Bioturbation and erosion rates along the soil‐hillslope conveyor belt, part 2: Quantification using an analytical solution of the diffusion–advection equation

Abstract

Particles on soil‐mantled hillslopes are subject to downslope transport by erosion processes and vertical mixing by bioturbation. Both are key processes for understanding landscape evolution and soil formation, and affect the functioning of the critical zone. We show here how the depth–age information, derived from feldspar‐based single grain post‐infrared infrared stimulated luminescence (pIRIR), can be used to simultaneously quantify erosion and bioturbation processes along a hillslope. In this study, we propose, for the first time, an analytical solution for the diffusion–advection equation to calculate the diffusivity constant and erosion–deposition rates. We have fitted this model to age–depth data derived from 15 soil samples from four soil profiles along a catena located under natural grassland in the Santa Clotilde Critical Zone Observatory, in the south of Spain. A global sensitivity analysis was used to assess the relative importance of each model parameter in the output. Finally, the posterior probability density functions were calculated to evaluate the uncertainty in the model parameter estimates. The results show that the diffusivity constant at the surface varies from 11.4 to 81.9 mm2 a‐1 for the hilltop and hill‐base profile, respectively, and between 7.4 and 64.8 mm2 a‐1 at 50 cm depth. The uncertainty in the estimation of the erosion–deposition rates was found to be too high to make a reliable estimate, probably because erosion–deposition processes are much slower than bioturbation processes in this environment. This is confirmed by a global sensitivity analysis that shows how the most important parameters controlling the age–depth structure in this environment are the diffusivity constant and regolith depth. Finally, we have found a good agreement between the soil reworking rates proposed by earlier studies, considering only particle age and depth, and the estimated diffusivity constants. The soil reworking rates are effective rates, corrected for the proportion of particles actually participating in the process. © 2019 John Wiley & Sons, Ltd.

Depth-dependent soil mixing persists across climate zones

“…1 and refs. [36][37][38]. We examine previously published measurements of luminescence as a function of depth in soil material where mixing is either reported by the authors or is likely to have occurred.…”

Luminescence as a Sediment Tracer and Provenance Tool

“…In their study, Johnson et al () compared both a linear and exponential depth profile for soil diffusivity and found that the exponential profile best fit the field data, which let them quantify both the diffusivity and the characteristic lengthscale of mixing. Román‐Sánchez, Reimann, et al, (),Román‐Sánchez, Laguna, et al, () merged both the downward velocity and advection‐diffusion approaches in their comprehensive study of the Santa Clotilde Critical Zone Observatory in southern Spain. Román‐Sánchez, Reimann, et al, (), Román‐Sánchez, Laguna, et al, () present a large body of work, including analytical solutions to the advection‐diffusion equation, a dataset spanning an entire hillslope, and careful analysis of the mixing and transport processes at their field sites.…”

“…Román‐Sánchez, Reimann, et al, (),Román‐Sánchez, Laguna, et al, () merged both the downward velocity and advection‐diffusion approaches in their comprehensive study of the Santa Clotilde Critical Zone Observatory in southern Spain. Román‐Sánchez, Reimann, et al, (), Román‐Sánchez, Laguna, et al, () present a large body of work, including analytical solutions to the advection‐diffusion equation, a dataset spanning an entire hillslope, and careful analysis of the mixing and transport processes at their field sites. The combined efforts of the above work are important because quantifying the soil mixing/diffusivity and lengthscales of movement opens the door for modeling other processes such as predicting the movement of nutrients and other soil properties.…”

“…The first is to divide the sample's apparent age by the depth to obtain a downward velocity (Heimsath et al, ) that can be interpreted in terms of soil mixing as a soil reworking rate (e.g., Reimann et al, ). 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).…”

Modelling soil and landscape evolution – the effect of rainfall and land use change on soil and landscape patterns

“…We will first consider vertical and lateral soil transport processes. Soils and hillslopes can be considered as a series of transport 465 ways or conveyor belts (Román-Sánchez et al, 2019). Vertical transport or mixing occurs by bioturbation including tree throw and clay translocation, whereas lateral transport occurs by creep, tree throw, water erosion and tillage erosion.…”