Hillslope Characteristics and Behavior in Relation to Nonlocal Sediment Transport

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.