The emergence of topographic steady state in a perpetually dynamic self-organized critical landscape

Abstract

Copyright (2015) American Geophysical Union. The definitive version citation is: Reinhardt, L., and M. A. Ellis (2015), The emergence of topographic steady state in a perpetually dynamic self organized critical landscape, Water Resour. Res., 51, doi:10.1002/2014WR016223. To view the published open abstract, go to http://dx.doi.org and enter the DOI.We conducted a series of four physical modeling experiments of mountain growth at differing rates of uplift and three distinct climates ranging from relatively wet to relatively dry. The spatial and temporal pattern of landscape behavior is characterized by ∼f-1 scaling in sediment discharge and power law scaling in the magnitude and frequency of ridge movement in all four experiments. We find that internally generated self-organized critical (SOC) processes generate dynamically stable catchment geometries after ∼1 relief depths of erosion: these regularly spaced catchments have an average outlet-spacing ratio of 2.16, well within the range of values reported in field studies. Once formed, large catchment bounding ridges oscillate about a critically balanced mean location, with occasional large-scale changes in catchment size. Ridge movement appears to be driven by the competition for discharge as landslides push ridges back and forth. These dynamics lead to the emergence of a complex twofold scaling in catchment dynamics that is fully established by 1.8 relief depths of erosion; at this stage, a clear threshold has emerged separating two distinct scaling regimes, where large ridge mobility is insensitive to relief and small ridge mobility is relief dependent. Overall, we demonstrate that the development of dynamically stable large-scale landforms is related to the emergence of a complex-system hierarchy in topographic dynamics. Once formed, these landscapes do not evolve; statistical properties such as average topography and discharge become stationary while topography remains highly dynamic at smaller length scales