Fractal analysis of surface topography

Abstract

Spectral and fractal analysis is applied to compute one-dimensional and two-dimensional power spectra of the surface topography in the Nopex and Folldal research areas. The power spectrum is used to estimate the fractal dimension of topography in a search for a scale-invariant topographic measure applicable for scaling and aggregation of hydrological processes and parameters. To evaluate their appropriateness as a tool in geomorphometry, the power spectrum is also used to analyse small-scale variability in topography. The analysis is accomplished by approximating a fractal model based on the Weierstraas Mandelbrot Function and Fast Fourier Transform to the surface topography. In this model the fractal dimension D describes the scaling of surface roughness. The results show that the topography of the Nopex and the Folldal areas cannot be described by a single fractal dimension D since this parameter seems to vary with the frequency range considered. This observed inhomogeneity in the scaling parameter implies that the extrapolation of roughness and other roughness-dependent physical parameters to other scales should be done with care in these areas. The power spectra show some promising properties in identification of specific surface characteristics related to small-scale variability in elevation.