Quantifying the influences of landscape gradient on urban spatial efficiency by using surface metrics in the central area of a mountainous city

• Landscape gradient impacts urban spatial efficiency, characterized by the Gradient Surface Model. • The impacts of landscape gradients on urban efficiency are explored through marginal effects. • NDVI Summit Density and elevation Root Mean Square Slope negatively impact urban spatial efficiency. • Urban spatial efficiency varies across block clusters with different landscape gradient characteristics. • The planning and design inspirations of mountainous urban blocks could be elicited by landscape gradient characteristics. Rapid urbanization in mountainous areas has caused unbalanced development, land use conflicts, and decreased urban spatial efficiency (USE) due to terrain constraints and disorderly land expansion, and this issue has not been fully explored. To address this gap, this study constructs a framework to quantify the impacts of landscape gradients on urban spatial efficiency. By developing indicator systems to characterize both landscape heterogeneity and urban spatial efficiency, the relationships between these factors are analyzed using the Boosting Regression Trees model, and clusters are identified to reveal spatial differentiation through key landscape gradient indicators. The results indicate that (1) the Summit Density (Sds) of Normalized Difference Vegetation Index (NDVI) exhibits the most significant negative impact on urban spatial efficiency, especially on spatial utilization efficiency; (2) the Root Mean Square Slope (Sdq) of Digital Elevation negatively affects traffic and public services efficiency; (3) the Texture Direction Index (Stdi) of building distribution has the most significant positive impact on public service efficiency. In mountainous environments, different landscape gradient types exhibit clear contrasts in urban spatial efficiency. Varied elevations lead to diverse construction sites and building layouts within urban blocks, resulting in spatial differentiation of urban spatial efficiency. This study enhances the use of gradient surface metrics in urban spatial research by describing landscape patterns and heterogeneity at the block scale. It offers valuable insights for urban planning and design with a focus on equity and sustainability.