Detrended fluctuation analysis of spatial patterns on urban impervious surface

Abstract

This paper analyzes satellite data from downtown Shanghai, China, to investigate the long-range dependence of spatial patterns on urban impervious surfaces (UIS) using two-dimensional detrended fluctuation analysis (DFA). The UIS fraction is estimated from Landsat Thematic Mapper and Enhanced Thematic Mapper Plus data from 1997 to 2010 using linear spectral mixture analysis. The results indicate that the spatial distribution of the UIS exhibits a positive spatial dependence, as revealed by Moran’s index, capturing the evolution from aggregation to dispersion and back to aggregation during the study period. The use of two-dimensional DFA reveals a strong long-range power-law dependence in the UIS spatial pattern during the study period. The DFA scaling exponent can be seen as a measure of the uniformity of the UIS spatial distribution, and exhibits an approximate 1/f behaviour. Two-dimensional multifractal detrended fluctuation analysis (MFDFA) confirmed that the UIS spatial pattern is not multifractal in nature, meaning that only a single scaling exponent is required to disclose the long-range dependence in the UIS spatial pattern. The application of two-dimensional DFA to UIS patterns should be viewed as a complementary tool to existing techniques, such as Fourier analysis, wavelets, and structure function, that can provide additional information about the structure of UIS patterns, including its 1/f behaviour.