Abstract: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.

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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.