Revealing the evolution of spatiotemporal patterns of urban expansion using mathematical modelling and emerging hotspot analysis.

The rapid expansion of cities in developing countries has led to many environmental problems, and the mechanism of urban expansion (UE), as a more complex human-land coupled system, has always been a difficult issue to research. This paper introduces a new approach by establishing an analytical framework for spatiotemporal pattern mining, exemplified by studying the urban growth of Changsha City from 1990 to 2019. Initially, an emerging hotspot analysis model (EHA) is employed to examine the spatiotemporal changes of urban growth on a macro scale. Mathematical models are subsequently utilized to quantify the correlations between urban expansion and selected infrastructural and topographical factors. Building on these findings, the paper constructs mathematical models to further quantify the spatiotemporal evolution of various urban sprawl patterns across different regions, aiming to elucidate and quantify the significant variations in UE over time and space. The study reveals that, as an emerging city, Changsha's hotspots of urban expansion prior to 2003 were primarily concentrated in the city centre, subsequently spreading to the periphery. The radial influence of metro stations on UE is notably less than that of railway stations-approximately 3 km versus 8 km-and the impact diminishes rapidly before gradually tapering off. Moreover, UE in Changsha predominantly occurs on slopes with gradients ranging from 1.1° to 7.5°, and significant development capacity is observed at elevations between 36.1 m and 78.3 m above sea level, with a tendency for urban sprawl to migrate to lower elevations. The paper also identifies three distinct patterns of urban expansion across different regions: an initial slow-growth phase, followed by a rapid escalation to a peak, and subsequently a swift decline to near stagnation. Additionally, it highlights a significant correlation between the proportion of built-up areas at the micro-regional scale and the stages of UE. This correlation was quantitatively analysed by constructing a logistic function, which demonstrated a robust fit that effectively captures spatiotemporal heterogeneity in the dynamics of UE. These insights enhance the selection of drivers in urban simulation models and deepen the understanding of the complex dynamics that influence urban development.