1 Introduction

The Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC 2014) states that anthropogenic influences are extremely likely as the dominant cause of the global warming that has been observed since the mid-twentieth century. The potential adverse impacts on the water resources systems are summarized by Simonovic (2017), and include: changes in surface runoff and groundwater recharge due to modifications in the amount and time distribution of precipitation and global rising of temperature; decrease of water quality; and increase in functional and operational requirements for the existing water infrastructure.

In line with the application of the sustainability concept, ecological flows should be considered in the operation of reservoir-dam systems. In the European Union, the Water Framework Directive (WFD - Directive 2000/60/EC) established a framework for the protection of inland surface waters, transitional waters, coastal waters and groundwater. The WFD does not include specifically the term “ecological flow”, although it states that action is necessary when water abstraction, water flow regulation or morphological alterations in surface water bodies may interfere in achieving the WFD objectives (Ramos et al. 2017). The term ecological flow appears explicitly in process of application of the WFD with the “Blueprint to Safeguard Europe’s Water Resources” (EC 2012). During the second cycle of the River Basin Management Plans (i.e., between 2016 and 2021), the Member States are requested to do significant advances in the implementation of ecological flows to “respect the needs of nature” (EC 2012). In Tharme (2003), the author classifies the majority of methodologies for defining environmental flows into hydrological (relying primarily on the use of hydrological data), hydraulic rating (approaches that use changes in simple hydraulic variables), habitat simulation (relying on physical habitat modelling to different flow regimes) and holistic (usually using tools of hydrological, hydraulic and physical habitat analysis) methodologies, generically of increasing complexity from the former to the last group. As claimed in Tharme (2003), hydrological methodologies lack of a clear linkage between hydrological variables and biological response but they are considered to be appropriate at the planning level in defining preliminary environmental flow targets.

As demonstrated in this paper, the application of water systems approach and modelling can enable an efficient decision-making for water problems in reservoir systems by considering simultaneously ecological flows and climate projections. Based on a general approach presented by Simonovic (2017) to bring the problematic of climate variability into practice, the methodology presented here includes the selection of projections of future climate to generate input data at the watershed scale for the simulation and evaluation of water reservoir systems operation considering the implementation of ecological flows.

Atmosphere Ocean coupled General Circulation Model-Regional Climate Models (in short, AOGCM-RCM) are able to generate climate projections at the watershed scale but they are still uncertain (IPCC 2014). European projects like PRUDENCE (Christensen and Christensen 2007) and ENSEMBLES (van der Linden and Mitchell 2009), and more recently the EURO-CORDEX initiative (Jacob et al. 2014), made available to the community large and consistent ensemble of AOGCM-RCM simulations that allow to explore uncertainties in climate projections related with different greenhouse gas emission scenarios, model structure, and/or parametrization schemes of the climate models. As in other recent impact studies considering future climate variability (e.g., Tseng et al. 2015; Gohari et al. 2017; Hernández-Bedolla et al. 2017), the methodology presented here should be applied to real case studies with the selection of multiple AOGCM-RCM simulations to explore the potential impacts of future climate variability associated to the uncertainties in climate projections.

Moreover, AOGCM-RCM simulations that are available to the scientific community exhibit frequently systematic errors when simulating the past climate. Teutschbein and Seibert (2012) or Ngai et al. (2017) present a number of post-processing techniques that have been used to adjust climate projections towards observed characteristics. In the context of the methodology presented here, AOGCM-RCM simulations are handled to generate input data only after their adjustment towards observed characteristics with one selected post-processing technique.

For evaluating the performance of reservoir systems considering future climate variability, different authors have used the performance criteria indicators introduced initially in the literature by Hashimoto et al. (1982). Although, there are today different metrics (i.e., mathematical expressions) of reliability, resiliency and vulnerability (RRV), one generic concept can be drawn for each performance criteria indicator. From Hashimoto et al. (1982), reliability is related with how often a system fails meeting the planned objectives (e.g., satisfying demand), resilience is defined as how quickly a system returns to a satisfactory state after a failure has occurred, and vulnerability refers to the likely magnitude of failures. In Asefa et al. (2014), these authors discussed the complementarity of RRV as each performance criteria measures different aspects of the operation of a water supply system, in a study considering varying climatic conditions. In another study about water system performance under future climate variability, Tseng et al. (2015) dedicated their attention investigating the behaviour of single (as RRV metrics) and composite performance criteria indicators (that combine RRV or other single metrics into a single value). Tseng et al. (2015) applied a monotonic test (Kjeldsen and Rosbjerg 2004) to verify if the performance criteria indicators showed an increased or decreased monotonically behaviour under sequential changes of the reservoir storage or the water demand (e.g., consider a storage-demand-reliability relationship in a reservoir system, for a given storage, if demand decreases and reliability continually increases, this performance criteria shows a monotonically behaviour, or non-monotonically otherwise). An in Kjeldsen and Rosbjerg (2004), Tseng et al. (2015) verified that not all metrics of resilience and vulnerability showed an monotonic behaviour, in particular those based on mean values (of duration and magnitude of failures) and not on worst events. Tseng et al. (2015) observed also a non-monotonic behaviour in composite performance indicators which can potentially give misleading information regarding the evaluation of water systems performance.

