Identification of Spatial Fairness and Obstacle Factor of Public Service Facilities from Multigradient Perspective: Lan-Bai Urban Agglomeration

Urban–rural development grapples with spatial inequality in public service facilities (PSFs). Understanding the spatial patterns of PSFs and promoting their equitable development is crucial for achieving equalization of PSFs, which is a key mechanism enhancing public resource utilization efficiency and resident satisfaction. Therefore, this paper uses the Lanzhou–Baiyin (Lan-Bai) urban agglomeration as a case study to investigate the spatial distribution of PSFs from a multigradient perspective by constructing a multidimensional gradient and utilizing function fitting. The study also evaluates the spatial equity of PSFs from a multigradient perspective. Finally, the paper identifies obstacle factors that impact the spatial equity of facilities. The results show the following: (1) Significant spatial aggregation of PSFs. (2) PSFs are situated predominantly in urban areas with flat terrain, high economic status, and proximity to urban centers. Topographic gradient and center–edge gradient (CEG) inversely correlate with facility density, while economic gradient (EG) and urban–rural gradient (URG) show a positive relationship. (3) The spatial equity of PSFs displays notable variations, with fairness being the foundation of facility matching but with areas exhibiting redundancy and insufficiency, particularly in EG. (4) EG and URG are the main obstacles to spatial equity in PSFs, with redundant inequity primarily attributed to CEG and deficient inequity affecting both URG and CEG. This study contributes to advancing sustainable urban–rural development by enhancing residents’ well-being through improved provision of various service facilities.