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.Mudd and Yoo (2010) summarize this topic in relation to the use of reservoir theory (e.g., Bolin & Rodhe, 1973;Eriksson, 1971) to calculate expected variations in the probability distributions of particle ages and residence Key Points:• We present an Eulerian-Lagrangian description of disturbance-driven transport with depth-dependent mixing • The mean particle age generally is less than the mean residence time; these converge with strong mixing • The analysis provides the foundation for examining the structure of cosmogenic nuclide and OSL tracers

Luminescence as a Sediment Tracer and Provenance Tool

“…Finally, Furbish, Roering, Almond, et al, (), Furbish, Roering, Keen‐Zebert, et al, (), 2018c), using a Fokker‐Planck equation, a specialized probabilistic form of the Master Equation (Fokker, ; Planck, ), demonstrated how the random paths of particles in a soil lead to changes in the depth profiles of luminescence ages. In, particular, Furbish, Schumer, et al () demonstrated that particles in soil undergo rarefied transport, meaning that continuum style formulations of advection and diffusion are not applicable in soils a priori.…”

“…Luminescence has the potential to help answer fundamental questions related to natural soil mixing as its light‐sensitive nature preserves information on the paths of grains throughout a soil column (Figure ). Broadly, particles in soil move via a combination of advective and diffusive motions (Furbish, Roering, Almond, et al, , Furbish, Roering, Keen‐Zebert, et al, ). These motions are related to the granular dynamics of creep and to external perturbations that alter soil velocity profiles and sediment flux rate (BenDror & Goren, ).…”

“…These motions are related to the granular dynamics of creep and to external perturbations that alter soil velocity profiles and sediment flux rate (BenDror & Goren, ). The quasi‐random motions of sand grains eventually lead to particles reaching the surface (Furbish, Roering, Almond, et al, ). When sand or silt grains reach the surface, their luminescence bleaches due to sunlight exposure.…”

“…The second is to apply advection‐diffusion style equations on the age versus depth structure of soil (Johnson et al, ; Román‐Sánchez, Reimann, et al, , Román‐Sánchez, Laguna, et al, ). The third is to apply a probabilistic model of rarefied sand grains and use the change in single grain luminescence ages versus depth to infer timescales of particle motion and soil Peclet numbers (Furbish, Roering, Almond, et al, , Furbish, Roering, Keen‐Zebert, et al, , 2018c). An additional method is to perform a regression of age versus depth to obtain an accumulation rate to track the movement of sediment (e.g., Bruening‐Madsen et al, ; Kristensen et al, ).…”

Morphodynamic Analysis and Statistical Synthesis of Geomorphic Data: Application to a Flume Experiment

“…Hence, the output of these models varies as a function of the random draw of input parameters. Stochastic models have been used in the Earth sciences to describe, for example, the occurrence of landslides and their impact on topography (Convertino et al, 2013;Moon et al, 2015), the synchronization of snowfall and avalanche release (Crouzy et al, 2015), the transport of sediment on hillslopes (Furbish et al, 2018) and in rivers (Ancey et al, 2008;Furbish et al, 2012;Liang et al, 2015;Lopez, 2003), or the buildup of stratigraphy (Straub & Wang, 2013). Compared with deterministic models, stochastic models are commonly less constrained to the physics governing the modeled system and are more likely to produce unrealistic configurations.…”