is a standard in the design of flood protections and often a potential threat to population and assets in case of failure of flood defences.

The final set of analyses is specifically addressed at detecting changes in the frequency of extreme peak discharges in each of the three future time slices, as compared to the baseline. The first of these analyses is focused on peak flows with return periods larger than 2 years and it is performed on each grid point of the European river network, given the robustness of the sample data set. Indeed, by definition these events occur with an average frequency of f2 = 0.5 events per year, which lead to a theoretical sample size of 15 events per ensemble member (i.e. 30 years × 0.5 = 15 events) for each grid point.

The second analysis investigates changes in the frequency of extreme events with return periods equal or larger than 100 years, in the three time slices. One can note that such events occur with a theoretical frequency of 0.01 per year and therefore 0.3 times every 30 years. To increase the robustness of the samples, results are aggregated at river basin and country levels. Two-proportion z test is applied to test the statistical significance of expected changes in the frequency of extreme events.

The frequency analysis of extreme events is based on a POT approach on the discharge time series of historical and future scenarios. A new algorithm was developed to select peak discharges from each grid point of the river network of a map stack of daily discharge over Europe. The main challenges faced in this task are related to the variable number of flow peaks above the threshold for each grid point and to the different peak timing. On the other hand the recursive application of the standard POT selection on each grid point is not a viable solution due to the excessive computation time required (i.e. for comparison, this option would have involved looping over more than 10 billion iterations). The considered threshold value is the 2-year return period Q2, taken from the analytical distribution fitted on the historical run of each of the seven climatic scenarios. Each event is defined by the portion of hydrograph larger than Q2 and it is identified by its peak discharge and the corresponding timing. The selection algorithm was then applied on both the baseline scenarios and the three future time slices, for a total of 43 200–43 830 discharge maps for each model run, depending on the calendar (see Table 1).

In Fig. 4 (top), the mean annual precipitation (prYear) and mean annual maximum daily precipitation (prMAX) are shown for the baseline period, together with the mean relative change (bottom) for the time slice 2080 (i.e. 2066–2095). The ensemble of climate projections agrees on up to a 30 % reduction of prYear in southern European countries, particularly in the Iberian Peninsula, Greece and southern Italy. Conversely, an increasing trend is projected over north-eastern Europe, with the largest changes in Iceland and Scandinavia, while in most of central Europe the ensemble spread is large in comparison to the mean change, so that a clear trend cannot be detected (i.e. grey area in Fig. 4 having CV > 1). These results are in line with those of the corresponding global climate models of CMIP5 (see Feng et al., 2014; Knutti and Sedláček, 2013), though the regional models give a more detailed representation of the spatial pattern of the projected changes. Significant changes in the future prMAX are instead mostly positive and have a patchy spatial pattern with the largest values of up to 40 % in northern and western Europe (see Fig. 4, bottom-right panel). Changes of prYear and prMAX in 2020 and 2050 are shown in Fig. S1 in the Supplement and look like the intermediate conditions between the baseline and 2080, though with a larger proportion of uncertain trends with CV > 1.

Annual values of prYear and prMAX are analysed at the basin scale for 22 large European river basins. The aims of this analysis are (1) to study long-term trends and the inter-annual variability of the underlying data, (2) to increase the sample robustness through spatial aggregation and detect possible weak but statistically significant trends, and (3) to link basin-wide changes of the precipitation regimes to possible implications on the future runoff. The ensemble range of prYear and prMAX for the historical runs and the future scenarios are shown in Fig. 5 for five European river basins shown in green in Fig. 1, together with the ensemble mean and the 10-year moving average (solid lines). In each panel, shades of green refer to basin-wide averages, while shades of blue refer to the largest point values within the river basin for each year, independently of their location.

In the two top panels one can see for the Kemijoki River basin a clear rising trend in the mean annual precipitation, with a basin average rate of b = 1.6 mm yr-2 and point maximum growing at the rate b = 2 mm yr-2 (i.e. 152 and 190 mm yr-1 increase by 2100, respectively), both statistically significant at pMK ≈ 0 using the Mann–Kendall trend test. Similarly, the maximum daily precipitation in the Kemijoki is projected to rise at a basin average rate of 0.07 mm day-1 yr-1 and at 0.17 mm day-1 yr-1 for local maxima. Both trends are statistically significant, though with a larger variability between local extremes and basin-wide averages. It is worth noting in Fig. 5 how maximum point accumulations (in blue shades) give a measure of the model's sharpness and of their ability to represent extreme values way larger than climatological averages, yet compatible with realistic observed past values (see e.g. WMO, 2009, Sect. 5.7). An overview of results for the 22 river basins indicates agreement with the pattern shown in Fig. 4. Considering a statistical significance level of 5 % for the Mann–Kendall test, 9 river basins out of 22 will experience a significant rise of prYear, in northern and eastern Europe, while a significant decrease of prYear is foreseen in 7 river basins in southern Europe (see Figs. 5 and S2). These figures become 6 and 8, respectively, if point maxima are considered. Significant changes in the future maximum daily precipitation are instead only positive (see Figs. 5 and S3) and are projected to occur in 19 (basin-wide average) and in 15 out of 22 cases (point maximum). The largest significant basin-wide average changes are projected to occur in the Po for prMAX (+0.11 mm day-1 yr-1), while for prYear the maximum positive change is in the Neva and Narva (+1.7 mm yr-2) and the maximum negative in the Guadalquivir (-1.9 mm yr-2).

