The analyses were performed on a set of 19 hydrological regions in Switzerland (Fig. ) with areas between 600 and 5000 km2, mean elevations between 550 and 2300 m a.s.l., and mean annual precipitation sums between 1000 and 1800 mm. The flow regimes north of the Alps (Plateau and Jura) are dominated by rainfall and characterized by high discharge in winter and spring but low discharge in summer. In contrast, the regimes in the Alps are dominated by snowmelt and ice melt and characterized by high discharge in summer. For illustration purposes, we chose four regions. Two of them (Jura and Thur) have a rainfall-dominated regime and the other two (Valais and Engadin) a melt-dominated regime under the current climate.

The analysis performed to detect changes in future extreme regimes consisted of three main steps (Fig. ). First, different procedures for estimating extreme flow regimes were tested (first step). Once a suitable procedure was identified, it was applied to estimate extreme high- and low-flow regimes under current and future climate conditions (second step). These extreme regimes were compared to mean regimes. Third, current and future estimates were compared to detect future changes in flow regimes (third step). We used simulated discharge representing both current and future climatology as the basis for the analysis. The current discharge series were derived by feeding a hydrological model with observed meteorological data and with meteorological data simulated by a set of climate models for the reference period. The future discharge series were obtained by driving the model with meteorological data from downscaled and bias-corrected climate model simulations.

The two estimation techniques applied use frequency analysis of different quantities. The first method applies frequency analysis to the individual percentiles of the FDC. The second method uses stochastically simulated discharge time series to identify annual hydrographs with a certain non-exceedance probability. We refer to these methods as FDC and stochastic, respectively. The two methods are compared to a benchmark method (univariate), which performs univariate frequency analysis of the monthly discharge values and neglects the dependence between individual months. We here focus on the estimation of high- and low-flow regimes with a return period of T=100 years since this return period is commonly used for planning purposes. The methods outlined in this study, however, can be generalized to other return periods. In the following paragraphs, we describe the data sets (Fig. a, Sect. ), the stochastic discharge generation procedure (Fig. b, Sect. ), and the estimation techniques used to derive extreme flow regimes (Fig. c, Sect. ).

We used discharge time series simulated with the PREVAH hydrological model as input for the analysis. To represent current conditions, the model was driven with observed meteorological data for the period 1981–2010. To represent future conditions, it was driven with meteorological data obtained by regional climate model simulations for the period 2071–2100 (see below). PREVAH is a conceptual process-based model. It consists of several sub-models representing different parts of the hydrological cycle: interception storage, soil water storage and depletion by evapotranspiration, groundwater, snow accumulation and snowmelt and glacier melt, runoff and baseflow generation, plus discharge concentration and flow routing . A gridded version of the model at a spatial resolution of 200 m was set up for Switzerland . For the calibration of the model parameters, meteorological and discharge time series from 140 mesoscale catchments covering different runoff regimes were used. The model calibration was conducted over the period 1993–1997. Validation on discharge was performed with the period 1983–2005. More details on the calibration and validation procedures can be found in . The parameters for each model grid cell were derived by regionalizing the parameters obtained for the 140 catchments with ordinary kriging . The hydrological model has been calibrated using observed meteorological data, but will subsequently be fed with meteorological data simulated by a set of GCM–RCM combinations. It is assumed that the parameter set derived in the calibration procedure will still produce reliable results since have confirmed in a review that a good performance of hydrological models in the historical period increases confidence in projected impacts under climate change. Future glacier extents were simulated with two glacier evolution models. We used the global glacier evolution model GloGEM; for short glaciers (glacier length < 1 km) and GloGEMflow for long glaciers (length > 1 km). GloGEM simulates glacier changes with a retreat parameterization relying on observed glacier changes . GloGEMflow is an extended version of GloGEM with a dynamic ice flow component. This new model was extensively validated over the European Alps through comparisons with various observations (e.g., surface velocities and observed glacier changes) and detailed 3-D projections from modeling studies focusing on individual glaciers e.g.,. The simulated glacier extents were transformed from the GloGEM(flow) 1-D model grid to the 2-D PREVAH model grid by ensuring that the area for each elevation band was conserved.

