Water Resources Management https://doi.org/10.1007/s11269-018-2101-7
Identifying the Relationship between Assignments of Scenario Weights and their Positions in the Derivation of Reservoir Operating Rules under Climate Change Wei Zhang 1 & Xiaohui Lei 2 & Pan Liu 1 & Xu Wang 2 & Hao Wang 1,2 & Peibing Song 3 Received: 5 March 2018 / Accepted: 28 August 2018/ # Springer Nature B.V. 2018
Abstract In order to mitigate the adverse impacts of climate change, adaptive operating rules (AOR) are generally derived using an ensemble of General Circulation Models (GCMs). Up to date, most of related literatures only focus on one fold of the following issues concerning the derivation of AOR using the GCMs ensemble, including: (1) consideration of different scenario weighing methods, or (2) analysis of different positions to locate scenario weights. And less concern is given to the latter compared with the former. However, few studies identify the relationship between (1) and (2) in the derivation of AOR based on the GCMs ensemble. In this study, we attempt to investigate where to use Equal and REA scenario weights in the derivation of reservoir operating rules under climate change. Equal weights (EW) and unequal weights based on the reliability ensemble average (REA) method are used in two positions: (I) the optimization objective of the reservoir operation model, which is to maximize the weighted average hydropower generation for all future scenarios; and (II) the incorporation of GCMs ensemble climate projections into the weighted climate conditions, and then it is input into the reservoir operation model with the objective of maximizing annual hydropower generation. Four AORs, including EW-AOR(I), REA-AOR(I), EW-AOR(II) and REA-AOR(II), are derived, and their optimized parameters are obtained by the simulation-based optimization (SBO) method with the Complex algorithm. The case study in the Jinxi Reservoir in China indicates that REA-AOR(I) outperforms the other three operation schemes, and EW-AOR(II) performs better than REA-AOR(II). Therefore, equal weights are preferably used to incorporate climate conditions, while unequal weights based on REA method can improve the performance of the reservoir operation model. Generally, REA-AOR(I) and EW-AOR(II) are suggested for adaptive reservoir management under climate change. Keywords Reservoir operation . Climate change . Adaptive operating rules . GCMs ensemble . Scenario weights . Position and assignment
* Xiaohui Lei
[email protected] Back Affiliation
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1 Introduction Climate change can result in changes in hydro-meteorological conditions at both global and regional scales and consequently great challenges in water resources management (Milly et al. 2008). Reservoirs, as one of the most important infrastructures for integrated water resources management (Loucks and Van Beek 2005; Liu et al. 2011), play an important role in mitigating the negative impacts of climate change. Till now, a number of studies have been conducted to design a series of adaptive strategies for reservoir operation in the changing environment. Adaptive reservoir operation is generally implemented to follow the “if-then” pattern of scenarios, in which several scenarios are firstly used to describe potential climate change and then reservoir operation is proposed and analyzed. There are two approaches to accounting for adaptive reservoir operation under climate change: (1) adaptive operation for each individual scenario derived from general circulation models (GCMs) (Eum and Simonovic 2010; Ward et al. 2013; Ahmadi et al. 2015; Yang et al. 2016; Mohammed and Scholz 2017; Zhang et al. 2017b) or alteration of inflow characteristics (Xu et al. 2015; Feng et al. 2017; Herman and Giuliani 2018); and (2) adaptive operation considering an ensemble of multiple scenarios (Brekke et al. 2009; Steinschneider and Brown 2012; Haguma et al. 2015; Zhang et al. 2017a; Karami and Dariane 2018). The consideration of future scenarios under climate change varies by case studies. For adaptive reservoir operation considering only individual scenario, Eum and Simonovic (2010) proposed an adaptive approach to optimize the rule curves of the multi-objective reservoirs, and then reservoir performance was evaluated under each selected emission scenario in the future. Zhou and Guo (2013) considered river ecology into the derivation of reservoir operating curves under the A2 emission scenario. Zhang et al. (2017b) presented a method to carry out adaptive reservoir management for agricultural irrigation and tested its application for the Dongwushi Reservoir under future climate change. However, the applicability of these adaptive operating rules (AOR) based on a single scenario may be problematic under uncertain future climates, which may give rise to the failure of AOR and tremendous economic losses. Since climate change could not be accurately predicted due to the inherent uncertainties in projection models, it is more appropriate to consider the ensemble of scenarios in deriving AOR in order to decrease potential risks. For AORs considering the ensemble of multiple scenarios, some use equal/unequal scenario weights to incorporate precipitation and temperature of multiple GCMs. Brekke et al. (2009) established the joint density functions of temperature and precipitation in which climate projection ensemble members were treated as equally plausible, and then discussed whether and how to weight climate change scenarios. Steinschneider and Brown (2012) considered GCM-based ensemble mean projection as future climate change, based on which a novel dynamically adaptive strategy was proposed for reservoir operation under non-stationary hydrologic conditions. Nevertheless, other literatures adopt scenario weights in the process of reservoir operation, instead of incorporation of climate information. Haguma et al. (2015) equally weighed future climate projections to evaluate their transition probabilities, which were used in the derivation of AOR based on stochastic dynamic programming. And Zhang et al. (2017a) equally assigned weights to all historical and future scenarios in the objectives of reservoir operation model, and consequently a balanced and robust adaptive operating rule was obtained to provide the guide for reservoir managers. Therefore, two concerns can be
Identifying the Relationship between Assignments of Scenario show...
