Transport time scales in soil erosion modelling

Unlike sediment transport in rivers, erosion of agricultural soil must overcome its cohesive strength to move soil particles into suspension. Soil particle size variability also leads to fall velocities covering many orders of magnitude, and hence to different suspended travel distances in overland flow. Consequently, there is a large range of inherent time scales involved in transport of eroded soil. For conditions where there is a constant rainfall rate and detachment is the dominant erosion mechanism, we use the Hairsine-Rose (HR) model to analyze these timescales, to determine their magnitude (bounds) and to provide simple approximations for them. We show that each particle size produces both fast and slow timescales. The fast timescale controls the rapid adjustment away from experimental initial conditions – this happens so quickly that it cannot be measured in practice. The slow time scales control the subsequent transition to steady state and are so large that true steady state is rarely achieved in laboratory experiments. Both the fastest and slowest time scales are governed by the largest particle size class. Physically, these correspond to the rate of vertical movement between suspension and the soil bed, and the time to achieve steady state, respectively. For typical distributions of size classes, we also find that there is often a single dominant time scale that governs the growth in the total mass of sediment in the non-cohesive deposited layer. This finding allows a considerable simplification of the HR model leading to analytical expressions for the evolution of suspended and deposited layer concentrations

Applicability of the landscape evolution model in the absence of rills

Despite numerous applications of physically-based models for incised landscapes, their applicability for overland flow on unchanneled surfaces is not known. This work challenges a widely used landscape evolution model for the case of non-uniform rainfall and absence of rills using laboratory flume experiment. Rainfall with an average intensity of 85 mm h−1 was applied for 16 h during which high resolution laser scans of the morphology were captured. The overland flow was modeled as a network that preserves the water flux for each cell in the discretized domain. This network represented the gravity-driven surface flow and determined the evolution direction. The model was calibrated using the first 8 h of the experiment and was then used to predict the second 8 h. The calibrated model predicted, as expected, a smoother surface morphology (and less detailed overland flow network) than that measured. This difference resulted from quenched randomness (e.g., small pebbles) within the experimental soil that emerged during erosion and that were captured by the laser scans. To investigate the quality of the prediction, a low-pass filter was applied to remove the small-scale variability of the surface morphology. This step confirmed that the model simulations captured the main characteristics of the measured morphology. The experimental results were found to satisfy a scaling relation for the exceedance probability of discharge even in absence of rills. However, the model did not reproduce the experimental scaling relation as the detailed surface micro-roughness was not accounted for by the model. A lower cutoff on the scale of applicability of the general landscape evolution equation is thus suggested, complementing other work on the upper cutoff underpinned by runoff-producing areas