# Soil Erosion by Water/Printable version

The current, editable version of this book is available in Wikibooks, the open-content textbooks collection, at
https://en.wikibooks.org/wiki/Soil_Erosion_by_Water

# Further Reading

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# Further reading
## en

* Morgan, R.P.C (2005). Soil Erosion and Conservation. 3rd ed., Blackwell, Oxford.
* Lal, R. (1994). Soil Erosion Research Methods. 2nd ed., Soil and Water Conservation Society, Ankeny, IA.
* Harmon, R.S., and Doe Ill, W.W. (2001). Landscape Erosion and Evolution Modelling. Kluver Academic/Plenum Publishers, New York
* Toy, T.J., Foster, G.R., and Renard, K.G. (2002). Soil Erosion: Processes, Prediction, Measurement, and Control. Wiley & Sons, New York

## de

* Morgan, R.P.C (1999). Bodenerosion und Bodenerhaltung. Thieme, Stuttgart.
* Richter, G. (1998). Bodenerosion: Analyse und Bilanz eines Umweltproblems. Wissenschaftliche Buchgesellschaft, Darmstadt
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# Process Basics

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# Process Basics

Soil erosion is a two-phase process consisting of the detachment of individual soil particles from the soil mass and their transport by erosive agents such as running water, wind or mechanical impact (e.g. tillage). When sufficient energy is no longer available to transport the particles, a third phase, deposition, occurs (Morgan, 2005).
Detaching agents loosen the soil so that it is easily removed by agents of transport.

## Detaching Agents

Detaching agents are
* Rainsplash:
       Kinetic energy of Raindrops striking bare soil surface detaches and breaks up soil aggregates. Continuous exposure to intense rainstorms considerably weakens the soil by surface sealing and crusting processes.
* Weathering processes:
       Both, mechanical, by alternate wetting and drying, freezing and thawing and frost action, as well as biochemical weathering breaks up the soil.
* Soil utilization:
       Soil ist disturbed by tillage operations and by the trampling of people and livestock.
* Running water and wind:
       Shear stress affecting the surface soil by running water and wind detaches soil particles.

## Transporting Agents

Transporting agents comprise those that act alreally and contribute to the removeal of a uniform thickness of soil (interrill erosion), and those that concentrate their action in channels (rill erosion).
Transporting agents in interrill zones are
* Rainsplash:
       Particles may be thrown through the air over distances of several centimeters. Soil surface slope effects a dominance of downslope transport.
* Overland flow:
       Surface runoff in the form of shallow flow of infinite width moves soil particles towards rills.
* Wind:
       Shear, the magnitude of which depends on wind velocity, moves particles of different sizes according to their critical shear velocity.
Transporting agents in rills are
* Rill runoff:
       Transport by concentrated water runoff in small rills, which can be obliterated by weathering and tillage operations.
* Gully runoff:
       Concentrated runoff in larger more permanent channel features with very specific formation threshold conditions and mechanisms.
* Brook/river runoff
The severity of erosion depends upon the quality of material supplied by detachment over time and the capacity of eroding agents to transport it. Where the agents have the capacity to transport more material than is supplied by detachment, the erosion is described as detachment-limited. Where more material is supplied than can be transported, the erosion is transport-limited.

## Available Energy

The energy available for erosion takes two forms: potential and kinetic.
Potential Energy $PE$ results from the difference in height of one body (e.g. particle) with respect to another (e.g. earth). It is the product of mass $m$, height difference $h$ and acceleration due to gravity $g$:
$PE=mgh$ (1.1)
The potential energy of erosion is converted into kinetic energy $KE$, the energy of motion. This is related to the mass $m$ and velocity $v$ of the eroding agent:
$PE={1 \over 2}mv^{2}$ (1.2)
Most of this energy is dissipated in friction with the surface over which the agent moves. Only 3-4 % of the energy of running water, and 0.2 % of that of falling raindrops is expeded in erosion (Pearce, 1976)
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## Bibliography

* ↑ Morgan, R. (2005). Soil Erosion and Conservation. Blackwell Publishing, Oxford.
* ↑ Pearce, A. (1976). Magnitude and frequency of erosion by hortonian overland flow. Journal of Geology,84:65–80.

# Soil Hydrologic Basics

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# Soil Hydrologic Basics

The processes of water erosion are closely related to the pathways taken by water.
* Direct throughfall:
   During a rainstorm, part of the water directly falls on land, either because there is no vegetation or because it passes through gaps in the plant canopy.
* Leaf drainage:
   Part of the rain is intercepted by the canopy, from where it impacts the ground by dripping from the leaves (or returns to the atmosphere by evaporation).
* Stemflow:
   Part of the rain finds its way to the ground by running down the plant stems.
The action of direct throughfall and leaf drainage produces rainsplash erosion. Rain that reaches the ground may be stored in small depressions or hollows on the surface or may infiltrate the soil, contributing to soil moisture starage, to lateral water movement downslope within the soil as subsurface or interflow or, by percolating deeper, to groundwater. From the moment on where soil is unable to take in more water (saturated conditions), the excess contributes to runoff on the surface, resulting in interrill, rill or gully erosion.

