In this study, low-flow projections of future climate scenarios are analysed by comparing future to past flows by using model forcing from a delta change approach. This concept allows one to remove biases resulting from simulations when regional climate model (RCM) outputs are used as an input in hydrologic modelling. Instead of using RCM simulations of daily air temperature and precipitation for hydrologic model calibration, the model is first calibrated by using observed climate characteristics in the reference period. In a next step, RCM outputs are used to estimate monthly differences between simulations in the reference (control) and future periods. These differences (delta changes) are then added to the observed model inputs and used for simulating future hydrologic changes. The daily precipitation is scaled by the relative monthly delta changes, with no change in the frequency of rainy days. The daily air temperature is changed by the absolute value of monthly delta changes. The differences between daily simulations of a hydrologic model in the reference and future periods are then used to interpret potential impacts of changing climate on future river flows.

The future low-flow changes are quantified by the Q95 low-flow quantile and seasonality index (SI). The Q95 represents river flow that is exceeded on 95 % of the days of the entire reference or future period. This characteristic is one of the low-flow reference characteristic, which is widely used in Europe (Laaha and Blöschl, 2006). SI represents the average timing of low flows within a year (Laaha and Blöschl, 2006, 2007). It is estimated from the Julian dates Dj of all days when river flows are equal or below Q95 in the reference or future periods. Dj represents a cyclic variable. Its directional angle, in radians, is given by θj=Dj⋅2π365.

The arithmetic mean of Cartesian coordinates xθ and yθ of a total of n single days j is defined as xθ=1n∑jcos⁡(θj)yθ=1n∑jsin⁡(θj).

From this, the directional angle of the mean vector may be calculated by θ=arctanyθxθ1stand4thquadrant:x>0,θ=arctanyθxθ+π2ndand3rdquadrant:x<0.

Finally, the mean day of occurrence is obtained from re-transformation to Julian date: SI=θ⋅3652π and the variability of the date of occurrence about the mean date (i.e. seasonality strength) is characterised by the length parameter r. The parameter r is estimated as (Burn, 1997) r=x¯2+y¯2n and ranges from r=0 (low strength, uniform distribution around the year) to r=1 (maximum strength, all extreme events of low flows occur on the same day).

The SI is estimated for observed and simulated low flows. The differences between model simulations (i.e. Q95 and SI estimates) in the reference and future periods are then used to quantify potential impacts of climate change on low flows. Both Q95 and SI measurements are estimated independently for the reference and future periods by the lfstat package in R software (Koffler and Laaha, 2014).

Low-flow projections are estimated by a conceptual semi-distributed rainfall–runoff model (TUWmodel; Viglione and Parajka, 2014). The model simulates water balance components on a daily time step by using precipitation, air temperature and potential evapotranspiration data as an input. The model consists of three modules, which allow for simulating changes in snow, soil storages and groundwater storages. The calibrated model parameters are presented in Table 1. More details about the model structure and examples of application in the past are given, e.g., in Parajka et al. (2007), Parajka and Blöschl (2008), Viglione et al. (2013) and Ceola et al. (2015).

In this study, the TUWmodel is calibrated by using the SCE-UA (Shuffled Complex Evolution) automatic calibration procedure (Duan et al., 1992). The objective function (ZQ) used in calibration is selected on the basis of prior analyses performed in different calibration studies in the study region (see e.g. Parajka and Blöschl, 2008; Merz et al., 2011). It consists of the weighted average of two variants of Nash–Sutcliffe model efficiency, ME and MElog⁡. While the ME efficiency emphasise the high flows, the MElog⁡ efficiency accentuates more the low flows. The maximised objective function ZQ is defined as ZQ=wQ⋅ME+(1-wQ)⋅MElog⁡, where wQ represents the weight on high or low flows. If wQ equals 1 then the model is calibrated to high flows, if it equals 0 then to low flows only. ME and MElog⁡ are estimated as ME=1-∑i=1nQobs,i-Qsim,i2∑i=1nQobs,i-Qobs‾2,MElog⁡=1-∑i=1nlog⁡(Qobs,i)-log⁡(Qsim,i)2∑i=1nlog⁡(Qobs,i)-log⁡(Qobs‾2, where Qsim,i is the simulated discharge on day i, Qobs,i is the observed discharge, Qobs‾ is the average of the observed discharge over the calibration (or verification) period of n days.