In this research, the authors use four RRV metrics as defined in Sandoval-Solis et al. (2011) that include the most frequent metric of reliability described in the literature, one common metric of resilience and two alternative metrics of vulnerability. The metrics are determined after water reservoir system operation has been simulated using a commercial software as in other recent studies that evaluated the performance of water systems under future climate variability with user-friendly applications (Ashofteh et al. 2017; Gohari et al. 2017; Hernández-Bedolla et al. 2017). Sandoval-Solis et al. (2011) also proposed a composite metric. However, only the single metrics were considered in this research because Tseng et al. (2015) verified a non-monotic behaviour in the composite metric described in Sandoval-Solis et al. (2011) and as aggregating too many indicators (say, more than three as claimed by Srdjevic and Srdjevic 2017) in one single value can hide information about different aspects of system performance.

In the remainder of this paper, the methodology proposed to explore potential impacts of future climate variability from present conditions on water reservoir systems with the implementation of ecological flows is described next (Section 2). The case study (Section 3) selected to demonstrate the application of the methodology was the Odeleite-Beliche multi-reservoir system located in southern Portugal. In a report on the implementation of the Water Framework Directive (Directive 2000/60/EC) in Portugal, the European Commission (EC 2015) identified as one main gap the definition of ecological flows. In the same report, the EC ( 2015) characterized the approach used in Portugal for implementation of ecological flows: all new surface reservoir-dams must have an ecological flow established; and in existing reservoir-dams the ecological flows must be revised (or implemented if absent) when renewing licensing permits. The ecological flow regime for Odeleite-Beliche system has not been defined yet but it is included in the corresponding River Basin Management Plan already adopted for the period 2016–2021 (APA 2016). The case study includes also references to previous studies in the same area by other authors (Ramos et al. 2014; Maia et al. 2015; Ramos et al. 2016) about the implications of future climate variablity on water resources management. The discussion of results (Section 4) is made from the analysis of the output of water system simulation with the implementation of ecological flows on Odeleite-Beliche multi-reservoir system. This paper ends (Section 5) with a summary of its main conclusions.

2 Methodology

The methodology presented here adapts the generic approach for bringing the problematic of climate variability into practice set by Simonovic (2017) to explore the potential impacts from the modification of present conditions on water reservoir systems with the implementation of ecological flows as follows:

  • Step 1 – Selection of AOGCM-RCM simulations with projections of future conditions about precipitation and temperature;

  • Step 2 – Adjustment of AOGCM-RCM simulations towards observed characteristics;

  • Step 3 – Use of adjusted AOGCM-RCM simulations to obtain natural inflows at the watershed scale for water system simulation;

  • Step 4 – Integrated water system simulation with the implementation of ecological flows, and evaluation of management with performance criteria indicators from the literature.

The sections that follow introduce the methods used in the application of the methodology to the selected case study.

2.1 Selection and Adjustment of Climate Projections

The climate projections used in this research to obtain natural inflows at the watershed scale are available from the EURO-CORDEX initiative database (http://www.euro-cordex.net/). This is one of the programmes sponsored by the World Climate Research Program to organize an internationally coordinated framework to produce improved regional climate projections for all land regions world-wide. From the EURO-CORDEX initiative, a large ensemble of AOGCM-RCM simulations with a resolution of 0.11 (~12.5 km) and 0.44 degree (~50 km) was made available to the community for the European domain within the timeline of the Fifth Assessment Report of the IPCC (IPCC 2014). In the last update (end of 2016), more than 40 modelling groups had already supported the EURO-CORDEX database to build a large ensemble of AOGCM-RCM simulations based on state-of-the-art RCM forced with different AOGCM projections from the Coupled Model Intercomparison Project phase 5 (Taylor et al. 2012), and different greenhouse gas concentration trajectories in the atmosphere following the Representative Concentration Pathways (RCP) scenarios, RCP 2.6, RCP 4.5 and RCP 8.5 (Moss et al. 2010) Table 1. The RCP 2.6 is a less severe scenario about the evolution of the global annual greenhouse emissions with the peak between 2010 and 2020. The RCP 4.5 scenario assumes a peak of the emissions around 2040, then decline. The RCP 8.5 is the most severe scenario in which emissions continue to increase throughout the twenty-first century.

