Self-dissimilar landscapes: Revealing the signature of geologic constraints on landscape dissection via topologic and multi-scale analysis

Climatic or geologic controls, such as tectonics or glacial drainage, might impose constraints on landscape self-organization resulting in spatial patterns of rivers and valleys which do not obey the typical self-similar relationships found in most landscapes. The goal of this study is to quantify how such geologic constraints express themselves on channel network topology, spatial heterogeneity of drainage patterns, and emergence of preferred scales of landscape dissection. We use as an example a basin located in the Upper Midwestern United States where successive glaciations over the past thousand years have led to a pronounced spatially anisotropic channel network structure which defeats most scaling laws of fluvial landscapes. This is contrasted with another river basin in the North-Central U.S. which has been organized under the absence of major geologic influences and follows a typical self-similar channel network organization. We show how the geologic constraints have imposed a competition for space which is captured in the slope-local drainage density probabilistic structure, in the failure of self-similarity in basin-wide river network topology, and in the length-area scaling relationship being not typical of fluvial landscapes. Via a two-dimensional wavelet analysis and synthesis, we demonstrate the occurrence of a gap in the power spectrum which corresponds to the presence of preferred scales of organization, and characterize them through multi-scale detrending. The developed methodologies can be useful in advancing our geomorphologic understanding of how external controls might manifest themselves in creating a landscape dissection that is outside the norm and how this dissection can be studied objectively for understanding cause and effect.