## Infiltration Rate

The rate at which water passes into the soil is known as infiltration rate. This excerts a major control over the generation of surface runoff. Water is drawn into the soil by gravity and by capillary forces, whereby it is attracted to and held as thin molecular film around soil particles. During a rainstorm, the soil pores become filled and capillary forces decrease. Hence infiltration rate starts high at the beginning of a storm and declines to al level that represents the maximum sustained rate at which water can pass through the soil to lover levels. This infiltration capacity or terminal infiltration rate corresponds theoretically to the saturated hydraulic conductivity $k_{s}$of a soil.
In practice, however, infiltration capacity is lower than $k_{s}$ because of air entrapped in the soil pores as the wetting front passes downwards through the soil. Soil physics knows various approaches have been established to describe the change in infiltration rate over time mathematically. One of the most widely used equations is a modification of the Green and Ampt (1911) equation proposed by Mein and Larson (1973):
$i=k_{s}+{\frac {b}{I}}$ (1.3)
where infiltrability $i$ is the instantaneous rate of infiltration, $k_{s}$ is the saturated hydraulic conductivity of the soil (assymptotic steady infiltration flux reached when $t$ and hence $I$become large), $I$ is the cumulative volume of water infiltrated in time $t$ per unit area of soil surface and b is the sorptivity, defined by Talsma (1969) as slope of the line when $i$ is plotted against the time $t$ elapsed since the onset of the rain.
The Green-Ampt equation as well as another approach proposed by Philip (1957) both arise out of mathematical solutions of well-defined physically based theories of infiltration, combining the Darcy (1856) equation with the continuity equation (conservation of mass) to obtain the general one-dimensional flow equation for water in soil. Both euqations however give errors when used to estimate saturated hydraulic conductivity. One reason is the faliure to predict infiltration correctly under conditions of surface ponding when the soil develops a viscous resistance to air flow. Morel-Seytoux and Khanji (1974) developed the following equation to overcome this:
$i={\frac {k_{s}}{\beta }}\left(1+{\frac {(\theta _{t}-\theta _{1})(h_{0}-\Delta \psi )}{I}}\right)$ (1.4)
where $k_{s}$ is the saturated hydraulic conductivity; $\beta$ is a viscous corretion factor varying in value between 1.1 and 1.7, depending on soil type and ponding depth but averages 1.4; $\theta _{i}$ is the initial volumetric soil moisture content; $\theta _{t}$ is the actual volumetric soil moisture content in the zone between the ground surface and the wetting front; $h_{0}$ is the depth of the ponded water; $\Delta \psi$ is the change in $\psi$ between the soil surface and the wetting front; $\psi$ is the difference in pressure between the pore-water and the atmosphere; and $I$ is the total amount of water already infiltrated. As a result of including the viscous correction factor, eqn 1.4 predicts lower infiltration rates than eqn 1.3 or the Philip equation.
Local variability in infiltration rates can be quite high because of differences in
* Soil structure,
* Soil compaction,
* Initial soil moisture content,
* Profile form of the soil,
* Vegetation density.
Infiltration rates depend upon the characteristics of the soil (cf. fig. 1.1). Coarse-textured soils such as sands and sandy loams have higher infiltration rates than clay soils because of the larger spaces between pores. Infiltration capacities may range from more than 200 mm h$^{−1}$ for sands to less than 5 mm h$^{−1}$ for tight clays.
In addition to the role played by the inter-particle spacing, the larger cracks or macropores exert an important influence over infiltration. They can transmit considerable quantities of water so that clays with well defined scructures can have infiltration rates that are much higher tan would be expected from their texture alone. Clays show a strong swelling and shrinking behaviour depending on soil moisture content.
Infiltration behaviour on many soils is also rather complex because the soil profiles are characterized by two or more layers of differing hydraulic conductivities. Most agricultural soils, for example, consist of a disturbed plough layer and an undisturbed subsoil.
The presence of stones or rock fragments also influences infiltration rates in a complex way depending on whether the stones are resting on top of the surface or are embedded within the soil. Rock fragments protect the soil against physical destruction and the formation of a crust, so that infiltration rates are higher than on a comparable stone-free bare soil. However, on soils that are subject to crusting, a high percentage stone cover will provoke decreased infiltration. A 75 % cover of rock fragments embedded in a crusted surface on a silt-loam soil reduced infiltration rates to 50 % of those on a stone-free soil (Poesen and Ingelmo-Sanches, 1992).