In this study, selected AOGCM-RCM simulations of monthly precipitation (P) and temperature (T) were adjusted using the quantile mapping as implemented by Gudmundsson et al. (2012). Unlike more simple methods such as linear scaling (e.g., Teutschbein and Seibert 2012) or delta change (e.g., Teutschbein and Seibert 2012; Vieira and Cunha 2017) in which only differences in average values are taken into account, the quantile mapping method uses information of cumulative distribution functions (CDF) to adjust climate projections. Gudmundsson et al. (2012) reviewed that a common approach is to use empirical CDF of observed and modelled values instead of assuming parametric distributions in the adjustment of precipitation and temperature projections. Here, precipitation and temperature were discretised with a monthly time step, and the climate projections were adjusted as follows:

$$ {P}_{aju\_ fut}={F}_{P_{obs}}^{-1}\left({F}_{P_{sim\_ con}}\left({P}_{sim\_ fut}\right)\right) $$
(1)
$$ {T}_{aju\_ fut}={F}_{T_{obs}}^{-1}\left({F}_{T_{sim\_ con}}\left({T}_{sim\_ fut}\right)\right) $$
(2)

where Psim _ fut (Tsim _ fut) = raw (or non-adjusted) future climate projection of monthly precipitation (temperature), \( {F}_{P_{sim\_ con}} \) (\( {F}_{T_{sim\_ con}} \)) = empirical CDF of simulated monthly precipitation (temperature) for the control period, \( {F}_{P_{obs}}^{-1} \) (\( {F}_{T_{obs}}^{-1} \)) = inverse empirical CDF of observed monthly precipitation (temperature). One critical assumption in the implementation of the quantile mapping method as described above is that differences in CDF of observed values and simulated values in the control period will not change in the future. All calculation were done using the R package made available to the community by Gudmundsson (2016).

2.2 Hydrological Modelling

The Temez model (Temez 1977) was used for estimating the inflows to Odeleite and Beliche reservoirs. The Temez model is a simplification of the classic Stanford Watershed Model (Crawford and Linsley 1966). Both models implement an aggregated approach to simulate rainfall-runoff processes occurring on a watershed. The formulation of the Temez model includes only four parameters that need to be calibrated: maximum soil holding capacity; maximum infiltration rate; runoff coefficient; and aquifer discharge coefficient. The other two inputs are precipitation and potential evapotranspiration. The Temez model provides values of specific runoff that can be multiplied by the drainage area of the reservoirs to get absolute values of runoff.

In this study, input precipitation was derived from the application of the quantile mapping method with (1), and evapotranspiration was determined by the Penman-Monteith method (Allen et al. 1998) combining adjusted temperature with (2), with air humidity, radiation, and wind speed.

2.3 Water System Simulation

The water system studied here was simulated with AQUATOOL software (Andreu et al. 1996). AQUATOOL is one of the representative simulation models used for preliminary analysis of performance on water resources systems (Sulis and Sechi 2013). As MODSIM (Labadie et al. 2000) and WEAP (SEI 2005) models, AQUATOOL applies an optimization method on every consecutive time step of the simulation to find a solution (e.g., releases from water reservoirs, water allocation to demand centres) compatible with physical constraints, operating rules, and other management constraints (Sulis and Sechi 2013; Lerma et al. 2015).

In a simple example, consider a single reservoir system that must satisfy a demand and downstream ecological flows. In AQUATOOL, the allocation of water to the satisfaction of demand (D) and the maintenance of minimum ecological flows (Ec) in each consecutive time step will be determined by the solution of an optimization problem that includes a water balance simulating changes of the water storage in the reservoir, minimum and maximum storage volumes in the reservoir, and an objective function (OF) defined internally by the software that can be written as follows:

$$ OF=\underset{Storage\ and\ spills\ in\ reservoir}{\underbrace{\left({C}_S\times S+{C}_{Sp}\times Sp\right)}}+\underset{Demand}{\underbrace{C_{Def\_D}\times Def\_D}}+\underset{Ecological\ flows}{\underbrace{C_{Def\_ Ec}\times Def\_ Ec\ }} $$
(3)

where S is the water storage in the reservoir in the end of the time step, Sp are the spills or non-controlled discharges of the reservoir, Def _ D is the deficit in the satisfaction of demand, Def _ Ec is the deficit in the minimum ecological flows, and CS, CSp, CDef _ D, and CDef _ Ec are weight factors that analysts can change to define the water management within AQUATOOL. When the values of the weight factors are selected so that CSp > CDef _ D > CDef _ Ec > CS, the solution of the optimization problem solved at each consecutive time step will give higher priority to avoid unnecessary spills from the reservoir (i.e., spills will be limited to keep storage within reservoir capacity); the satisfaction of demand will be prioritized over the maintenance of ecological flows; and all water available in the reservoir will be allocated to the satisfaction of demand and the maintenance of ecological flows following the standard policy operating rule of reservoirs (e.g., Kjeldsen and Rosbjerg 2004; Jain 2010). But a large variety of operating rules described in the literature for single- and multi-reservoir systems (e.g., Lund and Guzman 1999; Sulis and Sechi 2013) can be implemented and adapted in AQUATOOL to model different management policies.

