Data from flume studies are used to develop a model for predicting bed-load transport rates in rough turbulent two-dimensional open-channel flows moving well sorted non-cohesive sediments over plane mobile beds. The object is not to predict transport rates in natural channel flows but rather to provide a standard against which measured bed-load transport rates influenced by factors such as bed forms, bed armouring, or limited sediment availability may be compared in order to assess the impact of these factors on bed-load transport rates. The model is based on a revised version of Bagnold’s basic energy equation *ibsb *= *eb*ù, where *ib *is the immersed bed-load transport rate, ù is flow power per unit area, *eb *is the efficiency coefficient, and *sb *is the stress coefficient defined as the ratio of the tangential bed shear stress caused by grain collisions and fluid drag to the immersed weight of the bed load. Expressions are developed for *sb *and *eb *in terms of *G*, a normalized measure of sediment transport stage, and these expressions are substituted into the revised energy equation to obtain the bed-load transport equation *ib *= ù *G *3·4. This equation applies regardless of the mode of bed-load transport (i.e. saltation or sheet flow) and reduces to *ib *= ù where *G *approaches 1 in the sheet-flow regime. That *ib *= ù does not mean that all the available power is dissipated in transporting the bed load. Rather, it reflects the fact that *ib *is a transport rate that must be multiplied by *sb *to become a work rate before it can be compared with ù. It follows that the proportion of ù that is dissipated in the transport of bed load is *ibsb*/ù, which is approximately 0·6 when *ib *= ù. It is suggested that this remarkably high transport efficiency is achieved in sheet flow (1) because the ratio of grain-to-grain to grain-to-bed collisions increases with bed shear stress, and (2) because on average much more momentum is lost in a grain-to-bed collision than in a grain-to-grain one. Copyright © 2006 John Wiley & Sons, Ltd.

When open-channel flows become sufficiently powerful, the mode of bed-load transport changes from saltation to sheet flow. Where there is no suspended sediment, sheet flow consists of a layer of colliding grains whose basal concentration approaches that of the stationary bed. These collisions give rise to a dispersive stress that acts normal to the bed and supports the bed load. An equation for predicting the rate of bed-load transport in sheet flow is developed from an analysis of 55 flume and closed conduit experiments. The equation is i(b) = omega where i(b) = immersed bed-load transport rate; and omega = flow power. That i(b) = omega implies that e(b) = tan alpha = u(b)/u, where e(b) = Bagnold's bed-load transport efficiency; u(b) = Mean grain velocity in the sheet-flow layer; and tan alpha = dynamic internal friction coefficient. Given that tan alpha approximate to 0.6 for natural sand, u(b) approximate to 0.6u, and e(b)approximate to 0.6. This finding is confirmed by an independent analysis of the experimental data. The value of 0.60 for e(b) is much larger than the value of 0.12 calculated by Bagnold, indicating that sheet flow is a much more efficient mode of bed-load transport than previously thought.

%B Journal of Hydrologic Engineering %V 129 %P 159-163 %8 2003 %@ 0733-9429/2003/2-159-163 %G eng %U files/bibliography/JRN00378.pdf %M JRN00378 %L 00883 %) In File (8/8/2006) %R 10.1061/(ASCE)0733-9429(2003)129:2(159) %F 1286 %0 Journal Article %J Hydrological Processes %D 2003 %T Disposition of rainwater under creosotebush %A Athol D. Abrahams %A Parsons, Anthony J. %A Wainwright, John %K article %K articles %K creosotebush, hydrology %K creosotebush,also SEEIn desert shrubland ecosystems water and nutrients re concentrated beneath shrub canopies in 'resource islands'. Rain falling onto these islands reaches the ground as either stemflow or throughfall and then either infiltrates into the soil or runs off as overland flow. This study investigates the partitioning of rainwater between stemflow and throughfall in the first instance and between infiltration and runoff in the second. Two series of 40 rainfall simulation experiments were performed on 16 creosotebush shrubs in the Jornada Basin, New Mexico. The first series of experiments was designed to measure the surface runoff and was performed with each shrub in its growth position. The second series was designed to measure stemflow reaching the shrub base and was conducted with the shrub suspended above the ground. The experimental data show that once equilibrium is achieved, 16% of the rainfall intercepted by the canopy or 6.7% of the rain falling inside the shrub area (i.e., the area inside the shrubs circumscribing ellipse) is funneled to the shrub base as stemflow. This redistribution of the rainfall by stemflow is a function of the ratio of canopy area (i.e., the area covered by the shrub canopy) to collar area (i.e., a circular area centered on the shrub base), with stemflow rate being positively correlated and throughfall rate being negatively correlated with this ration. The surface runoff rate expressed as a proportion of the rate at which rainwater arrives at a point (i.e., stemflow rate plus throughfall rate) is the runoff coefficient. A multiple regression reveals that 75% of the variance in the runoff coefficient can be explained by three independent variables: the rainfall rate, the ratio of the canopy area to the collar area, and the presence or absence of subcanopy vegetation. Although the last variable is a dummy variable, it accounts for 66.4% of the variance in the runoff coefficient. This suggests that the density and extent of the subcanopy vegetation is the single most important control of the partitioning of rainwater between runoff and infiltration beneath creosotebush. Although these findings pertain to creosotebush, similar findings might be expected for other desert shrubs that generate significant stemflow and have subcanopy vegetation. Copyright © 2003 John Wiley & Sons, Ltd.