## Surface Runoff

According to Horton (1945), if rainfall intensity is less than the infiltration capacity $i$ of the soil (cf. 1.2), no surface runoff occurs and the infiltration rate equals the rainfall intensity. If the rainfall intensity exceeds the infiltration capacity, infiltration rate equals the infiltration capacity and the excess rain forms surface runoff, so called Hortonian runoff.
As a mechanism for generating surface runoff, however, this comparison of rainfall intensity and infiltration capacity in practice does not always hold due to the infiltration-diminishing influence of soil surface crusting and sealing. According to Boiffin (1985) crust forms in situ on the soil, due to physical destruction, elutrination and cubsequent drying (structural crust), or results from the deposition of fine particles in puddles (depositional crust) .
The prevailing control for runoff production on many soils is a limiting soil moisture content. When the actual moisture content is below this value, pore water pressure within the soil is less than atmospheric pressure and water is held in capillary form under tensile stress or suction. When the limiting moisture content is reached and all pores are full of water, pore water pressure equates to atmospheric pressure, suction reduces to zero and surface ponding occurs. E.g. Sands that have low levels of capillary storage can produce runoff very quickly even though their infiltration capacity is not exceeded by the rainfall intensity.
Since hydraulic conductivity is a flux partly controlled by rainfall intensity, increases in intensity can cause conductivity to rise. Therefore higher rainfall intensities do not always produce greater runoff, although runoff initially may have formed rapidly at a relatively low intensity (Nassif and Wilson, 1975). Also, infiltration capacity may raise with higher rainfall intensities because of their ability to disrupt surface seals and crusts that would otherwise keep infiltration rate low Bowyer-Bower (1993). These two mechanisms explain why infiltration rates sometimes increase with rainfall intensity .
Once water starts to pond on the surface, it is held in depressions or hollows and runoff does not begin until the storage capacity of these is satisfied. Depression storage varies seasonally depending on the type of cultivation that has been carried out and the time for the soil surface roughness to be reduced since cultivation by weathering and raindrop impact.
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## Bibliography

* ↑ Withers, B. and Vipond, S. (1974). Irrigation: design and practice. Batsford, London.
* ↑ Green, W. and Ampt, G. (1911). Studies on soil physics. i: The flow of air and water through soils. Journal of Agricultural Science, 4:1–24.
* ↑ Mein, R. and Larson, C. (1973). Modeling infiltration during a steady rain. Water Resources Research, 9:384–394.
* ↑ Talsma, T. (1969). In situ measurement of sorptivity. Australian Journal of Soil Research, 17:269–276.
* ↑ Philip, J. (1957). The theory of infiltration. i: The infiltration equation and its solution. Soil science, 83:345–57.
* ↑ Darcy, H. (1856). Les Fontaines Publiques de la Ville de Dijon. Dalmont, Paris.
* ↑ Morel-Seytoux, H. and Khanji, J. (1974). Derivation of an equation of infiltration. Water Resources Research, 10:794–800.
* ↑ Poesen, J. and Ingelmo-Sanches, F. (1992). Runoff and sediment yield from topsoils with different porosity as affected by rock fragment cover and position. Catena, 19:91–133.
* ↑ Horton, R. (1945). Erosional development of streams and their drainage basis: A hydrophysical approach to quantitative morphology. Bulletin of the Geological Society of America, 56:275–370.
* ↑ Boiffin, J. (1985). Stage and time-dependency of soil crusting in situ. In Callebaut, F., Gabriels, D., and De Boodt, M., editors, Assessment of surface crusting and sealing, pages 91–98. State University of Gent.
* ↑ Nassif, S. and Wilson, E. (1975). The influence of slope and rain intensity on runoff and infiltration. Hydrological Sciences Bulletin, 20:539–553.
* ↑ Bowyer-Bower, T. (1993). Effects of rainfall intensity and antecedent moisture on the steady-state infiltration rate in a semi-arid region. Soil unse and Management, 9:69–76.