In another simple example, consider a system with two reservoirs in series, one joint demand and minimum ecological flows set in both reservoirs, in which the objective function defined internally by AQUATOOL can be written as follows:

$$ OF=\underset{Storage\ and\ spills\ in\ upstream\ reservoir}{\underbrace{\left({C}_{S_U}\times {S}_U+{C}_{Sp_U}\times {Sp}_U\right)}}+\underset{Storage\ and\ spills\ in\ downstream\ reservoir}{\underbrace{\left({C}_{S_D}\times {S}_D+{C}_{Sp_D}\times {Sp}_D\right)}}+\underset{Demand}{\underbrace{C_{Def\_D}\times Def\_D}}+\underset{ Ec ological\ flows}{\underbrace{C_{Def\_ Ec}\times \left( Def\_{Ec}_U+ Def\_{Ec}_D\right)\ }} $$
(4)

where Def _ D, CDef _ D and CDef _ Ec were already defined in (3), \( {C}_{S_U} \) and \( {C}_{S_D} \) are, respectively, weight factors to be applied to the storage in the upper and downstream reservoirs (i.e., SU and SD), \( {C}_{Sp_U} \) and \( {C}_{Sp_D} \) are weight factors to be applied to the spills in both reservoirs (i.e., SpU and SpD), and Def _ EcU and Def _ EcD represent the deficit in the minimum ecological flows in the same reservoirs. One common operating rule for two reservoir in series is to fill upstream reservoir first, and empty downstream reservoir first. This operating rule can be implemented in AQUATOOL and combined with the same type of operation described above for the single reservoir system (i.e., spills should be minimum, satisfaction of demand with priority over the maintenance of ecological flows, and the storage in the reservoirs is allowed to increase only after the demand and ecological flows are totally satisfied) by defining the value of the weight factors as follows:

$$ \left({C}_{Sp_U}={C}_{Sp_D}\right)>{C}_{Def\_D}>{C}_{Def\_ Ec}>{C}_{S_D}>{C}_{S_U} $$
(5)

2.4 Performance Criteria Indicators

The performance criteria indicators used here to evaluate water system performance correspond to reliability (Rel), resilience (Res), vulnerability (Vul) and dimensionless maximum deficit (MaxDef) as defined in Sandoval-Solis et al. (2011). The first criterion corresponds to the most frequent metric of reliability described in the literature and the second criterion is one common metric of resilience. The last two criteria can be considered as alternative metrics of vulnerability as both refer to the likely magnitude of failures (see Introduction) with Vul based on an average deficit and MaxDef on the worst event but each metric can evince different aspects of water system operation. The RRV metrics described in Sandoval-Solis et al. (2011) have been used by different authors in recent studies about water resources planning and management (e.g., Tseng et al. 2015; Safavi et al. 2016; Hernández-Bedolla et al. 2017; Karamouz et al. 2017). Following Sandoval-Solis et al. (2011), consider that for each month t of the simulation, the water deficit of demand (Def _ Dt) is defined as follows:

$$ Def\_{D}_t=\left\{\begin{array}{cc}{D}_t-{C}_t& {D}_t>{C}_t\\ {}0& {D}_t={C}_t\end{array}\right. $$
(6)

where Dt is the water demand in month t and Ct is the water supply in month t.

Reliability (Rel) is defined as the proportion of time during the simulation period that the water demand is fully supplied. Using the water deficit as defined by (6), the value of Rel can be calculated as follows:

$$ Rel=\frac{\#_{\left( Def\_{D}_t=0\right)}}{N} $$
(7)

where \( {\#}_{\left({Def}_t=0\right)} \) is the number of months Def _ Dt = 0, and N is the total number of time steps/months of the simulation. By definition, the best value of Rel is one (i.e., no water deficits in any time period) and worse value is zero (i.e., water deficits occur in all periods).

Resilience (Res) is the probability that a month with no deficit fallows a month with deficit (\( {\#}_{\left( Def\_{D}_t=0\ |\ Def\_{D}_{t-1}>0\right)} \)) for all months with deficits (\( {\#}_{\left( Def\_{D}_t>0\right)} \)):

$$ Res=\frac{\#_{\left( Def\_{D}_t=0\ |\ Def\_{D}_{t-1}>0\right)}}{\#_{\left( Def\_{D}_t>0\right)}} $$
(8)

Res evaluates the recovery of the system once it has failed (meeting the demand). The value of Res is not defined when no water deficits occur, and with longer failures (a failure is defined by consecutive periods in which the demand is not satisfied) the value of Res goes to zero. With this metric, failures of high duration are flattened out when a high number of short events also occur.

Vulnerability (Vul) is a measure of severity of the deficits, and Sandoval-Solis et al. (2011) expressed it as the average of the dimensionless deficits if they occur:

$$ Vul=\frac{\sum_{Def\_{D}_t>0}\left(\frac{Def\_{D}_t}{D_t}\right)}{\#_{\left( Def\_{D}_t>0\right)}} $$
(9)

Vul is between zero and one with no deficits and maximum deficits in all periods, respectively.

The dimensionless maximum deficit (MaxDef) is another measure of severity used by Sandoval-Solis et al. (2011) that is defined by the ratio between the maximum annual deficit and the annual water demand:

$$ MaxDef=\frac{\max \left( Def\_{D}_{Annual}\right)}{D_{Annual}} $$
(10)

By definition, MaxDef is between zero (best value) and one (worse value).

