Proximity Expansion Index: An improved approach to characterize evolution process of urban expansion

The spatial relationship of newly grown urban patches to existing urban areas lies at the core of understanding the properties of urban expansion dynamics. Some existing landscape metrics have been used to identify patch expansion types, i.e., infilling, edge-expansion and outlying, capturing the evolution process of urban expansion patterns based on quantifying spatial relationship. However, these existing metrics cannot comprehensively describe the spatial distributions of all new patches relative to old built-up areas, especially for outlying patches, which are the significant elements affecting the urban expansion pattern. We propose a new landscape metric, the Proximity Expansion Index (PEI), to address this problem by incorporating two factors of proximity - distance and boundary sharing rate to old patches. The value of PEI is continuous and has the clear physical meaning for depicting the gradient of the spatial relationship. The landscape expansion types are then redefined by PEI, while the sprawl level of outlying patches is clearly reflected. The variants of PEI are designed as global indices to capture information of the dynamic process of urban expansion from a bottom-up view. We selected Wuhan, a metropolis in central China, as a case area to evaluate PEI based on four periods of remote sensing images (1995, 2000, 2005 and 2010). The results show that the spatial pattern of urban expansion becomes increasingly dispersed, demonstrating that PEI is capable of capturing information of urban expansion evolution. PEI can depict the spatial relationship between new and old patches in a more detailed way by comparing PEI and previous metrics. Using PEI, we can also discover regions of great significance, called outlying seed regions, which have a profound impact on the coalescence of urban morphology.