Assessing the reliability, resilience and vulnerability of water supply system under multiple uncertain sources

Journal of Cleaner Production 252 (2020) 119806

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Assessing the reliability, resilience and vulnerability of water supply system under multiple uncertain sources Kang Ren a, Shengzhi Huang a, *, Qiang Huang a, Hao Wang b, Guoyong Leng c, Wei Fang a, Pei Li a a

State Key Laboratory of Eco-Hydraulics in Northwest Arid Region of China, Xi’an University of Technology, Xi’an, 710048, China State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing, 100038, China c State Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, 100101, China b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 3 September 2019 Received in revised form 14 November 2019 Accepted 18 December 2019 Available online xxx

Water reservoirs often contain multiple runoff water sources, each of which is affected by a variety of uncertainties. The encounter situation defined in multiple water sources is the imbalance spatialtemporal distribution of water resources, which has a profound impact on the risk of water scarcity. This study presents a framework to evaluate the performance of a water supply system considering the encounter situations between different water sources. Based on the Han to Wei Inter-Basin Water Transfer (IBWT) project in the Shaanxi Province of China, the synchronous and asynchronous encounter probabilities are calculated using copula-based approach to characterize the encounter risks for water supply. Then, the synthetic monthly series of different water sources are generated through a synthetic streamflow-generated method based on the simulated annealing algorithm and fragment method, which is applied as the input variables of a reservoir optimization operation model. The metrics of reliability, resilience, and vulnerability are used to evaluate the performance of the water supply system. Results indicate that (1) regardless of whether the annual flow series is a full sequence or a pre- or post-changed sequence, the encounter probabilities between different water sources remain stable. However, there are obvious changes in the encounter probabilities of each month between different water sources; (2) The generated monthly flow series effectively preserves the internal composition of the historical data, which are adequate to evaluate the performance of the water supply system; (3) as the water demand increases, the reservoir’s storage capacity decreases, and the reliability of the water supply depends on the wet encounter situations for different water sources; (4) the ability to describe the states of the system varies significantly according to the metrics selected, and the choice of the metrics of reliability, resilience (max), and vulnerability (mean) can adequately describe the states of the water supply system. This study appropriately constrained the uncertain inputs of the reservoir operation model to improve the credibility of decision making. © 2019 Elsevier Ltd. All rights reserved.

^ as de Handling editor:Cecilia Maria Villas Bo Almeida Keywords: Uncertainty Encounter risk Synthetic runoff generator Water resources management

1. Introduction The exploitation and utilization of water resources by humans are affected by the planning and construction of various water conservancy projects. Presently, the infrastructure planning and water resources management of almost all projects are based on the assumption of hydrological stationarity (Hui et al., 2018).

* Corresponding author. E-mail address: [email protected] (S. Huang). https://doi.org/10.1016/j.jclepro.2019.119806 0959-6526/© 2019 Elsevier Ltd. All rights reserved.

However, climate change and intensifying human activities have changed the stationarity of hydrometeorological series (e.g. precipitation and runoff) (Han et al., 2019). The nonstationarity causes the increased uncertainty of human exploitation and utilization of water resources, followed by the increased potential for a loss of engineering-related benefits (e.g. water supply, flood control, and hydropower generation) (Milly et al., 2008; Min et al., 2013; Cheng and Aghakouchak, 2014). In the future, the dependence of population growth and urbanization on water resources will be further increased (Lu et al., 2016; Moran et al., 2018; Liu et al., 2017; Best,

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K. Ren et al. / Journal of Cleaner Production 252 (2020) 119806

2019), which subsequently leads to higher risks of water scarcity. Therefore, a key challenge of water resources management is to determine how to evaluate the reliability and vulnerability of water-related projects within the context of climatic uncertainties (Poff et al., 2016; Di Baldassarre et al., 2018). In water resource system analysis, the uncertainties are derived from the decision makers’ inability to adequately describe the alternative states of the world for quantizing possible risks of the system (Kasprzyk et al., 2012; Brown et al., 2015). To model a water supply system, the uncertainties include future water demand and supply growth, decision makers’ preferences, system structure, and incomplete input information. There are varying degrees of difficulty associated with these uncertainties in the system. First, the uncertainty of water supply is easily resolved because the water supply growth can be constrained between maximum and minimum water supply capacities of the system. Second, the decision makers’ preferences represent the optimistic/pessimistic attitudes of decision makers, which should be matched with their information needs (Giuliani and Castelletti, 2016; Quinn et al., 2019). Moreover, the inertia and myopia of decision makers in water resource management can be reduced by reasonably constructing the model’s formulation using multiple objectives and robust decision making (Kasprzyk et al., 2012; Giuliani et al., 2014; Ren et al., 2019a). Finally, the input information associated with the variability of hydrometeorological conditions is affected by various forcing factors, which cannot be precisely predicted using existing model and statistic methods (Shi et al., 2018). The weak predictability of input information is the most critical challenge which limits the application of water operation models in practice. Presently, water resource management has become a risk-based decision-making process under the deep uncertainties of input information (Wang and Blackmore, 2009; Burls and Fedorov, 2017; Hariri-Ardebili, 2018). In summary, reducing the uncertainties of input information will determine whether water management models can be used to support water management decisions. Although the assertion that ‘stationarity is dead’ has received many responses (Milly et al., 2008, 2015; Grafton et al., 2013; Bhave et al., 2016), the input information of existing water resource planning and management still depends on the hydrological frequency analysis of historical time series. The limitation for decision makers in the use of hydrological frequency analyses is that the historical streamflow sequences are parts of the whole sequences, and they do not represent the full conditions of streamflow. The uncertainty of historical time series can be reduced by making sufficient observations and efficient estimations. However, it is difficult for this limitation to be handled by traditional frequency analyses in a changing environment. Fortunately, the synthetic hydrology, which is a tool for sampling and expanding the user-specified characteristics of historical streamflow distributions, can be used to explore the performance of water resource systems under the deep uncertainties of streamflow (Jackson, 1975; Vogel and Stedinger, 1988; Borgomeo et al., 2015). Therefore, to reduce the uncertainty of input information, the key challenge becomes appropriately limiting the possible range of streamflow conditions. With the increasing user demand for the reliability of water resources in terms of quality and quantity, modern water supply systems often have multiple water sources (e.g. groundwater, surface water and desalinated water). Generally, water diversion projects are constructed when local water resources cannot meet these user requirements (Barnett et al., 2015). Owing to spatial variations between the diverted region and the benefiting region with respect to climatic conditions, hydrologic characteristics and human activities, there are also significant differences in the water resources