PREVAH is driven by time series of precipitation, temperature, relative humidity, shortwave radiation, and wind speed. The meteorological forcing for current simulations was observed time series provided by the , while the transient meteorological forcing for future simulations was derived from the CH2018 climate scenarios . The meteorological data were interpolated to a 2×2 km grid using detrended inverse distance weighting where the detrending was based on a regression between climate variables and elevation . The climate scenarios are based on the results from the EURO-CORDEX initiative , which are the most sophisticated and high-resolution coordinated climate simulations over Europe. The scenarios are based on representative concentration pathways (RCPs) and a regional downscaling approach based on quantile mapping . The quantile mapping procedure was calibrated on the period 1981–2010 and performed on a grid-by-grid basis for all meteorological variables. The meteorological data were derived from an ensemble of 39 GCM–RCM combinations for different scenarios (Table  in the Appendix), which provide temperature, precipitation, relative humidity, shortwave radiation, and wind speed for the locations of various meteorological stations. The selection of scenarios included the three RCPs2.6, 4.5, and 8.5 for which 8, 13, and 18 GCM–RCM combinations were available, respectively. Ten out of the 39 GCM–RCM combinations were available at a high resolution of 12.5 km and the remaining combinations at a resolution of roughly 50 km. Using combinations at both resolutions allows for a larger ensemble; however, it means that those GCM–RCM combinations which are available for both resolutions obtain more weight. During a model run, PREVAH reads the meteorological grids and further downscales the data to the computational grid of 200×200 m using bilinear interpolation. For temperature, a lapse rate of -0.65 ∘C/100 m was additionally used for topographic corrections.

The discharge simulated with the hydrological model for the current (1981–2010) and future (2071–2100) 30-year periods only represents small sets of possible annual hydrograph realizations. Among these realizations, certain hydrographs including extreme hydrographs such as a 100-year hydrograph were possibly not observed. We used a stochastic discharge simulation procedure to increase the number of possible annual hydrograph realizations. These realizations represent the discharge statistics and temporal correlation structure of the available data and extend the existing sample to as yet unobserved annual hydrographs. To simulate such hydrographs, we used the method of phase randomization . We combined this empirical procedure with the flexible four-parameter kappa distribution to allow for the extrapolation to as yet unobserved values. This phase randomization approach preserves the autocorrelation structure of the raw series by conserving its power spectrum . The procedure consists of three main steps . In a first step, the discharge series (here, the simulated discharge for past and future conditions) is converted from the time domain to the spectral domain by the Fourier transform . The Fourier transform of a given time series x=(x1, …, xt, …, xn) of length n is 1f(ω)=12πn∑t=1ne-iωtxt,-π≤ω≤π, where t is the time step, ω are the phases, and i=-1 is the imaginary unit. In this spectral domain, the data are represented by the phase angle and by the amplitudes of the power spectrum as represented by the periodogram. The phase angle of the power spectrum is uniformly distributed over the range -π to π. In a second step, the phases in the phase spectrum are randomized, while the power spectrum is preserved. In a third step, the inverse Fourier transform is applied to transform the data from the spectral domain back to the temporal domain. A step-by-step description of the stochastic simulation procedure and more background information on the Fourier transform are provided in , and references therein. An application of the simulation procedure to four example catchments in Switzerland has shown that both seasonal statistics and temporal correlation structures of discharge can be well reproduced . We therefore used this method to stochastically simulate 1500 years of discharge for each of the 19 regions in our data set. Stochastic series representing current conditions were generated by using the hydrological model simulations for 1981–2010 obtained by the 39 GCM–RCM combinations as input. Stochastic series representing future conditions were generated based on each of the hydrological model simulations generated with the 39 GCM–RCM combinations for different scenarios.

