Multiscale Frequency Table Analysis of Landscape Fragmentation in Thematic Raster Maps

This paper is concerned with extracting and summarizing the spatial pattern that may be present in landcover and other thematic raster maps. A sequence of rather large frequency tables is calculated by scanning the map and recording the landcover in configurations of four pixels whose inter-pixel distances become increasingly large. Perceived spatial pattern in a map is determined in part by dominance in the marginal landcover distribution. Likewise, the calculated frequency tables are much affected by the marginal landcover distribution. In order to adjust for this effect and extract a measure of intrinsic spatial pattern, we compare the actual frequency tables to what we would expect the tables to be if landcover were assigned to pixels as independent random draws from the marginal landcover distribution, i.e., for a pattern-free map. Discrepancy between the two sets of frequency tables is assessed using Kullback-Liebler distance, leading to several profiles of fragmentation in the landscape. Methods are illustrated with landcover maps for three Pennsylvania watersheds chosen to represent a range of human impact and disturbance.