Impact of Climate Change on water diversion risk of Inter฀basin Water Diversion Project

: Aiming at impact of climate Change on water diversion risk of Inter‑basin Water 20 Diversion Project, this paper constructs a risk operation system based on runoff forecast and risk 21 theory. Firstly, this study uses the EEMD-LSTM model to predict future runoff processes. Secondly, 22 the runoff forecast data is incorporated into the data source. The risk degree formula is deduced by 23 the risk theory. Finally, taking risk degree as decision variable established a risk operation model 24 and develop a risk operating scheme. Results indicate that: (1) The risk dispatching scheme transfers 25 the water diversion risk from the dry period to the wet period, to reduce the probability of extreme 26 risk. (2) The time distribution and variation law of water diversion risk are consistent between the 27 water source area and the water receiving area. The spatial law of water diversion risk is decreasing 28 transmission from the water source area to the water receiving area. (3) Risk source and risk bearing 29 body of the water receiving area are directly related to the water shortage and its probability 30 distribution. Rate of socio-economic loss decreases with the increase of water shortage probability. 31 The research results have important application value for risk control of inter-basin water diversion 32 projects and regional security of water supply.


Introduction
Under the influence of increasing global climate change, the uncertainty situation of future water resources is further increased.Strengthening risk assessment and countermeasure research of water resources become one of the important tasks of water security (Tian et al., 2018).
Since the risk was introduced into the field of water resources in the 1970 s, its application involves a wide range of contents, including hydrological risk, operating risk, management risk, engineering risk.Water conservancy project is an important engineering measure to regulate the change of water resources.With the uncertainty of climate change, the uncertainty situation of water resources is further increased (Immerzeel et al., 2020;Chen et al., 2020;Zhang et al., 2020).
Operating risk is the possibility of loss caused by the system failing to achieve the expected goal due to the influence of risk sources in the process of dispatching operation and management decision-making of water conservancy hub.The comprehensive operating risk increases dramatically due to the influence of multi-source risk factors such as uncertainty of incoming water, extreme weather, mismatch between supply and demand.Reservoir group operation and efficient utilization of water resources are facing more severe challenges.
In recent years, the research results on water resources risk operating have gradually increased.
Many organizations and individuals have carried out rich and in-depth research and practice based on applying operating schemes to reduce climate change impacts (Brown et al., 2012;He et al., 2020;Mandal et al., 2019;Zhang et al., 2021).Many achievements solve the risk problems by risk operation and risk evaluation (Romano et al., 2017;Bai et al., 2021;Lu et al., 2022).Risk operating mainly analyzes the impact of climate change on reservoir operating by inputting predicted runoff into the reservoir optimal scheduling model, to put forward strategies to alleviate the corresponding negative effects (Dong et al., 2022;Hunt et al., 2022;Liu et al., 2019).The risk assessment is based on the multi-objective water supply guarantee rate as the evaluation index, and select the operating scheme with the highest guarantee rate of water supply, result in reducing the impact of uncertain runoff changes on water resources allocation (Wei et al., 2015;Qian et al., 2021;Zhang et al., 2021).
In general, the research on the risk assessment and control strategy of reservoir operation is not deep enough, and lack a systematic, global and dynamic perspective to solve prevent risks.
Most risk operating studies quantify and evaluate the risk of operating results, or the results of runoff prediction model is nested in reservoir operation model.However, these methods ignore the impact of risk components on operating risk to varying degrees, result in the risk is not fed back to the actual operating decision.The reservoir operation model with nested runoff forecast and the single uncertain factors cannot accurately predict the possibility and severity of risk events, result in making it difficult to provide sufficient risk decision-making information for each user department and decision makers.
Therefore, aiming at the lack of research on risk factors and the imperfect construction of risk operating system, this study constructs a risk operating system based on runoff forecasting and risk theory (Fig. 1).First, the runoff forecast model is used to predict the future runoff change process, to reveal the future trend of runoff evolution.Second, the risk of water diversion is defined by considering the probability of occurrence of risk sources and the vulnerability of risk-bearing bodies, to deduce the calculation formula of risk degree of inter-basin dispatching water project.Finally, a risk operating model is established with the goal of minimizing the risk of water diversion, to reveal the space-time transmission law of water diversion risk and the transformation relationship between risk factors and risk degree.It provides more sufficient risk decision information for each user department and decision makers.The research results have important application value for the regulation of engineering multi-risk and regional water supply safety.  2 Theory and method