We employed two methods for estimating 100-year low- and high-flow regimes: FDC and stochastic. The extreme regime estimates were compared to the stochastically generated hydrographs to check for plausibility. Furthermore, they were compared to a lower-bound (for low-flow regimes) or upper-bound (for high-flow regimes) benchmark regime derived by combining 100-year monthly discharge estimates obtained from univariate frequency analysis. This frequency analysis was performed on the values of each month independently and the monthly values were fitted with a generalized extreme value (GEV) distribution. This distribution was not rejected according to the Anderson–Darling goodness-of-fit test computed using the procedure proposed by (α=0.05). The disadvantage of the univariate procedure is that the autocorrelation in the data, which is mainly visible for lags of 1 and 2 months, is neglected, which overestimates the extremeness of the 100-year low-flow regime and therefore produces unrealistic estimates. The univariate approach will therefore only be considered as a benchmark for model comparison and will not find consideration in the comparison of current and future extreme regime estimates.

The two methods and the benchmark approach for the estimation of 100-year low- and high-flow regime estimates were applied to discharge time series representing current and future climate conditions. First, 100-year regimes were estimated for current conditions (1981–2010). To generate a control regime, we used the discharge simulated with the observed meteorological data. To represent uncertainty due to different GCM–RCM combinations for different scenarios, we derived one reference regime for each discharge time series simulated by the 39 climate GCM–RCM combinations for different scenarios. This analysis provided us with a range of current regime estimates due to climate model uncertainty. The regime estimates derived from the 39 GCM–RCM combinations were used to derive a multi-model mean, which served as a reference for determining changes between current and future conditions. In a second step, 100-year estimates were derived for future conditions using the simulated time series for the period 2071–2100 for all GCM–RCM combinations and scenarios. We assessed changes in seasonality and magnitude of flow regimes in terms of their minimum, maximum, and mean discharges by comparing regime estimates derived for future conditions to the multi-model mean representing current conditions. (Figure ; results were grouped by RCP.)

The two estimation techniques and the benchmark approach provide distinct estimates for the 100-year low-flow regimes (Fig. ). The univariate technique leads to the most extreme regimes, whilst the FDC and stochastic methods lead to similar estimates. The univariate estimate should only be seen as a lower benchmark and not as an estimate for a “true” 100-year regime since the univariate approach neglects the dependence between monthly estimates. In contrast, the FDC and stochastic approaches produce more plausible estimates, i.e., estimates at the lower bound of the observed values. The summer low-flow regimes estimated by the FDC technique are comparable to the regimes of the year 2003, which included a very dry summer .

Similarly to low-flow regimes, the 100-year high-flow regimes derived by the three estimation techniques are distinct (Fig. ). The univariate approach, as mentioned previously, produces unrealistic results in terms of seasonality, since the predictions of the monthly 100-year flows neglect the dependence between the different months. The FDC and stochastic techniques produce more similar seasonalities and more realistic estimates at the upper bound of the observed annual hydrographs. Contrary to low-flow estimates, high-flow estimates generated with the FDC or stochastic techniques can be different. The stochastic approach generally leads to more conservative estimates than the FDC approach in melt-dominated regions. We attribute this to the fact that the stochastic approach performs frequency analysis of annual sums, while the FDC approach performs frequency analysis of the percentiles of the FDC.

The plausibility of the 100-year estimates derived by using the FDC and stochastic approaches is shown by a comparison with stochastically generated annual hydrographs (Fig.  in the Appendix for the low-flow estimates). The derived estimates, in fact, are embedded in the lower spectrum of the stochastically generated annual hydrographs. This is hardly the case for the univariate estimates, which lead to “unrealistically low” 100-year hydrographs partly outside of the range of the stochastically generated hydrographs. Similarly, the 100-year high-flow regime estimates derived by the FDC and stochastic methods are embedded in the higher spectrum of the stochastically generated hydrographs, while the univariate estimate is “unrealistically high”. Since the univariate approach yields unrealistic estimates, it is not considered for further analysis.