between them. In general, this difference becomes more pronounced as the spatial distance increases. If both regions are experiencing the wet season, the water demand of the benefiting region can be met easily, and vice versa. The ideal benefits of diversion projects can be achieved when the water resources of these two regions are in the wetness-dryness alternation. Therefore, the concept of a wetness-dryness encounter situation can be defined as ‘the combined event of dry and wet in different regions that is the result of the imbalance spatial-temporal distribution of water resources’ (Yuan et al., 2017). Wetness-dryness encounter situations are called asynchronous events, and wetness-wetness or dryness-dryness encounter situations are called synchronous events. These encounter situations exist not only in water diversion projects, but also in water supply systems with multiple water sources, which provide a comprehensive insight into the spatialtemporal distribution of water resources. The presence of multiple water sources leads to the problem of multi-process from climate- or human-related uncertainties to water resource systems (Borgomeo et al., 2016; Quinn et al., 2018). Herman et al. (2016) generated an artificial drought scenario using the streamflow generation method developed by Kirsch et al. (2013) to assess the urban water supply vulnerability of North Carolina, USA. Although their method intended to preserve the temporal autocorrelation of historical streamflow at each site as well as the spatial cross-correlation of historical streamflow between sites, the cross-correlations are biased slightly low in the logarithmic domain and cannot be exactly reproduced (Herman et al., 2016, see Fig. 4j and k). As reported by Herman et al. (2016), the question of bias in the cross-correlations is not easily resolved because changing one characteristic of streamflow inevitably results in undesired changes to the other characteristics. However, Trindade et al. (2017), Zatarain Salazar et al. (2017), and Quinn et al. (2019) adapted this method in their studies, which also neglected the question of bias. These studies failed to recognize that the synchronous and asynchronous encounter situations between different water sources have significant impacts on the risk of water scarcity. Considering the probability of encounter situations for a water supply system, it is important to determine how the reasonable time sequences can be generated to assess the performance of the system under deep uncertainties. The copulabased approach can combine two or more-dimensional time se€ lzel and Friederichs, 2008), quences into a joint distribution (Scho which can be used to calculate the probability of encounter situations between them. Therefore, our study uses the copula-based approach to more accurately reveal the spatial-temporal crosscorrelations (i.e. encounter situations) between different water sources, which are incorporated with the streamflow generated method to obtain more comprehensive input information and reduce the multiple uncertainties. In summary, the existing hydrological frequency analysis is not ideally suited for assessing the performance or risk of a water supply system. The streamflow-generated method incorporated with the copula-based approach, which considers the useful information (e.g. encounter situations) of multiple water sources, may provide an option to more reasonably limit the plausible range of input data. Hence, in this study, a framework is presented to evaluate the performance of a water supply system considering the encounter situations between different water sources. This paper is organized as follows. In Section 2, we describe the study area and formulate the problem for demonstrating our framework. In Section 3, we introduce our proposed framework for evaluating the performance of a water supply system under multiple uncertain sources. In Section 4, we present the results obtained after applying our framework, and in Section 5, we discuss the availability and final impacts.

K. Ren et al. / Journal of Cleaner Production 252 (2020) 119806

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2. Study area and problem description The Wei River, which is a monsoonal river system, is the largest tributary of the Yellow River basin, covers an area of 134,766 km2 and receives an average annual precipitation of 500e800 mm, which supports the greatest water demand of the Guanzhong Plain of Shaanxi Province, China. The Plain has 64% of the population, 56% of the arable land, 72% of the irrigated area, and accounts for 82% of the gross domestic product (GDP) of Shaanxi Province. The Wei River supplies water resources for a total population of 22 million in 76 major cities of the Guanzhong Plain, including drinking, industrial, and irrigated water demand. Over the past decades, population growth and urbanization have significantly increased the usage of water resources from the Wei River; meanwhile, several serious drought events have occurred in the Guanzhong Plain (Chang et al., 2015; Huang et al., 2017; Huang et al., 2019; Fang et al., 2019; Zhang et al., 2019). Owing to the impact of climate change and human activities, water shortage in the Wei River basin is likely to deteriorate further, and the risk of water shortage will profoundly affect human survival in the Guanzhong Plain (Zhao et al., 2019a). Within the last 10 years, efforts have been made by the government to reduce water shortage by constructing the Han to Wei inter-basin water transfer (IBWT) project. This project is the most significant water transfer project in the Shaanxi province, and there are plans to divert an annual average water of 1,000 and 1,500 million m3 (MCM) from the Han River basin to the Wei River basin in 2025 and 2030, respectively. In the years of abundant water resources, the maximum water transfer capacity of the project will be limited to 2,200 MCM by the water transfer pipelines. The main infrastructures of the project include the Huangjingxia reservoir and the Sanhekou reservoir; the former is located in the main stream of the Han River, and the latter is located on a tributary of this river. Both reservoirs are the water sources of the project, and they are connected by pumping stations and pipelines (Fig. 1). However, the Han River has been used as an important source of the South-to-North water transfer project (the world’s largest IBWT project). The transferable water of the Han to Wei IBWT project is projected by the Changjiang Water Resources Commission (CWRC) to be 2,200 MCM in wet years and 700 MCM in dry years. Therefore, the Han to Wei IBWT project will not satisfy the water demand of the Wei River basin in 2030, and a new water transfer project, i.e. the Jialing to Han IBWT project has been proposed by the government as a means of complementing the shortage proportion of water demand. As shown in Fig. 1, the point of diversion (POD) of the new project is located in the upper reach of the Jialing River, which will divert water from the Jialing River to the Han River (Ren et al., 2019b). In the future, the two projects will form a water supply system that undertakes the task of supplying water to the Guanzhong Plain. The formed water supply system will have three water sources, namely, the Huangjinxia reservoir, the Sanhekou reservoir and the available water at the POD. Owing to the geographical locations of the three sources, there are significant differences in the distribution of their water resources. Furthermore, the planning and construction of these projects is based on the deterministic runoff series, and their water supply plans and volumes have been pre-determined. In recent years, the runoffs from these rivers have shown a decreasing trend, and the uncertainty of their runoffs may increase in coming decades. Therefore, the key challenge of water management for the water supply system is to evaluate the robustness of the pre-determined plans under the multiple uncertain water sources. In this study, the monthly streamflow data of the three water sources are collected from the CWRC for the period of 1956e2010. To solve this challenge, the detailed analysis is presented in the following section.

Fig. 1. Map of the Wei River Basin, the Han River Basin, and the Jialing River Basin, and the components of the Han to Wei inter-basin water transfer project. The Danjiankou reservoir is the main water source of the mide line of the Sourth to North water transfer project.

Fig. 2. Flow chart of the methodologies of this study.