Runoff prediction
The EEMD-LSTM model is ' decomposition-prediction-reconstruction ' process in predicting runoff.Natural runoff series is a non-stationary nonlinear time series.The decomposed components contain the characteristics and periods of runoff.The runoff results by predicting different frequency components contain more specific information.The smoothed runoff component can improve the prediction accuracy of the neural network model and the LSTM network overcomes the short-term memory problem in traditional neural networks.Therefore, the EEMD-LSTM model can be applied to long-term runoff prediction (Liang et al., 2020;Yang et al., 2021;Luo et al., 2022).
Specific prediction steps (Fig. 2): (1) The original runoff sequence is preprocessed, the outliers are corrected, and the sequence is divided into 90 % training set and 10 % test set; (2) EEMD is used to decompose the original runoff sequence into intrinsic mode function and residual components; (3) The training set data of the intrinsic mode function and the residual components are input into the neural network for deep learning to form the memory state of each component after training; (4) The trained memory state is used to predict the components of the test set, and the runoff prediction results of the test set are obtained by linear superposition of the prediction results; (5) By calculating the prediction effect evaluation index to check whether the prediction results meet the accuracy requirements.If the prediction results do not meet the requirements, step 3 is returned; (6) The decomposed components of the original runoff series are input into the neural network after deep learning to predict the future components.Finally, the future runoff series is obtained by superposition.

Risk theory
This section considers the water diversion risk faced by the inter-basin water diversion project based on runoff prediction.Water diversion risk is defined according to disaster risk theory.The risk combination elements are quantitatively estimated by probability statistics.The expression formula of water diversion risk in water source area and water receiving area is deduced combined with the definition of risk, to provide decision variables for the subsequent risk scheduling model.

Risk definition
Risk rate refers to the possibility of adverse events after the interaction between risk sources and hazard-affected bodies (Bai et al., 2021).Risk = Hazard × Vulnerability proposed by the United Nations Department of Humanitarian Affairs has been widely recognized in the field of hydrology and water resources risk system (Zhao et al., 2019;Fell., 1994;Hearn., 1995).

R HV =
(1) where R is the risk; H is the Hazard; V is the Vulnerability.
Hazard is quantitatively expressed as the occurrence probability of risk source.Vulnerability is expressed as the loss rate and exposure of the risk-bearing body.Exposure refers to the proportion of an insured object exposed to the entire insured body.

R P e  =  
(2 where R is the risk；P is the occurrence probability of risk source； is the loss rate； e is exposure of the risk-bearing body.