Both mean and extreme regimes are subject to uncertainty when derived from simulated discharge. The uncertainty comes from the hydrological model and from the spread between the climate simulations. Figure  shows mean and extreme low- and high-flow regime estimates derived for the observed climatology for the four illustration catchments. It also shows the range of regimes obtained by using different GCM–RCM combinations and scenarios. This range of regimes generally encompasses the regime derived from meteorological observations, which suggests that the climate model output realistically reproduces the observed climate. An exception is the Engadin, where the low-flow regimes derived from the GCM–RCM combinations overestimate summer low flows. This overestimation might be related to the univariate bias correction applied, which might not perfectly reflect the interplay between temperature and precipitation and therefore the timing of snowmelt processes . The spread in the current regimes is larger for extreme than for mean conditions for the rainfall-dominated catchments Thur and Jura. In addition, the spread is larger for the high- than for the low-flow extreme regimes except for the Engadin region. This range should be kept in mind when analyzing future regime estimates.

Shifts in regimes are expected for both mean and extreme low-flow conditions (Fig. ). The shifts are weak for rainfall-dominated regions (e.g., Thur and Jura), while they are strong for melt-dominated regions (e.g., Valais and Engadin). For the rainfall-dominated regions, changes in mean and extreme regimes are most visible for RCP8.5. Here, the different realizations lead to regimes with more pronounced summer low flows. In addition, there is a reduction in spring discharge under RCP2.6 for both mean and extreme conditions when looking at the regimes derived from the FDC approach. In the case of melt-dominated regions, most GCM–RCM combinations lead to clear shifts towards regimes with earlier and reduced summer flows. These shifts are more pronounced for RCP8.5 than RCPs4.5 and 2.6. Note that the spread of future regimes is smaller for RCP2.6 than RCPs4.5 and 8.5 due to the smaller number of chains in the ensemble.

Differences between current (i.e., multi-model mean of reference simulations) and future mean and extreme low-flow regimes are summarized in Fig. . The detected changes for RCP2.6 and RCP8.5 are similar (results for RCP4.5 are not displayed, but lie in between those of RCPs2.6 and 8.5). Changes are projected for the minimum and maximum discharges of mean and extreme low-flow regimes and for their timing, but less for the mean of these regimes. The changes in the mean flow can reach up to 30 %, while the maximum and minimum flows can change up to 100 %.

Changes in melt- and rainfall-dominated regions are clearly different. Both the FDC and stochastic approach suggest changes in extreme low-flow regimes. In rainfall-dominated regions, an increase is expected for the discharge maximum independent of the estimation approach chosen. In contrast, a decrease is expected in the discharge minimum according to the stochastic approach, while no clear changes are expected using the FDC approach. For melt-dominated regions, the change pattern is different. There, a decrease in maximum discharge is expected. An increase in minimum discharge is expected for mean regimes, while changes are less clear for the extreme regimes. Shifts of 1 or 2 months are expected in timing for both rainfall- and melt-dominated regions. In most catchments, the timing of future maximum discharge is likely to occur earlier than under current conditions. Shifts towards later in the year are expected in the timing of the minimum flow. The changes in mean and maximum flows are similar for extreme low-flow regimes derived by the two estimation techniques FDC and stochastic. In contrast, the shifts in minimum flow and timing are different when applying the stochastic approach instead of the FDC approach.

High-flow regime estimates are also expected to change (Fig. ), with no consistent change pattern visible at first glance. Changes in high-flow extreme regimes are slightly more pronounced for RCP8.5 than for RCP2.6 (Fig. ; RCP4.5 not shown because it is expected to provide results somewhere in between RCPs2.6 and 8.5). They are similar for the estimation techniques used (FDC/stochastic). As for the low-flow regimes, only moderate and mostly positive changes of less than 30 % are expected in the mean discharge of extreme high-flow regimes. The changes in the maximum and minimum discharges of the high-flow regimes are much stronger, i.e., up to 100 %. In rainfall-dominated regions, changes in maximum discharge are mostly positive, while they can be negative for melt-dominated regions. In these melt-dominated regions, an increase is expected in the minimum discharge of high-flow extreme regimes, especially when using the FDC approach. In rainfall-dominated regions, changes in minimum discharge are mostly negative, especially for RCP8.5. Changes in timing are different for the FDC and stochastic approach and there is no consistent pattern across catchments. Minimum and maximum discharges can occur earlier or later in the year than under current conditions.