3. Methodologies In this section, we introduce several primary methods that are used to construct the evaluation framework. The copula-based approach is used to analyse the encounter situations between different water sources. The synthetic runoff generator method is employed to generate a set of monthly runoff time series with a wide range of climatic uncertainty. Moreover, a reservoir operation model for water supply is established to simulate the performance of the water resource system based on the generated monthly

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K. Ren et al. / Journal of Cleaner Production 252 (2020) 119806

Hðx1 ; :::; xd Þ ¼ C½F1 ðx1 Þ; :::; Fd ðxd Þ

Fig. 3. The differences of the synchronous encounter probabilities of the month flow under different water sources, (a) the Huangjinxia reservoir month inflow and the Sanhekou reservoir month inflow; (b) the Huangjinxia reservoir month inflow and the Lueyan POD month streamflow.

Fig. 4. Comparing the differences of the synchronous encounter probabilities of the month flow in the pre- and post-change point.

runoff. Finally, the reliability, resilience and vulnerability of the water supply system under multiple uncertain sources are specified in this study, and they can indicate the performance of the system and assist decision makers to efficiently manage water resources. The main steps of our framework are depicted in Fig. 2.

3.1. Copula-based approach Copulas are based on the coupling theory and are widely used in € lzel and Friederichs, 2008; Zhao et al., the hydrological field (Scho 2019b), such as flood risk analysis (Laux et al., 2009; Karmakar and Simonovic, 2009; Serinaldi, 2009), drought event assessment (Chanda et al., 2014) and streamflow simulation (Lee and Salas, 2011). The basic idea behind the copula-based approach is to synthesize multiple marginal distribution functions through the joint distribution function to become a function (Huang et al., 2014; Guo et al., 2019). Because this method was applied in hydrology, the hydrologic variables can be combined and analysed using this approach, which provides a comprehensive perspective for better understanding the internal mechanism of hydrological events. Copula’s theorem states that if H is a joint distribution function of d random variables with F1,…, Fd marginal distribution functions which are continuous, then a unique copula C exists and can be written as

(1)

The copula-based approach describes how the marginal distribution functions are tied together. This approach enables us to estimate the marginal distribution functions separately, and estimating the whole multivariate distribution requires a fitting process (e.g. goodness-of-fit tests) to identify the most appropriate copula from the copula families. In this study, based on this copulabased approach, the two-dimensional (2D) joint probability distributions of different runoff series are established to present the statistical characteristics of the synchronous and asynchronous encounter probabilities of a water supply system. For the values of a single flow series, if their cumulative frequencies are less than the low threshold frequency pf ¼ 25%, the states of the flow are classified as wet situations; if their cumulative frequencies are larger than the high threshold frequency pk ¼ 75%, the states of the flow are classified as dry situations, and the remaining states are classified as normal situations. The synchronous and asynchronous encounter situations between different flow series can be identified as states of these flow series which are in the same and different situations, respectively. If the marginal distributions of two flow series areFðxÞ andFðyÞ, respectively, the joint distribution function can be formulated asHðx; yÞ ¼ C½FðxÞ; FðyÞ. The synchronous and asynchronous encounter probabilities between different flow series can be calculated from the joint distribution function, and the detailed encounter probability representations are presented in Table A1 (Appendix A). Actually, the analysis of encounter situations is consistent with correlation analysis for analyzing the correlation between different time series. The former can be used to analyse the correlation between different runoff sequences having specific magnitudes according to the widely used classification criteria of water years (e.g. wetness and dryness). Furthermore, the probability of the occurrence of a synchronous encounter situation between two time series is higher, and their positive correlation is more obvious, and vice versa.

3.2. Synthetic streamflow generation method Synthetic hydrology has been widely used in water resource system analysis, which expands the set of plausible hydrological time series by the sampling of hydrological variability. The development history of synthetic streamflow generation methods is from the classical autoregressive models to the non-parametric methods (e.g. block bootstrapping and k-nearest neighbor resampling) (Hao and Singh, 2013), and then to the latest achievements (entropy theory-based methods and copula theory-based models) (Lee and Salas, 2011; Srivastav and Simonovic, 2014). All of these methods are based on the hypothesis of historical data stationarity (i.e. the future is going to be similar to the past). The reality of water resource systems analysis needs to extend beyond these methods and should be under a wider range of hydroclimate variables than historical data. Borgomeo et al. (2015) proposed a synthetic streamflow generation method which is based on a simulated annealing algorithm. This method allows for some user-specified runoff properties to be altered, while keeping unchanged some other important properties of the runoff distribution. The theoretical basis of this method is to consider the runoff generation as a combinatorial optimization problem for finding a time series which conforms to a statistical target (e.g. means, autocorrelation). This combinatorial optimization problem is solved by simulated annealing algorithm, which is generalized from the annealing process of metals (Scott, 1984). In simulated annealing, the states of metals at different temperatures denote

K. Ren et al. / Journal of Cleaner Production 252 (2020) 119806

different solutions of the combinatorial optimization problem, and the overall energy of the system is the objective function, which is minimized iteratively during optimization. The synthetic streamflow generation method reconstructs runoff time series with the simulated annealing algorithm to match a set of user-specified runoff properties, S ¼ {S1, S2,…Sk}. The objective function calculates the deviations between the target S and simulated properties Ss, which is formulated as 2

O¼

k   1X wk Sk  Ssk O0

(2)

k¼1

where k is the number of user-specified runoff properties, O0 is the initial value of the objective function, and wk is the weight factor of each property, which ensures the contribution of each component to the objective function. For detailed steps and an extended discussion of the method, the reader is referred to Borgomeo et al. (2015). In this study, the proposed method is used to generate the annual runoff time series. Although this method can be used to generate the runoff, which is impacted by the potential climate change, the purpose of this study is to address the problem of multiple water sources and match the different encounter situations. Therefore, the potential impact of climate change on runoff is not considered. To generate runoff time series that reproduce a wide range of runoff data, two components are selected in this study, that is, the autocorrelation coefficients and cross-correlation coefficients. The following sections introduce the specific steps for generating the runoff. First, the annual runoffs observed for the study area (the Han River, the Jialing River and the Ziwu River, from 1956 to 2010 in Section 2) are used to estimate the empirical distributions of the annual runoffs. Second, the no temporal dependence samples are sampled from the empirical distributions in order to establish the original datasets. Finally, depending on the selected components of the objective function and the datasets, the target runoff sequences can be generated using the simulated annealing algorithm. The objective function considered in this study can be formulated as