The uncertainty, defined as the range of simulated low-flow indices, is evaluated for two contributions. The first analyses the uncertainty (i.e. the range of Q95 and SI) estimated for different variants of hydrologic model calibration. Here, two cases are evaluated. In order to assess the impact of time stability of model parameters (Merz et al., 2011), the TUWmodel is calibrated separately for 3 different decades (1976–1986, 1987–1997, 1998–2008). The effect of objective functions used for the TUWmodel calibration is evaluated by comparing 11 variants of weights (wQ) used in ZQ. The following wQ are tested: 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1.0. The hydrologic model is calibrated for all 11 variants in each selected decade. Calibrated models are then used for flow simulations and hence Q95 and SI estimation in the reference and future periods.

The second contribution evaluates the uncertainty of Q95 and SI changes simulated for different climate scenarios. The effect of calibration uncertainty (case 1) is compared for four selected climate scenarios (more details are given in Sect. 3). The delta change approach is used to derive model forcing for selected future period and simulated future river flows are compared to model simulations in the reference period 1976–2008. The relative changes of Q95 and SI values between reference and future periods are estimated for 4 selected climate scenarios, 11 variants of model calibration and 3 selected decades. The relative contribution of the impact of model calibration (i.e. time stability and objective function selection) and climate scenario is evaluated for two low-flow regimes and for individual stations over Austria.

The uncertainty of low-flow projections is then compared to the range of low-flow indices obtained by different calibration variants in the reference period. In addition, the total uncertainty of future low-flow projections is decomposed to individual components by means of analysis of variance (ANOVA; e.g. von Storch and Zwiers, 1999, chap. 9 for a general introduction to ANOVA). The three-way ANOVA approach is employed to decompose total uncertainty of the projected low-flow changes into three main variance components. These variance components represent uncertainty contributions of three main effects: climate scenario (factor A with I=4 levels), decade used for model calibration (factor B with J=3, levels) and calibration variant representing different objective functions (factor C with K=11 levels). The ANOVA model is defined as follows: ΔQ95ijk=μ+αi+βj+γk+ϵijk. In this linear equation (Eq. 10), ΔQ95ijk denotes the ensemble projected changes in Q95 for the future horizon at a gauge. It is modelled by a global mean μ and the mean effects (deviations of factor-means from the global mean) of climate scenario (αi;i=1,…,I), decade (βj;j=1,…,J) and calibration variant (γk;k=1,…,K), and ϵijk are the residual errors of the model. In an ANOVA framework, the total variance of ΔQ95ijk is characterised by the total sum of squares SST, and is decomposed into additive variance components of individual effects: ST=SSA+SSB+SSC+SSE. The variance components of the main effects A, B and C are computed as follows: SSA=JK∑i=1Iy¯i..-y¯…2,SSB=IK∑j=1Jy¯.j.-y¯…2,SSC=IJ∑k=1Ky¯..k-y¯…2. The variance component of the residuals representing the unexplained variance is SSE=∑i=1I∑j=1J∑k=1Kyijk-yi..-y.j.-y..k+y…2. Based on the SSE, an estimate of the variance contributions of each effect A, B, C is computed as ηA2=SSASST;ηB2=SSBSST;ηC2=SSCSST;ηE2=SSESST. The measure eta square is also termed the coefficient of determination R2 (von Storch and Zwiers, 1999). Eta square tends to overestimate the variance explained by one factor and is therefore a biased estimate of the effect size. A less biased estimator is given by the measure ω2: ωA2=SSA-dfA⋅MSESST-MSE, where dfA denotes the degrees of freedom of a factor (e.g. for factor A with I levels, dfA=I-1), and MSe = SSE / dfe MSE is the residual mean square error. Similar equations to Eq. (17) may be written for factors B and C. The quantity MSeMSE denotes the mean residual sum of squares. It is computed by MSE=SSEdfE.

