Soil Particle Transport and Mixing Near a Hillslope Crest: 1. Particle Ages and Residence Times

Abstract

We examine probabilistic elements of soil particle ages and residence times measured from their entry into the mechanically active soil column, focusing on steady conditions near a hillslope crest, where particles steadily move into and through a soil mantle with fixed thickness in the presence of erosion. Our objective is to clarify consequences of the geometry of the particle trajectories and disturbance‐driven mixing in relation to the arrangement of the surfaces through which the particles enter and leave the soil element. We introduce an Eulerian‐Lagrangian description of particle motions to characterize effects of a nonuniform (two‐dimensional) mean motion with superimposed depth‐dependent mixing. With weak mixing, the forms and moments of the probability distributions of particle residence times and ages are distinct and are largely controlled by the geometry of the mean particle motion within the soil element. The average particle age is systematically less than the average residence time. These distributions converge to exponential forms with equal means only in the idealized limit of a “well‐mixed” system. The analysis provides the foundation for considering particle weathering and chemical losses in relation to residence times and ages and for describing the spatiotemporal structure of tracers, for example, cosmogenic nuclide concentrations and optically stimulated luminescence particle ages, in relation to what these reveal about particle mixing.