concluded from these comparative studies aforementioned. The first concern is the assignment of equal or unequal scenario weights in the field of adaptive management, and the second one is the use of scenario weights in the reservoir operation model or the generation of hydrometeorological conditions. However, most literatures of adaptive reservoir operation considering climate change ensemble merely focus on one individual aspect aforementioned, ignoring to investigate the relationship between scenario weighing methods and scenario weights uses in the derivation of AOR. Thus, this paper aims to further identify where to use Equal and REA scenario weights in the derivation of reservoir operating rules under climate change. Furthermore, one adaptive benchmark is expected through this investigation among proposed AOR. It would facilitate to illustrate the adaptability of novel adaptive managing strategies in the future research. The remainder of this paper is organized as follows. Section 2 described the methodological framework for AORs respectively considering two assignments and positions of scenario weights. Section 3 shows a case study of the Jinxi Reservoir in China, in which four AORs (EW-AOR(I), EW-AOR(II), REA-AOR(I), and REA-AOR(II)) are evaluated in terms of parameters of operating rules, hydropower benefits and uncertainty control. Finally, conclusions and recommendations are given in Section 4.
2 Methodology Figure 1 describes the proposed methodological framework, in which two assigning and two using approaches are considered into the derivation of adaptive operating rules. Two kinds of scenario weights are included, namely equal weights (EW) and unequal weights based on the reliability ensemble average (REA) method. And then, these scenario weights are used into two positions: (I) the optimization objective of the reservoir operation model, which aims to maximize the weighted average of hydropower generation for all future scenarios; and (II) the combination of precipitation and temperature of multiple scenarios, which is used to generate synthesized streamflow from a hydrological model as the input of the reservoir operation model with the objective of maximizing annual hydropower generation. Four AORs, including EW-AOR(I), REA-AOR(I), EW-AOR(II), and REA-AOR(II), are derived by the simulationbased optimization (SBO) method (Evenson and Moseley 1970).
2.1 Two Methods Used to Assign Scenario Weights (1) Equal weights (EW) Given the uncertainties inherent in all GCMs, it is difficult to choose an accurate GCM to predict future climate conditions. In this regard, it is reasonable to use identical weights among GCM ensembles. The weights depend only on the number of selected GCMs, regardless of the performance of these GCMs and the characteristics of streamflow changes. This has been supported by climate modeling community (Chen et al. 2017). The equal weights of scenarios can be described as follows: ωk ¼ 1
S
where ωk is the weight of the k-th scenario; and S is the number of scenarios.
ð1Þ
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Fig. 1 Flowchart for the derivation of EW-AOR(I), REA-AOR(I), EW-AOR(II), and REA-AOR(II))
(2) Unequal weights based on the reliability ensemble average method (REA) The REA method (Giorgi and Mearns 2002) can be used to evaluate the reliability of climate changes from GCM ensemble simulations, which considers not only the performance of the climate model to reproduce historical stationary conditions (precipitation and temperature), but also the convergence of future potential changes across models. The reliability factor Rk of the REA method is the product of two reliability criteria: Rk ¼
m n ½1=ðmnÞ RB;k RD;k ("
¼
∈ υ abs Bυ;k
#m
"
∈ υ abs Dυ;k
#n )½1=ðmnÞ
ð2Þ
where Rk is the reliability factor of the k-th future scenario, which is calculated for precipitation and temperature (Rk(Pre) and Rk(Temp)), respectively; RB, k is a factor measuring the reliability of the k-th scenario as a function of the bias (Bυ, k) of the model in simulating historical climate conditions; RD, k is a factor measuring the reliability of the k-th scenario in terms of the distance (Dυ, k) of the projected change by a GCM scenario from the REA average change; and m and n are used to discriminate each criterion and set to 3 and 2.5 in this study, respectively. Dυ, k is calculated using an iterative procedure proposed by Giorgi and Mearns (2002), and RB and RD are set to 1 when B and D are smaller than ∈υ.
Identifying the Relationship between Assignments of Scenario show...
