Using fractals and multifractals to characterize the spatiotemporal pattern of impervious surfaces in a coastal city: Xiamen, China

Abstract

Impervious surfaces (IS) constitute a quantifiable metric for urbanization and ecological environmental assessment. This study estimated the IS in the subtropical coastal area of Xiamen, southeastern China, from TM/OLI images obtained in 1994, 2000, 2004, 2010, and 2015. Two-dimension box-counting and two-dimension multifractal box-counting method were employed to quantitatively characterize the fractal and multifractal features of the spatial patterns of the IS. Results suggest that the spatial patterns observed during the study period are typical fractal structures with scale invariance, and the fractal dimension reveals the spatio-temporal complexity. Increasing the pixel binarization threshold decreases the spatial complexity of the IS pattern. The increasing dimension values over time show that the IS patterns become more complex and the spatial distribution becomes more clustered from 1994 to 2015. The two-dimension multifractal approach can transform an irregular IS pattern into a compact form and amplify small differences between different data series. The results revealed multifractality in the five study years, which varied throughout the study period, but the probability distribution shows a slightly decreasing trend. The probability of a given pixel having a high IS-fraction is consistently high in the study area, as indicated by the positive ratio between the regions where the probability measure appears most concentrated and most sparse.