TOPOGRAPHIC SLOPE DISTRIBUTIONS, PROCESS DOMINANCE, AND EQUIFINALITY

A systematic trend in the shape of topographic slope distributions is revealed by quantitative analysis of more than 10,000 slope distributions subsampled from digital elevation models (DEMs) of mountainous landscapes. The slope distributions are unimodal and change from positively skewed to negatively skewed as mean slope increases. This trend holds across 28 DEMs representing landscapes with diverse tectonic, lithologic, and climatic histories, and is recorded in DEMs of different spatial resolution. Slope skewness is a normalized index of slope distribution shape, and is unaffected by scaling of topographic relief (i.e. vertical exaggeration), which affects slope mean and standard deviation identically. Therefore the transition in skewness must reflect a change in landscape morphology as mean slope increases. To explain the skewness trend we use a process-based landscape model which incorporates creep, wash, and failure processes. We find that end-member landscapes which are creep and/or wash dominated have positively skewed slope distributions, while failure dominated end-member landscapes have negatively skewed slope distributions. This suggests that the skewness trend is caused by a change in hillslope process dominance, from creep and/or wash when mean slope is low, to slope failure when mean slope is high. In the model, this process transition is governed by a non-dimensional uplift number, and we reproduce the skewness trend by simulating a series of landscapes along a trajectory of increasing uplift number. The uplift number reflects the balance between processes of relief denudation and processes of relief generation. Since many different combinations of tectonic, climatic, lithologic and geomorphic variables can produce the same uplift number, this provides a basis for morphologic equivalences between the diverse landscapes in our study.