A nondimensional framework for exploring the relief structure of landscapes

Considering the relationship between erosion rate and the relief structure of a landscape within a nondimensional framework facilitates the comparison of landscapes undergoing forcing at a range of scales, and allows broad-scale patterns of landscape evolution to be observed. We present software which automates the extraction and processing of relevant topographic parameters to rapidly generate nondimensional erosion rate and relief data for any landscape where high-resolution topographic data are available. Individual hillslopes are identified using a connected-components technique which allows spatial averaging to be performed over geomorphologically meaningful spatial units, without the need for manual identification of hillslopes. The software is evaluated on four landscapes across the continental United States, three of which have been studied previously using this technique. We show that it is possible to identify whether landscapes are in topographic steady state. In locations such as Cascade Ridge, CA, a clear signal of an erosional gradient can be observed. In the southern Appalachians, nondimensional erosion rate and relief data are interpreted as evidence for a landscape decaying following uplift during the Miocene. An analysis of the sensitivity of this method to free parameters used in the data smoothing routines is presented which allows users to make an informed choice of parameters when interrogating new topographic data using this method. A method to constrain the critical gradient of the nonlinear sediment flux law is also presented which provides an independent constraint on this parameter for three of the four study landscapes.