Thus, the scenario weight based on the REA method is described as the average of Rk(Pre) and Rk(Temp): ωk ¼
1 ðRk ðPreÞ þ Rk ðTempÞÞ 2
ð3Þ
where Rk(Pre) and Rk(Temp) are the reliability factors of the k-th scenario based on the model performance in precipitation and temperature, respectively.
2.2 Incorporating Scenario Weights into Reservoir Operation Model 2.2.1 Objectives Two scenario weights (EW and REA) are used in the objective of the reservoir operation model considering all future scenarios. This way, simplified as (I) in the other parts of this paper, represents the impact of scenario weights in the view of adaption community. The following reservoir operation model is only to maximize the weighted average of annual hydropower generation for all future scenarios: S
MaxE ¼ ∑ ωk E k k¼1
ð4Þ
where E is the weighted average annual hydropower generation for all scenarios; ωk is the weight of the k-th scenario, whose value can vary with the method described in Section 2.1; and Ek is the mean annual hydropower generation of the k-th scenario, which can be expressed as follows: Ek ¼
1 M N ∑ ∑ Pi; j;k Δt i; j;k M j¼1 i¼1
ð5Þ
where Δti, j, k is the time step length; M is the number of years, N is the number of time steps per year; and Pi, j, k is the power output (kW) of the i-th time period in the j-th year under the kth scenario, which can be expressed as follows: ð6Þ Pi; j;k ¼ min ηRi; j;k H i; j;k ; Pmax where Ri, j, k is the reservoir release of the i-th time period in the j-th year under the k-th scenario; the net water head, Hi, j, k, is a function of the reservoir storage and tail water level; Pmax is the maximum power output constrained by the turbine-generator unit; and η is a comprehensive hydropower coefficient with the same unit as the gravitational acceleration (m/s2).
2.2.2 Constraints (1) Water balance constraints
V i; j;k
8 < V i−1; j;k þ Qi−1; j;k −Ri−1; j;k Δti−1; j;k −ei−1; j;k ; i ¼ 2; 3; …; N ¼ : V N ; j−1;k þ Q N; j−1;k −RN ; j−1;k Δt N; j−1;k −eN ; j−1;k ; i ¼ 1
ð7Þ
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where Vi, j, k is the reservoir storage of the i-th time step in the j-th year under the k-th scenario; Qi, j, k and Ri, j, k are the reservoir inflow and release of the i-th time step in the j-th year under the k-th scenario, respectively; and ei, j, k is the water loss resulting from reservoir seepage and evaporation. (2) Water storage capacity constraints
V i;min ≤V i; j;k ≤V i;max ; i ¼ 1; 2; …; N
ð8Þ
where Vi, min and Vi, max are the minimum and maximum reservoir storage of the i-th time step, respectively. (3) Reservoir release constraints
Rmin ≤Ri; j;k ≤Rmax ; i ¼ 1; 2; …; N
ð9Þ
where Rmin and Rmax are the minimum and maximum reservoir release, respectively. (4) Power output constraints
Pmin ≤Pi; j;k ≤Pmax ; i ¼ 1; 2; …; N
ð10Þ
where Pi, j, k is the power output of the i-th time step in the j-th year under the k-th scenario, which is constrained by the minimum output Pmin and maximum output Pmax.
2.2.3 The Pattern of AOR Reservoir operating rules are derived by specifying operational decisions (e.g., releases) as a function of available information, such as the current reservoir water level and hydrometeorological conditions (Guo et al. 2004). The widely used linear operating rules (Oliveira and Loucks 1997) are used in this study: ð11Þ Ri; j;k ¼ ai V i; j;k þ Qi; j;k Δti; j;k þ bi ; i ¼ 1; 2; …; N where ai and bi are the coefficients of the regression equation of the i-th time period; Ri, j, k is the reservoir release to be decided; Vi, j, k and Qi, j, k are the current reservoir storage (at the beginning of the i-th time period) and reservoir inflow, respectively; and Vi, j, k + Qi, j, kΔti, j, k represents the available reservoir water at the end of the i-th time period. The parameters of operating rules integrate multiple scenarios, which could contribute to the adaptive characteristics for EW-AOR(I) and REA-AOR(I).
2.2.4 The Derivation Method of AOR The operating rules can be derived by the fitting method (Young 1967) or the SBO method (Nalbantis and Koutsoyiannis 1997). Although the former is easy to implement,
Identifying the Relationship between Assignments of Scenario show...
it cannot be easily used to obtain parameters of operating rules when multiple inputs and outputs are simultaneously provided for the same variable. Therefore, SBO is used to derive AOR in this study, as it can directly optimize performance measures by adjusting the operating rule parameters as decision variables in an iterative manner. The Complex algorithm (Xu 1992; Zhang et al. 2017a) is used to determine the optimal parameters of AOR. The core steps of Complex algorithm has been described in the previous work (Zhang et al. 2017a). This algorithm, as a nonlinear method, considers equality and inequality constraints in searching for extreme values of an n-dimensional problem, and it can implement quick partial searches without any gradient information. It can update the set of parameters within parameter intervals, and find the optimal objective as well as its related parameter set.