O¼

2  2 i 1 h  wI SI  SsI þ wC SC  SsC O0

(3)

where SI and SsI are the autocorrelation coefficients of the observed and simulated time series, respectively, SC represents the crosscorrelation coefficients of the observed time series, and SsC represents the cross-correction coefficients between the observed and simulated time series, wI and wC are the weight factors, which are set to 1 in this study. The runoff time series matching the set of desired properties are generated when the objective function O ¼ 0, or when the maximum number of iterations is reached. 3.3. Method of monthly disaggregation The generation method based on the simulated annealing algorithm is applied to generate synthetic series of the annual runoff with a length which is equal to that of the historical runoff series. However, the monthly runoff series is usually used for reservoir storage-yield design and reservoir operation simulation. In this study, the monthly runoff series are applied as the inputs to test the reservoir optimization model and to evaluate the performance of the water supply system. Therefore, the generated annual runoff series should be disaggregated into monthly runoffs. This disaggregation can be achieved by the method of fragments, which is

5

based on a purely deterministic approach (Silva and Portela, 2012). For this method, the size of the segmentation probability is based on the observed monthly flows, Xk, j, which are divided by the corresponding annual runoff volume, Xk. For a given year, k, a set of 12 standardized monthly runoff establishes the fragment, gk, which can be formulated as:

gk ¼

 Xk;j Xk;1 ¼ Xk Xk

Xk;2 Xk

:::

Xk;11 Xk

Xk;12 Xk

 (4)

where Xk, j is the monthly runoff (j ¼ 1, 2,…,12). If the observations span a total of N years, the fragments can be formed and assembled into a fragment matrix, g. In this matrix, the annual runoff volumes should initially be ranked from smallest to largest:

2

X1;1 6 2 3 6 X1 6 ::: g1 6 6 ::: 7 6 6 7 6 Xk;1 6 7 g ¼ 6 gk 7 ¼ 6 6 4 ::: 5 6 Xk 6 ::: 6 gN 6 4 XN;1 XN

::: ::: ::: ::: :::

3 X1;12 7 X1 7 ::: 7 7 7 Xk;12 7 7 Xk 7 7 ::: 7 7 7 XN;12 5 XN

(5)

After the fragment matrix is formed, the fragment gi can be used to disaggregate the synthetic annual runoff, Xi, into 12 monthly runoffs, Xi,j, that is,

Xi;j ¼ gi Xi

(6)

where i ¼ 1, 2, …, N and j ¼ 1, 2, …, 12. The key challenge of this method is to choose the suitable fragment criteria for disaggregating the synthetic annual runoff. There are many different criteria which can be used to define and select the fragment. In this paper, the criterion proposed by Srikanthan and McMahon (1980) is used to define the fragment of the synthetic annual runoff. With this criterion, the relationship between the monthly runoff and the corresponding annual runoff is considered. This criterion considers one class per fragment. The first class is the lower limit, which is set to zero, and the next class is obtained by averaging every two adjacent ranked values of annual runoff until the last class, which has no upper limit. In the approach of disaggregation, each year value of the generated annual runoff series is checked to define the class to which it belongs. Once the class is determined, the generated annual runoff can be disaggregated into monthly runoffs according to the corresponding fragment.

3.4. Water supply system operation model The operator is responsible for maximizing the water supply reliability (or minimizing the water supply deficit) of a water supply system (Giuliani and Castelletti, 2016; Lu et al., 2018). For this example, there are three water sources which belong to two reservoirs, and they are connected by water diversion pipelines to form a water supply system. This water supply system has a key node (Fig. 1). Depending on the water supply at this node, the operator can assess whether the water demands of users are being met. The key target of the water supply system is to minimize the water shortage experienced by users. Therefore, minimizing the water shortage index (SI) is selected as the only objective function, that is,

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K. Ren et al. / Journal of Cleaner Production 252 (2020) 119806

min

 ! D S T 1 X max W i  W i ; 0  100% SI ¼ T i¼1 WD i

The vulnerability can be expressed as the mean or maximum deficit volume which describes the severity of failure events, that is,

(7)

3 where W D i is the total demand of the water users in the node (m ), W Si is the actual water supplied for the water users (m3), T represents the number of operation periods for all years (month), and i is the index of operational periods (ith month). This model minimizes the water shortage of water users with the long-term monthly runoff series, for 1955e2010. The water balance equation, water storage capacity constraints and release constraints are selected in this model. For more information about these constraints, readers can refer to the literature (Ming et al., 2017; Ren et al., 2019a,b). To solve the operation model, the cuckoo search (CS) algorithm is applied in this study. The CS is a bio-inspired optimization algorithm that has been widely used to solve complex and nonlinear optimization problem (Yang and Deb, 2014).

3.5. Defining reliability, resilience, and vulnerability The concept of reliability, resilience, and vulnerability (RRV) has been widely applied to assess the performance of water resource systems for more than a century. Since the publication by Hashimoto et al. (1982), the relevant discussion has extended beyond the analysis of water resource systems (Kundzewicz and Kindler, 1995). For example, the sustainability criterion derived from RRV has been established to quantify the trends of system sustainability (Adger, 2006), and a drought management index based on RRV was used to assess the drought propensity (Chanda et al., 2014). In this study, the goal of using RRV is to assess the performance of the water supply system of the Han to Wei IBWT project. Using the runoff generation method, we can obtain P (e.g. P ¼ 10,000) monthly runoff sets. Each set has three monthly runoff series with the observed series length of T month. These sets are used as the inputs of the water supply system operation model established in Section 3.4. When this model runs a total of P times with each set, we can obtain the corresponding sets of water supply series under different runoff conditions. For a specific water supply process p (p ¼ 1, 2,…, P), if the system can meet the water demand of users, indicating that it is in a satisfactory state; otherwise, the water supply system is said to be in a failure state. The reliability is defined by Hashimoto et al. (1982) as the probability that a water supply system is in a satisfactory state, and it is most widely accepted and estimated as M P

dðm; pÞ

Reliability ¼ 1  m¼1

(8)

T

where d (m,p) is the duration of the mth failure state of the pth water supply process, M is the total number of failure states, and T is the total duration of the water supply time. The resilience is defined by the mean or maximum recovery rate that the water supply system recovers from failure state to satisfactory state, and it can be estimated as the inverse of the mean or maximum duration:

"

M 1 X ResilienceðmeanÞ ¼ dðm; pÞ M m¼1

or

#1

  Resilience max ¼ fmax½dðm; pÞg1 m

(9)

VulnerabilityðmeanÞ ¼

M 1 X vðm; pÞ M m¼1

or

(10)

