The SDM was set up by integrating multiple sources of data (e.g. observations, modelled values and climate projections) to replicate past and to simulate future S. Giustina turbined water and stored reservoir volume. The model chain considered for this objective consists of three main modules, namely climate projections in box 1, hydrological model in box 2 and the SDM in box 3 (Fig. 2).

The climate projections provide information stemming from global climate models downscaled to the regional level and bias-corrected through the quantile mapping method (Maraun, 2016; Teutschbein and Seibert, 2012) using the downscaled daily ENSEMBLES daily gridded observational (E-OBS) dataset at 1 km resolution (Cornes et al., 2018) to better simulate climate local conditions. The regional climate model COSMO-CLM (Consortium for Small-scale Modeling Climate Limited-area Modelling) was selected for its spatial resolution of 0.0715∘ × 0.0715∘ (≈ 8 km × 8 km), allowing for a local-level climate impact assessment (Rockel and Geyer, 2008). Such model information was developed by the CLM community and provided by the Fondazione Centro Euro-Mediterraneo sui Cambiamenti Climatici (CMCC) as an external component for the application to the Noce catchment (Bucchignani et al., 2016). In the case of climate data from COSMO-CLM, precipitation and temperature baseline data were available from 1971 to 2005; they were also used to characterize the Noce catchment climatology and compare the baseline with future conditions of precipitation and temperature for the two Representative Concentration Pathways (RCPs).

Temperature and precipitation daily data were used as an input to the physically based model “GEOTRANSF” (external component, Bellin et al., 2016) together with topographical information to replicate streamflow conditions of the Noce River (box 2 in Fig. 2). These two boxes were obtained from simulations developed from the OrientGate project (http://m.orientgateproject.org/, last access: 30 April 2021) and used as an input to focus on the S. Giustina reservoir through the SDM (box 3 in Fig. 2). GEOTRANSF was calibrated and validated on past daily water flow data in the case study area considering a baseline time range from 1981 to 2010 with a performance of the Nash–Sutcliffe efficiency coefficient of 0.88 for calibration and 0.73 for validation at the S. Giustina control section (Bellin et al., 2016). GEOTRANSF provides a description of the water flow within the Alpine Noce River catchment relying on precipitation and temperature data (from box 1), land use and soil type (http://pguap.provincia.tn.it/#, last access: 30 April 2021), streamflow gauge data (https://www.floods.it/, last access: 30 April 2021), and glacier extension (https://webgis.provincia.tn.it/, last access: 30 April 2021). Water withdrawals for anthropogenic uses were modelled within GEOTRANSF at the subcatchment level, accounting for their licensed number and the physical constraints from the existing water infrastructures. Moreover, GEOTRANSF was applied with COSMO-CLM precipitation and temperature scenarios from 2021 until 2070 over the Noce catchment to assess future conditions of river discharge at the local level for RCP4.5 and RCP8.5 (Bucchignani et al., 2016). While climate was considered the only driver of change in future simulations, anthropogenic water withdrawals were assumed to be at their maximum physical discharge in order to account for possible future increases of water demands from sectors such as domestic and agricultural needs, sectors recognized to lead to possible increases in demand (Bellin et al., 2016; La Jeunesse et al., 2016).

The stochastic SDM relied on the inflow values from GEOTRANSF applications as one input variable. Other input variables were initially considered and tested as other variables data in the SDM to replicate turbined water and stored volume (excluded to the modelling; further information reported in the Supplement). The baseline simulation period was constrained by the reservoir volume data availability over 14 years with a range 1999–2004 and 2009–2016 and a data gap from 2005 to 2008. For this reason, the SDM was forced with past observations of inflow to S. Giustina (with data available for the period 1981–2016) and with GEOTRANSF values for future simulations due to the limited temporal overlap of past GEOTRANSF values (over 1981–2010) with observations of the S. Giustina stored volume (1999–2004 and 2009–2016, Table 1). The SDM was run at a daily time resolution to replicate the different outflow's regulations (e.g. minimum ecological flow and emergency outflows). Finally, simulations were aggregated to monthly values being a suitable time resolution for supporting reservoir volume management over long periods considering climate change effects (Solander et al., 2016).

This analysis aims to statistically describe the existence and type of interactions among the system variables. For the simulations of turbined outflows, different statistical models' and variables' interactions were tested and recursively implemented to simulate the stored water in S. Giustina by applying the reservoir water balance equation.