3 Case Study: Odeleite-Beliche Water System

3.1 Overview

The case study is focused on Odeleite-Beliche water system (Fig. 1) located in the Algarve region (south of Portugal) and built in the 1990s to supply domestic and intensive agricultural demands. As illustrated in Fig. 1, the water is discharged from Odeleite reservoir (min-max storage: 13–140 million m3) to Beliche reservoir (min-max storage: 0.4–48 million m3), and the withdrawals for the water supply are made exclusively from Beliche reservoir. Downstream, the water courses from each reservoir end in international Guadiana river that defines the official border between Portugal and Spain in this area.

Fig. 1
figure 1

Schematic representation of Odeleite-Beliche water system

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Previous studies have been made in Guadiana river basin about the impacts of future climate variability. Ramos et al. (2014) generated a large ensemble of adjusted climate projections for the entire Guadiana river basin for the periods 2011–2040 and 2041–2070. Those climate projections were used by Maia et al. (2015) to study the effects in water resources management in the Portuguese part of Guadiana river basin, while Ramos et al. (2016) combined the same climate projections with hydrological modelling to study the ecological risk based on projected hydrological alteration. Maia et al. (2015) and Ramos et al. (2016) had foreseen negative impacts as the climate projections in Ramos et al. (2014) agree generically with increasing temperatures and decreasing precipitations.

3.2 Previous Hydrological Modelling

The Temez model calibrated and validated for the case study area by Nunes et al. (2009) was used here to generate the natural inflows to Odeleite reservoir (drainage area: 348 km2) and Beliche reservoir (drainage area: 98 km2) using the adjusted AOGCM-RCM simulations.

3.3 Reservoir Simulation

Water storage in Odeleite (O) and Beliche (B) reservoirs is simulated in AQUATOOL by a water balance that can be written as follows:

$$ {S}_{i,t}={S}_{i,t-1}+{Inf}_{i,t}-{R}_{i,t}-{Ev}_{i,t}-{Sp}_{i,t} $$
(11)

where Si, t= storage at reservoir i (O or B) in the end of period t; Infi, t= total inflows to reservoir i in period t; Ri, t= total releases from reservoir i in period t; Evi, t= evaporation losses from reservoir i in period t; and Spi, t= excess discharges (i.e., spills) to remain within storage capacity in period t.

Beliche reservoir receives water transferred from Odeleite reservoir, the water withdrawals for meeting the demand are made only from Beliche reservoir, and ecological flows should be implemented in each reservoir for ecosystem maintenance (Fig. 1). Following this description, the total inflows and releases in (11) from the two reservoirs can be written as follows:

$$ {Inf}_{O,t}={Qn}_{O,t} $$
(12)
$$ {R}_{O,t}={Tr}_{O,t}+{Ec}_{O,t} $$
(13)
$$ {Inf}_{B,t}={Qn}_{B,t}+{Tr}_{O,t} $$
(14)
$$ {R}_{B,t}={Wd}_{B,t}+{Ec}_{B,t} $$
(15)

where QnO, t (or QnB, t)= natural inflows to Odeleite (or Beliche) reservoir in period t; TrO, t= water transfer from Odeleite to Beliche reservoir in period t; EcO, t (or EcB, t) = releases for ecological flows from Odeleite (or Beliche) reservoir in period t; and WdB, t= water withdrawals from Beliche reservoir in period t.

3.4 Composite Scenarios

In total, 12 different composite scenarios were considered in this study that resulted from combining (i) two prioritization schemes about withdrawals for water supply and releases of ecological flows with (ii) six regional climate projections for the period 2021–2050 from the EURO-CORDEX database with spatial resolution of 0.11 degree and adjusted with the quantile mapping method (see section 2.1). Period 1971–2000 was used as control period in the application of the quantile mapping method and as representative of the present-day climate in accordance with the use of EURO-CORDEX data.

The six climate projections used here were also selected to integrate the Portuguese Local Warming Website (LWW – http://portaldoclima.pt/en/) after a process of validation that compared simulated data in the historic period with observed data in Portugal. The LLW (Gomes et al. 2016) is for public use, and it is the result from a project promoted by the Portuguese Environment Agency on adaptation to climate change with the main goals of increasing the capacity to assess vulnerability to climate variability, and to raise awareness and education on climate change in Portugal. The climate model simulations selected for the assessment of performance of Odeleite-Beliche system tackled the uncertainty in climate projections from using the same RCM (RCA4: Samuelsson et al. 2011) forced by three different AOGCM (CNRM-CERFACS-CNRM-CM5: Voldoire et al. 2013; ICHEC-EC-EARTH: Hazeleger et al. 2010; MPI-M-MPI-ESM-LR: Giorgetta et al. 2013) and two different of greenhouse gas concentration trajectories in the atmosphere following the Representative Concentration Pathways (RCP) scenarios (RCP 4.5 and RCP 8.5: Moss et al. 2010). The designations CNRM-RCA4, ICHEC-RCA4, and MPI-RCA4 are used afterwards in this paper to identify the projections obtained from climate model simulations that use the same RCM with each AOGCM. Although it cannot be generalized to all situations, previous studies have shown significant differences on hydrology using the same RCM forced by different AOGCM (Kay et al. 2009; Chen et al. 2011; Dobler et al. 2012). The RCP scenarios 4.5 and 8.5 used here were the same as defined for the Fifth Assessment Report of the IPCC (IPCC 2014). Each combination of one RCP scenario with one AOGCM-RCM identifies each one of the six adjusted climate projections of precipitation and temperature used here.

