Abstract

Adaptation of water resources to climate change, drought management strategies, and hydrological and reservoir modelling have become serious issues in the context of climate change uncertainty. The aim of this paper is to introduce methods and tools for hydrological analysis and robust reservoir performance evaluation in this time of deep uncertainty. Newly developed lumped water balance and reservoir simulation models will be used to perform hydrological analysis, and a robust reservoir storage capacity reliability assessment will also be conducted. The hydrological data in relation to climate change will be constructed using two climatological datasets created by statistical downscaling tools LARS WG and ENSEMBLE Downscaling Portal. The hydrological analysis and the temporal reliability of the assessment of reservoir storage capacity and robustness in the context of climate change uncertainty will be presented as a case study of the Vir I reservoir and the Svratka River basin in the Czech Republic, in central Europe. The resulting models show a decrease in long-term mean flow, ranging from 6% to 32%, and in reservoir outflow from 1.5% to 26%, depending on the timescale, downscaling tools and emission scenarios.

INTRODUCTION

Climate change is a very serious topic, and an issue that has led to uncertainty in water management. These concerns have been discussed in academic, social and technical contexts (Kundzewicz et al. 2018). The World Meteorological Organization, NASA and NOAA have announced the years 2015, 2016 and 2017 as the warmest years registered in the history of measurements on a global scale (NOAA 2019). Hydrological extremes have been appearing more frequently in the Czech Republic, which further reinforces discussions on the issue of climate change (OECD 2013).

However, the development of tools and methods needed for climate change analysis targeted to water reservoirs has been limited. Globally, a range of hydrological models for climate change analysis relating to catchment hydrology and water resource management are available. As mentioned in Devia et al. (2015), the most well-known hydrological models include: the Hydrologic Modelling System (HEC-HMS) (2008); TOPMODEL, developed by Beven et al. (1984); the Soil and Water Assessment Tool (SWAT), developed by Arnold et al. (1993); HBV-96 (Lindström et al. 1997); MIKE SHE (Refsgaard & Storm 1995); and the Czech model BILAN (Vizina et al. 2015). The drawbacks of all these models include a high degree of complexity, catchment scale limits, open source limitations, and difficulty integrating the tools with other external applications. Reservoir models based on a reservoir simulation model use various mathematical methods and algorithms. Wurbs (2005) presented a broad up-to-date review of commonly used reservoir simulation models in the USA, where the best known are HEC-ResSim (Klipsch & Hurst 2013) and WRAP (Wurbs 2019). Vamvakeridou-Lyroudia et al. (2010) developed AquatorGA, which combines a single simulation model and computations of reservoir operation using Genetic Algorithm (GA) multi-objective optimisation.

To test against conditions of deep uncertainty, analysts can use computer simulations to generate an ensemble of plausible scenarios about the future (Lempert et al. 2003). If such a collection of plausible future climate scenarios under deep uncertainty is available, then the reservoir simulation model will be able to evaluate storage capacity and reliability for each climate scenario. In addition, the robustness approach (Lempert et al. 2003; Paton et al. 2014; Roach et al. 2016) involves appropriate methods for identifying an optimal adaptation strategy for reservoir operation against the uncertainty of climate change.

The overall aim of this paper is to introduce a comprehensive approach in order to conduct a robust assessment of reservoir storage capacity, which would help to manage water supplies under the deep uncertainty of climate change. The research approach consisted of developing two modelling tools: a hydrological model and a reservoir simulation model. To meet the research goal, a hydrological tool based on a new lumped water balance model and its two different optimisation approaches, and a reservoir simulation model that is suitable for robust reservoir performance assessment under climate change uncertainty, were developed in the form of software tools.

The new hydrological model is based on the water balance equations applied in Wang et al. (2013), which were first applied on a large arid basin in China. The model was modified for the different hydrological conditions of central Europe and the optimisation problem was specified. Hydrological data to simulate climate change were constructed based on statistical downscaling using two kinds of emission scenarios and downscaling methods. Two ensembles of future climate projections, taking into account the deep uncertainty of climate change, were created. The hydrological data were loaded into the reservoir simulation model, which is able to compute with datasets that contain deep uncertainty. Then, the method of robustness evaluation described in Paton et al. (2014) and Roach et al. (2016) was used to conduct an optimal temporal reliability assessment of reservoir storage capacity under conditions of deep uncertainty. An analysis of the results will be presented in this paper. The deep uncertainties were evaluated based on the robustness of the given temporal reliability of the storage capacity. The Svratka River basin and the Vir I reservoir in the Vysocina region, in the central area of the Czech Republic, were used as case studies to illustrate the functions of the models.

This paper develops the conference paper published at the 13th International Conference on Hydroinformatics – HIC 2018 (Marton & Knoppová 2018) and introduces an extensive summary of the results, which have been completed.