2.3 Using Scenario Weights in Streamflow Generation 2.3.1 Synthesized Streamflow Based on Scenario Weights Two scenario weights described in Section 2.1 are used to incorporate precipitation and temperature of multiple future scenarios, which can be expressed in Eqs. (12) and (13), respectively, and then the combined precipitation and temperature are input into a hydrological model to generate the synthesized streamflow, which can be described in Eq. (14). This is simplified as (II) in other parts of this paper. The synthesized precipitation and temperature are presented as follows: S
Pre syni; j ¼ ∑ ωk Prei; j;k k¼1
S
Temp syni; j ¼ ∑ ωk Tempi; j;k k¼1
ð12Þ
ð13Þ
where Pre _ syni, j and Temp _ syni, j are the synthesized precipitation and temperature of multiple scenarios, respectively; ωk is the k-th scenario weight, which is determined in Section 2.1; and Prei, j, k and Tempi, j, k are the precipitation and temperature of the i-th time step in the j-th year under the k-th scenario, respectively. The synthesized streamflow is produced by a hydrological model based on precipitation and temperature: ð14Þ Q syni; j ¼ f Pre syni; j ; Temp syni; j where Q _ syni, j is the synthesized streamflow of the i-th time step in the j-th year; and f() represents the relationship among precipitation, temperature and streamflow in the hydrological model. In this paper, a two-parameter monthly water balance model (Xiong and Guo 1999) is selected to generate streamflow.
2.3.2 Derivation of AOR on the Basis of the Synthesized Streamflow The two synthesized streamflows generated based on the two scenario weights are input into the reservoir operation model with the objective of maximizing the average annual
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hydropower generation, respectively. The optimization objective can be shown in the following equation: MaxE syn ¼
1 M N ∑ ∑ Pi; j Δti; j M j¼1 i¼1
ð15Þ
where E _ syn is the mean annual hydropower generation based on the synthesized streamflow; and other variables are the same as those in Section 2.2.1. The constraints in the reservoir operation model are the same as those in Section 2.2.2, but the only difference exits in the removed scenario subscript k due to unique model input. In addition, the linear description in Eq. (11) is also used in AOR based on the synthesized streamflow. And EW-AOR(II) and REA-AOR(II) are also derived using SBO with the Complex algorithm described in Section 2.2.4. More importantly, the parameters (ai and bi) of EW-AOR(II) and REA-AOR(II) reflect the reservoir decisions on the basis of synthesized streamflow, which differ significantly from results of EW-AOR(I) and REA-AOR(I) for all scenarios. In order to obtain operational results under multiple future scenarios, EW-AOR(II) and REA-AOR(II) are used in the simulation under each future scenario.
3 Case Study 3.1 Study Area and Data 3.1.1 The Jinxi Reservoir The Jinxi Reservoir is situated on the Yalong River of the upstream Yangtze Basin in Sichuan Province of China (Fig. 2). It has a drainage area of 102,560 km2 with a mean annual runoff at the dam site of approximately 4 × 1010 m3/yr. The dead water level is 1800 m mean sea level (msl), and the dead storage capacity is 28.5 × 108 m3. The normal pool water level is 1880 m, and the conservation storage capacity is 77.65 × 108 m3. The reservoir water level in flood season from July and August is kept at 1859 m to reduce flood risk of the downstream basin. There are 6 sets of 600 MW hydraulic turbo generators with a total installed capacity of 3600 MW, and a large proportion of its electricity is supplied to the southwestern China. The electricity output (kW) is calculated by Eq. (6) with η = 8.5, Ri, j, k in m3/s and Hi, j, k in meter. Since the total evaporation loss in the Jinxi Reservoir basin is much lower than the mean annual runoff, the corresponding term in Eq. (7) can be omitted. The minimum water level of the Jinxi Reservoir is 1800 m, while the maximum water level is 1859 m in July and August and 1880 m in other months. Both the initial and the final water levels are set to 1880 m (maximum) in the reservoir operation model. The maximum reservoir release is 15,400 m3/s due to the limited capacity of reservoir spillway, and the maximum electric power release is 2024 m3/s for hydraulic turbo generators.