In this study, the assessment of performance was based in the current maximum withdrawals that are authorized by the Portuguese Environment Agency and valid up to at least 2027–64 million m3/year; and the minimum releases for the satisfaction of ecological flows were set to 15% of the monthly natural inflows in each reservoir. This ecological flow regime is based on the application of the method proposed by Alves and Bernardo (2003) to a river in the south of Portugal. The method developed by Alves and Bernardo (2003) is focused on the characteristics of monthly flow series (as a hydrological method, it does not consider a clear linkage between hydrological variables and biological response – see Introduction) and it was designed to be applied to watersheds with homogenous hydrological characteristics. In the Algarve, this method was already used at the planning level for defining preliminary environmental flow targets (Hidroprojecto 2005), in a study about the expansion of the water supply to the region that included the simulation of reservoir’s operation located in a catchment with similar climatic, topographic and geological characteristics.

Under the two different prioritization schemes tested here, in one case water supply had a higher priority than ecological flows, while in the other case the priority between water supply and ecological flows was inverted (Table 1). This last prioritization scheme reflects a perspective that ecological flows are considered fundamental for achieving environmental objectives in the scope of the Water Framework Directive (Directive 2000/60/EC). The prioritization scheme was not relevant when, at each time step of the simulation, there was water available in the two reservoirs for the water supply and the maintenance of ecological flows. But when the water was scarce, a higher priority to one purpose (water supply or ecological flows) meant that water allocated would be allocated first to that purpose than to the other one.

Table 1 Future period and options considered in the definition of the composites scenarios
Full size table

The objective function used by AQUATOOL to determine the water allocation in each time step in any scenario was identical to (4). For the composite scenarios in which the water supply had a higher priority than the ecological flows the relation of the weight factors in (4) was as in (5). Following the examples described in section 2.3, such parametrization of the weight factors gave rise to a simulation of the water management within AQUATOOL that avoided unnecessary spills from the reservoirs, all water available in Odeleite-Beliche system could be allocated to satisfy the demand or to the maintenance of ecological flows following a standard policy operating rule of reservoirs; and water should be discharged from Odeleite (upstream) reservoir only when Beliche (downstream) reservoir was depleted. The other prioritization scheme between the water supply and the ecological flows was modelled by inverting the relation between CDef _ D and CDef _ Ec in (5).

4 Results

4.1 Adjusted Climate Model Simulations

Table 2 shows the average annual values of precipitation and temperature for the case study area based on observed values in the period 1971–2000 (OBS), and all climate model simulations for the period 2021–2050 after applying the quantile mapping method with (1)–(2).

Table 2 Average annual precipitation (mm) and temperature (°C) of the observed values in 1971–2000 (OBS) and all climate projections for the period 2021–2050
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Under RCP 4.5, the variation of the precipitation for the period 2021–2050 was estimated between −10.6 mm/year (−1%) and + 43.0 mm/year (+6%). Under RCP 8.5, the three AOGCM-RCM anticipate a decrease of the annual precipitation between −133.0 mm/year (−18%) and − 14.4 mm/year (−2%). These results evince the uncertainty about the variation of the precipitation in the future, in particular under RCP 8.5, which is even more evident looking at the average monthly values (Fig. 2).

Fig. 2
figure 2

Average monthly precipitation (mm) of the observed values in 1971–2000 (OBS), and all climate projections for the period 2021–2050: (a) RCP 4.5, and (b) RCP 8.5

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The changes in temperature are more consistent in all climate projections. The variation of the average annual temperature is between +1.4 °C (+8%) and + 1.7 °C (+10%) under RCP 4.5, and + 1.4 °C (+8%) and + 1.9 °C (+12%) under RCP 8.5 (Table 2) whereas Fig. 3 detail the changes in the average monthly temperatures.

Fig. 3
figure 3

Average monthly temperature (°C) of the observed values in 1971–2000 (OBS), and all climate projections for the period 2021–2050: (a) RCP 4.5, and (b) RCP 8.5

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Although the period and the area are not coincident, there is an agreement for increasing annual temperature and decreasing annual precipitation as foreseen in Ramos et al. (2014) for the all Guadiana river basin.

4.2 Natural Inflows

The natural inflows in Table 3 and Fig. 4 were determined using the observed values of precipitation and temperature in the period 1971–2000 and the adjusted climate model simulations for the period 2021–2050 (section 4.1), turned into runoff with the Temez model (sections 2.2 and 3.2).

