Urban Expansion, Entropy Dynamics, and Ecological Quality: A District-Based Assessment

Abstract. Urban expansion in rapidly developing metropolitan regions reshapes not only the spatial structure of built environments but also the ecological functioning of surrounding landscapes. This study examines district-level urban expansion and ecological change between 2007, 2018, and 2025 in a rapidly growing region of north-west Sydney, Australia. Multi-temporal Landsat imagery was classified to extract built-up land, and Shannon’s entropy was used to quantify the spatial dispersion of development. In parallel, ecological conditions were assessed using the Remote Sensing Ecological Index (RSEI), while temporal differences (ΔRSEI) and Getis–Ord Gi hotspot analysis were applied to identify spatial clusters of improvement or degradation. Results show that entropy increased from 0.88 (2007) to 0.91 (2018), indicating a phase of suburban expansion, then stabilised at 0.90 by 2025 as development became more uniform across districts. Ecological quality declined steadily, with mean RSEI decreasing from 0.72 to 0.70 and further dropping to 0.61 in the final period. Hotspot patterns reveal ecological improvement in central districts during early development (2007–2018), whereas a distinct cold spot emerges in the southern district between 2018–2025, associated with intensified construction activity and vegetation loss. These spatial patterns are further supported by socio-economic indicators. Population grew by over 50%, housing prices tripled, and transport investments such as the Sydney Metro Northwest contributed to increasing development pressure, accelerating suburbanisation and ecological stress. Overall, the integrated entropy-RSEI hotspot approach provides a framework for linking urban with ecological quality and offers insights to support planning and management in rapidly growing metropolitan regions.