3.1.2 Data Historical monthly temperature and precipitation of the Jinxi Reservoir basin from June of 1953 to May of 2003 are collected from the Climate Research Unit at a spatial resolution of 0.5° × 0.5° (https://crudata.uea.ac.uk/cru/data). And historical monthly inflow observations
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Fig. 2 The location of the Jinxi Reservoir and its basin
over the same period are directly collected. The future period from 2023 to 2073 is selected in this study, and future climate conditions (precipitation and temperature) are projected by the Coupled Model Intercomparison Project Phase 5 (CMIP5) models (http://cmip-pcmdi.llnl. gov/cmip5/index.html) based on the Representative Concentration Pathway 4.5 scenario (RCP 4.5) (Moss et al. 2010). Moreover, the Bias Correction and Spatial Disaggregation Method (BCSD) (Wood et al. 2004) is adopted for downscaling and bias correction at the regional scale. As a result, ten GCMs are selected in this study, including access1-0, canesm2, cesm1cam5, csiro-mk3-6-0, gfdl-esm2m, giss-e2-r, hadgem2-ao, ipsl-cm5a-lr, miroc5, and mpi-esmlr, which are referred to as Scenario 1 (S1) to Scenario 10 (S10), respectively. And two criterions are used to evaluate the simulation ability of selected GCMs, including the root mean square error (RMSE) and correlation coefficient (CC) with respect to precipitation and temperature. Results indicate that: (1) the RMSE for all future scenarios lies in the small range of [20, 24] for precipitation (mm) and [1.3, 1.5] for temperature (°C); and (2) the CC for all future scenarios is higher than 80% for precipitation and 95% for temperature, respectively. Thus, all selected scenarios can be used for future projections. Since streamflow directly depends on precipitation and evapotranspiration, the Hargreaves method (Hargreaves and Samani 1982) is used to convert temperature into potential evapotranspiration. A two-parameter monthly water balance model (Xiong and Guo 1999) is used to
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generate streamflow, i.e., inflow projections. This hydrological model is calibrated in the period from 1953 to 1988 and then validated in the following 15 years. And the NashSutcliffe efficiency coefficient (NSE) and the Relative Error (RE) are given to evaluate the hydrologic model. As a result, the NSE is 92.25 and 92.03%, and the RE is −0.63 and 2.04% in the calibration and validation periods, respectively. It consequently indicates that streamflows can be well projected under future scenarios using the two-parameter monthly water balance model with trained parameters. Figure 3 shows the average annual changes in the precipitation ratio, temperature difference and inflow ratio of the 10 collective future scenarios in the future period compared with that in the historical period. Clearly, the precipitation is increased from 0.15% to 14.14% and temperature is increased from 1.6 to 2.5 °C, and thus the inflow varies between −3.48% and 15.52%.
3.1.3 Historical Operating Rules (HOR) Historical operating rules (HOR), which are established in the stationary condition, are introduced as a comparative benchmark. The derivation of HOR is similar to AOR(II), while the difference exists in the fact that historical inflow and maximum historical benefits severe as the input and the optimization objective of reservoir operation, respectively. The description of HOR is the same as Eq. (11), and the SBO is also used to obtain the parameters of HOR. In order to evaluate performance of HOR, HOR is used for simulation under selected 10 future scenarios.
3.2 Results 3.2.1 Scenario Weights Based on the Two Weighing Methods Figure 4 presents the scenario weights of the equality and the REA method. Figure 4a shows significantly distinct reliability factors for precipitation and temperature under 10 selected future scenarios. The reliability factor of precipitation/temperature can be indicative of the
Fig. 3 Average annual changes of 10 collective future scenarios relative to the historical period
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Fig. 4 Results of the REA method. a The reliability factor of precipitation and temperature for each scenario; and b equal weights and unequal weights based on the REA method
ability of GCMs in simulating historical conditions and projecting future climate change. With regard to precipitation, four scenarios, including S1, S4, S5 and S6, perform better than others; whereas in terms of temperature, scenarios with a reliability factor over 0.10 accounts for more than half of the selected scenarios. Thus, different scenarios have different reliability levels for historical simulation and future change projections in terms of precipitation and temperature. And Fig. 4b clearly presents that scenario weights based on the REA method differ from equal weights. As shown in this figure, there are four scenario weights more than 0.10, including S1, S5, S6, and S10. Since the scenario weight based on the REA method is the average of the reliability factors of precipitation and temperature, it can balance the reliability of precipitation and temperature for each scenario.
3.2.2 Parameters for Four AORs In this study, two reservoir operation models are established to derive AORs (i.e., EW-AOR(I) and REA-AOR(I) vs. EW-AOR(II) and REA-AOR(II)): (1) the objective of the first reservoir
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operation model is to maximize the weighted average of hydropower generation of all future scenarios; and (2) that of the second model is to maximize the mean annual hydropower generation for the synthesized streamflow. The SBO method with the Complex algorithm is used to determine the optimized parameters of AOR in both reservoir operation models. The range of ai and bi for each time step is set to [−50, 150] and [−4000, 3000], respectively. The intervals of these two parameters are obtained based on the deterministic optimization model with inflow of individual scenario as the input and the linear fitting method. The parameter intervals for ai and bi take all collective scenarios into account. Parameter optimization is performed on the basis of different initial solutions, and then the best solution is selected as the parameter set of AOR. Table 1 lists the results of optimal parameters (a and b) for EW-AOR(I), REA-AOR(I), EWAOR(II), and REA-AOR(II), respectively. There is a similar change trend with time among the four AORs, and the parameter intervals of the four adaptive operation schemes lie in the range of [0, 50] for a and [−4000, 2600] for b. However, those AORs considering all future scenarios (EW-AOR(I) and REA-AOR(I)) have more values in parameter ∣a∣ but less values in parameter ∣b∣ compared with those AORs based on synthesized streamflow (EW-AOR(II) and REA-AOR(II)). It may result in different operational results for the four AORs.
