Comparison of concentrated-flow detachment equations for low shear stress

Several equations exist to describe the relationship between concentrated-f low detachment and shear stress (tau). However, the advantages and disadvan tages of these equations for specific circumstances remain unclear. This st udy examines the performance of linear and power equations with and without a critical shear stress (tau (c)) term for concentrated-flow detachment at low shear stress. Equations were fit to data collected from experiments on five midwestem US soils using flume experimental data at low shear stress levels. Field experimental data were also available for these soils. The li near equation was simple to use and parameter values were easily estimated with linear regression. However, significant lack of fit was found when the linear equation was applied to data collected from low to medium shear str ess levels. The value of soil erodibility (K) for a soil varied by a factor of 3 and critical shear stress (tau (c)) varied by a factor of 2.5. The li near equation prediction underestimated detachment (D) by 25% at high shear stress and overestimated detachment by 30% at low shear stress. In contras t, the power equations gave more stable erodibility parameters because thes e equations reduced the systematic nature of the observation residuals foun d with the linear equation. Correlation between rill detachment D and tau w as generally lower with the linear compared to the power equations for cond itions tested. For higher shear stresses and longer slopes, the linear equa tion may be acceptable where field experiments show a linear trend. It is s uggested that tau (c) only be used when it has a value significantly differ ent from zero. (C) 2001 Published by Elsevier Science B.V.