Figure 6 (left column) shows the ensemble mean of the average streamflow Q‾, of the mean annual daily peak flow Q‾MAX, and of the 100-year daily peak flow Q100 for the baseline scenario, while the relative changes for the time slice 2080 are shown on the right. The corresponding changes for 2020 and 2050 are shown in Fig. S4. Changes in Q‾ reproduce similar patterns as those of the mean annual precipitation in Fig. 4, with negative changes in southern Europe, positive in northern and eastern Europe, and uncertain behaviour in the western part of central Europe where CV > 1 over a large area. In the considered study region, Q‾ is projected to increase in 73 % of the river network by 2080, while the overall mean relative change is 8 %. However, the largest projected changes of Q‾ are negative and in some cases lower than -40 % in southern Spain. One can note that such changes are in absolute value larger than the corresponding reduction in the annual precipitation (∼ 30 % for the same area), as a consequence of the increased evapotranspiration rates caused by the projected warming.

Changes of Q‾MAX and Q100 in the three future time slices have similar patterns. Although in the majority of the river network the projected changes have large uncertainty (CV > 1), some significant trends are found, particularly in 2080, where in 38 (for Q‾MAX) and 27 % (for Q100) of the river network the ensemble of climate projections points towards a clear change from the baseline. For both variables, positive changes are found in central and southern Europe, though with a rather discontinuous pattern and the alternation of good and poor agreement of the ensemble models. Significant negative changes are instead mainly located in southern Spain and in north-eastern Europe, including the Baltic countries, Scandinavia and north-western Russia. For the Iberian case, reasons are sought in the overall reduction in the components contributing to the surface runoff of rivers. On the other hand, negative changes in northern Europe are likely to be linked to the temperature rise and the consequent reduced contribution of snow accumulation and melting on spring floods, as already found in previous studies (Dankers and Feyen, 2008; Kundzewicz et al., 2006).

The average annual frequency of peak discharges larger than Q2, for brevity referred to as f2, is shown in Fig. 7 for the baseline scenario (top left), together with the relative changes for the three future time slices. It is not surprising to see several river reaches with f2 considerably larger than the theoretical frequency of 0.5. Indeed the analytical distributions are fitted on the samples of annual maxima (i.e. one event per year), while the empirical frequencies in Fig. 7 are counted on the entire time series. As shown by Mallakpour and Villarini (2015), this approach enables a more consistent assessment of event frequency, particularly for those years when more than one event above threshold is recorded. In the future scenarios, changes are particularly consistent in the north-eastern Europe, where a reduction of the frequency of extreme events is clearly visible since the first time slice. In 2080, the pattern of projected relative changes looks similar to that of Q‾MAX in Fig. 6, though with a wider range, where 50 % of grid points exhibit changes in absolute value larger than 35 %.

The expected annual frequency (EAF) of peak flow events larger than Q2 is shown in Figs. 8 and S5, by aggregating output for the 22 large European river basins considered in this study. Figure 8 also includes Europe-wide aggregated data (top-left panel). For each time slice, the ensemble mean and range are shown with a solid line and a colour shading delimited by dashed lines. The information content of this graphical representation is manifold, and the main points are summarized in the following:

The y axis shows the EAF of peak flow events with return periods between 2 and any chosen value of the abscissa up to 500 years. Return periods are calculated by inverting Eq. (2), using the discharge peaks over threshold extracted from the hydrological simulations. Peak flows above a 500-year return period are added as lump contribution at the position x = 500 years of the abscissa. In other words, values at the far right of the abscissa are read as EAF(2 < RP < ∞) ≡ f2, as those in Fig. 8. It is worth noting that the estimated return period of simulated flood peaks of both the baseline and the future time slices is derived from the corresponding analytical extreme value distribution computed only on the baseline scenario. This step is crucial to compute coherent estimates of future extremes with return periods larger than the length of the time slice and thus represent a substantial improvement as compared to approaches comparing statistical values with the same probability of occurrence but taken from different analytical distributions.

The frequency analysis of extreme peak flow events above a 100-year return period is of particular interest, given that the average protection level of the European river network is of the same magnitude (Rojas et al., 2013), with some obvious differences among different countries and river basins (Jongman et al., 2014). In other words, a substantial increase in the frequency of peak flows below the protection level is likely to have a lower impact, in terms of population affected and economic losses, in comparison to a small but significant change in extreme events causing settled areas to be inundated by the flood flow. In this regard, Figs. 8 and S5 denote a visible increase of extreme events above a 500-year return period in a number of river basins (e.g. Po, Dniester, Duero, Garonne, Ebro, Loire, Maritsa, Rhine, Rhone), including some where the overall frequency f2 of events above threshold is projected to decrease (e.g. Guadiana, Narva). A summary of country-aggregated estimates of f100 and the relative changes from the baseline in future time slices is shown in Table 2. Values are obtained by counting the average frequency of occurrence in all grid points of the river network within each country. It is worth noting that larger countries have on average a larger sample of historical events (Ne) with return periods larger than 100 years to estimate relative changes. The statistical significance of the estimated change in the ensemble mean was tested with a two-proportion z test. A stringent p value of 1 ‰ is chosen as threshold for significance, to compensate for the autocorrelation of extreme events in neighbouring grid points along the drainage direction. In addition, this issue is mitigated by the use of an ensemble of seven independent models.

The striking outcome of Table 2 is the large dominance of positive changes in f100 since the first future time slice, although in some areas the overall frequency f2 of peak flows over threshold is projected to decrease considerably, such as in Spain (Guadiana and Guadalquivir) and in some river basins in north-eastern Europe (Kemijoki, Daugava, Neva and Narva) as shown in Figs. 8 and S5. In time slice 2080, projected changes are positive and significant in all the considered countries, with values ranging between 18 % in Finland and up to 982 % in Iceland.