The statistical model for turbined water was calibrated and validated over 5061 d of available data for the baseline period, representing a total of 14 years from 1999 to 2004 and from 2009 to 2016. A forward time window approach was applied as a cross-validation technique to better estimate model fitting (i.e. based on training data) and predictive performance (i.e. based on temporally independent test data) using the root mean square error (RMSE). The applied methodology is based on multiple separations of training and testing datasets. Within the first repetition, the predefined model set-ups (i.e. turbined outflows models) are calibrated using a subset of the original data that relates to the first 3650 d of available data. The derived relationships are then tested using both training data (i.e. fitting performance) and the dataset that relates to the remaining (not yet) considered days (i.e. predictive performance). The following 1410 repetitions are based on the same procedure but on increasingly larger training datasets (i.e. consecutively adding 1 d within the forward time window approach). The mean value for RMSE was calculated considering all 1411 repetitions over the increasingly larger dataset, providing a more robust estimation of model performance and its variability using multiple temporally independent subsets of the original data (Hastie et al., 2009; Kohavi, 1995; Tashman, 2000; Varma and Simon, 2006). This methodology allows for overcoming some limitations of common one-fold non-temporal validation methods (splitting of training and test data randomly; e.g. hold-out validation) associated with data temporal dependencies (i.e. autocorrelation) and an arbitrary choice of training and validation subsets. A major advantage of such multi-fold partitioning strategies is the possibility to exploit all the available data for the generation of the final prediction model.

Future water inflow to the reservoir (coming from the GEOTRANSF application) was used to simulate future turbined outflow and volumes stored in the S. Giustina reservoir. GEOTRANSF simulations considered unchanged maximum water withdrawals in the Noce catchment in the future, and although possible variations in the future may affect river water flows, this set-up provided a conservative assumption accounting for future water demand increases, such as from domestic and agricultural needs, in future scenarios. Moreover, integrated downscaled COSMO-CLM climate scenarios were considered (Bellin et al., 2016; Bucchignani et al., 2016). Such climate projections have been demonstrated to represent climate forcing variables (i.e. precipitation and temperature) over Alpine regions well (Montesarchio et al., 2013).

The RCP4.5 and RCP8.5 scenarios were selected according to the IPCC AR5 (Intergovernmental Panel on Climate Change Fifth Assessment Report; IPCC, 2014). Simulations stretched over two 30-year time horizons to represent short-term (2021–2050) and long-term (2041–2070) future climate conditions affecting the Noce River flow and the S. Giustina reservoir management.

Differences between the future and baseline simulated turbined water and volume stored were statistically tested through the Wilcoxon rank sum test, a non-parametric test selected since it allows for dealing with non-normally distributed, unpaired groups of data (Hollander and Wolfe, 1973). It was implemented to test whether future predicted values of stored volume were significantly different than the baseline and to reject the null hypothesis (i.e. same tendencies among the tested groups) in the case of a p value ≤ 0.05.

This study explored and analysed critical conditions of low and high future stored volume considering the 10th and 20th and 80th and 90th percentile thresholds calculated from water stored from the baseline (1999–2004 and 2009–2016). Such thresholds provided a symmetrical reference of extreme conditions and were already identified in previous studies as significant levels to assess critical states in hydrological studies (Yilmaz et al., 2008). Considering these thresholds, a set of different metrics were calculated to characterize the frequency, duration and severity of future critical volume conditions (Table 3) based on existing metrics used to describe extreme events (Vogt et al., 2018). In particular, frequency was considered in relative terms as the ratio of the overall number of months below or above the selected threshold used to define the level of volume critical conditions over 14 years, hence describing yearly conditions of extreme events. Maximum duration was described considering the maximum number of consecutive months below or above the selected thresholds. The severity metric describes the accumulated deficit/surplus of simulated volume values with respect to the total volume stored over a 14-year window (relative severity). This last metric provides information on the fraction of the total stored volume in deficit or surplus as the average annual severity.

Moreover, a Monte Carlo approach was implemented to account for the uncertainty related to the simulations in future conditions. The water balance equation considered the lower and upper turbined outflow from the prediction bands to generate a range of simulated volume values. A set of 1000 replications of 30-year length per each future climate scenario was generated by randomly sampling from the simulated volume values and their prediction bands. In addition, for each replication a subset was iteratively extracted considering a time window of 14 years moving progressively at a monthly time step along the simulated 30 years of future volume. Extreme condition metrics of relative frequency, maximum duration and relative severity were calculated on the subset at each iteration. This procedure allowed for comparing the calculated metrics of each subset replication with the 14 years of available data for the baseline volume (1999–2004 and 2009–2016). By doing so, it was possible to account for the uncertainty related to the modelling and provided a wider range of low and high future volume values for a more robust characterization of their conditions.