The measure omega square is also termed the adjusted R2, in analogy to the adjusted coefficient of determination of multiple regression. Note that the degrees of freedom of the error term dfE depend on the total number of effects in the ANOVA design. For three-way ANOVA without interactions, dfE is obtained by dfE=dfT-dfA-dfB-dfC=IJK-I-J-K+2. Clearly, the adjustment of effect size increases if the residual degrees of freedom are small, which is the case when overall sample size is small. Hence, the difference between both measures of effect size will be negligible for designs with large dfE, as is the case for our study. In our assessment, we will therefore only present ω2, which is the more general measure of effect size at each catchment. A spatial synthesis of uncertainty contributions for basins with summer and winter low-flow regime is finally obtained from the distribution of variance components across basins falling into each low-flow regime group.

The runoff model efficiency (ZQ) in the three calibration periods obtained for different variants of the objective function is presented in Fig. 3. The results show that ZQ is larger and thus runoff simulations are more accurate in basins with winter (blue colour) than summer low-flow minimum (red colour). Most of the basins with a winter low-flow regime are situated in the alpine western and central part of Austria, where the runoff regime is snow dominated. Such a regime has stronger runoff seasonality (see e.g. Fig. 5 in Laaha et al., 2015) and less difference in rainfall regime, which allows one to model the rainfall–runoff process easier than in basins with rainfall-dominated runoff regime. ZQ increases with decreasing weight wQ, which indicates that the runoff model performance likely tends to be better for low than high flows. The comparison of ZQ in the three calibration periods indicates that the difference in model performance between basins with winter and summer low-flow regime is the largest in the period 1976–1986. While ZQ for basins with winter low-flow regime is very similar in all three calibration periods, ZQ has an increasing tendency in basins with summer low-flow regime. For example, the median of ZQ for wQ=1.0 increases from 0.64 in the period 1976–1986 to 0.71 in the period 1998–2008. This increase is likely related to the increasing number of climate stations and data quality (Merz et al., 2009).

How the different calibration variants and periods translate into low-flow 95 %-quantile Q95 and seasonality SI is examined in Fig. 4. The model calibrated for an 11-year period is used to simulate daily flows in the entire reference period 1976–2008. The results show that the model calibrated in the period 1976–1986 significantly overestimates Q95 of the reference period particularly in basins with summer low-flow regime. The period 1976–1986 is characterised by lower air temperatures with less evapotranspiration and relatively higher runoff generation rates, which translates into different soil moisture storage (FC model parameter) and runoff generation (BETA) model parameters. Such effects are consistent with findings of Merz et al., (2011). The hydrologic model applied to the entire reference period hence produces larger runoff contribution, which tends to overestimate Q95 particularly in the warmer and drier parts of the reference period and drier and warmer parts of Austria. The overestimation is consistent for large range of wQ (wQ in the range 0.0–0.9) and the median of Q95 difference exceeds 20 %. Also the scatter around the median is rather large, where 25 % of the basins with the summer low-flow regime have Q95 differences larger than 35 %. The simulated Q95 in basins with winter low flows fit closer to the observed estimates. The median is less than 10 % for variants wQ < 1. Interestingly, the model simulations based on calibration periods 1987–1997 and 1998–2008 are much closer to the observed values. The results for both groups of basins are very similar and essentially unbiased in terms of 95 % low-flow quantile. The exception is the calibration variant wQ=1 that tends to underestimate Q95. There are many significant differences between calibration to low-flow only (wQ=0.0) and other weights, with the exception of wQ=1, which represents a typical calibration of using classical Nash–Sutcliffe coefficient.