Table 3 Average annual natural inflows to Odeleite and Beliche reservoirs (×106 m3) estimated for the period 1971–2000 (OBS) and all climate projections for the period 2021–2050
Full size table
Fig. 4
figure 4

Average monthly natural inflows (million m3) estimated with the observed values of precipitation and temperature in 1971–2000 (OBS), and all climate projections for the period 2021–2050: (a) RCP 4.5, and (b) RCP 8.5

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Under RCP 4.5, the hydrological modelling with the Temez model showed a variation of the average natural inflows between −3.9 million m3/year (−3%) and + 32.2 million m3/year (+27%) from the natural inflows estimated with the observed precipitation and temperature. The significant increase of the natural inflows estimated with climate projection RCP 4.5-MPI-RCA4 is related with higher precipitation between December and March (Fig. 2a). Historically, these are important months for the generation of surface runoff, and, thus, an increase of precipitation in these months should have a positive impact on the natural inflows in the same period (Fig. 4a).

Under RCP 8.5, the hydrological modelling showed a variation of the average natural inflows between −34.7 million m3/year (−29%) and − 1.8 million m3/year (−2%). The three AOGCM-RCM agree with decreases of the annual precipitation, leading to proportional reductions of the annual natural inflows. The higher reduction of the annual natural inflows estimated with climate projection RCP 8.5-ICHEC-RCA4 can be justified with significant decreases of precipitation between December and February (Fig. 2b) with impact on hydrological modelling (Fig. 4b).

4.3 Water System Simulation

The results presented next detail the output of simulation in AQUATOOL. No failures were registered meeting the aggregated demand of 64 million m3/year and with the implementation of ecological flows when the natural inflows were based on the observed values of precipitation and temperature in the period 1971–2000. By definition, Rel= 1, Res is not defined, Vul= 0, and MaxDef= 0 when no failures (i.e., total satisfaction of demand) occur.

The sections that follow describe the results of the simulation in AQUATOOL by using all climate projections, first with a higher priority set to the satisfaction of demand (4.3.1), and next with a higher priority given to the satisfaction of the ecologic flows (4.3.2).

4.3.1 Prioritzation of Water Supply

Table 4 shows that failures only occurred with two of the adjusted climate projections considering RCP scenario 8.5: RCP 8.5-ICHEC-RCA4 and RCP 8.5-MPI-RCA4. These climate projections anticipate higher decrease of precipitation and higher increase of temperature (Table 2) with impact on the reduction of the natural inflows estimated by hydrological modelling (Table 3).

Table 4 Performance criteria indicators for all climate projections with water supply with higher priority than ecological flows in water allocation
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In Table 4, the lowest values of reliability (Rel) and resilience (Res) from water system simulation with climate projection RCP 8.5-ICHEC-RCA4 can be justified with the lowest average natural inflows (Table 3), as these performance criteria indicators are frequently related with average conditions.

The simulation in AQUALTOOL with climate projection RCP 8.5-ICHEC-RCA4 is characterized by low natural inflows between approximately 2030 and 2041 (Fig. 5a). In this period, the annual natural inflows estimated to Odeleite and Beliche reservoirs were always lower than the volumes necessary to the satisfaction of demand (64 million m3/year) and the maintenance of the ecological flows (12.8 million m3/year). As the system was simulated with a standard policy operating rule that always tried to satisfy the demand and the ecological flows at each time step, the water storage in the reservoirs between 2030 and 2041 first decreased and then remained consistently at low values (Fig. 5b). The deficits in the water supply occurred in this period (Fig. 5c and Fig. 5d) when the minimum storage was reached in both reservoirs. The value of Rel= 0.85 (or 85%) corresponds to the percentage of months of the simulation with no deficits (305 months in 30 × 12 = 360 months). The value of Rel= 0.26 corresponds to the inverse of the average time mean value of the time the system is in failure in consecutive periods. From the analysis of the monthly deficits (Fig. 5c), the system was in failure for an average duration of 6.11 months, when they occurred.

Fig. 5
figure 5

Details from water system simulation with climate projection RCP 8.5-ICHEC-RCA4 and priority of the water supply greater than the maintenance of the ecological flows: (a) natural inflows, b) storage in reservoirs, (c) monthly deficits, and (d) annual deficits

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The two other performance criteria indicators in Table 4, vulnerability (Vul) and dimensionless maximum deficit (MaxDef), are related with severity of the deficits in the water supply. The value of Vul= 0.75 with climate projection RCP 8.5-ICHEC-RCA4 indicates that in average the deficits were 75% of the demand (this average value is calculated considering only the time periods in which deficits have occurred). MaxDef aggregates the deficits at the annual level, and the maximum deficit was 87% of the demand in year 2040 (Fig. 5d). The high values of these two performance criteria indicators resulted from the simulation of the water management with the standard policy operating rule. As at each time step all the water available could be allocated if necessary to the water supply demand, this caused significant deficits when the water storage in the reservoirs was minimum at the end of one time step and the natural inflows in the next time step were low and clearly insufficient to satisfy the demand.

In Table 4, the better values of Rel and Res with climate projection RCP 8.5-MPI-RCA4 can be associated to higher average natural inflows (Table 3), but the values of Vul and MaxDef evince more severe deficits that can be related with more extreme situations. The value of MaxDef was given by a deficit in the water supply of 93% in year 2036. Analysing in detail the input (Fig. 6a) and output (Fig. 6b, c and d) of the simulation in AQUATOOL with climate projection RCP 8.5-MPI-RCA4, one can confirm that both reservoirs were at minimum storage in the end of year 2035, and the natural inflows in the first eleven months of 2036 was only 2 million m3. Climate projection RCP 8.5-MPI-RCA4 had associated significant inflows in December 2036, the storage in both reservoirs recovered, but the maximum annual deficit was still extremely high.