The low-flow regime estimates derived with the univariate method are implausible because the method neglects the interdependence between flows of adjacent months. In contrast, both other methods, FDC and stochastic, lead to similar results. The differences between the two methods mainly lie in how the seasonality is derived. In the case of the FDC approach, mean seasonality is used. In the case of the stochastic approach, a rather “random” seasonality is used since the regime is chosen according to the annual discharge sum. The use of one potential realization of seasonality in the stochastic approach compared to the use of a mean seasonality in the FDC approach has the disadvantage that it is less representative but the advantage that it is consistent with the corresponding annual discharge sum. The direction of changes derived from the two estimates are similar except for changes in minimum discharge in the low-flow regime and minimum discharge in the high-flow regimes. Both types of estimates seem to be plausible in the light of the stochastically generated hydrographs, which represent a large set of possible realizations among which extreme hydrographs can be found. While the estimates derived by the two methods do not differ much, both methods have their advantages and disadvantages. The FDC approach is relatively simple to implement but decouples seasonality from the distribution of daily discharge values. In contrast, the stochastic approach jointly considers magnitude and seasonality but requires the implementation of a stochastic discharge generator. The main advantage of such a generator is that the individual hydrograph realizations can be used for specific impact studies, which allows for direct performance of the frequency analysis of the quantity of interest. There are several possible solutions to the multivariate problem of estimating extreme regimes, and none of these two methods can therefore be said to be the better one.

The estimation of extremes, be it of regimes or individual flow characteristics, is associated with several sources of uncertainty. These comprise the choice of an extreme value distribution used to fit the data (i.e., percentiles of FDCs, annual sums, daily discharge sums) and the estimation of its parameters . When applied to time series representing future conditions simulated with a hydrological model, additional uncertainty sources are involved. These include the assumptions underlying the applied future global climate scenarios, global climate model structures, initial conditions, downscaling methods, modeled future glacier extents, the uncertainties inherent in the hydrological model results, and the calibration of its parameters . Despite these uncertainties, the extreme regime estimates can be used to identify future changes, and as such these estimates can be further used in climate impact studies. Potential fields of application include water scarcity assessments, where such regime estimates are combined with estimates of water demand , eco-hydrological studies , or analyses of the future potential of hydropower production .

Changes in all types of regimes (mean/extreme low flow/extreme high flow) were found to be distinct for melt-dominated and rainfall-dominated regions. This refers not only to the entire regime, but also to individual regime characteristics such as minimum, maximum, and mean flow as well as the timing of the minimum flow. The direction of change was different in rainfall- and melt-dominated regions for all regime types. An increase of up to 50 % in the maximum discharge of mean and extreme low- and extreme high-flow regimes was found for rainfall-dominated regions. In contrast, a decrease in the minimum discharge by up to 100 % is projected to occur for these catchments and all types of regimes. The opposite is true for melt-dominated regimes, where the minimum discharge increases while the maximum and mean discharges decrease. The changes in extreme regimes can be explained by a reduction or an earlier contribution of snowmelt and glacier melt and by an increase in winter precipitation , which coincide with the high-flow season in rainfall-dominated regions but with the low-flow season in melt-dominated regions. For mean regimes, changes in melt-dominated regimes were found in previous studies . found a projected discharge decrease in melt-dominated regions due to reduced contribution of ice melt in the Po and Rhine river basins. The regime shifts in the rainfall-dominated regions are also influenced by increases in precipitation in the winter season and decreases in the summer season. Precipitation increases in the high-flow winter season lead to increases in the discharge maximum, while precipitation decreases in the low-flow summer season lead to decreases in the discharge minimum. The results of confirm that changes in rainfall-dominated regions are more uncertain since the projected changes in precipitation mostly lie within the range of natural variability of the control scenario. Similar results were found by for several catchments in Switzerland and by on a global scale. We have shown here that these previous findings also apply to extreme regimes. The regime shifts detected have implications for various sectors. Regime shifts and more severe low flows were found to lead to more severe water scarcity situations, where water supply is insufficient to meet water demand . In the hydropower sector, future regime shifts are anticipated to lead to a reduction in production .