# Rainsplash

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# Rainsplash

The downslope component of the momentum of a single raindrop falling on a sloping soil surface is transferred in full to the soil surface. However, only a small proportion of the component normal to the surface is transferred, the remainder being reflected. The transfer of momentum to the soil particles has two effects:
Consolidation:
    It provides a consolidationg force compacting the soil and consequently intensifying crust formation. The formation of a surface crust results from clogging of the pores by soil compaction and by the infilling of surface pore spaces by fine particles detached from soil aggregates by the raindrop impact. Crusts have a dense surface skin or seal, about 0.1 mm thick, with well oriented clay particles. Beneath this is al layer, 1-3 mm thick, where the larger pore spaces are filled by finer washed-in material (Tackett and Pearson, 1965). Most aggregates on the soil surface are destroyed during an rainfall, while those in the lower layer of the crust remain intact, even though completely saturated (Farres, 1978). Although saturation reduces the internal strength of soil aggregates, they will not disintegrate until directly struck by raindrops.
Dispersion:
    The transfer of momentum to the soil particles produces a disruptive force as the water rapidly disperses from and returns to the point of impact in laterally flowing jets. The impact velocity of falling raindrops striking the soil surface varies from 4 m s$^{−1}$ for a 1 mm diameter drop to 9 m s$^{−1}$ for a 5 mm diameter drop. Local velocities of the lateral jets are about twice these (Huang et al., 1982). These fast moving water jets impart a velocity to some of the soil particles and launch them into the air, entrained within water droplets that are temselves formed by the break-up of the raindrop on contact with the ground (Mutchler and Young, 1975). Thus Raindrops are agents of both consolidation and dispersion.
The actual response of a soil to a given rainfall depends upon its moisture content and, therefore, its structural state and the rainfall intensity (kinetic energy). Le Bissonnais (1990) describes three possible responses:
* If the soil is dry and rainfall intensity is high, soil aggregates break down quickly by slaking. This is the breakdown by compression of air ahead of the wetting front. Infiltration capacity reduces rapidly and on smooth surfaces runoff can be generated after only a few millimeters of rain. With rougher surfaces, depression storage is greater and runoff takes longer to form
* If the aggregates are initially partially wetted or rainfall intensity is low, mircocracking occurs and the aggregates break down into smaller aggregates. Surface roughness thus decreases but infiltration remains high because of large pore spaces between the microaggregates.
* If the aggregates are initially saturated, large quantities of rain are required to seal the surface and infiltration capacity depends on the saturated hydraulic conductivity to the soil. Nevertheless, soils with less than 15 % clay are vulnerable to sealing if the intensity of the rain is high.
Over time, the percentage are of the soil surface affected by crust development intreases exponentially with cumulative rainfall energy (Govers and Poesen, 1985), which, in turn, brings about an exponential decrease in infiltration capacity (Boiffin and Monnier, 1985). Crustability decreases with increasing contents of clay and organic matter since these provide greater aggregate stability to the soil. Thus loams and sandy loams are the most vulnerable to crust formation.
Studies of the kinetic energy required to detach one kilogram of sediment by raindrop impact show that minimal energy is needed for soils with a geometric mean particle size of 0.125 mm and that soils with geometric mean particle size between 0.063 and 0.250 mm are the most vulnerable to raindrop detachment (Poesen, 1985): Silt loams, loams, fine sands and sandy loams. Coarser soils are resistant to detachment because of the weight of the large particles, finer soils are resistant because the raindrop energy has to overcome the adhesive or chemical bonding forces that link the minerals comprising the clay particles. Selective removal of particles by rainsplash can cause variations in soil texture downslope, affecting soil aggregates as well as primary particles.
The wide range in energy required to detach clay particles is a function of different levels of resistance in relation to the type of clay minerals and the relative amounts of ${\ce {Ca^2+}}$, ${\ce {Mg^2+}}$ and ${\ce {Na^+}}$Na cations in the water passing through the pores (Arulanandan et al., 1975). Overall, silt loams, loams, fine sands and sandy loams are the most detachable.
Besides texture, the detachability of a soil also depends on the shear strength of the top soil (Cruse and Larson, 1977). The detachment of soil particles represents a failure of the soil by the combined mechanism of compression and shear under raindrop impact, which is most likely to occur under saturated conditions when the shear strength of the soil is lowest (Al-Durrah and Bradford, 1982). Detachment decreases exponentially with increasing shear strength.
During a storm Raindrops sometimes do not directly fall on to the soil surface, but on surface water in the form of puddles or overland flow. As the thickness of the surface water layer increases, so does splash erosion (Palmer, 1964). This is due to the durbulence that impacting raindrops impart on to the water. Only on sandy soils splash erosion does not increase with water depth (Poesen, 1981).
There is, however, a critical water depth beyond which erosion decreases exponentially with increasing water depth because more of the rainfall energy is dissipated in the water and does not affect the soil surface. This critical depth is approximately equal to the diameter of the raindrops (Palmer, 1964).