The results of the seasonality estimation are presented in the bottom panels of Fig. 4. It is clear that this hydrologic model tends to estimate the low-flow period later. This shift is larger in basins with summer low-flow regimes. While the median of SI difference in basins with winter low flows is around 10–12 days in the period 1976–1986 and increases to 12–19 days in the period 1998–2008, the median of SI difference in basins with summer low flows is in the range of 18–32 days. The scatter is, however, much larger for basins with summer low-flow regime. Here the model simulates the season of low-flow occurrence with more than 2 months shift (earlier or later) in almost 50 % of the basins. A typical example of such shift is provided in Fig. 5. The periods with flows below 95 % quantile are often very short and the timing of simulated low flows does not fit well with these periods. In some cases there is also a difference in the length of observed and simulated low-flow periods. Some small rainfall–runoff events in the summer or autumn cause an interruption of the observed low-flow periods, but the model simulates a complete absorption of the precipitation event by the soil storage and hence a longer low-flow period.

The spatial pattern of the variability of Q95 estimation in the reference period 1976–2008 is presented in Fig. 6. Figure 6 shows the range of differences between simulated and observed Q95 for the different calibration variants. The results indicate that the Q95 differences vary more between the different objective functions (right panels); however, in many basins the range exceeds 60 % even if the model is calibrated by one objective function but in the different calibration periods. As already indicated in Fig. 4, the differences are larger in basins with summer low flows, particularly for variants calibrated in the period 1976–1986. For particular basins, the differences are not strongly related to the weight wQ used in the calibration, with an exception of wQ=1, which tends to have the largest difference to observed Q95. Some examples of the model performance for individual basins are given in the companion paper by Laaha et al. (2015).

Spatial variability of the model variability in terms of low-flow seasonality is presented in Fig. 7. The results clearly indicate that basins with winter low-flow regime (i.e. situated in the Alps) vary significantly less for different calibration settings than the basins with summer low-flow regime. The range of differences is typically less than 14 days in the mountains, compared to more than 90 days in many basins with the summer low-flow regime.

The comparison of SI and Q95 ranges indicates that large SI variability does not systematically mean large variability in terms of Q95. For example, a cluster of basins situated in the south-eastern part of Austria (Styria) has a large SI range of difference (i.e. more than 90 days) for 11 calibration variants in the period 1976–1986, but the variability in Q95 is in many basins less than 20 % for this case. The same applies for the opposite case of small SI and large Q95 variability in the alpine basins.

Low-flow projections for selected climate scenarios and different calibration weights wQ are presented in Fig. 8. Rather than to evaluate in detail the projections in terms of absolute values of low-flow changes, the main focus is to assess the range of possible changes caused by different scenarios and objective function used for model calibration. The results show projections based on model calibration in 1998–2008, but the results are almost identical with results for the other two calibration periods (i.e. the average difference is around 1 %). Figure 8 clearly shows the difference in projections for basins with summer and winter low-flow regime, particularly for Q95 changes. It is hence important to evaluate the projections and their variability separately for different regimes. The comparison of different scenarios indicates that they are similar in terms of projecting an increase of winter low flows and a tendency for no change or decreasing low flows in the summer period. The increase of winter Q95 slightly varies between climate scenarios and tends to increase for calibration variants with larger wQ. The difference in median between wQ < 0.4 and wQ > 0.8 is approximately 9 %. The projections of Q95 changes in basins with summer low flows have significantly smaller variability and do not depend on wQ. The change in low-flow seasonality (Fig. 8, bottom panels) is less pronounced. The median of projections is around 5 and 10 days earlier than in the reference period for basins with summer and winter low-flow regime, respectively. Interestingly, the variability between basins and wQ is significantly smaller than that obtained for different calibration variants in the reference period (Fig. 4).