Risk assessment
Risk is the adverse events possibility after the risk source acts on the risk-bearing body.Risk includes the probability of occurrence of risk sources and the exposure and vulnerability of the insured.Risk assessment is to use empirical, statistical or conceptual models to estimate the probability of occurrence of risk sources and exposure and vulnerability of the undertaker.
(1) Occurrence probability of risk source Based on the time series data of historical and future predicted risk sources, the occurrence times of different risk sources were counted.The probability of occurrence of risk sources is estimated by mathematical statistics.According to the probability distribution function, the probability of exceeding the value of the risk source at this time is calculated as the probability of occurrence of the risk source.
Under the single risk source scenario, according to the sample data, the risk source sequence is fitted by continuous distribution functions such as P-III, GEV and LN3 (Chen et al., 2020).KS is used as an evaluation index to check the feasibility of continuous distribution.RMSE is used as an evaluation index to evaluate the fitting quality of edge distribution.Finally, the optimal theoretical probability distribution is determined by AIC.
Under the multi-risk source scenario, the marginal probability distribution of a single risk source is determined.Copula function constructs the connection function to determine the optimal joint distribution, to calculate the probability of multiple risk sources (He et al., 2013).The goodness of fit of Copula function is evaluated by OLS and AIC.The probability estimation process of single / multiple risk sources is shown in Fig. 3. (2) Vulnerability of the risk-bearing body Vulnerability is the ratio of the value of losses suffered by various types of underwriters to the target value under normal circumstances.In order to calculate the loss rate of each risk bearing body, this study first determine the object or department threatened by the risk source.Secondly, Secondly, this study estimates the possible loss degree of these objects or parts under the risk source event.
The loss rate of the bearing body is divided into single loss rate and comprehensive loss rate.The single loss rate is the separate loss rate of each hazard bearing body.The comprehensive loss rate is the overall loss rate calculated by weighting each individual loss rate.The single loss rate can be obtained by statistical calculation of historical loss.The comprehensive loss rate can be obtained according to the weighted average of the individual loss rate of each type of insurance body and its proportion in the total loss.
where i  is the single loss rate of the i risk-bearing body; i W is the amount of value after the loss of the third type of risk bearing body; i,obj W is the target quantity of the i risk-taking body.
where  综 is comprehensive loss rate; i  is the single loss rate of the ith risk-bearing body; i w is the loss value of the first type of risk bearing body; i  is The proportion of the loss value of the first type of risk bearing body to the total loss.

Risk degree calculation
The risk theory is applied to the inter-basin water diversion project.The shortage of inflow runoff in water source area will threaten the satisfaction of water diversion target, to cause water diversion risk.Therefore, the risk source of water source area is the inflow runoff of the reservoir group.The bearing body is the single loss rate of water diversion.According to the water quantity planning of water receiving area of the water diversion project, the water diversion risk of water receiving area includes urban life, production and ecology outside the river.Because the water shortage of ecological water outside the river is very little, it can be ignored.Therefore, the risk source of water receiving area is the water shortage of water diversion, and the bearing body is mainly the production and living department.
The expression formula of water diversion risk in water source area and water receiving area where is Risk degree value of water diversion in water source area in t period; ( ,1) is the inflow runoff of reservoir group in t period (m 3 ); ( , ) f x y is the joint probability distribution function for fitting runoff risk sources; () Wt , obj W is the total water diversion and Planning water demand (m 3 ); e is exposure.When the amount of water diversion is satisfied, e = 0.When the amount of water diversion is not satisfied, all risk-bearing bodies in the water source area are exposed to the influence range, e = 1.
is Risk degree value of water diversion in water receiving area in t period; () Wt , obj W is the total water diversion and Planning water demand (m 3 ); () of industrial production, target industrial output value (10 4 yuan); () Dt , obj D is water consumption norm of per capita, life-water quantity Target of per capita (m3); I  , D  is the proportion of water loss in industrial economy to total loss, the proportion of water loss in life economy to total loss; e is exposure.When water diversion amount is satisfied, e = 0.When water diversion amount is not satisfied, production and living dangerous bodies in the water-affected area are exposed to the influence range, e = 1.
According to formulas ( 5) and ( 6), the water diversion loss or social economic loss is calculated by water diversion risk acting on different risk-bearing bodies under the influence of specific intensity risk source can be calculated, to calculate the water diversion risk degree of inter-basin water diversion project.

Case study
The water diversion project from Hanjiang to Weihe River, the largest inter-basin water diversion project in Shaanxi Province stretches across the Yangtze River and the Yellow River valley, the overview of the study area is shown in Fig. 4 (Bai et al., 2022).It can effectively alleviate the contradiction of water shortage in Guanzhong area of Shaanxi Province (Bai et al., 2021;Jin et al., 2018;Wu., 1995).The Hanjiang-to-Weihe River Water Diversion Project includes the water diversion project in the water source area and the water transmission and distribution project in the  River Water Diversion Project will be able to meet the multi-year average water diversion of 1.5 billion m3 in 2030 (Du et al., 2017;Kong et al., 2020).However, due to the interaction of multisource risks such as extreme weather and uncertain incoming water, it is difficult to guarantee 95 % of the water supply guarantee rate in the water source area.During the operation of the project, the mismatch between supply and demand of water resources and the lack of operating experience will aggravate the risk of water diversion in the water source area and the risk of water allocation in the water receiving area.The quantitative size of the risk of water diversion and the risk factors causing the risk are not clear, result in the risk of inter-basin water diversion is prominent.

