Directional multi-scale analysis and simulation of urban expansion in Auckland, New Zealand using logistic cellular automata

Abstract

In characterising urban expansion, existing landscape indices lack consideration for directional changes. This limitation is overcome with the proposed directional perspective (urban expansion vector) in this study, which can identify both the urban expansion mode and local changes at the patch and sectorial levels, and reveal the varying importance of the same urbanisation factors at multi-scales. Landscape (expansion) indices (LEI) and directional characteristics of newly grown urban patches were derived / extracted from time-series (1975–2016) satellite images in the Auckland metropolitan area, based on which urban expansion was simulated using logistic regression cellular automata at both the global and sectorial levels. The results show that Auckland urban development was mostly compact with “organic” being the dominant mode of expansion throughout the last 40 years. Most urban development took place in the southeast (270° - 360°) and northwest (90° - 180°) sectors, within which urban expansion occurred mostly in places that had favourable transportation infrastructures and are close to the CBD. The influence of the nine factors of urbanisation studied varies with scale and sector. In general, accessibility (e.g., proximity to roads and the CBD) and amenity (e.g., distance to transportation and schools) are more important than physical variables (e.g., terrain) in affecting urban development. The localised sectorial simulation result is in a closer agreement with the observed urbanisation than the global, sectorless result. The directional perspective, in conjunction with the LEI and other landscape indices, can effectively characterise the spatiotemporal patterns of urban expansion. More importantly, it improves the simulation accuracy of urban expansion (e.g., simulation kappa rising from 0.024 to 0.161 in the northwest sector, and from 0.31 to 0.40 in the southeast sector) for a monocentric city whose urbanisation is strongly sectorial.