Fractal Surfaces of Synthetical DEM Generated by GRASS GIS Module r.surf.fractal From ETOPO1 Raster Grid

Abstract

The research problem is about to generate artificial fractal landscape surfaces from the Digital Elevation Model (DEM) using a stochastic algorithm by Geographic Resources Analysis Support System Geographic Information System (GRASS GIS) software. Fractal surfaces resemble appearance of natural topographic terrain and its structure using random surface modelling. Study area covers Kuril- Kamchatka region, Sea of Okhotsk, North Pacific Ocean. Techniques were included into GRASS GIS modules (r.relief, d.rast, r.slope.aspect, r.mapcalc) for raster calculation, processing and visualization. Module 'r.surf.fractal' was applied for generating synthetic fractal surface from ETOPO1 DEM GeoTIFF using algorithm of fractal analysis. Three tested dimensions of the fractal surfaces were automatically mapped and visualized. Algorithm of the automated fractal DEM modelling visualized variations in steepness and aspect of the artificially generated slopes in the mountains. Controllable topographic variation of the fractal surfaces was applied for three dimensions: dim=2.0001, 2.0050, 2.0100. Auxiliary modules were used for the visualization of DEMs (d.rast, r.colors, d.vect, r.contour, d.redraw, d.mon). Modules 'r.surf.gauss' and 'r.surf.random' were applied for artificial modelling as Gauss and random based mathematical surfaces, respectively. Univariate statistics for fractal surfaces were computed for comparative analysis of maps representing continuous fields by module 'r.univar': number of cells, min/max, range, mean, variance, standard deviation, variation coefficient and sum. The paper includes 9 maps and GRASS GIS codes used for visualization.