Many geomorphic systems act as conveyor belts onto which material is loaded at a particular rate and is transported in one direction toward another system that serves as a sink. As the material travels, it ages, it changes in grain size, it accumulates cosmogenic radionuclides, it adsorbs or releases nutrients, and it weathers. Here I address the hillslope conveyor. As many geochemical processes are depth-dependent, the depth history of a particle becomes important to know. I calculate soil particle trajectories in the horizontal-depth plane and address three cases, one in which horizontal speeds decline exponentially with depth, a second in which they are uniform with depth, and a third in which horizontal speeds are also uniform but all profile values are vertically well-mixed. Vertical speeds are governed by continuity in an incompressible medium and by the boundary condition of zero vertical particle speed at the soil surface. Particle trajectories must therefore become surface parallel at the surface. Knowledge of soil particle trajectories allows calculation of residence times and concentration profiles of 10Be in the soil. The results inform strategies for interpretation of nuclide concentrations in soils and stream sediments and for inference of transport rate profiles. In all steady cases, the particle age and 10Be structure are uniform with distance from the divide. When significant vertical gradients in horizontal speed occur, the patterns of particle age and of 10Be concentration are dominated by the depth scale of the transport process. In unmixed cases, the particle age and 10Be concentration in near-surface samples can greatly exceed the vertically averaged values, reflecting the fact that the vertical speeds of particles slow dramatically as they near the surface. In cases in which horizontal speed varies significantly with depth, the vertically averaged concentration of 10Be within the soil can significantly underpredict the mean 10Be concentration of sediment delivered to the channel. Proper averaging requires weighting by particle speed. These results provide the backdrop for addressing chemical evolution of soil on a hillslope.
Anderson, R.S. (2015): Particle trajectories on hillslopes: Implications for particle age and 10Be structure. JGR-Earth Surface 120: 1626–1644. DOI: 10.1002/2015JF003479
This Paper/Book acknowledges NSF CZO grant support.