METHODOLOGY

In the search for an optimal approach and reliable results, several methods were tested and new software tools were developed. Firstly, the system of equations of the lumped water balance model described by Wang et al. (2013) was tested to find out whether it could be applicable to Czech catchment hydrology. Microsoft Excel was used for the initial testing. The Generalised Reduced Gradient (GRG) algorithm (Lasdon et al. 1978) was used for model calibration and the LARS WG method was applied to generate climate data. Secondly, the software tool Runoff Prophet in Fortran 77 and a C# user interface were developed and the Differential Evolution method (DE) (Storn & Price 1997; Zelinka 2002) for model calibration was applied. The ENSEMBLE Downscaling Portal (ED portal) (Gutiérrez et al. 2012) was used as a climate data generation tool. The reservoir simulation model software UNCE Climate Change was developed in Fortran 77 and Delphi 7 and tested on the two sets of future climate projection ensembles. Lastly, the robustness approach (Paton et al. 2014; Roach et al. 2016) was used to evaluate the impact of deep uncertainty on reservoir storage capacity. Finally, the results were statistically evaluated. The basic statistical characteristics of mean value, standard deviation, minimum and maximum values and percentage variance were used.

Lumped water balance model

The lumped water balance model was the hydrological modelling tool used as the basis of the modelling process. The rainfall–runoff equations first published by Wang et al. (2013) were modified for different climate and hydrological conditions (Marton & Knoppová 2018).

Once the system of equations had been established, the optimisation problem was defined. The 37 parameters in the control equations had to be optimised as a calibration set. The parameters were: 12 coefficients of monthly surface flow; 12 coefficients of monthly groundwater flow; 12 coefficients of monthly evapotranspiration; and one parameter of initial surface-soil moisture. These 37 coefficients were the decision variables for model optimisation. The objective function was to maximise the Nash–Sutcliffe Efficiency (NSE) coefficient (Nash & Sutcliffe 1970). The intervals of NSE are between −∞ and 1.0. Moriasi et al. (2007) highlighted that values between 0.0 and 1.0 are generally viewed as acceptable levels of performance and established four performance ratings: (i) Unsatisfactory (NSE < 0.50); (ii) Satisfactory (0.50 < NSE <0.65); (iii) Good (0.65 < NSE < 0.75); and (iv) Very Good (0.75 < NSE < 1.00). Based on these acceptable levels, the model calibration was considered satisfactory when the NSE reached values of 0.5 and above.

Two optimisation techniques were used to obtain an optimal calibration setup: the GRG nonlinear algorithm in the testing phase (Lasdon et al. 1978), and the DE method in the software algorithm (Storn & Price 1997; Zelinka 2002).

Statistical downscaling

In each case a hydrological model that had been calibrated and validated using the optimisation method was used to create hydrological data for climate change conditions. The downscaled climatological datasets representing climate change scenarios for the studied river basin were then added into the model. In the first case the hydrological model was calibrated and validated by the GRG method and statistical downscaling was conducted using LARS WG software (Racsko et al. 1991; Semenov et al. 2013). Using LARS WG, an ensemble of 29 climate scenarios was created based on the first generation of Special Report on Emissions Scenarios (SRES) emission scenarios (Nakićenović et al. 2000). In the second case the hydrological model was calibrated and validated using the DE method. The statistical downscaling was carried out using the ED portal (Gutiérrez et al. 2012) and an ensemble of eight climate scenarios based on the second generation of Representative Concentration Pathways (RCP) emission scenarios (Moss et al. 2010) was created. To ensure that the output data could be used and then compared with real values, a simplified BIAS correction of the hydrological data was applied. The ratio between the BIAS data and the historical data was calculated and the ensemble of hydrological datasets was modified according to this figure.

Reservoir simulation model

A reservoir simulation model was developed based on the mass balance equation described in Marton et al. (2015, 2016).

During simulation the temporal reliability RT was evaluated. The general reliability of the water management system was calculated following the model of Hashimoto et al. (1982).

After a reliability assessment of all hydrological time series, the robustness (ROB) of the reservoir storage capacity reliability assessments was calculated. In this case the robustness could be viewed as a statistical evaluation of uncertain results in the uncertain context of climate change. Robustness was calculated according to Equation (1), based on Paton et al. (2014) and Roach et al. (2016): 
formula
(1)
where ROB is robustness; Sj is the system evaluation of boundary conditions loaded by uncertainty for j = 1, …, N; and j is the number of input hydrological time series created by the input ensemble. A value of 1 would indicate satisfactory evaluation, while 0 stands for an unsatisfactory evaluation. System evaluation was defined as in Equation (2): 
formula
(2)
where RT,j is the temporal reliability for j = 1,…, N solutions and RT is the required temporal reliability.