The linear mixed-effects model was used to replicate observations of turbined water outflows from the S. Giustina reservoir (Fig. 3). The model was run at a daily time step, and values were aggregated and reported at a monthly resolution. The model gave an R2 of 0.75 and a mean RMSE of 16.57 Mm3. Figure 3 shows the modelled and real values, with the y scale ranging from 0 % (i.e. no turbined water) to 100 % (i.e. maximum turbined water of 176 Mm3 per month for 31 d of full turbine operations). Coloured bands outline areas above or below the percentile values defining critical thresholds that were considered throughout the analysis.

The modelled turbined water was then used in the iterative implementation of the water balance equation together with the operational rules for the minimum ecological flow and the emergency releases. Figure 4 shows the modelled and real volume ranging from 0 % to 100 % of stored volume (equal to 159.3 Mm3, maximum volume allowed for flood prevention), where the simulation of the stored volume resulted in an R2 of 0.60 and a mean RMSE of 19.74 Mm3 per month. In Figs. 3 and 4 the general behaviours of real turbined outflows and stored water were replicated by the regression models. Some specific very high and low conditions were not completely represented or missed due to abrupt changes in the reservoir management, such as the 2001 summer peak of turbined outflows in Fig. 3, due to persistent inflows to S. Giustina forcing dam managers to turbine at the maximum outflow for 23 d consecutively, as well as the low values in spring 2003 in Fig. 4, when the S. Giustina reservoir was emptied due to construction works on a penstock.

Future GEOTRANSF model results forced by the COSMO-CLM climate projections depict a situation of general decreases in precipitation and water inflowing to the reservoir (Table 4 and Fig. 5). In particular, changes in RCP4.5 are rather similar for the short and long terms, whereas changes are larger in the long term for RCP8.5 compared to the short term. These results are consistent with the precipitation trends from COSMO-CLM projections with RCP8.5 showing higher values of total precipitation in the short term but a higher decrease in the long term compared to RCP4.5 (Bucchignani et al., 2016). In RCP8.5, inflow, outflow and volume reductions are lower for the short-term future compared to the baseline (-7.8 %, -11.5 % and -10.2 %) and are associated with the only case of precipitation increase (+1.4 %), pointing to the increase of evapotranspiration due to the relatively larger increase in temperature (+29.4 %). In the long term, results show the greatest increase of temperature (+58.8 %) and reduction of precipitation (-4.3 %) as well as of inflow, outflow and volume (-21.3 %, -26.2 % and -20.8 %).

A summary overview of future conditions for inflow, turbined water and stored volume is reported in Fig. 5. For all variables, four coloured bands representing areas lower than the 10th and 20th and greater than the 80th and 90th percentile are reported as a reference, which allows for comparing the 30-year time slices. Values show a generalized decrease into the 20th and 10th percentile thresholds of the long-term RCP8.5 scenario. This trend is clearly visible for future water inflow, while values larger than boxplots whiskers can be identified in all inflow scenarios and hence point to single future conditions greater than baseline maximum recorded values (Fig. 5a). Future turbined outflows show boxplot values with the lowest interquartile range expected to reach 10th percentile conditions. Consistently with the results from Table 4, volume values show significant reductions already for RCP4.5 with interquartile levels below with the 20th percentile calculated from the baseline (i.e. 1999–2004 and 2009–2016). These results were further investigated through the application of the Wilcoxon rank sum test (Table 5), which provides more quantitative insights into the statistical significance of changes considering the whole 30-year period of data for the baseline and the four scenarios (Fig. 5) as well as considering monthly averaged values (Figs. 6 and 7). While p values considering the whole time series are below the 0.05 threshold of significance, monthly averages for the short-term RCP8.5 scenario (2021–2050) provided non-significant results both for stored volume and turbined outflow.