3.2.3 Hydropower Benefits of Five Operation Schemes Hydropower Generation The objectives of both EW-AOR(I) and REA-AOR(I) are to maximize the weighted average of hydropower generation of all future scenarios, whereas those of both EW-AOR(II) and REA-AOR(II) are to maximize the mean annual hydropower generation for the synthesized streamflow. Thus, all future scenarios have been used for the calibration of EW-AOR(I) and REA-AOR(I), and furthermore historical observations are needed for the validation of AOR(I). However, in order to compare the four AORs, EWAOR(II) and REA-AOR(II) have to simulate the respective process of reservoir operation under each future scenario and historical condition. Table 2 shows the mean annual hydropower generation of HOR and four AORs in the historical stationary condition. It can be seen that: (1) all AORs underperform HOR, since HOR and AORs are derived based on historical inflow and future projections, respectively; (2) Table 1 Parameters of the four AORs Time
Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.
EW-AOR(I)
EW-AOR(II)
REA-AOR(I)
REA-AOR(II)
a
b
a
b
a
b
a
b
37.34 43.16 37.34 51.07 22.36 4.21 22.74 37.24 40.72 37.34 38.58 37.34
−2899.00 −3224.36 −2899.12 −2314.38 2392.22 1192.90 −1269.19 −2448.99 −3791.81 −2899.03 −2996.22 −2898.98
36.29 40.47 36.21 41.86 8.58 1.17 20.20 36.55 39.62 34.26 38.58 35.34
−2957.92 −3282.26 −2963.49 −2674.44 1799.49 1027.87 −1584.36 −2533.67 −3952.33 −2929.90 −3368.78 −3058.82
36.99 43.85 37.34 55.02 27.54 5.86 23.49 37.45 41.22 37.34 38.58 37.34
−2910.80 −3193.29 −2899.05 −2178.21 2599.26 1303.81 −1163.39 −2412.22 −3698.25 −2899.14 −2995.89 −2899.06
36.27 40.40 36.19 41.62 8.21 1.07 20.12 36.54 39.59 34.20 38.58 35.30
−2959.14 −3284.02 −2964.84 −2683.86 1785.40 1020.94 −1594.30 −2535.91 −3957.89 −2930.54 −3376.55 −3062.15
Identifying the Relationship between Assignments of Scenario show... Table 2 Comparison of hydropower generation among HOR and four AORs under historical and future conditions Scenario type
Historical observation Future scenarios Average S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
Mean annual hydropower generation (108 kWh) & Its relative change (%) HOR
EW-AOR(I)
EW-AOR(II)
REA-AOR(I)
REA-AOR(II)
176.17 184.90 181.57(−) 193.04(−) 193.88(−) 178.14(−) 179.87(−) 178.30(−) 180.19(−) 189.41(−) 192.23(−) 182.35(−)
175.45 185.67 (0.36) (0.28) (0.42) (0.76) (0.47) (0.46) (0.36) (0.42) (0.41) (0.24)
176.16 184.98 (0.39) (0.11) (0.15) (−0.28) (−0.48) (0.18) (0.26) (0.43) (−0.21) (−0.15)
176.14 185.57 (0.48) (−0.45) (−0.41) (0.26) (1.36) (1.15) (−0.02) (0.01) (0.04) (1.35)
176.10 184.92 (0.35) (0.06) (0.11) (−0.34) (−0.51) (0.21) (0.27) (0.39) (−0.27) (−0.19)
REA-AOR(I) produces much more (0.69 × 108 kWh) hydropower than EW-AOR(I), while EW-AOR(II) produces slightly more (0.06 × 108 kWh) hydropower than REA-AOR(II); and (3) REA-AOR(I) outperforms REA-AOR(II) with little more hydropower generation of 0.04 × 108 kWh, while EW-AOR(I) underperforms EW-AOR(II) since the former produces 0.71 × 108 kWh less than the latter. Additionally, Table 2 also presents the mean annual hydropower generation under each future scenario, in which the hydropower generation for all future scenarios is averaged in order to test the mean adaptability of operating rules under uncertain climate change. As a result, the AOR’s overall performances are better than HOR under climate change. Moreover, both of EW-AOR(I) and REA-AOR(I) have better adaptability than EW-AOR(II) and REA-AOR(II), since all future scenarios are considered in the derivation of AOR(I). In order to evaluate the hydropower generation among four AORs, the change relative to HOR under each corresponding future scenario are considered in Table 2 shown in the brackets. Compared with HOR, EW-AOR(I) can improve the hydropower benefit for each scenario, while EW-AOR(II), REA-AOR(I), and REA-AOR(II) could obtain higher hydropower generation under 60, 70 and 60% of the selected scenarios, respectively. And the number of scenarios where the relative increase/decrease change occurs, is same for both EWAOR(II) and REA-AOR(II), but the former has larger increases (0.11–0.43%, averagely more than REA-AOR(II) by 0.04%). and smaller decreases changes (0.15–0.48%, averagely less than REA-AOR(II) by 0.05%). Generally, REA-AOR(I) and EW-AOR(II) can balance hydropower generation for both historical and future conditions, and thus they can serve as the benchmark in adaptive reservoir operation, especially considering an ensemble of GCMs.