## Rainsplash Detachment

Experimental Studies have shown that the rate of detachment of soil particles with rainsplash varies with the 1.0 power of the instantaneous kinetic energy of the rain (Free, 1960; Quansah, 1981). The detachment rate $D_{r}$D r on bare soil can be expressed by equations of the form:
$d_{r}\propto KE^{a}s^{b}e^{-ch_{0}}$ (1.5)
$KE$ is the kinetic energy of the rain and $h_{0}$ is the depth of surface water film. $s$ is the local slope for a distance equivalent to only a few drop diameters from the point of raindrop impact (e.g. on the side of a soil clod), and not the average ground slope. $a$ may vary from 0.8 for sands to 1.8 for clays (Bubenzer and Jones, 1971). Values for $b$ are in the range of 0.2-0.3 (Torri and Sfalanga, 1986), those for $c$ in the range of 0.9-3.1 (Torri et al., 1987b), varying with the texture of the soil.

## Rainsplash Transport

In contrast, average ground slope S is important when considering the overall transport of splashed particles. On a sloping surface more particles are thrown downslope than upslope during the detachment process, resulting in a net movement of material downslope. Splash transport $T_{r}$per unit width of slope can be expressed by the relationship:
$T_{r}\propto I^{d}S^{e}$ (1.6)
where $d=1.0$(Meyer and Wishmeier, 1969), and $e$ decreases from 1.0 to minimum values of 0.8 and 0.75 where ground slope angles rise to 20 and 25°, respectively (Mosley, 1973; De Ploey et al., 1976), and becomes negative on steeper slopes (Foster and Martin, 1969; Bryan, 1979).
These relations ignore the role of wind. Windspeed imparts a horizontal force to a falling raindrop until its horizontal velicity component equals the wind velocity. As a result, the kinetic energy of the raindrop is increased. Detachment of soil particles by impacting wind-driven raindrops can be 1.5-3 times greater than resulting from rain of the same intensity without wind (Disrud and Krauss, 1971; Lyles et al., 1974). Wind also causes raindrops to strike the surface at an angle from vertical. This affects the relative proportions of upslope versus downslope splash (Moeyersons, 1983).
Splash erosion is most important for detaching the soil particles that are subsequently eroded by running water (interrill overland flow, rill flow). However, on upper sections of hillslopes, splash transport may be the dominant erosion process. As runoff and soil loss increase, the importance of splash transport declines. Since splash erosion acts uniformly over the land surface its effexts are seen best where stones or tree roots selectively protect the underlying soil and splash pedestrals or soil pollars are formed.
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## Bibliography

* ↑ Tackett, J. and Pearson, R. (1965). Some characteristics of soil crust formed by simulated rainfall. Soil Science, 99:407–413.
* ↑ Farres, P. (1978). The role of time and aggregate size in the crusting process. Earth Surface Processes, 3:243–254.
* ↑ Huang, C., Bradford, J., and Curshman, J. (1982). A numerical study of raindrop impact phenomena: the rigid case. Soil science of America Journal, 46:14–19.
* ↑ Mutchler, C. and Young, R. (1975). Soil detachment by raindrops. In Present and prospective technologyfor predictiong sediment yields and sources, volume 40, pages 113–117. USDA-ARS Publication.
* ↑ Le Bissonnais, Y. (1990). Experimental study and modelling of soil surface crusting processes. Catena Supplement, 17:13–28.
* ↑ Govers, G. and Poesen, J. (1985). A field-scale study of surface sealing and compaction on loam and sandy loam soils. part i. spatial variability of soil surface sealing and crusting. In Callebaut, F., Gabriels, D., and De Boodt, M., editors, Assessment of soil surface crusting and sealing, pages 171–182. Flanders Research Centre for Soil Erosion and Conservation, Gent.
* ↑ Boiffin, J. and Monnier, G. (1985). Infiltration rate as affected by soil surface crusting caused by rainfall. In Callebaut, F., Gabriels, D., and De Boodt, M., editors, Assessment of soil surface crusting and sealing, pages 210–217. Flanders Research Centre for Soil Erosion and Conservation, Gent.
* ↑ Poesen, J. (1985). An improved splash transport model. Zeitschrift für Geomorphologie, 29:193–211.
* ↑ Arulanandan, K., Loganathan, P., and Krone, R. (1975). Pore and eroding fluid influences on the surface erosion of a soil. Journal of the Geotechnical Engineering Division ASCE, 101:53–66.
* ↑ Cruse, R. and Larson, W. (1977). Effect of soil shear strength on soil detachment due to raindrop impact. Soil science of America Journal, 41:777–781.
* ↑ Al-Durrah, M. and Bradford, J. (1982). Parameters for describing soil detachment due to single water drop impact. Soil science of America Journal, 46:836–840.
* 1 2 Palmer, R. (1964). The influence of a thin water layer on water-drop impact forces. International Association of Hydrological Sciences Publication, 65:141–148.
* ↑ Poesen, J. (1981). Rainwash experiments on the erodibility of loose sediments. Earth Surface Processes and Landforms, 6:285–307.
* ↑ Free, G. (1960). Erosion characteristics of rainfall. Agricultural Engineering, 41:447–449,455.
* ↑ Quansah, C. (1981). The effect of soil type, slope, rain intensity and their interactions on splash detachment and transport. Journal of Soil Science, 32:325–332.
* ↑ Bubenzer, G. and Jones, B. (1971). Drop size and impact velocity effects on the detachment of soil under sumulated rainfall. Transactions of the American Society of Agricultural Engineers, 14:625–628.
* ↑ Torri, D. and Sfalanga, M. (1986). Some problems on soil erosion modelling. In Giorgini, A. and Zingales, F., editors, Agricultural nonpoint source pollution: Model selection and application, pages 161–171. Elsevier, Amsterdam.
* ↑ Torri, D., Sfalanga, M., and Del Sette, M. (1987b). Splash detachment: Runoff depth and soil cohesion. Catena, 14:149–155.
* ↑ 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.
* ↑ Mosley, M. (1973). Rainsplash and the convexity of badland divides. Zeitschrift für Geomorphologie, Supplementband, 18:103–107.
* ↑ Foster, R. and Martin, G. (1969). Effect of unit weight and slope on erosion. Journal of the Irrigation and Drainage Division ASCE, 95:551–561.
* ↑ Disrud, L. and Krauss, R. (1971). Examining the process of soil detachment from clods exposed to wind driven simulated rainfall. Transactions of the American Society of Agricultural Engineers, 14:90–92.
* ↑ Lyles, L., Dickerson, J., and Schmeidler, M. (1974). Soil detachment from clods by rainfall: effects of wind, mulch cover and initial soil moisture. Transactions of the American Society of Agricultural Engineers, 17:697–700.
* ↑ Moeyersons (1983). Measurements of splash-saltation fluxes under oblique rain. Catena Supplement, 4:19–31.

