An analysis for features of geospatially rescaled range analysis method and spatial scaling behavior

We apply the rescaled range analysis (R/S) method to analyze the geospatial scaling behavior and its relevant features, including spatial heterogeneity, a spatially short-range correlation, spatial scale effects and spatial nonstationarity. Our goal is to provide a tentative finding about a theoretical framework construction of geospatial multifractality of attribution-variable-value distribution. To investigate the spatial scaling behavior, the conventional R/S method is extended to a two-dimensionally geographical space and a two-dimensional geospatially rescaled range analysis method is presented. Our analysis shows that this proposed method is reliable and effective in the analysis of spatial scaling behavior and its characteristics. Furthermore, on the basis of this approach, the theoretical framework of spatial multifractality associated with spatial distribution of attribution value is preliminarily developed. Our findings contribute by providing a potential method to investigate spatial scaling behavior and spatial multifractality.