Hillslope Characteristics and Behavior in Relation to Nonlocal Sediment Transport
Doane, Tyler Hill
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2014-07-26
Abstract
Mathematical descriptions of sediment transport are essential for our understanding of the evolution and form of Earth's surface. Recent work has highlighted the potential strengths of a nonlocal mathematical description of the hillslope sediment flux in steepland settings. Theory for nonlocal hillslope sediment transport has largely outpaced field or empirical studies designed to inform it. Here I present topographic data from tectonically and climatically diverse regions that is largely consistent with theory from nonlocal sediment transport. I use these data to show how one may extract the ratio of uplift rate to transport activity, which is the central factor in determining relief. I further isolate transport activity and show a direct connection between transport mechanisms and mean annual precipitation. This ultimately offers a physically-based connection between climate, sediment transport mechanisms, and hillslope relief. A second part of this thesis explores the stability behavior of hillslopes evolving by nonlocal sediment particle motions. A stable system unconditionally returns to an initial condition whereas an unstable system amplifies perturbations at characteristic wavelengths. Results suggest that nonlocal formulations of sediment transport with non-uniform entrainment rates are unstable. Numerical analyses suggest that hillslope roughness scales of 1-4 meters may be caused by instability introduced by nonlocal transport. Indeed these scales are consistent with $approx10$ meter scale roughness observed in natural settings. This result has implications for how geomorphologists interpret spatial variability of soil thickness which may reflect unstable hillslope behavior.