No abstract

In China, studies on water supply and water demand balance have received much attention, but risk between water supply and water demand lacks the same focus. This paper presents evaluation criteria of risk between water supply and water demand, which includes threat, susceptibility, and vulnerability. A new quantitative definition of threat is given based on fuzzy probability; Susceptibility is proposed for evaluating the inherent state of the water resource systems; Vulnerability is qualitatively defined and computed in terms of economic losses. A model for risk evaluation is developed based on the maximum entropy principle and discriminant analysis. Risks in Beijing, used as a case study, are evaluated under different scenarios of inflow. The results show that all the risks in 2020 are first or second grade. After using reclaimed water and transferred water, the third grade and fourth grade risk account for 75 %, with 25 % of the first grade and second grade risk. Therefore, risks are still high in the situations of low precipitation periods.

A new method of parameter estimation in data scarce regions is valuable for bivariate hydrological extreme frequency analysis. This paper proposes a new method of parameter estimation (maximum entropy estimation, MEE) for both Gumbel and Gumbel-Hougaard copula in situations when insufficient data are available. MEE requires only the lower and upper bounds of two hydrological variables. To test our new method, two experiments to model the joint distribution of the maximum daily precipitation at two pairs of stations on the tributaries of Heihe and Jinghe River, respectively, were performed and compared with the method of moments, correlation index estimation, and maximum likelihood estimation, which require a large amount of data. Both experiments show that for the Ye Niugou and Qilian stations, the performance of MEE is nearly identical to those of the conventional methods. For the Xifeng and Huanxian stations, MEE can capture information indicating that the maximum daily precipitation at the Xifeng and Huanxian stations has an upper tail dependence, whereas the results generated by correlation index estimation and maximum likelihood estimation are unreasonable. Moreover, MEE is proved to be generally reliable and robust by many simulations under three different situations. The Gumbel-Hougaard copula with MEE can also be applied to the bivariate frequency analysis of other extreme events in data-scarce regions.

In terms of drought years, the assessment of water shortage risk is a significant precondition for taking effective measures to reduce the potential losses. This paper proposes a new multiple integral model for evaluating the risk of water shortage. First, the probability density function for water shortage was simulated. Second, a nonlinear function between vulnerability and its indicators was developed based on projection pursuit. Third, a function of consequence was proposed from the perspective of water-use benefit, and data envelopment analysis was applied to compute the water-use benefit coefficients. Fourth, risk was defined as a double integral in monetary units. Risks in Beijing, used as a case study, are assessed under different inflow scenarios by using the model. The findings of the study were as follows: In 2020, the vulnerability was shown to vary from 0.93 to 0.99, and the maximum value occurs with the inflow conditions of 1980 and 2009. The probable maximum loss occurs with the inflow condition of 2006, and risk is approximately equal to 0.7 billion CNY. After using the transferred water and reclaimed water, all of the values for consequence vulnerability and risk are reduced, but the situation regarding supply and demand remains at a disadvantage in 2020.