# Soil Detachment by Interrill Overland Flow

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# Soil detachment by interrill overland flow

Interrill overland flow on a soil surface is a mass of anastomosing or braided water courses with no pronounced channels rather than a sheet of water of uniform depth. The flow is broken up by stones and cobbles and by the vegetation cover, often swirling around tufts of grass and small shrubs.

## Shear Stress of Flow

The important factor in the basic hydraulic relationships of Reynolds, and Froude numbers is the flow velocity, commonly expressed by the Manning equation:
$v={\frac {r^{\frac {2}{3}}s^{\frac {1}{2}}}{n}}$ (1.7)
where $r$ is the hydraulic radius, $s$ is the slope and $n$ is Manning’s coefficient of roughness. The equation assumes fully turbulet flow moving over a rough surface.
Because of an inherent resistance of the soil, velocity must attain a threshold value before erosion commences. Basically, the detachment of an individual soil particle from the soil mass occurs when the forces exerted by the flo exceed the forces keeping the particle at rest. The processes involved and the forces at work when particle movement over relatively gentle slopes in rivers is initiated are controlled by critical conditions of the dimensionless shear stress of the flow $\Theta$, and the particle roughness Reynolds number $Re$, respectively, defined by:
$\Theta ={\frac {\rho _{w}u_{*}^{2}}{g(\rho _{s}-\rho _{w})D}}$ (1.8)
$Re^{*}={\frac {u_{*}D}{v}}$ (1.9)
where $\Theta$ is the Shields (1936) number, $\rho _{w}$ and $\rho _{s}$ are the densities of water and soil respectively, $g$ is the acceleration of gravity, $D$ is the diameter of the respective soil particle and $u_{*}$ is the shear velocity of the flow, expressed as:
$u_{*}=(grs)^{\frac {1}{2}}$ (1.10)
When the value of $Re^{*}$ is greater than 40 (turbulent flow), the critical value of $\Theta$ for particle movement assumes a constant value of 0.05. Unfortunately, this value does not hold when the particles are not fully submerged or the flow has Reynolds numbers in the laminar range, as it is the case with overland flow. Studies with rock fragments in shallow flows suggest that $\Theta$ is about 0.01 in value (Poesen, 1987; Torri and Poesen, 1988).
Other research (Govers, 1987; Guy and Dickinson, 1990; Torri and Borselli, 1991) indicates that Shields number consistently overpredicts the hydraulic requirements of particle movement. This implies that the initiation of particle movement is not solely a phenomenon of fluid shear stress but is enhanced by further factors:
* Effects of raindrop impact on the flow,
* Angle of repose of the particle in relation to ground slope,
* Strong influence of gravity as slope steepness increases,
* Cohesion of the soil,
* Changes in density of the fluid as sediment concentration in the flow increases,
* Abrasion between particles moving in the flow and the soil beneath.
Since the above approach has not proved satisfactory, empirical procedures have been adopted by Savat (1982), based on a critical value of the flow’s shear velocity for initiating particle movement (fig. 1.2). Once the critical conditions for particle movement are exceeded, soil partilces may be detached from the soil mass at a rate that is dependent on the shear velocity of the flow and the unit discharge (Govers and Rauws, 1986).
However this is only valid, if the shear velocity is exerted solely on the soil particles, which implies that the resistance to the flow wold entirely be due to grain resistance. This situation is only true for completely smooth bare soil surfaces. In practice, resistance due to the microtopographic form of the soil surface and the plant cover is usually more important and grain resistance may be as little as 5 % of the total resistance offered to the flow (Abrahams et al., 1992).

