Fractal physiography?

Abstract

Fractal geometric parameters were employed to assess the morphometric viability of traditionally defined physiographic provinces using relatively coarse 30-arc-second digital elevation models (DEM) within 1[deg] x 1[deg] blocks of the conterminous United States. Four DEM samples were analyzed for each of the eight areas examined. Six of the eight physiographic provinces plot as strong clusters in fractal parameter space, indicating regional terrain homogeneity. Two displayed weak spatial clustering, suggesting that samples from these regions lacked the spatial homogeneity to be easily detectable in digital form. The terrain parameters for these problematic blocks were calculated using a multi-cell area with a pseudo-inversion solution to the resulting over-constrained matrix equations. The study indicates that use of the Hausdorff-Besicovitch Dimension as an index of surface roughness, the explained variance of the power-law fit to the variance spectrum, and the elevation range of the terrain block are powerful parameters for abstracting surface information. Use of relatively coarse DEMs in high-relief terrain produced fractal dimensions somewhat larger than those reported by other workers who employed finer arrays covering smaller areas. In regions of low relief there was little disparity, suggesting invariance across the scale of the DEMs. The 30-arc-second DEM is capable of resolving features with periods of up to 85 km, and successfully captures the directional texture of morphotectonic terrains.