Hydrological Data
In this study, the inflow runoff data of HJX and SHK reservoirs from July 1954 to July 2010 were used for runoff prediction.The characteristic parameters of HJX and SHK reservoirs, hydropower stations, and pump stations in the water source area of the project are shown in Table 1.

Risk operation
Taking runoff uncertainty as the risk source of water diversion, based on the traditional reservoir group scheduling, the risk degree of water diversion is defined according to the risk loss rate and the probability of risk source occurrence.Aiming at minimizing the average risk degree of water diversion in the water source area, a risk operating model for inter-basin water diversion is established.

Risk operation model
Using the predicted runoff data of HJX and SHK reservoirs, the risk operating model is established with the minimum average risk of water diversion in the water source area as the goal and the month as the scheduling period.
where R 源 is the average risk degree of water diversion in the water source area during the dispatching period; ( ,1) i Qt is the HJX reservoir inflow in t period (m 3 ), the SHK reservoir inflow in t period (m 3 ); ( , ) f x y is fitting joint probability distribution function of HJX and SHK runoff; Wt is the total water diversion flow in t period (m 3 /s), the water required flow in t period (m 3 /s); e is exposure ( e =0 or 1).
(1) Water balance constraint (5) Power station and pumping station design flow constraint where ( ) , V t j is water storage of reservoir j in t period (m 3 ); ( ) , Z t j is water level of reservoir j in t period (m); ( ) max Wt is maximum water diversion amount (m 3 ); ( ) Q t j are inflow, outflow, water diversion flow, power generation flow of power station, pumping flow of pumping station of reservoir j in t period (m 3 /s); Nj is installed output of hydropower station j in t period (MW).

Optimal operation model
In order to verify the superiority of the risk scheduling model, this section establishes a traditional deterministic optimal scheduling model with the largest water diversion amount and the smallest water shortage rate under the same conditions.
(1) Operation model 1: Maximum water diversion amount (2)Operation model 2: Minimum average water shortage rate where W is the total of water diversion amount during the operating period (m 3 ); F is the average water shortage rate during the operating period; () g Q t is water diversion in t period (m 3 /s); () g Wt and () obj Wt are total water diversion and water demand in t period (m 3 ); T and t total operating period and different periods during the operating period.
The constraint condition is the same as the risk operating constraint, which is not repeated here.

Solution procedure
In this study, Genetic Algorithm (GA) is selected to solve the optimal operation and risk operation model of reservoir group.The GA can simulate the process of biological evolution according to natural selection and genetic mechanism, to obtain optimal solution of the most value problem.Therefore, the GA is suitable for the risk scheduling model with the minimum average risk degree as the objective function (Getachew et al., 2020).
The calculation of risk operating model mainly includes two parts: the process of risk source probability and loss estimation of the insured body in the objective function, the optimization process of the risk operating model.Firstly, the optimal risk source probability distribution is determined by fitting the risk source sequence with continuous distribution.Then the risk degree of water diversion is defined according to the result of the loss of the risk bearing body, to establish the reservoir risk scheduling target fitness function.Finally, the GA solve the risk scheduling model to obtain the optimal water diversion risk sequence.
The optimal operating model is solved by GA algorithm to obtain the optimal water diversion sequence.Then the risk degree formula calculates the risk degree of water diversion in each period.
This algorithm is widely used in the solution of traditional reservoir operation model, and it is not repeated here.

Scheme settings
Due to the water consumption complexity in the receiving area of the Hanjiang-to-Weihe River Interbasin Water Diversion Project, three simulated water demand schemes are set up according to the relevant planning and the water demand process in the receiving area.The schemes are shown in Table 2.