VulnerabilityðmaxÞ ¼ max½vðm; pÞ m

where v (m,p) is the deficit volume of the mth failure state of the pth water supply process. In order to properly assess the performance or risk of water resource systems, it is necessary to select suitable metrics (Giuliani and Castelletti, 2016). When the metrics are used to characterize the performance of water resource systems, the results obtained from these metrics under different definitions (mean or maximum) will differ (Kjeldsen and Rosbjerg, 2005). According to the publication by Kundzewicz and Kindler (1995), the performance assessment based on the maximum value is better than that based on the mean value. Kjeldsen and Rosbjerg (2005) argued that the estimates of resilience and vulnerability based on mean values may lead to non-monotonic behavior. Furthermore, a previous study has also shown that the selection of indicators under different definitions has a significant impact on the robustness of a system (Giuliani and Castelletti, 2016). However, to date, there are no widely accepted selection criteria for these measures. Therefore, the selection of these benefit assessment indicators should be carefully made in practical applications. 4. Results and discussion In this section, the copula-based approach was first used to evaluate the synchronous and asynchronous encounter probabilities of different water sources with the annual and each monthly flow series. Secondly, according to the analysis of the encounter situations, the annual flow series were sampled from the historical parametric distributions. The sampled series were reconstructed and fragmented into monthly time series using the simulated annealing algorithm and fragment method. Finally, the fragmented monthly series were applied as the inputs for the water supply operation model to evaluate the performance of the system. 4.1. Synchronous and asynchronous encounter situations and encounter probabilities of different water sources In our case study, the water supply system has three water sources, namely the Hunagjinxia reservoir, the Sanhekou reservoir, and the Lueyan POD. The two reservoirs connected by the pipelines are the main water sources of the system. The Lueyan POD is a supplement water source which enhances the reliability of the system and supplies water to the Huangjinxia reservoir. According to the design of the system, the inflow of the Hunagjinxia reservoir and the Sanhekou reservoir, and the streamflow of the Lueyan POD are applied to evaluate their synchronous and asynchronous encounter probabilities, respectively. Meanwhile, the statistical methods of the Mann-Kendall test method (Mann, 1945) and the heuristic segmentation method (Bernaola-Galvan et al., 2001) are used to detect the possible change points in these flow time series. The identified change points in the annual flow time series for the Hunagjinxia reservoir, the Sanhekou reservoir, and the Lueyan POD are the years 1991, 1993 and 1994, respectively. For consistency, the year 1993 was selected to divide the annual flow time series into the pre- and post-changed time series. The full and changed time series are applied to calculate the

K. Ren et al. / Journal of Cleaner Production 252 (2020) 119806

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Table 1 The synchronous and asynchronous encounter probabilities of the annual flow of different water sources, (a) the Huangjinxia reservoir annual inflow and the Sanhekou reservoir annual inflow; (b) the Huangjinxia reservoir annual inflow and the Lueyan POD annual streamflow. Scenarios

Synchronous probability (%) Huang San

Wet

Normal

Dry

Asynchronous probability (%) Sum

Wet

Wet

Normal

Normal

Dry

Dry

Sum

Normal

Dry

Wet

Dry

Wet

Normal

72.73 73.94 71.81

9.42 9.08 9.67

0.07 0.05 0.09

9.42 9.08 9.67

4.14 3.90 4.33

0.07 0.05 0.09

4.14 3.90 4.33

27.27 26.06 28.19

Wet

Normal

Dry

Full series Pre-changed series Post-changed series

15.51 15.87 15.24

36.44 37.02 36.00

20.79 21.05 20.58

Scenarios

Synchronous probability (%) Wet Normal Dry Wet Normal Dry

Sum

Asynchronous probability (%) Wet Wet Normal Normal Dry Wet

Normal Dry

Dry Wet

Dry Normal

Sum

12.98 11.60 11.43

63.80 58.60 57.97

11.56 12.44 12.53

6.09 7.30 7.45

0.46 0.96 1.04

6.09 7.30 7.45

36.20 41.40 42.03

Huang Lueyan Full series Pre-changed series Post-changed series

32.36 30.26 30.03

18.46 16.74 16.51

encounter probabilities between different water sources using the copula-based approach. The encounter situations and encounter probabilities of the annual flow time series for the three water sources are shown in Table 1. As shown in Table 1a, the synchronous encounter probabilities of the annual inflow for the two reservoirs are significantly larger than the asynchronous encounter probabilities, indicating that the annual inflows of the two reservoirs are almost in the same states. As a result, the water requirements of the water supply system may not be satisfied in their Dry-Dry encounter situation. The asynchronous encounter probabilities of their fully opposite situations (Wet-Dry) are near to zero, indicating that regardless of which reservoir is experiencing the low-flow conditions, the water supply of the system may not be satisfied. The reliability of the water supply system is severely affected by droughts because the two reservoirs are in very close proximity and in the same basin (the Han River basin), and their control areas have similar surface conditions and climatic characteristics. Furthermore, the encounter probabilities of the pre- and post-changed annual flow time series for the two reservoirs also show the similar patterns mentioned above. The deviations of the encounter probabilities between the pre- or post-changed annual series and the full annual series are very small in all encounter situations. This result indicates that although runoff stationarity is undermined by climate change and human activities, this variation in stationarity occurs synchronously in the annual flow of the two reservoirs. Therefore, the encounter probabilities remain constant, indicating the stability of the encounter relationship between the annual inflows of the two reservoirs. Table 1b shows the encounter probabilities of the annual flow for the Hunagjinxia reservoir and the Lueyan POD. As the distance between the water sources increases, the synchronous encounter probabilities decrease and the asynchronous encounter probabilities increase. However, the differences in the encounter probabilities between the full annual series and the pre- or postchanged annual series are very small, indicating that the encounter relationship between the inflow of the Hunagjinxia reservoir and the streamflow of the Lueyan POD is stable. To further evaluate the encounter situations of different water sources, we also analysed the encounter probabilities of each month for these water sources (Fig. 3). As shown in Fig. 3a, the differences in the encounter probabilities between the monthly inflow of the Huangjinxia reservoir and the monthly streamflow of the Lueyan POD vary in different months. These differences are more pronounced in the low-flow season (e.g. January) and the high-flow season (e.g. June). The differences in the encounter probabilities between the monthly inflow of the Huangjinxia reservoir and the Sanhekou reservoir reach their maximum in the

