A Comprehensive Study of Water Resource–Environment Carrying Capacity via a Water-Socio-Ecological Framework and Differential Evolution-Based Projection Pursuit Modeling

Water resources are fundamental to sustaining life, fostering social development, and maintaining ecological balance. This study focuses on Anhui Province (AP) as the research area, employing 22 indicators from the Water-Socio-Ecological (WSE) framework for the water resource-water environment carrying capacity (WR-WECC) of AP. The WR-WECC of AP is assessed via differential evolution projection pursuit modeling (DE-PPM). Additionally, the degree of coupled coordination model (DCCM) is utilized to analyze the coordinated development among the municipalities of AP, whereas the obstacle degree model is employed to identify the primary obstacles affecting the enhancement of the WR-WECC and to forecast them via autoregressive composite moving averages. The findings of the study are as follows: (1) WR-WECC in AP showed a steady upward trend, and the water, socio-economic, and ecological subsystems showed a fluctuating upward trend, with ES increasing the fastest. The overall WR-WECC of each city shows a fluctuating upward trend, and the spatial gap narrows, with Southern Anhui (SA) > Central Anhui (CA) > Northern Anhui (NA). (2) The DCC of the WSE carrying capacity of AP also shows a fluctuating upward trend, gradually transitioning from barely coordinated to well coordinated. The DCC level of the WR-WECC in SA is better than that in CA and NA, and the growth rate is greater than that in CA and NA, whereas the DCC level in CA is better than that in NA, and the DCCs of the three major regions show an upward trend. (3) The degree of obstruction at the criterion level of AP’s WR-WECC basically maintains the following order: WS > SS > ES. In the indicator layer, the water supply modulus, water production modulus, and proportion of tertiary industry are the main obstacle factors restricting the enhancement of the WR-WECC of AP. (4) The prediction results for 2025–2040 indicated that the WR-WECC level and the three subsystem levels of AP showed a continuous increasing trend. Measuring WR-WECC plays a crucial role in regional sustainable development.