CASE STUDY

The methods and tools were tested on the Vir I reservoir in the Svratka River basin. This reservoir was chosen for many reasons. It is one of the main surface-water resources in the South Moravia region of the Czech Republic. The basin and reservoir are covered by a long history of climatological and hydrological measurements, but a climate change analysis has never been conducted on this reservoir. Additionally, as mentioned in the introduction, the whole region is under hydrological stress caused by recent drought episodes. The reservoir volume provides mainly water supply capacity, flood protection capacity, and capacity for hydropower production. The location of the Vir I reservoir is shown in Figure 1.

Figure 1

Vir I reservoir location in the Czech Republic, central Europe.

Figure 1

Vir I reservoir location in the Czech Republic, central Europe.

The Svratka River is the main water inflow into the reservoir. The mean long-term inflow into the reservoir is calculated from historical data measurements from 1950 to 2016 and Qa is 3.28 m3s−1. The mean annual value of evaporation from the water surface EANNUAL is 700 mm.

The total reservoir volume VTOTAL is 56.193 mil m3, the active storage volume VZ,max is 44.056 mil m3 and the flood reservoir volume VFLOOD is 8.337 mil m3. The total outflow OP consists of the ecological flow OECO and the water withdrawal for water supply OWS (drinking water and industry). The total outflow OP is 2.53 m3 s−1, divided into OECO = 0.53 m3 s−1 and OWS = 2 m3 s−1. The reservoir managers' estimated temporal reliability of the reservoir storage capacity RT is 99.5%. Technical data were obtained from the reservoir management guidelines, provided by the reservoir management authority.

The Svratka's catchment area upstream of the reservoir is 366.94 km2. The climatological data are measured at the climatological stations Policka and Svratouch by the Czech Hydrometeorological Office (CHMI). The range of the time series is 1964–2016. The climatological observation covers daily air temperatures and daily precipitation. The hydrological data are provided in the form of mean monthly flows, with a time series range of 1950–2016. The measurements are obtained from the hydrometric profile of Dalecin, located on the river near to the reservoir's main tributary. The data for the case study were unified to the same time series range of 1964–2016.

Model calibration was carried out using the 40 years from 1964 to 2003, and validation with the 13 years from 2004 to 2016. The calibration inputs were mean monthly air temperatures, precipitation levels and river flows. As mentioned in the methodology section, two ensembles of climatic data were created, each simulating the deep uncertainty of climate change.

First, LARS WG downscaling software was applied to the input data of the mean daily air temperature and daily precipitation data from the local climatological stations of Policka and Svratouch. The adapted statistical characteristics data from 12 climate models for SRES emission scenarios A1B, A2 and B1, as implemented in the software, were the basis of the input data. The ensemble of 29 possible climate data scenarios containing mean daily temperature and daily precipitation predictions were the outcome of the LARS WG (from here, referred to as the SRES ensemble).

Next, the ED portal was used to generate climatic data based on the global historical climatic database. Historical data from three climatological stations in Vienna, Milesovka and Oravska Lesna, one global climate model, four downscaling methods and two RCP emission scenarios (RCP 4.5/RCP 8.5) were used to gather data for the Czech Republic. The output, in the form of an ensemble of eight possible climate data scenarios containing mean daily temperature and daily precipitation figures, was created using the ED portal (from here, called the RCP ensemble).

Three time-periods and their combinations for both ensembles were then defined: P1 (2011–2030), P2 (2046–2065), and P3 (2080–2099). The combinations of the P1 + P2 periods (2011–2065) and P1 + P2 + P3 periods (2011–2099) were also modelled. Prior to usage in the hydrological model, the ensemble was recalculated to monthly values, so that the time step was uniform for all the computations.

RESULTS AND DISCUSSION

Firstly, the hydrological model was calibrated and validated based on the historical data time series. Using the GRG method for hydrological model calibration, the resulting NSE was 0.699, and the NSE for model validation was 0.6. Using the DE method, the NSE for hydrological model calibration was 0.6905 and that for model validation was 0.6905.

The separate SRES and RCP ensembles of climatic data representing climate change were then added into the calibrated and validated model. Each ensemble of hydrological data in the form of mean monthly inflow to the reservoir under climate change is the result of hydrological transformation. Before the reservoir simulation model was used, hydrological analysis in the catchment upstream of the reservoir had been completed.

Results based on SRES ensemble

The SRES ensemble was divided into the groups A1B, B1 and A2, according to the SRES scenario, and each group was statistically evaluated. The mean values of the long-term mean flow μ(Qa), minimal and maximal values min(Qa) and max(Qa) and the percentage variance ΔQa were determined for the P1, P2, P3 periods and then their combination P1 + P2 + P3. The results were compared with the real value Qa = 3.28 m3 s−1 and the statistical characteristics μ(Qa), min(Qa), max(Qa) and ΔQa for the Svratka River. Table 1 shows the results of the analysis.