0.46 0.96 1.04

11.56 12.44 12.53

high-flow season (Fig. 3b), and the differences in the encounter probabilities between the full series and the pre- or post-changed series exhibit the similar patterns. These results indicate that the runoff variabilities of each month are increased, leading to the encounter situations between the pre- and post-changed monthly series having significant differences (Fig. 4), which are more obvious in the Huangjinxia reservoir and the Lueyan POD than those in the two reservoirs. According to the above results, it can be concluded that the nonstationarity of runoff has mainly altered the encounter situations of monthly flow between different water sources, and the encounter situations of annual flow remain stable. Therefore, the sampling from the parametric distribution of historical annual flow series may maintain the encounter situations between different water sources. 4.2. Generating monthly streamflow 4.2.1. Sampling no temporal dependence annual series from parametric distribution In this section, 10,000 sets of annual flow series, each of which is 55 years long, are sampled to reproduce the annual flow statistics of each observed series in order to maintain the encounter situations. The no temporal dependence annual series is generated by sampling from the parametric distribution of the annual flows observed for the three water sources from 1956 to 2010. The parametric distributions are estimated from empirical distributions, which should make assumptions with respect to distribution parameters and density estimation methods. The Pearson Type III distribution was selected to randomly sample the annual flows because this distribution can only take values between 0 and þ∞, and it agrees well with the annual empirical distribution (Fig. B1). Fig. 5 shows the mean, median, standard deviation and interquartile range for each sampled annual flow series, and these characteristic values are uniformly distributed between the maximum and minimum values. This result indicates that historical annual flow distributions are adequately represented by the sampled series. Although these sampled annual series reproduce the historical data characteristics, they are not temporal dependence series. 4.2.2. Constructing annual streamflow series using simulated annealing algorithm The annual flow series with no temporal dependence have been generated from the historical data distributions. To reconstruct these flow series into the temporal configurations whihc reproduce the encounter situations between the different water sources, the simulated annealing algorithm is used to reconstruct the flow

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Fig. 5. The mean (Me), median (Med), standard deviation (Std), and interquartile range (Iqr) for sampled 10,000 annual flow series, each 55 years long, where the values are normalized between the minimum and maximum values.

series for matching target statistics. In this reconstruction approach, two selected components are included in the objective function, that is, the autocorrelation coefficient of each water source and the cross-correlation coefficient of different water sources. The objective function of the Huangjinxia reservoir is crucial because it needs to consider the encounter situations between the Huangjinxia reservoir and two other water sources. Therefore, three components (two cross-correlation coefficients and one autocorrelation coefficient) are included in this objective function. To improve the diversity of the reconstructed series, a deviation of 0.1 in each component was retained when setting the objective functions; the algorithm stops when the deviation is reached. The cross-correlation coefficients between the historical flow series of the two reservoirs is 0.89, and that of the Huangjinxia reservoir and the Lueyan POD is 0.74. The initial autocorrelation coefficients of the historical series are 1. The reconstructed temporal dependence series of the three water sources are shown in Fig. 6. This result indicates that the reconstructed series and the historical series are roughly consistent, and the overall situations of the flow series do not change. The diversities of the reconstructed series are reflected in the magnitude of flows, and the maximum values are more likely to appear outliers than the minimum values. As shown in Fig. 7, the autocorrelation coefficients of the reconstructed series for the three water sources range between 0.9 and 1. The cross-correlation coefficients between the historical series of the Huangjinxia reservoir and the reconstructed series of the Sanhekou reservoir and the Lueyan POD are distributed within the reasonable intervals. These results indicate that the components of the objective functions have been achieved by the simulated annealing algorithm. Furthermore, the reconstruction approach does not disturb the initial configurations of the historical annual series and retains the initial encounter situations of different water sources into the simulated annual flow series. 4.2.3. Monthly disaggregation of streamflow The input flow data of reservoir operation model usually comprise monthly data, and the reconstructed annual flow series should therefore be disaggregated into monthly flow series. The observed flow series of the three water sources are applied to form the fragmented matrixes, and the criterion proposed by Srikanthan and McMahon (1980) is used to define the fragment of the reconstructed annual flows. The 10,000 sets of reconstructed annual flow series of the three water sources are fragmented into monthly flow series. The effectiveness of the fragmented approach is assessed by comparing the statistical indicators of each month for each

fragmented monthly flow series. These indicators are the mean, median, standard deviation and interquartile range. Fig. 8 displays the box plots of these indicators for the 10,000 sets of fragmented monthly flow series and the historical data (solid green line) of the three water sources. The mean and median of historical flows are well preserved in the fragmented monthly flow series, and the intra-annual flow distributions are also well preserved during the fragmented approach. The outliers of these indicators occur more frequently in the high-flow seasons than in the low-flow seasons. The fragmented monthly flow series show slightly underestimated values of the standard deviation and interquartile range for the high-flow seasons, but they still agree well with match the standard deviation and interquartile range of the historical flows. Compared with the low-flow seasons, the differences in flow magnitude in the high-flow season are very obvious. This result indicates that the variations in the fragmented monthly flow decrease in the highflow seasons relative to the historical flows. Actually, the intraannual distributions of historical monthly flows do not have the identical pattern for any two or more years. However, in the fragmented approach, the fragment matrixes are subjected to the length of the observed data. Therefore, it is inevitable that the annual flow for some years may be classified into the same class that is used to fragment the reconstructed annual flows. In the reservoir operation model, the Sanhekou reservoir is a multi-year reservoir, and the influence of the intra-annual distributions of monthly flow on reservoir operation may be limited during the operation period. In conclusion, 10,000 sets of monthly flow series were generated for the three water sources, and in the next section, these are applied as the inputs of the reservoir operation model to evaluate the performance of the water supply system. 4.3. Results of reservoir optimization model 4.3.1. Water supply processes and reservoir water level To minimize the water shortage of the water supply system, a water shortage index for minimizing the average month water deficit is considered as the objection function of the operation model. The 10,000 sets of generated monthly flow series are applied to evaluate the performance of the operation model. The emphasis of this operation model is on the performance of the water supply. Therefore, two scenarios are applied to obtain the water supply processes for different water demands, i.e. the annual water demand of 1,500 MCM and 2,200 MCM. The operation model allocated the annual water demand uniformly throughout each month. This strategy of allocation can more adequately assess the reliability of the water supply system in the low-flow season than the allocation which depends on the magnitude of the river flow in different seasons. Fig. 9 shows the monthly water supply processes and the average annual water level of the Sanhekou reservoir obtained from the observed flow series and the generated flow series under different water demands. The water supply processes obtained from the observed flow series show several events of water scarcity over the operation period, and the most critical water scarcity event occurred in the 1990s (Fig. 9a and b). During this scarcity period, runoffs of all rivers were in long-term low-flow conditions (see green lines in Fig. 6), while water scarcity exceeded the reservoir’s capacity for storage leading to the reservoir depletion. The water supply cannot meet the water demand of the corresponding period (Fig. 9c and d). As the water demand increased from 1,500 MCM to 2,200 MCM, the frequency of occurrence of water scarcity events increases, and the reservoir is at low water levels for most of the period. This result indicates that there is a decreased storage capacity of the reservoir to regulate runoff for water supply. The water

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Fig. 6. The reconstructed temporal dependence series of the three water sources using the simulated annealing, (a) Huangjinxia, (b) Lueyan POD, and (c) Sanhekou.

