To quantitatively evaluate and diagnose the carrying capacity of regional water resources under uncertain conditions, an index system and corresponding grade criteria were constructed from the perspective of carrying subsystem. Meanwhile, an improved entropy weight method was used to determine the objective weight of the index. Then, an evaluation model was built by applying set pair analysis, and a set pair potential based on subtraction was proposed to identify the carrying vulnerability factors. Finally, an empirical study was carried out in Anhui Province. The results showed that the consistency among objective weights of each index was considered, and the uncertainty between the index and grade criterion was reasonably dealt with. Furthermore, although the carrying situation in Anhui was severe, the development tended to be improved. The status in Southern Anhui was superior to that in the middle area, and that in the northern part was relatively grim. In addition, for Northern Anhui, the fewer water resources chiefly caused its long-term overloaded status. The improvement of capacity in the middle area was mainly hindered by its deficient ecological water consumption and limited water-saving irrigation area. Moreover, the long-term loadable condition in the southern part was due largely to its relatively abundant water resources and small population size. This evaluation and diagnosis method can be widely applied to carrying issues in other resources and environment fields.

To quantitatively access the effects of drought stress during different growth stages of soybean on development process and yield, a pot-culture experiment was conducted in China’s Huaibei Plain with different irrigation treatments over two seasons (2015 and 2016). Two drought stress levels (mild and severe) were applied at four growth stages for the experiment (S: seedling stage; B: branching stage; FPS: flowering and pod-setting stage; and PF: pod-filling stage). The effects of drought stress at different stages on growth and yield were evaluated and compared. Results of this two-year study showed that all growth and yield parameters were significantly affected by the water deficit during the sensitive FPS. Compared to the full irrigation treatment, severe drought stress during FPS caused a 22% loss of final plant height, 61% loss of the leaf area per plant (LAP), and 67% loss of final aboveground dry matter (ADM). Yield components also declined dramatically with water deficits during FPS and PF. Significant seed yield losses of 73–82% per plant were observed in the plants exposed to drought stress during FPS, and were also associated with the highest nonviable pod percentage of 13%. The greatest losses in 100-seed weight (42–48%) were observed under drought stress during PF. A rising trend in response to increasing soil water deficit (SWD) was observed for LAP, yield, and ADM losses. The slope (k) values of these fitting curves varied at different treatments, the highest value of k (7.37 and 8.47 in two years, respectively) was also observed in the sensitive FPS.

As a new development form for evaluating the regional water resources carrying capacity, forewarning regional water resources of their carrying capacities is an important adjustment and control measure for regional water security management. Up to now, most research on this issue have been qualitative analyses, with a lack of quantitative research. For this reason, an index system for forewarning regional water resources of their carrying capacities and grade standards, has been established in Anhui Province, China, in this paper. Subjective weights of forewarning indices can be calculated using a fuzzy analytic hierarchy process, based on an accelerating genetic algorithm, while objective weights of forewarning indices can be calculated by using a projection pursuit method, based on an accelerating genetic algorithm. These two kinds of weights can be combined into combination weights of forewarning indices, by using the minimum relative information entropy principle. Furthermore, a forewarning model of regional water resources carrying capacity, based on entropy combination weight, is put forward. The model can fully integrate subjective and objective information in the process of forewarning. The results show that the calculation results of the model are reasonable and the method has high adaptability. Therefore, this model is worth studying and popularizing.

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.

Assessment and diagnosis of regional agricultural drought resilience (RADR) is an important groundwork to identify the shortcomings of regional agriculture to resist drought disasters accurately. In order to quantitatively assess the capacity of regional agriculture system to reduce losses from drought disasters under complex conditions and to identify vulnerability indexes, an assessment and diagnosis model for RADR was established. Firstly, this model used the improved fuzzy analytic hierarchy process to determine the index weights, then proposed an assessment method based on connection number and an improved connection entropy. Furthermore, the set pair potential based on subtraction was used to diagnose the vulnerability indexes. In addition, a practical application had been carried out in the region of the Huaibei Plain in Anhui Province. The evaluation results showed that the RADR in this area from 2005 to 2014 as a whole was in a relatively weak situation. However, the average grade values had decreased from 3.144 to 2.790 during these 10 years and the RADR had an enhanced tendency. Moreover, the possibility of RADR enhancement for six cities in this region decreased from east to west, and the drought emergency condition was the weak link of the RADR in the Huaibei Plain.

This paper establishes a water resources vulnerability framework based on sensitivity, natural resilience and artificial adaptation, through the analyses of the four states of the water system and its accompanying transformation processes. Furthermore, it proposes an analysis method for water resources vulnerability based on connection entropy, which extends the concept of contact entropy. An example is given of the water resources vulnerability in Anhui Province of China, which analysis illustrates that, overall, vulnerability levels fluctuated and showed apparent improvement trends from 2001 to 2015. Some suggestions are also provided for the improvement of the level of water resources vulnerability in Anhui Province, considering the viewpoint of the vulnerability index.