Extreme low and high flows can have negative economic, social, and ecological effects and are expected to become more severe in many regions due to climate change. Besides low and high flows, the whole flow regime, i.e., annual hydrograph comprised of monthly mean flows, is subject to changes. Knowledge on future changes in flow regimes is important since regimes contain information on both extremes and conditions prior to the dry and wet seasons. Changes in individual low- and high-flow characteristics as well as flow regimes under mean conditions have been thoroughly studied. In contrast, little is known about changes in extreme flow regimes. We here propose two methods for the estimation of extreme flow regimes and apply them to simulated discharge time series for future climate conditions in Switzerland. The first method relies on frequency analysis performed on annual flow duration curves. The second approach performs frequency analysis of the discharge sums of a large set of stochastically generated annual hydrographs. Both approaches were found to produce similar 100-year regime estimates when applied to a data set of 19 hydrological regions in Switzerland. Our results show that changes in both extreme low- and high-flow regimes for rainfall-dominated regions are distinct from those in melt-dominated regions. In rainfall-dominated regions, the minimum discharge of low-flow regimes decreases by up to 50 %, whilst the reduction is 25 % for high-flow regimes. In contrast, the maximum discharge of low- and high-flow regimes increases by up to 50 %. In melt-dominated regions, the changes point in the other direction than those in rainfall-dominated regions. The minimum and maximum discharges of extreme regimes increase by up to 100 % and decrease by less than 50 %, respectively. Our findings provide guidance in water resource planning and management and the extreme regime estimates are a valuable basis for climate impact studies.

Estimation of 100-year low- and high-flow regimes using annual flow duration curves and stochastically simulated discharge time series

Both mean and extreme regimes will change under future climate conditions.

The minimum discharge of extreme regimes will decrease in rainfall-dominated regions but increase in melt-dominated regions.

The maximum discharge of extreme regimes will increase and decrease in rainfall-dominated and melt-dominated regions, respectively.

Low flows can have severe impacts on ecology and economy. Potential ecological impacts include fish-habitat conditions or water quality

Previous studies have focused on the detection of changes in mean flow regimes

Commonly, extreme flow estimates derived by frequency analysis focus on one characteristic of the hydrological regime, e.g., summer low flows, drought durations, drought deficits

Estimating extreme flow regimes with a given exceedance frequency is not straightforward since discharge values at several points in time are correlated. Because of the multivariate nature of the problem, no single solution exists. We here aim at estimating extreme high- and low-flow regimes with a defined return period for current and future climate conditions. We propose two possible approaches for the estimation of such extreme regimes.
The first approach is based on flow duration curves (FDCs). FDCs describe the whole distribution of discharge and are particularly suited for planning purposes

Map of Switzerland with 19 large hydrological regions (grey outline) and the four illustration regions (black border): Thur, Jura, Valais, and Engadin. The main orographic regions Jura, Plateau, and Alps are outlined by the brown lines.

Many different approaches have been proposed for the stochastic simulation of streamflow time series. Often, indirect approaches, which combine the stochastic simulation of rainfall with hydrological models, have been used for the generation of stochastic discharge time series

The analyses were performed on a set of 19 hydrological regions in Switzerland (Fig.

The analysis performed to detect changes in future extreme regimes consisted of three main steps (Fig.

Illustration of the study framework. (1) Comparison of the different estimation techniques

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

We used discharge time series simulated with the PREVAH hydrological model

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

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

We employed two methods for estimating 100-year low- and high-flow regimes:

A first extreme regime estimate was derived by performing the frequency analysis of annual FDCs. According to

The second method for the estimation of extreme regimes performs the frequency analysis directly on a large set of stochastically simulated annual hydrographs (here 1500 years). The frequency analysis was performed on the annual sums of the stochastically generated hydrographs. We identified the hydrograph corresponding to the empirical 100-year annual discharge sum as the 100-year regime. The application of this procedure is only possible for long time series as given by the stochastic series, since a 100-year annual sum is not necessarily observed in a short record of, say, 30 years. Like the FDC estimates, the regimes derived from the stochastic approach were aggregated to a monthly resolution.

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

Illustration of the main characteristics of an annual rainfall-dominated flow regime under current and future conditions: maximum, mean, and minimum.

The two estimation techniques and the benchmark approach provide distinct estimates for the 100-year low-flow regimes (Fig.

100-year

Similarly to low-flow regimes, the 100-year high-flow regimes derived by the three estimation techniques are distinct (Fig.

100-year

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.

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

Current 100-year mean regimes (grey), low-flow regimes (blue lower line), and high-flow regimes (blue upper line) estimated by using the FDC method on the control discharge simulations derived by observed meteorological data (bold line) and the reference discharge simulations derived by meteorological data simulated by the 39 GCM–RCM combinations for different scenarios for the reference period (shaded polygons).

Shifts in regimes are expected for both mean and extreme low-flow conditions (Fig.

Comparison of current multi-model mean (solid line) and future 100-year

Differences between current (i.e., multi-model mean of reference simulations) and future mean and extreme low-flow regimes are summarized in Fig.

Differences between current (i.e., multi-model mean of reference simulations) and future mean (grey) and extreme

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.

Comparison of current multi-model mean (solid line) and future 100-year

High-flow regime estimates are also expected to change (Fig.

Differences between current (i.e., multi-model mean of reference simulations) and future mean (grey) and extreme

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

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

Extreme regime estimates were derived by frequency analysis performed on (1) annual flow duration curves (FDCs) and (2) the discharge sums of stochastically generated annual hydrographs. Both were found to provide realistic, similar results. A range of future extreme regime estimates was obtained for both extreme and mean conditions. In rainfall-dominated regions, the range of these future low- and high-flow estimates comprised the current estimate. In contrast, in melt-dominated regions, future high-flow and especially low-flow regimes were distinct from the current estimate. Changes in mean discharges were moderate for all types of regimes and catchments and did not exceed 30 %. Projected changes in the minimum discharge of mean and extreme high- and low-flow regimes were positive in melt-dominated regions due to increases in winter precipitation and amount to up to 100 %. In contrast, mostly positive changes of up to 50 % in maximum discharge were found in rainfall-dominated regions for all types of regimes. These positive changes in maximum discharge are linked to increases in winter precipitation, which coincide with the high-flow season. High- and low-flow regime estimates derived using the approaches proposed in this study are important for climate impact studies addressing, e.g., the future hydropower production potential or the occurrence of water shortage situations. The estimates also provide guidance for hydraulic design, emergency planning, and drought and water management.

The climate model simulations are available on the web page of the Swiss National Centre for Climate Services (

The idea and setup for the analyses were developed by MIB. MZ did the hydrological model simulations. HZ, MH, and DF provided the future glacier extents. The analyses were performed by MIB and discussed with MZ and DF. MIB wrote the first draft of the manuscript, which was revised by all the co-authors and edited by MIB.

The authors declare that they have no conflict of interest.

We thank MeteoSwiss for providing observed meteorological data and the Swiss National Centre for Climate Services (NCCS) for providing the climate model simulations.

This research has been supported by the Swiss Federal Office for the Environment (FOEN) (grant no. 15.0003.PJ/Q292-5096).

This paper was edited by Axel Bronstert and reviewed by two anonymous referees.