Assurance Rate of Hydropower The assurance rate of hydropower generation (indicative of the reliability of hydropower generation of a reservoir) is also evaluated in this study. Since this indicator is not considered in the optimization objective, it can reflect the inherent hydropower reliability of an operating rule. It is calculated by recording the number of time steps when hydropower output meets the requirement of firm output (Hashimoto et al. 1982; Ming et al. 2017). The results of the assurance rate of
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hydropower generation are shown in Fig. 5. It presents that EW-AOR(II), REA-AOR(I) and REA-AOR(II) perform more reliably than HOR under each future scenario, despite their underperformances compared with HOR in the historical condition. Among four AORs, it indicates that EW-AOR(I) and REA-AOR(I) have the lowest and highest hydropower reliabilities, respectively, and the hydropower reliability of EW-AOR(II) equals that of REA-AOR(II).
3.2.4 Uncertainty Control for Four AORs Given the same input uncertainty for the four AORs in simulating reservoir operation under future climate change, the uncertainty in the outputs can indicate their ability to perform robustly and withstand the impact of unknown climate change. Thus, the lower the output uncertainty is, the higher the robustness an AOR will have (Haguma et al. 2015; Herman et al. 2015; Zhang et al. 2017a). The operating rule with higher robustness could be more likely to avoid potential losses in the context of climate change, which essentially demonstrates the adaptability of the operating rule. Figure 6 shows the comparison of the monthly uncertainties in reservoir storage and reservoir surplus for EW-AOR(I), EW-AOR(II), REA-AOR(I), and REA-AOR(II) during the future period. The median and interquartile range (25 to 75%) for all future projections are also shown. In addition, the uncertainty range is indicated by the maximum and minimum uncertainty values. It can be seen in Fig. 6 especially in its gray area that REA-AOR(I) has the most robust performance in both reservoir storage and unproductive spill, while EW-AOR(II) performs poorest. For reservoir storage, both EW-AOR(I) and REA-AOR(I) have lower uncertainties compared with EW-AOR(II) and REA-AOR(II), respectively. Additionally, REA-AOR(I) and REA-AOR(II) perform more robustly than EW-AOR(I) and EW-AOR(II), respectively. The
Fig. 5 Comparison of assurance rate of hydropower from five operation schemes in the historical and future condition
Identifying the Relationship between Assignments of Scenario show...
(1) Reservoir Storage
(2) Reservoir Surplus Fig. 6 Comparison of uncertainty range in (1) reservoir storage and (2) reservoir surplus, among (a) EW-AOR(I), (b) EW-AOR(II), (c) REA-AOR(I), and (d) REA-AOR(II) under all future scenarios
second subfigure of Fig. 6 shows that EW-AOR(I) and REA-AOR(I) are better able to resist uncertainties of unproductive spill, when relative to EW-AOR(II) and REA-AOR(II), respectively. And REA-AOR(I) has lower surplus uncertainty than EW-AOR(I). It simultaneously should be noticed that the uncertainty level of reservoir surplus is similar for EW-AOR(II) and REA-AOR(II). Therefore, REA-AOR(I) is the best choice under multiple future change scenarios due to its good ability to control uncertainty. However, EW-AOR(II) is less robust, despite its good economic benefits under an ensemble of scenarios.
