Self-dissimilar Landscapes: Probing into Causes and Consequences via Multi-scale Analysis and Synthesis

Abstract:

External climatic or geologic controls on landscape topography such as tectonics or glacial drainage might impose constraints on the landscape resulting in a spatial organization of rivers and valleys which does not obey the typical self-similar or self-affine relationships found in most landscapes. The goal of this study is to quantify the multi-scale landscape organization, extract the range of scales at which self-similarity breaks down, and provide insight into how such an analysis can be used as a diagnostic tool for understanding landscape evolution and external controls that might have shaped the landscape dissection. The Headwaters and Methow River Basins (located in North-West Minnesota and North-Central Washington, respectively) are selected as our case studies as they have completely different geologies, river network topology, and surface topography. A two-dimensional discrete wavelet transform with its powerful localization property is applied both as a multi-scale decomposition and reconstruction tool and its superiority over the Fourier decomposition is demonstrated. The wavelet spectrum of the Headwaters topography reveals the emergence of a spectral gap at certain range of scales, which is the first signature of dissimilarity for this landscape. The characteristic scales attached to the spectral gap were found to correspond to the distance between the quasi-periodic ridges and valleys forming regularity in the landscape topography, as forced by larger-scale geologic controls. Furthermore, by applying entropy-based metrics on the multi-scale reconstructed landscapes, we identify the scales at which the organization is “very tight” documenting once again the influence of external controls on such a preferential organization.