Runoff prediction
Based on the historical measured runoff sequence of the water source area of the Hanjiang-to-Weihe River Water Diversion Project, the EEMD-LSTM model is used to predict the runoff.Taking Nash-Sutcliffe efficiency coefficient (short as NES) as the evaluation index, the prediction accuracy of the EEMD-LSTM model is evaluated.As shown in Tab.3, the NES of reservoirs are above 0.87.
The model results are reliable.(2) The runoff of SHK and HJX reservoir began to decrease more significantly in 1997 and continued for a long time.This continuous dry period is extremely unfavorable to the guarantee of the water diversion target of the Hanjiang-to-Weihe River Water Diversion Project.Therefore, the relevant part should pay attention to such continuous dry period.

Risk source estimation of water source
This study clarifies that the risk source of water diversion in water source area is inflow runoff of the two reservoirs.The data amount is increased by runoff prediction, to make the reaction information more complete, to improve the stability of probability distribution fitting.The P-III According to the edge distribution function and the connection function, the contour map of the joint distribution of the inflow runoff of the HJX and SHK reservoirs is drawn (Fig. 6).From the three-dimensional and two-dimensional contour maps, the occurrence probability of various runoff risk source combinations between the two reservoirs can be quantitatively viewed.

Risk source estimation of water receiving area
The risk source of water diversion in water receiving area is the water shortage at the control gate, to take the probability of exceeding the water shortage during the period as the probability of the occurrence of the risk source at this time.The water shortage in the three water demand schemes may occur in the future.Therefore, the water shortage sequences under the three schemes are combined to form a more representative and extensive water shortage sequence.In this study, the generalized extreme value distribution is used as the optimal fitting distribution of annual water shortage (Fig. 7& Tab.3).

Comparison of water diversion and annual water diversion risk process
The annual water diversion amount and annual water diversion risk process of each model from the guarantee rate of water diversion.
(3) The time distribution of annual water diversion risk degree of each model in water demand scheme 3 is more discrete and the maximum value is more.The reason is that under different inflow conditions, it is very difficult to ensure the annual water diversion of 1.5 billion m 3 .Therefore, the dynamic water demand target should be set according to the incoming water situation, and it is more favorable for the centralized regulation and reduction of water diversion risk.

Risk transfer law of water diversion under extreme inflow and water demand
Taking the water demand scheme 3 with the most unfavorable water diversion risk as the water demand process, the water diversion risk process of the risk operating model from 1993 to 1998 is analyzed (Fig. 9).runoff prediction.The time of risk occurrence in 1994 was earlier than that in 1997, when the runoff decreased significantly.It shows the sensitivity of water diversion risk.When the runoff reduction is not significant, the water diversion risk is generated in advance.
(2) From 1993 to 1998, with the decrease of water inflow, the risk of water diversion increased time by time, but the rate of change is decreasing.It shows that when the inflow is insufficient in the early stage, the SHK reservoir uses the reservoir capacity to replenish water to offset the risk of water diversion.However, with the continuous decline of reservoir water level, water inflow influence on water diversion risk is enhanced, and the risk of water diversion increases gradually.After 1997, water inflow increased and the storage capacity of the reservoir increased.Therefore, the rate of change of risk gradually decreases.