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3.3 Discussion The hydropower generation (listed in Table 2) is related to both locating and assigning approaches of scenario weights. Unequal scenario weights based on the REA method are preferable in AOR(I), because REA-AOR(I) can not only be applied under stationary conditions, but also have good adaptability under future scenarios. Nevertheless, equal scenario weights are more suitable for AOR(II), since EW-AOR(II) can produce more hydropower under both historical and future scenarios. Besides, the assignment of scenario weights exerts significant impacts on the assurance rate of hydropower generation of AOR(I), but little on that of AOR(II). To be more specific, scenario weights based on the REA method promote the hydropower reliability in AOR(I), while the opposite is observed for equal weights. Uncertainty control (shown in Fig. 6) represents the robustness of an operating rule under uncertain climate change. It can be indicated that: AOR(I) is more robust than AOR(II), and unequal scenario weights of the REA method are better able to improve the robustness of operating rules than equal scenario weights (EW). Besides, the operational process is distinct between AOR(I) and AOR(II) regardless of the scenario weights, as shown in Fig. 6. It attributes to the impact of parameters of operating rules on the reservoir decisions. The further reason is that the two different use positions of scenario weights determine differences in optimization objectives and inputs of the reservoir operation models. Thus, the operational process depends much more highly on where scenario weights are used than on how weights are assigned. It is evident that scenario weights should be used in the optimization objective of the reservoir operation model (saying AOR(I)), for it can take the benefit of all future scenarios into consideration. This approach helps to obtain more and balanced hydropower generation as well as higher robustness of reservoir decisions. In addition, unequal scenario weights based on the REA method can remarkably improve the performance of AOR(I) in hydropower generation and robustness during the future period. Although equal scenario weights (EW) can slightly facilitate AOR(II) to generate more hydropower under both historical conditions and future projections, EW sacrifices the robustness of AOR(II). Chen et al. (2017) investigated the impacts of weighting climate models for hydrometeorological climate change studies. Their results illustrated that weighting GCMs had a limited impact on not only projected future climate described via precipitation and temperature changes but also hydrology based on nine different streamflow criteria. Therefore, they supported the view that climate models should be considered equiprobable. The comparison between EW-AOR(II) and REA-AOR(II) in this study agrees well with the work of Chen et al. (2017). Moreover, Steinschneider and Brown (2012) used a scheme similar to EW-AOR(II) as a comparative adaption benchmark, and their work demonstrated the applicability of EWAOR(II) in adaptive reservoir operation.
4 Conclusions This study focuses on identifying the relationship between assignments and positions of scenario weights in the derivation of reservoir operating rules under climate change. Equal weights and unequal ones based on the REA method are chosen as scenario weight assignments. These two weighing methods are used into the optimization objective of the reservoir operation model and the combination of precipitation and temperature of multiple scenarios,
Identifying the Relationship between Assignments of Scenario show...
respectively. And then, four AORs, including EW-AOR(I), REA-AOR(I), EW-AOR(II) and REA-AOR(II), are obtained, and their optimized parameters are determined by the SBO method with the Complex algorithm. Their performances in the Jinxi Reservoir (i.e., mean annual hydropower generation, hydropower assurance rate, and uncertainty control) are compared. Some conclusions can be drawn as follows: (1) Equal weights are preferably used to incorporate climate conditions, while unequal weights based on the REA method can better improve the performance of the reservoir operation model. (2) The parameters and operational processes for both AOR(I) and AOR(II) are mainly determined by the position of scenario weights, and the hydropower generation and robustness of both AOR(I) and AOR(II) can be affected by how scenario weights are assigned. The REA method have a positive effect on AOR(I), while EW leads to a slight improvement of hydropower generation but a decrease of robustness of AOR(II). (3) REA-AOR(I) and EW-AOR(II) can balance hydropower generation for both historical and future changes. Unequal weights can increase the hydropower reliability of AOR(I), while the opposite is observed for equal weights. However, scenario weighing method has no effect on the hydropower reliability of AOR(II). (4) REA-AOR(I) performs best in the uncertainty control of reservoir storage and unproductive spill, while EW-AOR(II) performs worst. Both EW-AOR(I) and REA-AOR(I) can be better able to control uncertainties of operational outputs compared with EWAOR(II) and REA-AOR(II). Therefore, REA-AOR(I) and EW-AOR(II) are preferably used in the reservoir operation under climate change. In future studies, it is necessary to consider other weighing methods, such as representation of the annual cycle (RAC) (Christensen and Lettenmaier 2007) and upgraded reliability ensemble averaging (UREA) (Xu et al. 2010). Additionally, more studies should be conducted in other reservoirs to verify the results of this study. Acknowledgements The authors would like to thank the editor and anonymous reviewers for their valuable suggestions, which helped to improve the quality of the paper. This study was supported by National Key Research and Development Project (2016YFC0402208), National Natural Science Foundation of China (Grant No.51709276) and National Key Technology R&D Program (2015BAB07B03).
Compliance with Ethical Standards Conflict of Interest The authors declare that they have no conflict of interest.
Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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Affiliations Wei Zhang 1 & Xiaohui Lei 2 & Pan Liu 1 & Xu Wang 2 & Hao Wang 1,2 & Peibing Song 3 1
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
2
State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China
3
College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