Fig. 7. The correlation coefficient between the reconstructed sequences and the historical sequences, where H-L and HeS denote the cross-correlation between the historical sequences of the Huangjinxia reservoir and the reconstructed sequences; L-H and SeH denote the cross-correlation between the historical sequences and the reconstructed sequences of the Huangjinxia reservoir.

supply processes obtained from the generated flow series also exhibit similar patterns which have been outlined above, but there are increases or decreases in the frequency of water scarcity events and the reservoir at low water levels with different generated flow series. The reliabilities of the two water supply scenarios obtained from the observed flow series are 0.91 and 0.59, respectively, and the reliabilities obtained from the generated flow series are shown in

Fig. 10. Meanwhile, to compare the reliability with the encounter probabilities, the encounter probabilities of the three water sources were calculated. The encounter probability of wet conditions obtained from the observed flow series is 0.56, and these probabilities obtained from the generated flow series are also shown in Fig. 10. As shown in the figure, wet encounter probabilities are distributed within a narrow range and are concentrated around the encounter probability of observed flow series, indicating that the encounter situations are reproduced by the generated flow series. Compared with the water supply for 1,500 MCM, the reliabilities of the water supply for 2,200 MCM significantly decrease, and the distribution of these reliabilities is more discrete. Furthermore, the reliabilities of the water supply for 2,200 MCM are closer to the wet encounter probabilities than the water supply for 1,500 MCM. These results further indicate that the storage capacity of the reservoir to regulate runoff for water supply is decreased under the water supply for 2,200 MCM, and most of the supplied water for the system depends on the encounter situations of the rivers instead of the reservoir’s storage.

4.3.2. Relationship between reliability, resilience and vulnerability In this paper, RRV functions as variables which change with the number of simulations. The limited number of simulations may not adequately assess the characteristics of these metrics. In particular, when using the mean values of these metrics to estimate resilience and vulnerability, it leads to the non-monotonic behavior with a limited number of simulations. To obtain the robust assessment of the three metrics, 10,000 sets of generated monthly flow series are

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Fig. 8. The mean, median, standard deviation, and interquartile range for fragmented monthly streamflow series.

Fig. 9. The monthly water supply processes and the Sanhekou reservoir water level, (a), (c) the annual water demand of 1,500 MCM; (b), (d) the annual water demand of 2,200 MCM.

used to generate large sets of water supply processes, and thereby more values of these metrics. Fig. C1 shows the mean values of reliability, resilience and vulnerability with different simulated times. These results indicate that the 10,000 sets of generated monthly flow series are adequate to estimate the three metrics which can obtain the robust levels. According to the simulated results of reliability, resilience (mean

and max) and vulnerability (mean and max) under water demands of 1,500 MCM and 2,200 MCM, the relationships between them are illustrated in Fig. 11. The values of reliability, resilience (mean) and vulnerability (mean) are plotted on the x-axis, y-axis and z-axis, respectively. The values of resilience (max) are represented by the size of spheres, which range from 0.2 to 0.1(large size) to 0.06 and 0.03 (small size), respectively. The colour of the spheres indicates

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Fig. 10. The reliability of the water supply system and wet encounter probability of the three water sources.

the values of vulnerability (max) which vary from 5.20  108 and 12.09  108 (yellow) to 12.75  108 and 29.11  108 (red), respectively. The arrows show the directions of increasing preference, and the best situations of the water supply system are located toward the left lower corners, which have the maximum reliability and resilience as well as minimum vulnerability. This result indicates that when the water supply system has a very reliable water supply, the system also has a short duration and low severity of water deficit. As shown in Fig. 11, the relationship between the reliability and vulnerability (mean) is obviously negative. The negative relationship can also be observed from the relationship between the resilience (mean) and vulnerability (mean). The reliability and resilience (mean) are positively correlated, and their positive relationship indicates the states of the stable stage, which depend on the water supply process of the water supply system. As the values of reliability and resilience (mean) increase, the size of spheres varies from small to large, indicating that the resilience (max) is also positively correlated with the reliability and resilience (mean). There are two very different colour regions in the metric space. The red region has a high vulnerability (mean and max) and low reliabilities and resilience (mean and max). The yellow region shows the opposite result to what is shown in the red region. This result indicates that the vulnerability (max) of the water supply system with different streamflow scenarios may be consistent and depends on the maximum water demand and the water supply capacity of the system.

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4.3.3. Reasonable selection of reliability, resilience and vulnerability Regardless of the complex relationships between reliability, resilience and vulnerability, it is important to determine how to choose the reasonable metrics to assess the performance of the system. Different metrics represent diverse information about a system, but there are significant differences in the effectiveness when these metrics are used to evaluate the performance of the system. To further analyse the differences between these metrics, a parallel axes plot is applied to illustrate the results. Fig. 12 shows each value of reliability using a line crossing the vertical axes at the values of their corresponding resilience and vulnerability. The values of these metrics are normalized between the minimum (bottom) and maximum (top) values, and the directions of increased preference are from the blue lines to the red lines. The ideal situation of the water supply system would be a diagonal line running along the top of the reliability and resilience axes and the bottom of the vulnerability axes. When the situations of simulated streamflow are changed, the values of reliability show the corresponding changes and have no duplicate values. Hence, the reliability is considered as a monotonic metric with respect to the streamflow situations. Furthermore, some of the values of resilience and vulnerability estimated as the maximum and mean duration and deficit volume of simulated failure events are obscured by their other values, which are more pronounced when the water demand is 1,500 MCM (Fig. 12a). These results indicate that both the resilience (mean and max) and vulnerability (mean and max) have nonmonotonic behaviours. The values of resilience and vulnerability would be fixed at a certain value when the situations of simulated streamflow are changed. As a result, decisionmakers may be unable to determine the quality of the system. For a more detailed illustration of the differences of these metrics, parts of Fig. 12 are magnified (see grey boxes in Fig. 12). As shown in the grey boxes, the left and right states of the resilience (max) axis are opposite, indicating that the resilience (mean) is negatively correlated to the vulnerability (mean). Although this negative relationship has been reported in Fig. 11, it is shown more precisely in the grey boxes. To date, it can be shown that if the resilience (mean) has a lower value, the vulnerability (mean) would have a higher value, and vice versa. Two specific cases (see green and yellow lines in Fig. 12) that have the same values of resilience (mean) and vulnerability (mean) are selected. Although the two

Fig. 11. The relationships of Reliability, Resilience, and Vulnerability.