Fig. 6
figure 6

Details from water system simulation with climate projection RCP 8.5-MPI-RCA4 and priority of the water supply greater than the maintenance of the ecological flows: (a) natural inflows, b) storage in reservoirs, (c) monthly deficits, and (d) annual deficits

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4.3.2 Prioritization of Ecological Flows

When a higher priority was given to the release of ecological flows, failures in the water supply occurred with the same climate projections as previously: RCP 8.5-ICHEC-RCA4 and RCP 8.5-MPI-RCA4 (Table 5). By comparison with Table 4, there is a deterioration of all performance criteria indicators, but only more significant in the metrics related with the severity of the deficits. Nonetheless, the values of Vul and MaxDef in Table 4 and Table 5 are extremely high. The occurrence of such situations would be very unacceptable, and emergency measures would have to be taken by the authorities to minimize the impacts associated with such situations.

Table 5 Performance criteria indicators for all climate projections with water supply with lower priority than ecological flows in water allocation
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The evolution of the performance criteria indicators from Table 4 to Table 5 is a consequence of having simulated water system operation with an operating rule that at each consecutive time step gave higher priority to the satisfaction of the ecological flows than to the satisfaction of demand so that water was allocated to the water supply only after ecological flows have been fulfilled.

Table 6 shows the impact of the prioritization scheme in satisfying the demand and the ecological flows with climate projection RCP 8.5-ICHEC-RCA4. When the ecological flows had a lower priority that water supply, the discharges for environmental purposes were not met in 16% of the periods of the simulation. The lower priority of the ecological flows can be verified in Table 6 as in the periods coincident with failures in the water supply, no water was released for ecological flows in both reservoirs and; in January 2035, when the releases minimum releases for environmental purposes were not met, the water supply demand was totally fulfilled (i.e., no failure was registered). When a higher priority was given to the satisfaction of the ecological flows these were always met, and two longer failures were registered in the water supply (uninterruptible failures from August 2034 to September 2035 and, from August 2039 to October 2041). Furthermore, the total deficit of the demand increased from 253.1 million m3 to 302.3 million m3 when a higher priority was given to the discharges for environmental purposes.

Table 6 Failures in satisfying water supply demand (and corresponding total deficit) and minimum ecological flows with climate projection RCP 8.5-ICHEC-RCA4 with the two prioritization schemes in water allocation between water supply and ecological flows
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5 Conclusions

The methodology presented in this paper, aiming at exploring the potential impacts of future climate variability on water reservoir systems with the implementation of ecological flows, adapts a generic approach set by Simonovic (2017) for bringing the problematic of climate variability into practice. Adjusted AOGCM-RCM simulations are used to obtain input data at the watershed scale. Using an integrated water system simulation that allows to represent water storage in reservoirs, likely operating rules and the implementation of ecological flows, water management is evaluated with performance criteria indicators from the literature. Different methods can be applied in each step upon the data and modelling tools available.

The case study selected to demonstrate the application of the methodology was the Odeleite-Beliche multi-reservoir system located in southern Portugal. Until now the Odeleite-Beliche water system has been operated without the obligation of doing discharges for the maintenance of ecological flows downstream but these are implicitly required for the fulfilment of the environmental objectives defined under the Water Framework Directive (Directive 2000/60/EC).

In this study, six climate projections were combined with two management perspectives by prioritizing in one case the water supply and in the other case the ecological flows. The prioritization scheme was only relevant when, at each time step of the simulation, there was not water available for the two purposes. A higher priority to one purpose meant that water allocated would be allocated first to that purpose than to the other one. The results showed greater variation in the impacts on the water supply due to differences in the natural inflows generated from diverse climate projections compared to the results obtained with a different prioritization scheme.

Failures in meeting the current maximum withdrawals that are today authorized for Odeleite-Beliche multi-reservoir system with the implementation of ecological flows were registered with the two climate projections that anticipate more significant reductions of the natural inflows (higher than 10%). Given the high uncertainty in climate projections (the variation of the natural inflows estimated with the climate projections used in this study ranged between −29% to +27% from the natural inflows estimated with historical data), the potential impacts of future climate variability should be still explored with the methodology presented here by using other AOGCM-RCM simulations; other realizations of the same AOGCM-RCM simulations with different model parameters and initial conditions; or alternative techniques for the adjustment of climate model simulations. Uncertainty could be tackled as well in the field of hydrological modelling with the use of other hydrological models and/or parameters. Updated information in the simulation of the water management such as the establishment of additional priorities within the water supply, for example, between urban use and agriculture; the definition of ecological flows from reservoirs with new criteria; or the use more sophisticated management policies than following the standard policy operating rule of reservoirs, can also be addressed in future studies.