This paper developed a multiobjective stochastic fractional goal programming (MOSFGP) model for optimal water resources allocation among industries based on analyses of water resources quantity, quality, and uncertainty. The model integrated chance constrained programming, fractional programming, and multiobjective goal programming. The developed model was then applied in a real-world case study. The developed MOSFGP has the following advantages: (1) the model deals with economic and social objectives simultaneously, thus reflecting the actual situation more realistically; (2) the model in fractional form can determine water resources use efficiency directly; (3) water quantity and water quality are coupled in the model; and (4) the model can generate different optimal schemes under different risk probabilities. Based on the results of the MOSFGP model, decision makers could use water resources efficiently and obtain higher economic and social benefits. The model is also of great significance to i...

This paper presents an extended two-stage data envelopment analysis (DEA) method for analyzing water resource use efficiency (WRUE) and related WRUE issues, which was developed by introducing regional water resource metabolic theory into the two-stage DEA method. It has the following advantages: (1) it has the ability to reflect the inner difference and connection of the regional water resource consumption process, which developed the corresponding physical model instead of making it a “black box”; (2) the built physical model for WRUE divided the main body of water resource consumption into social and economic subsystems, which can thus elaborate WRUE; (3) it can analyze not only WRUE but also related WRUE issues. The proposed method was applied to a real-case study in Gansu Province, China. Results show that decision makers can determine the comprehensive and accurate WRUE and negative factors of WRUE in Gansu Province. Moreover, the results offer recommendations for decision makers to plan for efficient use of water resources in different cities.

The stationarity of observed hydrological series has been broken or destroyed in many areas worldwide due to changing environments, causing hydrologic designs under stationarity assumption to be questioned and placing designed projects under threat. This paper proposed a data expansion approach—namely, the cross-reconstruction (CR) method—for frequency analysis for a step-changed runoff series combined with the empirical mode decomposition (EMD) method. The purpose is to expand the small data on each step to meet the requirements of data capacity for frequency analysis and to provide more reliable statistics within a stepped runoff series. Taking runoff records at three gauges in western China as examples, the results showed that the cross-reconstruction method has the advantage of data expansion of the small sample runoff data, and the expanded runoff data at steps can meet the data capacity requirements for frequency analysis. In addition, the comparison of the expanded and measured data at steps indicated that the expanded data can demonstrate the statistics closer to the potential data population, rather than just reflecting the measured data. Therefore, it is considered that the CR method ought to be available in frequency analysis for step-changed records, can be used as a tool to construct the hydrological probability distribution under different levels of changing environments (at different steps) through data expansion, and can further assist policy-making in water resources management in the future.

The aim of this paper is to evaluate water resources use efficiency (WRUE), which focuses on the entire water consumption process by utilizing data envelopment analysis (DEA) and the Malmquist index (MI). A comprehensive analysis of WRUE both on the spatial and temporal scale has been conducted. For the spatial scale, the difference of WRUEs among cities is presented, and the negative factors by analyzing and decomposing relative water resources use efficiency (RWRUE) are examined. Similarly, the dynamic changes of WRUE over time is presented to analyze the temporal scale. Moreover, a real-world case study in Guansu Province, China, from 2003 to 2013 is employed to evaluate the performance of the proposed WRUE analysis. Results show that the decision makers can determine the comprehensive and accurate WRUE and negative factors of WRUE in Gansu. Furthermore, the results provide alternative recommendations to decision makers to plan for efficient use of water resources in different cities.

Water competing conflict among water competing sectors from different levels should be taken under consideration during the optimization allocation of water resources. Furthermore, uncertainties are inevitable in the optimization allocation of water resources. In order to deal with the above problems, this study developed a fuzzy max–min decision bi-level fuzzy programming model. The developed model was then applied to a case study in Wuwei, Gansu Province, China. In this study, the net benefit and yield were regarded as the upper-level and lower-level objectives, respectively. Optimal water resource plans were obtained under different possibility levels of fuzzy parameters, which could deal with water competing conflict between the upper level and the lower level effectively. The obtained results are expected to make great contribution in helping local decision-makers to make decisions on dealing with the water competing conflict between the upper and lower level and the optimal use of water resources under uncertainty.