Evaluation of water resource carrying potential and barrier factors in Gansu Province based on game theory combined weighting and improved TOPSIS model

• The carrying capacity of water resources in Gansu Province is evaluated comprehensively. • The combination weights of different indicators were determined through the application of game theory. • The TOPSIS evaluation model improved by using grey relational analysis was applied to calculate the WRCC of Gansu Province. • The water-carrying capacity of 14 cities and prefectures in Gansu Province has been progressively increasing over the years. • The future water resource carrying capacity has been forecasted using the ARIMA model. The water resource carrying capacity, as a pivotal component of the overall regional natural resource carrying capacity, plays a fundamental role in determining the feasibility of achieving harmonious coexistence among population, economy, and environment in regions with limited water resources. It holds paramount significance for regional development.“Based on the theoretical framework of the four subsystems, namely water resources, society, economy, and ecology, this article employs the entropy weight method and CRITIC method to calculate individual weights. The combined weights are then determined using game theory. Subsequently, an improved TOPSIS model based on grey relational analysis is applied to comprehensively evaluate the water resources carrying capacity in Gansu Province from 2009 to 2022. The main obstacles impacting water resources carrying capacity are diagnosed using an obstacle degree model. Finally, a time series model is utilized to predict future trends in water resources carrying capacity from 2023 to 2030. The findings suggest that (1)over the study period, Gansu Province exhibited an upward trend in its overall water resource carrying capacity, with a value of 0.55 (weakly bearable) in 2022, representing a significant 20% increase compared to the baseline year of 2009. (2) In terms of regional changes, before 2015, the water resources carrying capacity of Wuwei, Linxia, Dingxi, and other places were in a weakly bearable carrying range [ 0.5,0.6), while other cities and prefectures were in a critical carrying state [ 0.4,0.5). After 2015, the carrying state of most cities and prefectures has improved, especially in Jiuquan, Jiayuguan, Wuwei, and other places, which may be related to the local government’s efforts to increase water resources management and water-saving measures. (3) The key factors influencing the carrying capacity of water resources in Gansu Province include ecological water consumption, industrial wastewater emissions of chemical oxygen demand (COD), urban sewage treatment capacity, effective irrigation area in agricultural land, overall water consumption rate, and per capita daily water consumption in urban areas. To promote sustainable utilization of water resources, it is crucial to strengthen the management and regulation of these major hindering factors. (4) The future carrying capacity of water resources in various cities and states is expected to witness significant improvement. By 2030, it is anticipated that the carrying capacity of all provinces within Gansu Province will reach a bearable state [0.6,1], thereby progressing towards an overall green and sustainable trajectory.