With the rapid economic development and the acceleration of urbanization, the pressure on the water resources system is becoming intense. As an important indicator of water resources security and sustainable development, the water resources carrying capacity has become a hot issue. To overcome the limitation of commonly used methods for weight determination and to evaluate the regional water resources carrying capacity reasonably, the index weight determined by the Analytic Hierarchy Process method was revised by the subtraction set pair potential to calculate the dynamic index weight. Then, the dynamic weight was combined with the set pair analysis method to evaluate the regional water resources carrying capacity dynamically. In addition, the Dagum Gini coefficient and its decomposition method were used to analyze the overall difference of water resources carrying capacity in the whole region and the differences within and between subregions considering the lack of quantitative research in spatial equilibrium. Finally, a case study was carried out in Anhui Province, China. The results showed that from 2011 to 2018, most of the water resources carrying capacity for 16 cities in Anhui Province were in a critical state, with the strongest in the south of Anhui Province and the weakest in the north. The overall spatial difference of carrying capacity in Anhui Province showed an increasing trend from 2011 to 2018. Furthermore, the slightest difference within the subregion was in the north of Anhui Province, while the largest was in the south. The most significant difference between the subregions was between the south and the north of Anhui Province. The primary source of carrying capacity spatial difference in Anhui Province was from the difference between subregions. The results of the case study suggested that the method proposed in this paper are conducive to the early find of possible disadvantages of spatial equilibrium and can effectively identify the main source of regional spatial difference in water resources carrying capacity, which means that the method can be widely applied to similar issues.

Quantifying the lasting effects of drought stress on crop growth is a theoretical basis for revealing agricultural drought risk mechanism and formulating adaptive irrigation strategies. Based on two-season pot experiments of soybean in the Huaibei Plain, quantitative responses of plant evapotranspiration and aboveground biomass at each growth stage from a drought were carried out. The results showed that drought stress at a certain stage of soybean not only significantly reduced the current evapotranspiration and aboveground biomass accumulation during this stage, compared with full irrigation, but also generated the after-effects, which resulted in the reductions of evapotranspiration and biomass accumulation at the subsequent periods. Furthermore, the damaged transpiration and growth mechanism caused by drought gradually recovered through the rewatering later, and the compensation phenomenon even occurred. Nevertheless, the specific recovery effect was decided by both the degree and period of drought before. It is practical to implement deficit irrigation at the seedling and branching stages, but the degree should be controlled. Meanwhile, it is crucial to ensure sufficient water supply during the reproductive growth phase, especially at the flowering and pod-enlargement stage, to guarantee a normal transpiration function and a high biomass yield for soybeans in the Huaibei Plain.

Currently, the implementation of water resource spatial equilibrium strategy is a fundamental policy of water resource integrated management in China; it is also a considerable challenge to explore the relationship structure features of water resources, society, economy and ecological environment (WSEE) complex system. For this purpose, firstly, we applied information entropy, ordered degree and connection number coupling method to reveal the membership characteristics between different evaluation indicators and grade criterion. Secondly, the system dynamics approach was introduced to describe the relationship features among different equilibrium subsystems. Finally, the ordered degree, connection number, information entropy and system dynamics integrated model was established to conduct relationship structure simulation and evolution trend evaluation of the WSEE system. The application results in Hefei city, Anhui Province, China, demonstrated that: (1) the variation of overall equilibrium conditions of WSEE system in Hefei city, 2020–2029 was higher compared to that of 2010–2019, though the increasing rate of ordered degree and connection number entropy (ODCNE) became slower after 2019; and (2) the annual ODCNE value from 2020 to 2029 of WSEE system under dry year scenarios increased about 0.0812, which indicated that the construction of Yangtze-Huaihe Diversion (YHD) project could play significant positive role in mitigating the equilibrium situation of WSEE system in Hefei city in the future. On the whole, this study is capable of providing the guidance basis for constructing a theoretical framework of structure simulation and equilibrium evaluation analysis of WSEE complex system.

To promote the application of entropy concepts in uncertainty analysis of water resources complex system, a quantitative evaluation and obstacle factor diagnosis model of agricultural drought disaster risk was proposed using connection number and information entropy. The results applied to Suzhou City showed that the agricultural drought disaster risks in Suzhou during 2007–2017 were all in middle-risk status, while it presented a decreasing trend from 2010. The information entropy values of the difference degree item bI were markedly lower than those of the difference degree b, indicating that bI provided more information in the evaluation process. Furthermore, the status of drought damage sensitivity and drought hazard were improved significantly. Nevertheless, high exposure to drought and weak drought resistance capacity seriously impeded the reduction of risk. Thus, the key to decreasing risk was to maintain the level of damage sensitivity, while the difficulties were to reduce exposure and enhance resistance. In addition, the percentage of the agricultural population, population density, and percentage of effective irrigation area were the main obstacle factors of risk and also the key points of risk control in Suzhou. In short, the results suggest that the evaluation and diagnosis method is effective and conducive to regional drought disaster risk management.

Water Supply issues a formal retraction in relation to the above article by Zheng Li, Juliang Jin, Yi Cui, Libing Zhang, Chengguo Wu, Shaowei Ning and Yuliang Zhou. The publisher issues this retraction due to concerns relating to unreliable quality and data. The journal did not receive a satisfactory response from the authors to these concerns and as such, the Editors-in-Chief no longer have confidence in the integrity of the article. We apologize for any confusion this may have caused.