Coupled length scales in eroding landscapes

Abstract

We propose a method to study natural topography by means of local transform. A nonlinear local transform Alc[h(x)] of the elevation field h(x) is used to determine a director field of anisotropy a(x). The director field is directly related to local small-scale channel-like features. From study of the correlations of these with large-scale structure of drainage basins, characteristic coupling length scales are found which indicate an important breaking of scale invariance. We also show that these length scales are related to the average sizes of the individual drainage basins. Our study demonstrates one way in which landscape patterns of unknown origin may be quantitatively analyzed to determine the kind of mechanisms that have eroded them.