The value distribution of risk degree
The bubble diagram and box plot are used to analyze the statistical indexes of water diversion risk sequence in water source area under each model.Taking the water demand scheme 3 with the most unfavorable water diversion risk as an example, the water diversion risk bubbles and box plots of each model water source area are shown in Fig. 10.The water demand scheme 1 is the annual dynamic water demand.The water demand scheme 2 is the annual dynamic average water demand.
The water demand scheme 3 is the annual average water demand.As shown in Fig. 10, (1) the risk degree of water diversion in Model 1 is between 0.01 and 0.52.
Model 2 is distributed between 0.03 and 0.62.Model 3 is distributed between 0.03 and 0.44.The data variation range under the risk scheduling model is the smallest, the data point continuity is higher, the transition is stable, and the distribution is more concentrated.It verifies the time distribution of risk, and also shows that the risk operating model can reduce the probability of sudden increase in the risk level.(2) Under different water demand schemes, the risk degree distribution of the same model is different.The risk of water diversion under water demand scheme 3 is the most serious, and the average, median and maximum values are higher than other water demand schemes.
Moreover, its bubble distribution diverges, and the probability of sudden increase in risk is large.
Therefore, scheme 3 can reflect the water demand under the most unfavorable conditions of water diversion.The water demand scheme 2 has lower risk and is easier to satisfy the water diversion target.
(3) The median of the water diversion risk sequence of the risk operating model is lower than that of the other two models, and the its average is basically the same as that of Model 1.It shows that the risk scheduling model can optimize the risk degree of water diversion in each period, increase the number of small water diversion risks and reduce the probability of extreme risks on the basis of maintaining the high annual average water diversion volume and low average risk degree.
The results of each model have very few outliers, to prove the stability of the model solution.The median of each model is less than the average, to estimate that the risk degree fitting may be right skewed distribution.

Water diversion risk in water receiving area
Scheme 3 is the most unfavorable situation of inter-basin water diversion, which can better reflect the risk transfer law of inter-basin water diversion.Therefore, taking the water demand scheme 3 with the most unfavorable water diversion risk as the water demand process, to calculate changes of water receiving area.

Comparison of water diversion risk between water source area and water receiving area
The water diversion loss of water source area is transmitted to water receiving area, to transform into social and economic losses caused to life and production.Water diversion risk of water receive area is calculated based on the probability distribution of water shortage.The time comparison process of water diversion risk between the water source area and the receiving area is shown in Fig. 11.(2) The risk degree of the water source area is less than that of the water receiving area, but the risk degree range is different.The water diversion risk presents a spatial law of decreasing transmission from the water source area to the water receiving area.Because the water amount of water source area is input to water receiving area, it also transfers the risk of water diversion from the water source area to different water use units in the water receiving area.The water diversion from the water source area is allocated to the production and living industries in proportion.
Therefore, water diversion risk of water receiving area is flattened.In addition, the supply of local water sources makes the risk transmission decrease, to reduce the impact of water diversion risk on the social economy of the water receiving area.

The influence law of risk components on risk degree
The risk degree of water source area and water receiving area and the scatter corresponding diagram between the two are drawn respectively, and the trend line with the highest fitting degree is selected as Fig. 12.As shown in Fig. 12, (1) The risk degree of water diversion is positively correlated with the loss rate and negatively correlated with the probability of risk source.The larger loss of risk-bearing body will lead to the greater risk, and the larger probability of risk source generally leads to the smaller risk.It shows that the probability of risk source and the loss rate are opposite, and the risk degree is produced by the joint action.When the risk of water diversion is transmitted from the water source area to water receiving area, the risk source is reduced, the corresponding relationship between the probability of risk source and the risk degree of water diversion is enhanced, and the risk degree of water diversion is reduced.Due to the supplement of local water source in the water receiving area, the loss of the risk bearing body is reduced, the influence of water source area on water receiving area decreases, and the risk degree of water diversion is reduced; (2) The probability scatter distribution of risk sources in the water source area is scattered, and the fitting degree with the trend line is low.The scatter distribution of loss rate and water diversion risk degree is concentrated, and the fitting degree with linear trend line is higher.Therefore, the runoff probability reflects the potential before the risk outbreak.After the reservoir regulation, the influence of runoff probability on the risk of water diversion is weakened, resulting in a weakening of the corresponding relationship.The loss rate occurs after the outbreak of the risk, and the potential danger of the risk is transformed into the actual loss.Therefore, the loss rate is mainly distributed on and on both sides of the fitting line; (3) The scatter distribution of risk source probability-risk degree and loss-risk degree of risk bearing body in the water receiving area is more concentrated than that in the water source area.They have a higher degree of fitting with the trend line and have obvious linear and exponential laws.The reason is that the risk of water diversion in the water receiving area is transferred from the water source area, which is caused by the probability of water shortage.The social and economic losses of water shortage are distributed by various departments in the water receiving area.Therefore, the risk source and the risk bearing body of the water receiving area are directly related to the water shortage and its probability distribution.The alternating growth and decline regularity of water shortage probability and socio-economic loss rate is stronger.The corresponding relationship between the risk degree of water diversion and each factor is more significant after the joint action.

