Transport Time Scales in Soil Erosion Modeling

Abstract

Core Ideas Erosion timescales inherent in the Hairsine–Rose soil erosion are exposed. Both fast and slow timescales are isolated and can be estimated a priori. The maximum sediment settling rate controls the possible range of timescales. In practice, the full range of erosion timescales are not seen in flume experiments. 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 timescales 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 timescales 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 timescales 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 timescale 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.