Results of future turbined outflows are reported in Fig. 6 with values averaged for each month over the 30-year simulation and compared to the baseline (i.e. percentage change). Negative reductions of outflows for all scenarios are reported for spring and summer, starting in April and going until September with differences up to -56.3 % in August for the long-term RCP4.5 scenario. All climate scenarios agree on a water flow reduction during November reaching a minimum of -33.5 % of turbined outflow for the long-term RCP8.5 scenario. In all other months, scenarios depict varying conditions of water flow. In particular, the short-term RCP4.5 scenario depicts conditions of negative differences for every month of the year. An increased number of positive differences are predicted for the long-term RCP4.5 scenario during January (+5 %) and December (+5.3 %). The short-term RCP8.5 scenario shows larger positive differences during January (+10.3 %), February (+1.8 %), March (+2.9 %), October (+0.8 %) and December (+6.5 %). The long-term RCP8.5 scenario projects a negative trend from April until the end of the year, reaching persistent negative conditions in summer down to -55.5 % in August, overlapping with the summer electricity peak loads and calling for particular attention (Terna, 2019). Nevertheless, small but positive values are expected for January (+0.7 %), February (+1.4 %) and March (+3.7 %), when the winter electricity peak load usually occurs (Terna, 2019).

Comparative results with the baseline for the monthly average over the 30-year simulation are reported for the stored volume in Fig. 7. All climate scenarios agree on the general volume decrease from May until the end of the year. The short- and long-term RCP4.5 scenario depicts conditions of minimum peaks in May (-43.8 % and -40.6 %) and June (-44.1 % and -41.9 %), while the long-term RCP8.5 scenario shows fewer negative minimum values, although persistent negative values in November and December lower than the other scenarios (-26.8 % and -19 %). Scenarios agree on the positive variation during February and March with a maximum increase of +32.5 % for the short-term RCP8.5 case. However, scenarios disagree in terms of stored volume for January, with RCP4.5 scenarios representing a positive variation both in the short- and long-term cases (+1.4 % and +2.2 %), while the short-term RCP8.5 case depicts a positive variation (+7.3 %) but a negative one for the long-term case (-7.1 %). Conditions in April are reversed with the short-term RCP4.5 scenario depicting a decrease (-8.3 %) and RCP8.5 increases for short- and long-term cases (+5.5 % and +3.5 %).

Months of positive variation and scenario disagreement provide important information on the timing of potential reservoir management adaptation, while the small volume increases are insufficient to counterbalance persistent volume reductions. The short-term RCP8.5 scenario shows the most favourable conditions of water volume, depicting positive differences in January (+7.3 %), February (+22.5 %), March (+32.5 %) and April (+5.5 %).

Critical conditions of stored reservoir water volumes (both high and low) were explored to further understand how climate change may impact long-term reservoir vulnerability. A set of different metrics were calculated to characterize frequency, duration and severity of future critical volume conditions considering values lower than the 10th and 20th and higher than the 80th and 90th percentiles of stored volume (Figs. 8 and 9). The metrics were calculated from 1000 replications per scenario randomly sampled from the simulated future volume values and their prediction bands. Reductions were shown to have similar trends across the metrics between the 10th and 20th as well as between the 80th and 90th percentiles, with the four future scenarios having statistically significant differences compared to the baseline.

Boxplots for low-volume conditions (Fig. 8) show increasing average values for all metrics and scenarios compared to the baseline: conditions of low volume are expected to become more frequent, having a longer maximum duration and larger severity. In particular, for both values lower than the 10th and 20th percentile, the short-term RCP4.5 scenario shows the highest average increase. Relative frequency and relative severity are expected to have a higher increase for average values below the 10th percentile (+157 % for frequency, from 1.64 to 4.21 monthsyr-1, and +250 % for severity, from 0.2 % to 0.7 %) compared to values below the 20th percentile (+105 % for frequency, from 2.86 % to 5.86 %, and +300 % for severity, from 0.3 % to 1.2 %), while maximum duration is expected to have a higher increase for values below the 20th percentile (+100 %, from 5 to 10 months) compared to values below the 10th percentile (+75 %, from 4 to 7 months). These results point to events of low-volume conditions below the 10th percentile becoming more frequent and with a higher severity, while low-volume events below the 20th percentile are expected to last for a longer time in the case of the most extreme events. RCP8.5 in the short term depicts fewer negative conditions for both thresholds in line with results in Fig. 6: for values below the 10th percentile, +40 % in relative frequency (from 1.64 to 2.29 monthsyr-1), +0 % in maximum duration (4 months) and +50 % in relative severity (from 2 % to 3 %) and for values below the 20th percentile, +38 % in relative frequency (from 2.86 to 3.93 monthsyr-1), +20 % in maximum duration (from 5 to 6 months) and +67 % in relative severity (from 0.3 % to 0.5 %).