Table 1

The results of hydrological analysis of the Svratka River basin upstream of the Vir I Reservoir – SRES ensemble

Scenario (period)μ(Qa) [m3 s−1]min(Qa) [m3 s−1]max(Qa) [m3 s−1]ΔQa [%]
Real Qa (1950–2016) 3.280 – – – 
P1 - A1B 3.018 2.732 3.297 −7.970 
P2 - A1B 2.779 2.454 2.985 −15.279 
P3 - A1B 2.436 2.003 2.828 −25.722 
P1 + P2 + P3 - A1B 2.744 2.397 2.914 −16.324 
P1 - A2 3.087 2.875 3.460 −5.865 
P2 - A2 2.705 2.605 2.896 −17.524 
P3 - A2 2.218 1.998 2.393 −32.369 
P1 + P2 + P3 - A2 2.670 2.525 2.819 −18.586 
P1 - B1 3.055 2.731 3.522 −6.859 
P2 - B1 2.883 2.693 3.237 −12.104 
P3 - B1 2.727 2.269 3.312 −16.868 
P1 + P2 + P3 - B1 2.888 2.564 3.109 −11.944 
Scenario (period)μ(Qa) [m3 s−1]min(Qa) [m3 s−1]max(Qa) [m3 s−1]ΔQa [%]
Real Qa (1950–2016) 3.280 – – – 
P1 - A1B 3.018 2.732 3.297 −7.970 
P2 - A1B 2.779 2.454 2.985 −15.279 
P3 - A1B 2.436 2.003 2.828 −25.722 
P1 + P2 + P3 - A1B 2.744 2.397 2.914 −16.324 
P1 - A2 3.087 2.875 3.460 −5.865 
P2 - A2 2.705 2.605 2.896 −17.524 
P3 - A2 2.218 1.998 2.393 −32.369 
P1 + P2 + P3 - A2 2.670 2.525 2.819 −18.586 
P1 - B1 3.055 2.731 3.522 −6.859 
P2 - B1 2.883 2.693 3.237 −12.104 
P3 - B1 2.727 2.269 3.312 −16.868 
P1 + P2 + P3 - B1 2.888 2.564 3.109 −11.944 

The last step of the computation was analysis of the reservoir storage capacity in terms of the deep uncertainties of climate change. The target of the analysis was to identify the mean value of total outflow μ(OP) that would fit the requested criterion: min {μ(RT) − (RT = 99.5%)}. When the optimal μ(OP) was found, the resulting RT set gained from the input data-ensemble calculation was statistically evaluated. The standard deviation σ(RT) and intervals min(RT) and max(RT) were determined. Finally, the robustness ROB was evaluated for the optimal solution. ROB was computed for a temporal reliability limit of RT = 99.5%; thus, the system was evaluated as satisfactory when RT ≥ 99.5% and VZ,max = 44.056 mil m3. The results of the reliability assessment and of robustness based on the SRES ensemble can be seen in Table 2.

Table 2

Results of storage reliability assessment and robustness – SRES ensemble

Periodμ(OP) [m3 s−1]μ(RT) [%]σ(RT) [%]min(RT) [%]max(RT) [%]ROB
P1 2.491 99.509 0.630 97.620 99.940 0.690 
P2 2.282 99.504 1.047 95.400 99.940 0.793 
P3 1.923 99.505 1.292 94.100 99.940 0.897 
P1 + P2 2.362 99.502 0.859 96.130 99.970 0.759 
P1 + P2 + P3 2.035 99.503 1.139 95.410 99.980 0.862 
Periodμ(OP) [m3 s−1]μ(RT) [%]σ(RT) [%]min(RT) [%]max(RT) [%]ROB
P1 2.491 99.509 0.630 97.620 99.940 0.690 
P2 2.282 99.504 1.047 95.400 99.940 0.793 
P3 1.923 99.505 1.292 94.100 99.940 0.897 
P1 + P2 2.362 99.502 0.859 96.130 99.970 0.759 
P1 + P2 + P3 2.035 99.503 1.139 95.410 99.980 0.862 

As assumed, the results show that river flows in the basin will decrease. In Table 1 we can see a decline of about 8% in P1 and 25.7% in P3 for the A1B emission scenario, which is considered as balanced. For the A2, so-called pessimistic, scenario, a flow-drop effect is seen in P1 to P3 of 5.9% to 32.4%. The optimistic B1 scenario shows flow decreasing from 6.9% to 16.9% between P1 and P3. According to the applied climate change scenarios, it is clear that the long-term river flows will decline significantly in the coming years. This fact will inevitably influence the reservoir outflow. The mean value of total outflow will decrease by 1.54% with ROB = 0.690 in P1 compared with the present value OP = 2.53 m3 s−1. This means that 20 out of the 29 scenarios will satisfy the RT and VZ,max requirements. In P2, the reservoir outflow will decrease by 9.8% with a ROB value of 0.793. Consequently, 23 out of the 29 scenarios will fulfil the water demands. P3 will see the highest percentage outflow decrease, potentially reaching 24% with ROB = 0.897, which matches 26 out of the 29 scenarios. The P1 + P2 combination shows a decrease of 7% with ROB = 0.759, which matches 22 out of the 29 scenarios. In the period combination P1 + P2 + P3 the outflow will decrease by 19.6% with ROB = 0.862, which matches 25 out of the 29 scenarios.

