Scaling and physical thresholds: the case of continental topography

Thresholds derived from statistical inference are used frequently to detect some properties of geometrical distributions. Here, in the case of continental topography, it is shown that an intrinsic physical threshold with a characteristic dimension exists which must be taken into account before applying any standard analysis. For distances ranging from 100m to 100km, the elevation statistical distribution is well approximated by a standard Brownian surface with a fractal dimension D = 2·5. However, this pattern is unable to explain a global drainage. The hypsornetric curve of watersheds is used as an approximation of a drainage profile. Then dealing with continental wide hydrographic basins, it is shown that beyond a threshold around 150km the large-scaleelevation follows a logarithmic trend constrained by two boundary conditions: the sea level and the tectonic ridge.