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= Transport of Soil Particles by Interrill Flow =

== Transporting Capacity of Flow ==
Once sediment has been entrained within the flow, it will be transported until actual sediment concentration in the flow exceeds it’s transporting capacity and deposition occurs. The ''transporting capacity'' of the flow <math>T_f</math> varies with the fifth power of velocity (Meyer and Wishmeier, 1969)<ref>Meyer, L. and Wishmeier, W. (1969). Mathematical simulation of the process of soil erosion by water. ''Transactions of the American Society of Agricultural Engineers'', 12:754–758,762.</ref>:

<math>T_f \propto Q^\frac{5}{3} s^\frac{5}{3}</math> &nbsp;&nbsp;&nbsp;(1.18)

This relationship relates to the action of overland flow on its own, whereas, in practice, flow is usually accompanied by rainfall. The interaction with ''raindrop impact'' causes a slight rise in the value of the exponents (Quansah, 1982)<ref>Quansah, C. (1982). ''Laboratory experiments for the statistical derivation of equations for soil erosion modelling and soil conservation design''. Phd thesis, Cranfield Institute of Technology.</ref>:

<math>T_f \propto Q^{2.13} s^{2.27}</math> &nbsp;&nbsp;&nbsp;(1.19)

While detachment capacity of flow is reduced by raindrop impact (eqn. 1.12, cf. section [[Soil Erosion by Water/Soil Detachment by Interrill Overland Flow|→ Rill Erosion]]), ''transporting capacity is enhanced'' (Savat, 1979<ref>Savat, J. (1982). Common and uncommon selectivity in the process of fluid transportation: field observations and laboratory experiments on bare surfaces. ''Catena Supplement'', 1:139–160.</ref>; Guy and Dickinson, 1990<ref>Guy, B. and Dickinson, W. (1990). Inception of sediemnt transport in shallow overland flow. ''Catena Supplement'', 17:91–109.</ref>; Proffitt and Rose, 1992<ref name=":0">Proffitt, A. and Rose, C. (1992). Relative contributions to soil loss by rainfall detachment and runoff entrainment. In Hurni, H. and Tato, K., editors, ''Erosion, conservation and small-scale farming'', page 75.89. Geographica Bernensia, Bern.</ref>). The degree of enhancement depends on the resistance of the soil, the diameter of the raindrops and the depth and velocity of the flow.

Nearing et al. (1989)<ref>Nearing, M., Foster, G., Lane, L., and Finkner, S. (1989). A process-based soil erosion model for usda-water erosion prediction project technology. ''Transactions of the American Society of Agricultural Engineers'', 32(5):1587–1593.</ref> derives an equation for <math>T_f</math> by simplifying the ''general transport equation'' to:

<math>T_f = k_t \tau^{\tfrac{3}{2}}</math> &nbsp;&nbsp;&nbsp;(1.20)

where <math>k_t</math> is an empiric transport coefficient and <math>\tau</math>is hydraulic shear stress exerted flow (according to the [[w:Darcy-Weisbach_equation|Darcy-Weisbach equation]], cf. section [[Soil Erosion by Water/Rill Erosion|→ Rill Erosion]]).

== Maximum Sediment Concentration ==
Transport capacity of overland flow is defined as the ''maximum sediment concentration'' <math>C_{max}</math> that can be carried (Govers, 1990)<ref>Govers, G. (1990). Empirical relationships for the transporting capacity of overland flow. ''International Association of Hydrological Sciences Publication'', 189:45–63.</ref>:

<math>C_{max} = a (s v - 0.4)^b</math> &nbsp;&nbsp;&nbsp;(1.21)

where <math>a</math> and <math>b</math>are empirical coefficients dependent on grain size. For particles with median grain diameters (''D''<sub>50</sub>) of 33, and 390 μm, respectively, <math>b</math> amounts at values from 1.5 to 3.5 (Everaert, 1991)<ref>Everaert, W. (1991). Empirical relations for the sediment transport capacity of interrill flow. ''Earth Surface Processes and Landforms'', 16:513–532.</ref>. The impact of rainfall has an negligible influence on the relationship for fine particles but reduced <math>b</math> to 1.5, indicating that rainfall diminishes the ability of overland flow to transport coarse material.

== Deposition Rate ==
Instead of trying to define transport capacity olny in terms of flow properties, some researchers have attempted to relate transport capacity to the maximum sediment concentration that a flow can carry when a balanced condition exists between detachment and deposition (Rose et al., 1983<ref>Rose, C., Williams, J., Sander, G., and Barry, D. (1983). A mathematical model of soil erosion and deposition processes. i. theory for the plane element. ''Soil science of America Journal'', 47:991–995.</ref>; Styczen and Nielsen, 1989<ref>Styczen, M. and Nielsen, S. (1989). A view of soil erosion theory, process research and model building: possible interactions and future developments. ''Quaderni di Scienza del Suolo'', 2:27–45.</ref>). The ''rate of deposition'' <math>D_p</math> is:

<math>D_p = v_s C</math> &nbsp;&nbsp;&nbsp;(1.22)

where <math>v_s</math> is the settling velocity of particles (Proffitt et al., 1991)<ref>Proffitt, A., Rose, C., and Hairsine, P. (1991). Detachment and deposition: experiments with low slopes and significant water depths. ''Soil Science Society of America Journal'', 55:325–332.</ref>.

Given the rather shallow depths of interrill overland flow, the considerable role played by surface roughness and the generally low Reynolds and Froude numbers, it can be proposed that most of the sediment transported is derived by ''raindrop impact'' and that grain shear velocity rarely attains the level necessary to detach soil particles (except on steep slopes or smooth bare soil surfaces).

In contrary to raindrop impact, where ''particles'' between 0.063 and 0.250 mm in size are most detachable (cf. section [[Soil Erosion by Water/Rainsplash|→ Rill Erosion]]), those most detachable by overland flow are within the 0.1-0.3 mm range, and the sediment carried in overland flow is deficient in particles larger than 1 mm and enriched in finer material.

Over time, areas of erosion on a hillside will become progressively sandier and areas of deposition will be enriched with clay particles. Most of the sediment splashed into the flow is moved only relatively short ''distances'' before being deposited. Since deposition is a ''particle-size selective process'', with the coarser particles being deposited first, the deposited layer becomes progressively coarser (Proffitt et al., 1991)<ref name=":0" /> and may develop into a ''depositional crust'' (cf. section [[Soil Erosion by Water/Rainsplash|→ Rill Erosion]]). Less of the finer material is then exposed to erosion. This mechanism can take place even within an individual storm so that detachment is highest ant the beginning of the storm and transport capacity is reached very quickly.

However, the relationship between sediment transport by interrill overland flow and discharge, as measured in the field, does not always conform with what may be expected from the research described above. The transport process may under certain conditions be dominantly one of rolling of the particles over the soil surface as ''bed load''. The sediment component contributed to overland flow by raindrop impact is moved as bed load, whereas the component contributed through detachment by the flow itself is moved as ''suspended load'' (Kinnell, 1990)<ref>Kinnell, P. (1990). The mechanics of raindrop-induced flow transport. ''Australian Journal of Soil Research'', 28:497–516.</ref>. The process is extremely dynamic, so that the most relevant equation for describing sediment transport by interrill overland flow continually changes through time.

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== Bibliography ==
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