Results based on RCP ensemble

The ensemble was divided into the groups RCP 4.5 and RCP 8.5 according to the RCP scenarios and statistically evaluated based on long-term mean flow μ(Qa), minimal and maximal values min(Qa) and max(Qa) and the percentage variance ΔQa for P1, P2, P3 and then their combination P1 + P2 + P3. The results were compared with the real value of Qa and the statistical characteristics of the Svratka River. Table 3 shows the results of the analysis.

Table 3

Results of hydrological analysis of the Svratka River basin upstream of the Vir I reservoir – RCP ensemble

Scenario (period)μ(Qa) [m3 s−1]min(Qa) [m3 s−1]max(Qa) [m3 s−1]ΔQa [%]
Real Qa (1950–2016) 3.280 – – – 
P1 - RCP 4.5 3.079 2.910 3.259 −6.109 
P2 - RCP 4.5 2.621 2.499 2.763 −20.080 
P3 - RCP 4.5 2.421 2.199 2.673 −26.182 
P1 + P2 + P3 - RCP 4.5 2.707 2.536 2.899 −17.457 
P1 - RCP 8.5 2.698 2.096 3.207 −17.750 
P2 - RCP 8.5 2.376 2.001 2.715 −27.563 
P3 - RCP 8.5 2.239 2.014 2.643 −31.736 
P1 + P2 + P3 - RCP 8.5 2.437 2.076 2.854 −25.683 
Scenario (period)μ(Qa) [m3 s−1]min(Qa) [m3 s−1]max(Qa) [m3 s−1]ΔQa [%]
Real Qa (1950–2016) 3.280 – – – 
P1 - RCP 4.5 3.079 2.910 3.259 −6.109 
P2 - RCP 4.5 2.621 2.499 2.763 −20.080 
P3 - RCP 4.5 2.421 2.199 2.673 −26.182 
P1 + P2 + P3 - RCP 4.5 2.707 2.536 2.899 −17.457 
P1 - RCP 8.5 2.698 2.096 3.207 −17.750 
P2 - RCP 8.5 2.376 2.001 2.715 −27.563 
P3 - RCP 8.5 2.239 2.014 2.643 −31.736 
P1 + P2 + P3 - RCP 8.5 2.437 2.076 2.854 −25.683 

After hydrology analysis, the same analysis of the reservoir storage capacity in terms of the deep uncertainties of climate change was conducted. The goal of the analysis was to identify the μ(OP) that would fit the requested criterion: min {μ(RT) – (RT = 99.5%)}. When the optimal μ(OP) was found, the resulting RT set gained from the input data-ensemble calculation was statistically evaluated. The σ(RT) and intervals min(RT) and max(RT) were determined and ROB was evaluated to determine the optimal solution. ROB was computed for the RT = 99.5% limit: in other words, the system was evaluated as satisfactory when RT ≥ 99.5% and VZ,max = 44.056 mil m3. The results of the reliability assessment and of robustness based on the RCP ensemble can be seen in Table 4.

Table 4

Results of storage reliability assessment and robustness – RCP ensemble

Periodμ(OP) [m3 s−1]μ(RT) [%]σ(RT) [%]min(RT) [%]max(RT) [%]ROB
P1 1.953 99.533 0.734 97.590 99.810 0.875 
P2 1.8972 99.531 0.502 98.420 99.810 0.750 
P3 1.885 99.533 0.734 97.590 99.810 0.875 
P1 + P2 1.895 99.503 0.954 96.990 99.900 0.875 
P1 + P2 + P3 1.902 99.511 0.771 97.810 99.940 0.750 
Periodμ(OP) [m3 s−1]μ(RT) [%]σ(RT) [%]min(RT) [%]max(RT) [%]ROB
P1 1.953 99.533 0.734 97.590 99.810 0.875 
P2 1.8972 99.531 0.502 98.420 99.810 0.750 
P3 1.885 99.533 0.734 97.590 99.810 0.875 
P1 + P2 1.895 99.503 0.954 96.990 99.900 0.875 
P1 + P2 + P3 1.902 99.511 0.771 97.810 99.940 0.750 