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Fig. 12. Parallel-axes representation of Reliability, Resilience, and Vulnerability with maximum simulated times, where the values are normalized between the minimum and maximum values.

cases have the same values of these metrics and even the same values of reliability, there are significant differences in their values of resilience (max) and vulnerability (max). The durations of the water shortages of case one and case two are consistent. However, the severity of the water shortage in case one is significantly larger than that of case two. This result indicates that the resilience and vulnerability estimated as the mean duration and deficit volume of simulated failure events cannot correctly reflect the states of the system. Furthermore, another two specific cases (see black and yellow lines in Fig. 12) having the same values of resilience (max) and vulnerability (max) are chosen. This result also cannot correctly reflect the states of the system. Therefore, regardless of which mean or maximum value is selected individually, the states of the system cannot be properly assessed. The reasonable selection of reliability, resilience and vulnerability should include the resilience and vulnerability, which are estimated from both the mean and maximum values. Based on the above results, it is recommended that the reliability, resilience (max) and vulnerability (mean) are employed to evaluate the performance of the system. 5. Conclusion Facing the increased uncertainties of hydrometeorological variabilities, it is important to carry out a comprehensive risk analysis of water resource systems in order to mitigate the risk associated with these uncertainties. Such a risk analysis is even more urgent in regions of water shortages, such as the Shaanxi province in China. This study presents a framework for the evaluation of water supply system performance, considering the encounter situations between different water sources to properly limit the range of plausible water resource conditions. Moreover, this framework combines the methods of coupling, simulation, and optimization, and has been proven to be effective by case study of the Han to Wei IBWT project in Shaanxi province, China. The analysis framework using the copula-based method captures the encounter situations of different water sources at different time scales. The differences in the water resource

distribution between different water sources increase with increases in the distance, and are more pronounced on the monthly scale than on the annual scale. This result indicates that the importance of these differences in spatial-temporal dimension is underestimated when building water management models (Herman et al., 2014). As reported by previous studies (Adger, 2006; Giuliani and Castelletti, 2016), the potential inaccuracy of the analysis relying on static estimates of a system’s performance will compromise the system’s regulation. The method of generating monthly flow series considering the encounter situations extends the possible range of input information and prompts the dynamic estimation of system’s performance. It should be noted that the integration of our proposed framework with the generated streamflow provides a new perspective for performance analysis, that is, the reliability of the water supply depends on the wet encounter situations between different water sources. This study evaluates the system’s benefits from data input to output process and gives a reasonable choice of strategy to describe the system performance under alternative states of the world. Moreover, although the water supply system in our case study has three water sources which are all stream flows, this proposed framework can be extended to the uncertainty assessment of water supply systems, including multiple types of water sources (e.g. surface water, groundwater and desalinated water). A single-objective optimization model has been established in our case study, which may be insufficient to explore the competing objectives of water supply systems. Further research efforts should establish a multi-objective optimization model for combining the analysis of the trade-offs and sensitivity in the full range of the decision-making space. Furthermore, by focusing on the current encounter situations between different water sources, the encounter situations were set to fixed values. In the future, with the increasing impact of human activities on the surface conditions of river basins, the difference between runoffs will increase. Meanwhile, the runoff is also affected by climate uncertainty, so the encounter situations are expected to change. Therefore, in future studies, it is important to research encounter situations which change with the runoff alteration.

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Author contribution section R.K., H.S.Z. and H.Q. designed the study, developed the model and conducted the analysis. R.K. wrote the original draft of the manuscript with input from H.S.Z. H.Q., W.H. and L.G.Y. reviewed and edited the manuscript. All authors discussed the results and contributed to the final version of the manuscript. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements We sincerely appreciate the helpful and constructive comments provide by the editor and three anonymous reviewers. This research is jointly funded by the National Natural Science Foundation of China (51879213 and 51709221), the National Key Research and Development Program of China (2017YFC0405900), the Planning Project of Science and Technology of Water Resources of Shaanxi (2017slkj-16 and 2017slkj-19), Key laboratory research projects of the education department of Shaanxi province (17JS104), the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin (China Institute of Water Resources and Hydropower Research) (IWHRSKL-KF201803), and the Belt and Road Special Foundation of the State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering (2018490711). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.jclepro.2019.119806. References Adger, W.N., 2006. Vulnerability. Glob. Environ. Chang. 16 (3), 268e281. https:// doi.org/10.1016/j.gloenvcha.2006.02.006. Barnett, J., Rogers, S., Webber, M., Finlayson, B., Wang, M., 2015. Transfer cannot meet China’ s water needs. Nature 527, 295e297. https://doi.org/10.1038/ 527295a. Bernaola-Galvan, P., Ivanov, P.C., Amaral, L.a.N., Goldberger, A.L., Stanley, H.E., 2001. Scale invariance in the nonstationarity of physiological signals. Phys. Rev. Lett. 87 (16), 1e4. https://doi.org/10.1103/PhysRevLett.87.168105. Best, J., 2019. Anthropogenic stresses on the world’s big rivers. Nat. Geosci. 12 (1), 7e21. https://doi.org/10.1038/s41561-018-0262-x. Bhave, A.G., Conway, D., Dessai, S., Stainforth, D.A., 2016. Barriers and opportunities for robust decision-making approaches to support climate change adaptation in the developing world. Climate Risk Management 14, 1e10. https://doi.org/ 10.1016/j.crm.2016.09.004. Borgomeo, E., Farmer, C.L., Hall, J.W., 2015. Numerical rivers: a synthetic streamflow generator for water resources vulnerability assessments. Water Resour. Res. 51 (7), 5382e5405. https://doi.org/10.1002/2014WR016827. Borgomeo, E., Mortazavi-Naeini, M., Hall, J.W., O’Sullivan, M.J., Watson, T., 2016. Trading-off tolerable risk with climate change adaptation costs in water supply systems. Water Resour. Res. 52 (2), 622e643. https://doi.org/10.1002/ 2015WR018164. Brown, C.M., Lund, J.R., Cai, X., Reed, P.M., Zagona, E.A., Ostfeld, A., Brekke, L., 2015. The future of water resources systems analysis: toward a scientific framework for sustainable water management. Water Resour. Res. 51 (8), 6110e6124. https://doi.org/10.1002/2015WR017114. Burls, N.J., Fedorov, A.V., 2017. Wetter subtropics in a warmer world: contrasting past and future hydrological cycles. Proc. Natl. Acad. Sci. 114 (49), 12888e12893. https://doi.org/10.1073/pnas.1703421114. Chanda, K., Maity, R., Sharma, A., Mehrotra, R., 2014. Spatiotemporal variation of long-term drought propensity through reliability-resilience-vulnerability based Drought Management Index. Water Resour. Res. 50 (10), 7662e7676. https:// doi.org/10.1002/2014WR015703. Chang, J.X., Wang, Y.M., Istanbulluoglu, E., Bai, T., Huang, Q., Yang, D., Huang, S.Z., 2015. Impact of climate change and human activities on runoff in the Weihe River Basin, China. Quat. Int. 380e381, 169e179. https://doi.org/10.1016/

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