Retraction

Science is fully retracting the report "Detection of an infectious retrovirus, XMRV, in blood cells of patients with chronic fatigue syndrome" (V. C. Lombardi et al., Science 326, 585 (2009); 10.1126/science.1179052)     

Comparison of concentrated-flow detachment equations for low shear stress

Several equations exist to describe the relationship between concentrated-flow detachment and shear stress (τ). However, the advantages and disadvantages of these equations for specific circumstances remain unclear. This study examines the performance of linear and power equations with and without a critical shear stress (τ_c) term for concentrated-flow detachment at low shear stress. Equations were fit to data collected from experiments on five midwestern US soils using flume experimental data at low shear stress levels. Field experimental data were also available for these soils. The linear 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 stress levels. The value of soil erodibility (K) for a soil varied by a factor of 3 and critical shear stress (τ_c) varied by a factor of 2.5. The linear equation prediction underestimated detachment (D) by 25% at high shear stress and overestimated detachment by 30% at low shear stress. In contrast, the power equations gave more stable erodibility parameters because these equations reduced the systematic nature of the observation residuals found with the linear equation. Correlation between rill detachment D and τ was generally lower with the linear compared to the power equations for conditions tested. For higher shear stresses and longer slopes, the linear equation may be acceptable where field experiments show a linear trend. It is suggested that τ_c only be used when it has a value significantly different from zero.