The results based on the RCP ensemble, similar to those from the SRES ensemble, show that river flows in the basin will decrease. In Table 3 a decline of about 6.1% in P1 and 26.2% in P3 can be seen for the RCP 4.5 emission scenario, which is considered as balanced. For the pessimistic RCP 8.5 scenario, decrease values for P1 and P3 are 17.8% and 31.7% respectively. According to the developed climate change scenarios, the long-term river flow will decline significantly. This fact will inevitably influence the reservoir outflow. The mean value of total outflow will decrease by more than 22.8% with ROB = 0.875 in P1, compared with the present value OP = 2.53 m3 s−1. In this case, seven out of the eight scenarios will satisfy the RT and VZ,max requirements. In P2, the reservoir outflow will decrease by 25% with ROB value 0.75; thus, six out of the eight scenarios will fulfil the water demands. In P3, the outflow decrease percentage will reach 25.5% with ROB = 0.875, which matches seven out of eight scenarios. The combination of P1 + P2 shows a decrease of 25.1% with ROB = 0.875, which matches seven out of the eight scenarios. In the combination P1 + P2 + P3 the outflow decreases by 24.8% with ROB = 0.75, which matches six out of the eight climate change scenarios.

Discussion

The results of both climate change ensembles show a falling trend for river flows and reservoir outflows. The degree of the resulting river flow recession in the catchment corresponds to the climate change magnitude in the emission scenarios. The pessimistic A2 and RCP 8.5 scenarios show the highest flow decrease (A2: P1 to P3 from 5.9% to 32.4%; RCP 8.5: P1 to P3 from 17.8% to 31.7%.). On the other hand, in the B1 scenario the river flow decreases are the lowest (6.9% and 16.9% for P1 and P3 respectively).

The reservoir outflow results indicate that for the input RT and VZ,max, the total outflow will decrease. The results from the SRES ensemble indicate the mean value of total outflow decreasing by 1.54% with ROB = 0.69 in P1, and by 24% with ROB = 0.897 in P3. The combination of P1 + P2 shows a decrease of 24% with ROB = 0.897 and the P1 + P2 + P3 combination shows a decrease of 19.6% with ROB = 0.862.

Based on the RCP ensemble results, the mean total outflow will decrease by more than 22.8% with ROB = 0.875 in P1, and 25.5% with ROB = 0.875 in P3. In the P1 + P2 combination, the decrease is 25.1% with ROB = 0.875, and in the P1 + P2 + P3 combination, the decrease is 24.8% with ROB = 0.75.

As they take into account the deep uncertainties of the climate change patterns created by the climatic and hydrological data ensembles, the final outflow values μ(OP) of the Svratka River are quite robust, and they should be satisfactory even under future climate change conditions.

Comparing the results from SRES and RCP ensembles, the benefit of SRES ensembles generated by LARS WG is their capability to focus on a specific area, and the ability to define a larger number of SRES emission scenarios describing the deep uncertainty of climate change; while the main disadvantage is using the first generation of emission scenarios defined by Nakićenović et al. (2000). Whereas the RCP ensemble generated by the ED portal is based on the new generation of emission scenarios defined by Moss et al. (2010), the disadvantage is in fewer setting options in the ED portal to create a detailed ensemble when modelling the deep uncertainty of climate change.

CONCLUSIONS

The main goal of this study was to introduce two modelling tools (hydrological and reservoir simulation models) which together create a comprehensive approach to allow robust assessment of reservoir storage capacity in the context of the deep uncertainty of climate change.

Generally, the governing equations of the lumped water balance model were successfully tested in central European hydrology conditions. The NSE results of calibration and validation of the hydrological model using GRG were 0.699 and 0.6, while those using DE were 0.6905 for both calibration and validation. Based on categories by Moriasi et al. (2007), the performance rating model was thus evaluated as good. The results showed decreasing values of long-term mean flow ranging from 6% to 32% depending on the time period, downscaling tools and emissions scenarios. The water balance model equations will be applicable to other catchments with different climatic and hydrological conditions if the model is set up correctly. This means that a suitable calibration and validation dataset ratio was found, and appropriate optimisation methods were used.

The paper also showed how to establish a link between the hydrological model and the reservoir simulation model in relation to the deep uncertainties of climate change. Thus, a new method of expressing the deep uncertainties of hydrological reliability assessment and the resulting robustness connection has been found. Based on the results, it could be expected that the reservoir outflow will decrease by values ranging from 1.5% to 26%, with robustness of 0.69 to 0.875, depending on period, downscaling tools and emissions scenarios. Consequently, reservoir storage capacity will be more sensitive to water shortages caused by drought and increasing water deficits.

The latest version of LARS WG, which was not available when the research was carried out, takes into account the new RCP emission scenarios standards. This creates opportunities for future research to compare the results from all the downscaling methods with each other.

