Water is essential for sustainable development, and river basins like the Yellow River in China are crucial for socioeconomic development and ecological security. The Yellow River basin (YRB) supports a large population and significant economic activity despite limited water resources. Existing WRCC assessments often rely on dimensionless indices, lacking clarity in representing regional carrying capacity. This study aims to overcome this limitation by characterizing WRCC using population size and economic scale. The Yellow River faces water scarcity issues due to reduced runoff and contamination, exacerbated by the projected decrease in runoff by 2030 as outlined in the "Yellow River Basin Comprehensive Planning (2012-2030)". This plan allocates 39.485 billion m³ of freshwater for the nine provinces in the YRB, with a projected population of 0.13094 billion. The study addresses whether this water allocation is sufficient and determines the supportable population size and economic scale under different development scenarios.

The introduction extensively reviews existing literature on water resource carrying capacity (WRCC), highlighting the limitations of using dimensionless indices. It cites studies that employ composite indices or 0-1 scales to evaluate water resource suitability and environmental carrying capacity. The authors argue that these methods lack the conciseness and visual clarity needed for effective regional carrying capacity representation. The review also includes studies on the Yellow River’s declining runoff, water scarcity issues, and the "Yellow River Basin Comprehensive Planning (2012-2030)" which provides the basis for the study's water allocation scenario.

The study uses a WRCC prediction model based on previous research by Guo et al. (2022). The model maximizes population (P) subject to constraints on total water use (TW), which includes domestic (WD), production (WP), and ecological (WE) water use. Equations are developed to model each component of water use, considering factors like population size (P), urbanization rate (uR), per capita domestic water use (QU, QR), per capita GDP (Ya), water use per CNY10,000 of GDP (QGDP), and the growth rate of per capita GDP (gr) and the decrease ratio of water use per CNY10,000 of GDP (dr). Data from 2020 serves as the benchmark, with future values projected using historical trends analyzed via the Mann-Kendall method and artificial neural networks where applicable. The upper limits for per capita domestic water use were based on WHO standards and literature. Ecological water use is assumed to decrease substantially by 2030. The model calculates the 2030 population size (P2030) and economic scale (TWGDP2030) for each province. Multiple scenarios are simulated by varying the gr and dr parameters, representing high, moderate, and low development pathways. The study considers both province-level and regional analyses of the results.

The study's simulations show that the available freshwater of 39.845 billion m³ in 2030 can support population sizes exceeding the projected 0.13094 billion. Under high, moderate, and low development scenarios, the supportable populations are 0.16 billion, 0.152 billion, and 0.147 billion, respectively. The corresponding economic scales are CNY17.5 trillion ($2.52 trillion), CNY15.01 trillion ($2.18 trillion), and CNY13.2 trillion ($1.91 trillion). Spatial analysis reveals significant disparities in WRCC between the middle and upper reaches and the middle and lower reaches of the YRB. The middle and lower reaches can support a considerably larger population and economic scale, despite a slightly higher water allocation compared to the middle and upper reaches. This disparity is primarily attributed to differences in economic development and water use efficiency. The middle and lower reaches exhibit higher per capita GDP and significantly lower water use per CNY10,000 of GDP compared to the middle and upper reaches. The study highlights substantial variations in per capita GDP and water use efficiency across the nine provinces, emphasizing the importance of balanced development and improved water use efficiency.

The findings demonstrate that the projected available freshwater in 2030 can support a larger population and economic scale than initially predicted. However, the significant spatial disparities in WRCC highlight the need for targeted policies focusing on balanced regional development and water resource management. Improving water use efficiency, particularly in the less developed regions of the middle and upper reaches, is crucial for maximizing the YRB's water resource carrying capacity. The results underscore the complex interplay between economic development, population growth, and water resource availability. The study's methodology offers a valuable tool for informing water resource allocation and sustainable development planning in the YRB.

This study successfully simulates the population size and economic scale supportable by the Yellow River's limited freshwater resources in 2030. The results show sufficient water availability to sustain projected population growth and considerable economic development across various scenarios. The method improves upon prior WRCC assessments, highlighting regional disparities and suggesting targeted policies. Future research should incorporate population density and utilize finer spatial scales for enhanced accuracy.

The study assumes an even distribution of population density, which may not accurately reflect the reality in the YRB. The analysis is conducted at the provincial level, which might overlook variations at smaller spatial scales. The projections for water use efficiency and ecological water requirements include inherent uncertainties due to potential future technological advancements and policy changes.