Three-dimensional land footprint assessment of land capital sustainability in ecological fragile areas: a case study of Sanjiangyuan Region, China

Traditional assessments of land capital have largely relied on two-dimensional (2D) models that fail to capture the dynamic heterogeneity and spatial-temporal evolution of ecological resource utilization, particularly in ecologically sensitive regions like the Sanjiangyuan region, China. To address this gap, this study develops an innovative analytical framework by integrating an improved three-dimensional (3D) land footprint model with statistical methods, including the standard deviation ellipse and Tapio decoupling models, to systematically evaluate land capital dynamics from 2000 to 2022. The results reveal that: First, while the Sanjiangyuan region maintained an overall land capital surplus, this surplus was progressively shrinking due to a consistent increase in per capita land footprint coupled with declining land carrying capacity, a trend signaling growing ecological stress. Second, the footprint breadth demonstrated a distinct U-shaped trajectory, initially decreasing before rebounding, while spatial heterogeneity exhibited fluctuating growth, highlighting uneven regional development patterns. Third, the decoupling analysis indicated that only a small proportion of prefectures achieved strong decoupling between land use and economic growth, suggesting that most local economies remained dependent on land-intensive development models. The findings highlight the urgent need for differentiated land protection policies to address increasing spatial heterogeneity and deficit risks, offering a scientific basis for sustainable land resource allocation in ecologically fragile areas. • Three-dimensional land footprint model constructed and improved. • Integrating methods such as the Tapio decoupling model and the standard deviation ellipse. • The per capita 3D land footprint exhibits a southwest-northeast distribution pattern. • Sanjiangyuan's expanding land footprint versus declining carrying capacity. • Land surplus in the Sanjiangyuan region generally exists but is showing a declining trend.