The hydrological model was programmed as an integrated algorithm in FORTRAN with a user interface in C#, creating a user-friendly software tool called Runoff Prophet. The potential universality of such software, in combination with a calibration-parameter setup and suitable optimisation techniques, makes it applicable to all types of catchments in the Czech Republic and possibly across Europe.

The reservoir simulation model can be also described as a universal algorithm, which might be adapted for any reservoir under hydrological stress due to climate change conditions if the inflow data and the reservoir area and volume curves are available. The present algorithm version of the reservoir simulation model is in the form of a user-friendly software tool called UNCE Climate Change, programmed in FORTRAN and with a user interface developed in Delphi 7.

All software tools described in this paper performed on PC with the MS Windows 7 operating system. After further testing, these hydrological and reservoir simulation models may prove to be appropriate tools for decision makers to identify an optimal strategy for adaptation of reservoir operation to protect against the uncertainty of climate change.

ACKNOWLEDGEMENTS

This paper was supported by the specific research project FAST-S-18-5341 ‘Climate Change Uncertainty Propagation in the Hydrological and Water Management Applications’.

REFERENCES

REFERENCES
Arnold
J. G.
Allen
P. M.
Bernhardt
G.
1993
A comprehensive surface-groundwater flow model
.
Journal of Hydrology
142
,
47
69
.
doi:10.1016/0022-1694(93)90004-S
.
Beven
K. J.
Kirkby
M. J.
Schofield
N.
Tagg
A. F.
1984
Testing a physically based flood forecasting model (TOPMODEL) for three UK catchments
.
Journal of Hydrology
69
,
119
143
.
Devia
G. K.
Ganasri
B. P.
Dwarakish
G. S.
2015
A review on hydrological models
.
Aquatic Procedia
4
,
1001
1007
.
doi:10.1016/j.aqpro.2015.02.126
.
Gutiérrez
J. M.
San-Martín
D.
Cofiño
A. S.
Herrera
S.
Manzanas
R.
Frías
M. D.
2012
User guide of the ENSEMBLES downscaling portal, Santander Meteorology Group: technical note
.
GMS
2
,
1
16
.
Hashimoto
T.
Stedinder
J. R.
Loucks
D. P.
1982
Reliability, resiliency, and vulnerability criteria for water resource system performance evaluation
.
Water Resources Research
18
(
1
),
14
20
.
doi:10.1029/WR018i001p00014
.
Hydrologic Engineering Center
2008
HEC-HMS Applications Guide: Version 3.1.0. Institute for Water Resources
,
Hydrologic Engineering Center
,
Davis, CA, USA
.
Klipsch
J. D.
Hurst
M. B.
2013
HEC-ResSim Reservoir System Simulation, User's Manual, Version 3.1
.
US Army Corps of Engineers, Hydrologic Engineering Center
,
Davis, CA
,
USA
. .
Kundzewicz
Z. W.
Krysanova
V.
Benestad
R. E.
Hov
Ø.
Piniewski
M.
Otto
I. M.
2018
Uncertainty in climate change impacts on water resources
.
Environmental Science & Policy
79
,
1
8
.
doi:10.1016/j.envsci.2017.10.008
.
Lasdon
L. S.
Waren
A. D.
Jain
A.
Ratner
M.
1978
Design and testing of a generalized reduced gradient code for nonlinear programming
.
ACM Transactions on Mathematical Software
4
(
1
),
34
50
.
doi:10.1145/355769.355773
.
Lempert
R. J.
Popper
S. W.
Bankes
S. C.
2003
Shaping the Next One Hundred Years: New Methods for Quantitative Long-Term Strategy Analysis
.
MR-1626-RPC
,
The RAND Pardee Center
,
Santa Monica, CA, USA
.
Lindström
G.
Johansson
B.
Persson
M.
Gardelin
M.
Bergström
S.
1997
Development and test of the distributed HBV-96 hydrological model
.
Journal of Hydrology
201
(
1–4
),
272
288
.
doi:10.1016/S0022-1694(97)00041-3
.
Marton
D.
Knoppová
K.
2018
Robust reliability assessment of water reservoir under uncertainty of climate change
. In:
13th International Conference on Hydroinformatics HIC 2018, Manchester
(G. La Loggia, G. Freni, V. Puleo & M. De Marchis, eds), The EPiC Series: EasyChair Proceedings and Collections 2018, pp.
1316
1323
.
doi:10.29007/s5s1
.
Marton
D.
Starý
M.
Menšík
P.
2015
Analysis of the influence of input data uncertainties on determining the reliability of reservoir storage capacity