%B Hydrological Processes %V 17 %P 2555-2566 %8 2003 %G eng %U files/bibliography/JRN00382.pdf %M JRN00382 %L 00816 %) (10/13/2003) %R 10.1002/hyp.1272 %F 1245 %0 Journal Article %J Earth Surface Processes and Landforms %D 2001 %T A sediment transport equation for interrill overland flow on rough surfaces %A Athol D. Abrahams %A Li, Gary %A Krishnan, Chitra %A Atkinson, Joseph F. %K article %K articles %K hydrology, bedload %K hydrology, hillslopes %K hydrology, interrill flow %K hydrology, overland flow %K hydrology, sediment transport %K hydrology, soil erosion %K journal %K journals %K model, hydrology %K model, interrill overland flow %K model, sediment transport %XA model for predicting the sediment transport capacity of turbulent interrill flow on rough sur4faces is developed from 1295 flume experiments with flow depths ranging from 3.4 to 43.4 mm, flow velocities from 0.09 to 0.65 m s^{-1}, Reynolds numbers from 5000 to 26949, Froude numbers from 0.23 to 2.93, bed slopes from 2.7° to 10°, sediment diameters from 0.098 to 1.16 mm, volumetric sediment concentrations from 0.002 to 0.304, roughness concentrations from 0 to 0.57, roughness diameters from 1.0 to 91.3 mm, rainfall intensities from 0 to 159 mm h^{-1}, flow densities from 1002 to 1501 kg m^{-3}, and flow kinematic viscosities from 0.913 to 2.556 x 10^{-6} m^{2} s^{-1}. Stones, cylinders and miniature ornamental trees are used as roughness elements. Given the diverse shapes, sizes and concentrations of these elements, the transport model is likely to apply to a wide range of ground surface morphologies. Using dimensional analysis, a total-load transpot equation is developed for open-channel flows, and this equation is shown to apply to interrill flows both with and without rainfall. The euation indicates that the dimensionless sediment transport rate Ø is a function of, and therefore can be predicted by, the dimensionless shear stress è, its critical value è_{c}, the resistance coefficient u/u_{*}, the inertial settling velocity of the sediment w_{i}, the roughness concentration C_{r}, and the roughness diameter D_{r}. Testing reveals that the model gives good unbiased predictions of Ø in flows with sediment concentrations less than 0.20. FLows with higher concentrations appear to be hyperconcentrated and to have sediment transport rates higher than those predicted by the model. Copyright © 2001 John Wiley & Sons, Ltd.

Modeling soil erosion requires an equation for predicting the sediment transport capacity by interrill overland flow on rough surfaces. The conventional practice of partitioning total shear stress into grain and form shear stress and predicting transport capacity using grain shear stress lacks rigor and is prone to underestimation. This study therefore explores the possibility that inasmuch as surface roughness affects flow hydraulic variables which, in turn, determine transport capacity, there may be one or more hydraulic variables which capture the effect of surface roughness on transport capacity sufficiently well for good predictions of transport capacity to be achieved from data on these variables alone. To investigate this possibility, regression analyses were performed on data from 1506 flume experiments in which discharge, slope, water temperature, rainfall intensity, and roughness size, shape and concentration were varied. The analyses reveal that 89.8 per cent of the variance in transport capacity can be accounted for by excess flow power and flow depth. Including roughness size and concentration in the regression improves that explained variance by only 3.5 per cent. Evidently, flow depth, when used in combination with excess flow power, largely captures the effect of surface roughness on transport capacity. This finding promises to simplify greatly the task of developing a general sediment transport equation for interrill overland flow on rough surfaces. ©1998 John Wiley & Sons, Ltd.

%B Earth Surface Processes and Landforms %V 23 %P 481-492 %8 1998 %G eng %U files/bibliography/JRN00261.pdf %M JRN00261 %L 00725 %) In File %R 10.1002/(SICI)1096-9837(199812)23:12<1087::AID-ESP934>3.0.CO;2-4 %F 5