Multifractal surfaces and terrestrial topography

We analyze terrestrial topographic data from four Digital Elevation Models which collectively span the range 20000 km to 50 cm. We use power spectra and trace moment analysis techniques to show that topography is multifractal from planetary scales down to around 40 m, where the multiscaling is broken by trees. We show that over this range the topography is reasonably described by a global nonlinear moment scaling function, itself determined by three parameters. We argue that these isotropic analyses are insensitive to the anisotropies and are hence compatible with different geomorphologies.