## Soil Detachment

Since it is difficult to determine the level of grain resistance, only very generalized relationships can be developed for describing detachment rate $D_{f}$, depending on a simplified relationship between detachment and flow velocity. Integrating the continuity and Manning’s velocity equations, Meyer (1965) showed that:
$v=s^{\frac {1}{2}}Q^{\frac {1}{3}}$ (1.11)
for constant roughness conditions, where $Q$ is discharge or flow rate. Assuming that the detachment rate $D_{f}$ varies with the square of the velocity Meyer and Wishmeier (1969) showed that:
$D_{f}\propto Q^{f}s^{j}$ (1.12)
with $f={\tfrac {2}{3}}$, and $j={\tfrac {2}{3}}$. Quansah (1985) obtained more accurate exponent values of f = 1.5 and j = 1.44 experimentally for a range of soil types from clay to sand. Both versions relate only to the action of water flow over the soil surface. When flow is accompanied by rainfall, he found that the exponents decreased in value to f = 1.12 and j = 0.64 indicating that raindrop impact inhibits the ability of flow to detach soil particles.
However, detachment depends on the amount of sediment already suspended in the flow (Meyer and Monke, 1965), $D_{f}$ in eqn. 1.12 applies to the detachment capacity that only occurs when the flow is clear. Unter other conditions, $D_{f}$ depends on the difference between the actual sediment concentration in the flow $C$ and the maximum concentration that the flow can hold $C_{max}$ (Foster and Meyer, 1972):
$D_{f}\propto (C_{max}-C)$ (1.13)
This implies that in theory the detachment rate declines as sediment concentration in the flow increases and that when the maximum sediment concentration is reached, the detachment rate becomes zero.
Flanagan and Nearing (1995) describe the interrill detachment rate $D_{f,i}$ as explicit function of baseline interrill erodibility $K_{i}$, effective rainfall intensity $I_{e}$, interrill runoff rate $Q_{i}$, canopy, ground cover and interrill slope adjustment factors $C_{c}$, $C_{g}$ and $C_{s}$, spacing and width of rills $R_{s}$and $w$, and a sediment delivery ratio ${SDR}$:
$D_{f,i}=K_{i}I_{e}Q_{i}C_{c}C_{g}C_{s}{\frac {R_{s}}{w}}{SDR}$ (1.14)
with
$C_{c}=1-F_{c}e^{-0.34h_{c}}$ (1.15)
$C_{g}=e^{-2.5f_{g}}$ (1.16)
$C_{s}=1.05-0.85e^{4\sin \alpha }$ (1.17)
where $f_{c}$ is the fraction of the soil protected by canopy cover, $h_{c}$ is the effective canopy height, $f_{g}$ is the fraction of interrill surface covered by plant residue, and $\alpha$ is the interrill slope angle. According to Foster (1982) ${SDR}$ may be estimated as function of soil surface random roughness, interrill slope and interrill sediment particle size distribution.
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## Bibliography