For values lower than the 20th percentile, a larger number of values outside the boxplot whiskers are depicted for all scenarios and especially towards higher number of months for relative frequency as well as maximum duration and relative severity, hence pointing to potential single conditions of lower volume stored in the future with respect to the represented median. These results point to the possibility of the most extreme water scarcity conditions lasting longer than 1 hydrological year and pointing to chronic consequences of low stored volume, especially considering the short-term RCP4.5 scenario (maximum values of 19 months and 31 months for values below the 10th and 20th percentile) and the long-term RCP8.5 scenario (maximum values of 15 and 30 months for values below the 10th and 20th percentile), where the highest outlier values are expected.

Boxplots for high-volume conditions (Fig. 9) also show a generalized decrease in all metrics of high stored volume for all scenarios and for both thresholds. The long-term RCP4.5 and RCP8.5 scenarios depict conditions of higher percentage reductions for relative frequency (-75 % for both scenarios) and maximum duration (-60 % for both scenarios) above the 90th percentile compared to the 80th percentile (-68 % in relative frequency and -50 % in maximum duration for both scenarios). On the contrary, relative severity reductions are expected to be higher for RCP8.5 for values above the 80th percentile (-97 %) compared to the 90th percentile (-80 %). Above the 90th percentile, values are expected to be less frequent than baseline conditions, while they show smaller severity reductions compared to values above the 80th percentile. The short-term RCP8.5 scenario predicts a smaller decrease in all metrics in comparison with the other scenarios with -48 % of relative frequency (from 3.14 to 1.64 monthsyr-1), -50 % of maximum duration (from 6 to 3 months) and -75 % in relative severity (from 0.4 % to 0.1 %) for values above the 80th percentile compared to the baseline, as well as -56 % of relative frequency (from 2.29 to 1 monthsyr-1), -60 % of maximum duration (from 5 to 2 months) and -68 % of relative severity (from 0.3 % to 0.08 %) for values above the 90th percentile compared to the baseline. A summary table with median, maximum, minimum and standard deviation values for low- and high-volume conditions is provided in the Supplement.

The applied SDM mainly considers outputs from the GEOTRANSF applications integrating the COSMO-CLM climate projections. However, several assumptions and limitation in this study are noted.

Accounting for the GEOTRANSF application means not only relying on a very accurate water streamflow within the catchment (Bellin et al., 2016) but also considering the COSMO-CLM climate model for future projections. A wider range of inflow values driven by a set of climate models could provide a larger set of results that can be used for further stochastic analysis of turbined water and stored volume. Nevertheless, the climate model has been demonstrated to represent conditions in mountain regions well (Montesarchio et al., 2013) and different than other climate models, depicts general conditions of decreased precipitation over the catchment (Table 4). Hence it provides conservative information on possible impacts on streamflow and volume management. The results from the GEOTRANSF application assumed a conservative condition of upstream water use set at the maximum licensed withdrawal values. This information was kept unchanged for future scenarios, although possible variations in the future (e.g. from agricultural and touristic uses) may affect river water flows.

Moreover, the presented study considered precipitation, water flow and volume trends over a 30-year period considering their monthly average values, important for long-term large-reservoir management. For this reason, conditions of a high volume with a very short duration might have been potentially underrepresented.

The statistical models are an effective tool to replicate past observations of water volume and turbined water outflows. Applying such a regression to future conditions of predictors, reservoir management in terms of turbined outflow as well as minimum ecological flows was assumed to be stationary over time. Nevertheless, such a constraint is justified by the high uncertainty associated with future changes in hydropower production patterns affected by societal conditions (e.g. energy price fluctuations; Gaudard et al., 2014; Ranzani et al., 2018). Moreover, the minimum ecological flow was always set to the values established by law, although critical conditions in water availability (e.g. streamflow) may lead to extraordinary changes in minimum flow which can affect the stored volume as well as the turbined outflow.

Finally, the selected models considered a few tested and selected variables. Although other variables play important roles within the management of the reservoir at different temporal resolutions (e.g. hourly energy market price), the simulation on monthly aggregated values supported the objective of analysing long-term variations in the stored volume for the large S. Giustina reservoir.