Trajectories of soil particles on a hillslope conveyor: Implications for particle age and Be-10 field

Abstract:

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. In general the material will evolve as it travels: it ages, it changes in grain size, it absorbs and releases nutrients, it weathers and it accumulates cosmogenic radionuclides. Here I address the hillslope conveyor. As many geochemical and physical 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 steady state 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 conservation of mass, which requires that strain rates in the horizontal enact strains rates of opposite sign in the vertical, and by the boundary conditions of zero vertical particle speed at the soil surface and the particle release rate at the saprolite interface. Particle trajectories must become surface-parallel at the surface. Knowledge of soil particle trajectories allows calculation of residence times and concentration profiles of ¹⁰Be in the soil. 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 vertical profiles of particle age and 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 slowing of vertical speeds as particles approach the surface. Where horizontal speeds vary significantly with depth, the vertically-averaged concentration of ¹⁰Be within the soil can significantly under-predict the mean ¹⁰Be concentration of sediment delivered to the channel; proper averaging requires weighting by particle speed.