.
Journal of Hydrology and Hydromechanics
63
(
4
),
287
294
.
doi:10.1515/johh-2015-0036
.
Marton
D.
Paseka
S.
Knoppová
K.
2016
Reservoir storage capacity analysis under conditions of uncertainty and climate change
. In:
Conference Proceedings: International Conference Computing and Control for the Water Industry CCWI 2016
,
Amsterdam, The Netherlands
.
Moriasi
D. N.
Arnold
J. G.
Van Liew
M. W.
Bingner
R. L.
Harnel
R. D.
Veith
T. L.
2007
Model evaluation guidelines for systematic quantification of accuracy in watershed simulations
.
Transactions of the American Society of Agricultural and Biological Engineers
50
(
3
),
885
900
.
Moss
R. H.
Edmonds
J. A.
Hibbard
K. A.
Manning
M. R.
Rose
S. K.
van Vuuren
D. P.
Carter
T. R.
Emori
S.
Kainuma
M.
Kram
T.
Meehl
G. A.
Mitchell
J. F. B.
Nakicenovic
N.
Riahi
K.
Smith
S. J.
Stouffer
R. J.
Thomson
A. M.
Weyant
J. P.
Wilbanks
T. J.
2010
The next generation of scenarios for climate change research and assessment
.
Nature
463
,
747
756
.
Nakićenović
N.
Alcamo
J.
Grübler
A.
Riahi
K.
Roehrl
R. A.
Rogner
H.-H.
Victor
N.
2000
Special Report on Emissions Scenarios (SRES), A Special Report of Working Group III of the Intergovernmental Panel on Climate Change
.
Cambridge University Press
,
Cambridge, UK
.
NOAA
2019
State of the Climate: Global Climate Report – 2018
.
National Centers for Environmental Information. Available from: https://www.ncdc.noaa.gov/sotc/global/201813 (accessed 21 June 2019)
.
OECD
2013
Water and Climate Change Adaptation: Policies to Navigate Uncharted Waters
.
OECD Studies on Water, OECD Publishing
,
Paris, France
.
doi:10.1787/9789264200449-en
.
Racsko
P.
Szeidl
L.
Semenov
M. A.
1991
A serial approach to local stochastic weather models
.
Ecological Modelling
57
(
1–2
),
27
41
.
doi:10.1016/0304-3800(91)90053-4
.
Refsgaard
J. C.
Storm
B.
1995
MIKE SHE
. In:
Computer Models of Watershed Hydrology
(
Singh
V. P.
, ed.),
Water Resources Publications
,
Highlands Ranch, CO, USA
, pp.
806
846
.
Roach
T.
Kapelan
Z.
Ledbetter
R.
Ledbetter
M.
2016
Comparison of robust optimization and info-gap methods for water resource management under deep uncertainty
.
Journal of Water Resources Planning and Management
142
(
9
),
04016028
.
doi:10.1061/(ASCE)WR.1943-5452.0000660
.
Semenov
M. A.
Pilkington-Bennet
S.
Calanca
P.
2013
Validation of ELPIS 1980–2010 baseline scenarios using the observed European Climate Assessment dataset
.
Climate Research
57
(
1
),
1
9
.
doi:10.3354/cr01164
.
Storn
R.
Price
K.
1997
Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces
.
Journal of Global Optimization
11
(
4
),
341
359
.
doi:10.1023/A:1008202821328
.
Vamvakeridou-Lyroudia
L. S.
Morley
M. S.
Bicik
J.
Green
C.
Smith
M.
Savić
D. A.
2010
AquatorGA: Integrated optimisation for reservoir operation using multiobjective genetic algorithms
. In:
Integrating Water Systems – 10th Int. Conf. Comput. Control Water Ind.
(
Boxall
J.
Maksimović
Č.
, eds),
CRC Press, Taylor & Francis Group
,
London, UK
, pp.
493
500
.
Vizina
A.
Horáček
S.
Hanel
M.
2015
Recent developments of the BILAN model
.
Water Management Technical and Economical Information Journal
57
(
4–5
),
7
10
.
Wang
G.
Zhang
J.
Xuan
Y.
Liu
J.
Jin
J.
Bao
Z.
He
R.
Liu
C.
Liu
Y.
Yan
X.
2013
Simulating the impact of climate change on runoff in a typical river catchment of the Loess Plateau, China
.
Hydrometeorology
14
(
5
),
1553
1561
.
doi:10.1175/JHM-D-12-081.1
.
Wurbs
R. A.
2005
Comparative Evaluation of Generalized Reservoir/River System Models
.
Technical Report 282
,
Texas Water Resources Institute
,
College Station, TX, USA
.
Wurbs
R. A.
2019
Reference and Users Manual for the Water Rights Analysis Package (WRAP)
.
Technical Report
,
Texas Water Resources Institute
,
College Station, TX, USA
.
Zelinka
I.
2002
Umělá inteligence: v problémech globální optimalizace (Artifical Intelligence: In Problems of Global Optimization)
.
BEN
,
Prague
,
Czech Republic
, pp.
71
87
.