Conclusion
Aiming at uncertainty factors insufficient research and imperfect construction of risk operating system, this study takes the Hanjiang-to-Weihe River Water Diversion Project as the research object to construct the water diversion risk operating system of inter-basin water diversion project.The conclusions are as follows: (1) Based on the theory of disaster risk, the risk of inter-basin water diversion project is defined.
The probability statistics method is used to quantitatively estimate the risk source probability of risk combination factors and the loss of risk-bearing body, and calculate the expression formula of water diversion risk in water source area and water receiving area, to provide decision variables for the subsequent risk scheduling model.
(2) The runoff forecasting model, risk definition and scheme decision process are coupled to establish risk operating model.Through runoff forecast and risk theory, the actual risk is fed back to the scheduling decision, to Reduce the likelihood and severity of risk events.It provides a new idea for multi-risk decision-making evaluation and establishment of regional water supply safety model.
(3) The risk operating system considering multiple uncertain factors is applied to the Hanjiangto-Weihe River Water Diversion Project.The results showed the risk operating system can transfer the risk of water diversion from the dry period to the wet period, and reduce the probability of extreme risk.It effectively reduces the risk of system water diversion and verifies the scientificalness and advancement of the risk dispatching system.
(4) This study reveals the influence of risk source probability and risk-bearing body loss on risk degree.The risk source and risk bearing body of the water receiving area are directly related to the water shortage and its probability distribution.The alternating growth and decline regularity of water shortage probability and socio-economic loss rate is stronger.The corresponding relationship between the risk degree of water diversion and each factor is more significant after the joint action.
After the risk operation of the reservoir group in the water source area of the Hanjiang-to-Weihe River Water Diversion Project, the risk of inter-basin water diversion is alleviated.However, the high-risk problem of water diversion in individual years is still prominent.The next step will be to propose corresponding risk prevention and control measures for the risk of water diversion in individual years to reduce the impact of uncertain runoff changes on water resources allocation.

Fig. 3
Fig.3 Calculation process of occurrence probability of single/multiple risk sources water receiving area.The water diversion project includes HJX Reservoir, SHK Reservoir and 98.3 km Water Conveyance Tunnel in Qinling.The water transmission and distribution project are composed of HCG water distribution hub, north-south trunk line and 20 branch lines(Liu et al., 2015).

Fig. 4
Fig.4 Overview of water diversion project from Hanjiang to Weihe River are output of hydropower station j in t period (MW), Output of pumping station j in t period (MW);

Tab. 3 Fig. 5
Fig.5 Annual runoff variation trend as the optimal marginal distribution function of the annual runoff series of the HJX and SHK reservoirs.The Calyton Copula function is selected as the connection function of the risk source of the inflow of the three estuaries and the golden gorge.

Fig. 6
Fig.6 Contour map of joint distribution of inflow runoff of two reservoirs

Fig. 7
Fig.7 Comparison of generalized extreme value distribution fitting of three models

Fig. 8
Fig.8Comparison of water diversion process and risk degree process in water source area

Fig. 9
Fig.9 Risk degree process of water diversion in continuous dry years Fig.10 Distribution of risk degree of water diversion in water source area

Fig. 11
Fig.11Comparison of risk degree process of water diversion between water source area and water receiving area Fig. 12 Comparison of relationship between risk combination elements and risk degree of water diversion

Table 1
The characteristic parameters of hydro-junctions

Table 2
In this study, the above theories and methods are applied to the case study of Hanjiang-to-Weihe River Water Diversion Project.Runoff forecasting, probability statistics, reservoir operation