Impacts of spatial scale on the delineation of spatiotemporal urban expansion

The delineation of spatiotemporal urban expansion highly depends on the selection of moving window size. Few studies examine the effects of moving window size and the scaling mechanism when analyzing urban expansion patterns. This study selected nine moving windows from 450 m to 4050 m with a scale (size) interval of 450 m to examine the urban expansion dynamics of Shanghai from 1995 to 2005, and from 2005 to 2015. Three urban expansion rate indicators were selected to explore the scale dependence of urban expansion, and these indicators include the overall urban expansion rate (OUER), the gridded urban expansion rate (GUER), and the boxed urban expansion rate (BUER). In addition, Global Moran's I was used to measure the spatial autocorrelation of urban expansion on different scales. The results show that the changing moving window size has varying impacts on delineating urban dynamics when using these three indicators. Specifically, OUER and GUER yield polynomial relationships with the moving window size, while BUER does not comply with any known functions in terms of the scaling relations. All three indicators reach their extreme points and/or inflection points at sizes of 1800 m, 2250 m and 2700 m, and the optimal size is speculated in the range of 1800-2700 m. This study should help to choose appropriate moving window sizes and suitable urban expansion indicators to more accurately capture the spatial differences in urban expansion dynamics and assist land-use planning.