Topography of large-scale watersheds: fractal texture and global drift. Application to the Mississippi basin

Abstract

The topography of large-scale hydrographic basins is assumed to involve two components: a meso-scale isotropic fractal pattern and a polarized large-scale trend which is oriented by large-scale tectonics and supports the global drainage. An algorithm is developed which splits up topography into a fractional Brownian function and a trend gradient C. Focusing on the large scales a logarithmic profile and a rectangular planform are detected through either the relationship between the gradient C and the normalized elevation E or by the basin hypsometric curve and the inertia tensor of the basin area. This is successfully applied to the digital terrain model of eight large-scale sub-basins of the Mississippi. The profile belonging to the basin main valley is also logarithmic but its slope is twice smaller than that of the mean profile, denoting a trend surface with converging slopes towards the mid-valley. The scaling transition is investigated through angular distributions. This is synthesized by a ternary diagram involving the following poles according to increasing scales: a pure isotropic fractal F, a transient off-centred fractal O and a tilted tectonic plane T. The fractal parameters are the intensity σ at scale s = 1 km and the Hurst exponent H. Over a basin area H is constant while σ is proportional to the trend slope C whatever the elevation E. This implies a constant horizontal scale ξ f for each basin, around 30 km separating the fractal-dominated topography from the trend-dominated topography.