Examples of spatial patterns of low-flow projections are presented in Figs. 9 and 10. The projections of Q95 changes (Fig. 9) indicate an increase of low flows in the Alps, typically in the range of 10–30 %. A decrease is simulated in south-eastern part of Austria (Styria) mostly in the range of -5 – (-20) %. The most spatially different projection is provided by the HADCM3 A1B climate scenario, which simulates the strongest gradient between an increase of Q95 in the Alps in winter and a decrease in the south-eastern region in summer. The change in the seasonality varies between the scenarios, but there is a tendency for earlier low flows in the northern Alps and a shift to later occurrence of low flows in eastern Austria (Fig. 10). As already indicated in Fig. 8, the shift in seasonality is greater than 1 month only in a few basins.

Figures 9 and 10 show projections of low flows for four climate scenarios, but only one set of hydrologic model parameters. The evaluation of the impacts of different calibration variants on the variability of low-flow projections is presented in Figs. 11 and 12. These figures indicate the range of Q95 (Fig. 11) and the seasonality occurrence (Fig. 12) changes obtained by 11 calibration variants and 3 calibration periods. The range of Q95 changes is interestingly the largest in basins with the winter low-flow regime. In the Alps, the increase of Q95 is often in the range of 15 % to more than 60 %. On the other hand, the future Q95 estimates vary only slightly between the calibration variants in basins with the summer low flows. The change is less than 20 % in most of the basins. The impact of the selection of objective function is, however, much larger for the estimation of the seasonality changes. Depending on the calibration variant, the change in seasonality can vary within more than 3 months, e.g. in the south-eastern part of Austria.

The total uncertainty of low-flow projections of Q95 and SI is presented in Fig. 13. While the top panels show the range of low-flow characteristics for all climate scenarios, calibration variants and periods, the bottom panels show the ratio between the uncertainty of future low-flow projections to the range of low-flow indices simulated in the reference period. The results show that the Q95 range is less than 25 % in approximately one-third of analysed basins. On the other hand, 20 % of basins have a range larger than 50 %. These are the basins with the winter low-flow regime. The variability in the date of low-flow occurrence is less than 3 months in 40 % of the basins. In almost 20 % of the basins, however, it is larger than 5 months. The ratio between the range of projections to the range of calibration differences (bottom panels in Figs. 13 and 14) indicates that only in 15 % of the cases is the climate projection uncertainty of Q95 larger than the range obtained in the calibration period. Most of these basins are situated in the mountains (mean basin elevation above 1000 m a.s.l.) and have winter low-flow regime. The range of calibrated Q95 is larger in almost all basins with the summer low-flow regime, which are characterised by lower mean basin elevation and larger aridity (i.e. ratio of mean annual potential evaporation to mean annual precipitation). On the other hand, the climate projection uncertainty dominates for the low-flow seasonality and is more than 3 times larger in 50 % of basins, particularly in the Alps. The SI projection uncertainty is only in 15 % of the basins lower than the SI range obtained in the calibration period. The SI uncertainty ratio tends to be lower with increasing mean basin elevation and the basin area, but there is no apparent relationship with the aridity of the basins.

The relative contribution of the three main variance components (i.e. climate scenario, decade used for model calibration and calibration variant representing different objective function) to the overall uncertainty of future low-flow projections is evaluated in Fig. 15. Left and right panels show the distribution of ANOVA variance components for basins with winter (left panel) and summer (right panel) low-flow regime, respectively. The results indicate that the variability from climate scenarios has a dominant contribution to the overall projection uncertainty in basins with summer low-flow regime. While in basins with winter low flows the median contribution of the three variance components is 29 % (climate scenario), 13 % (calibration decade) and 13 % (objective function), in basins with summer low-flow regime the median contribution from climate scenario is larger than 76 %.