Analysis and prediction of urban agglomeration ecological footprint based on improved three-dimensional ecological footprint and shared socioeconomic pathways

• From 2000 to 2020, Guanzhong's ecological footprint grew, carrying capacity fell, and the ecological deficit widened. • Ecological security levels varied across Guanzhong. • Under SSP1-SSP5, population impact on the ecological footprint peaks in 2025-2027, while urbanization's influence declines. Ecological degradation has significantly affected many regions of the nation, particularly those undergoing rapid economic expansion. In recent years, Shaanxi’s Guanzhong region has experienced sustained economic growth, with industrialization and urbanization imposing considerable pressure on the local environment. This study analyzes the spatial–temporal dynamics of ecological security, sustainability, and driving factors in Shaanxi’s Guanzhong urban agglomeration. Using an extended nonlinear STIRPAT model, this study projects population and urbanization rates under Shared Socioeconomic Pathways (SSP1-SSP5) scenarios. The results reveal a 4.3-fold increase in the ecological footprint in the Guanzhong region during the study period, alongside a decline in carrying capacity, resulting in a pronounced ecological deficit. Despite some progress in coordinated development, ecological security and sustainability levels remain low. Population growth and per capita GDP are identified as the primary drivers of the three-dimensional ecological footprint expansion. Projections indicate that the population-driven ecological footprint will peak between 2025 and 2027, with the highest peak under SSP5. By 2050, urbanization’s contribution to the ecological footprint is expected to decrease significantly, with the sharpest reductions expected under SSP1, SSP2, and SSP3. This study provides valuable guidance for addressing the ecological-economic imbalance in rapidly urbanizing and industrializing urban agglomerations.