* ↑ Shields, A. (1936). Anwendung der Aehnlichkeitsmechanik und der Turbulenzfoschung auf die Geschiebebewegung, volume 26 of Mitteilungen der Preussischen Anstalt Wasserbau und Schiffbau.
* ↑ Poesen, J. (1987). Transport of rock fragments by rill flow: a field study. Catena Supplement, 8:35–54.
* ↑ Torri, D. and Poesen, J. (1988). Incipient motion conditions for single rock fragments in simulated rill flow. Earth Surface Processes and Landforms, 13:225–237.
* ↑ 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.
* ↑ Govers, G. (1987). Initiation of motion in overland flow. Sedimentology, 34:1157–1164.
* ↑ Guy, B. and Dickinson, W. (1990). Inception of sediemnt transport in shallow overland flow. Catena Supplement, 17:91–109.
* ↑ Torri, D. and Borselli, L. (1991). Overland flow and soil erosion: some processes and their interactions. Catena Supplement, 19:129–137.
* ↑ Savat, J. (1979). Laboratory experiments on erosion and deposition of loess by laminar sheet flow and turbulent rill flow. In Vogt, H. and Vogt, T., editors, Colloque sur l’erosion agricole des sols en milieu tempere non Mediterraneen, pages 139–143. L’Universite Lois Pasteur, Strasbourg.
* ↑ Govers, G. and Rauws, G. (1986). Transporting capacity of overladn flow on a plane and on irregular beds. Earth Surface Processes and Landforms, 11:515–524.
* ↑ Abrahams, A., Parsons, A., and Hirsch, P. (1992). Field and laboratory studies of resistance to interrill overland flow on semi-arid hillslopes, southern arizona. In Parsons, A. and Abrahams, A., editors, Overland flow: hydraulics and erosion mechanics, pages 1–23. UCL Press, London.
* ↑ Meyer, L. (1965). Mathematical relationships governing soil erosion by water. Journal of Soil and Water Conservation, 20:149–150.
* ↑ 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.
* ↑ Quansah, C. (1985). Rate of soil detached by overland flow, with and without rain, and its relationship with discharge, slope steepness and soil type. In El-Swaify, S., Moldenhauer, W., and Lo, A., editors, Soil erosion and conservation, pages 406–423. Soil Conservation Society of America, Ankeny, IA.
* ↑ Meyer, L. and Monke, E. (1965). Mechanics of soil erosion by rainfall and overland flow. Transactions of the American Society of Agricultural Engineers, 8:572–577.
* ↑ Foster, R. and Meyer, L. (1972). A closed-form soil erosion equation for upland areas. In Shen, H., editor, Sedimentation. Department of Civil Engineering, Colorado State University, Cort Collins.
* ↑ Flanagan, D. and Nearing, M. (1995). USDA-Water Erosion Prediction Project (WEPP: Technical Documentation, volume 10 of NSERL Report. National Soil Erosion Research Laboratory, West Lafayette, IN.
* ↑ Foster, G. (1982). Modelling the soil erosion process. In Haan, C., Johnson, H., and Brakensiek, D., editors, Hydrologic modelling of small watersheds, volume 5, pages 940–947. American Society of Agricultural Engineers Monograph.

# Transport of Soil Particles by Flow

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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 $T_{f}$ varies with the fifth power of velocity (Meyer and Wishmeier, 1969):
$T_{f}\propto Q^{\frac {5}{3}}s^{\frac {5}{3}}$ (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):
$T_{f}\propto Q^{2.13}s^{2.27}$ (1.19)
While detachment capacity of flow is reduced by raindrop impact (eqn. 1.12, cf. section → Rill Erosion), transporting capacity is enhanced (Savat, 1979; Guy and Dickinson, 1990; Proffitt and Rose, 1992). 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) derives an equation for $T_{f}$ by simplifying the general transport equation to:
$T_{f}=k_{t}\tau ^{\tfrac {3}{2}}$ (1.20)
where $k_{t}$ is an empiric transport coefficient and $\tau$is hydraulic shear stress exerted flow (according to the Darcy-Weisbach equation, cf. section → Rill Erosion).

## Maximum Sediment Concentration

Transport capacity of overland flow is defined as the maximum sediment concentration $C_{max}$ that can be carried (Govers, 1990):
$C_{max}=a(sv-0.4)^{b}$ (1.21)
where $a$ and $b$are empirical coefficients dependent on grain size. For particles with median grain diameters (D$_{50}$) of 33, and 390 μm, respectively, $b$ amounts at values from 1.5 to 3.5 (Everaert, 1991). The impact of rainfall has an negligible influence on the relationship for fine particles but reduced $b$ 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; Styczen and Nielsen, 1989). The rate of deposition $D_{p}$ is:
$D_{p}=v_{s}C$ (1.22)
where $v_{s}$ is the settling velocity of particles (Proffitt et al., 1991).
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 → 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) and may develop into a depositional crust (cf. section → 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). 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

* ↑ 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.
* ↑ 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.
* ↑ 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.
* ↑ Guy, B. and Dickinson, W. (1990). Inception of sediemnt transport in shallow overland flow. Catena Supplement, 17:91–109.
* 1 2 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.
* ↑ 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.
* ↑ Govers, G. (1990). Empirical relationships for the transporting capacity of overland flow. International Association of Hydrological Sciences Publication, 189:45–63.
* ↑ Everaert, W. (1991). Empirical relations for the sediment transport capacity of interrill flow. Earth Surface Processes and Landforms, 16:513–532.
* ↑ 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.
* ↑ 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.
* ↑ 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.
* ↑ Kinnell, P. (1990). The mechanics of raindrop-induced flow transport. Australian Journal of Soil Research, 28:497–516.

# Rill Erosion

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# Rill Erosion
## Rill Initiation

Rills are initiated at a critical distance downslope, where overland flow becomes channelled. Overland flow breaks up into small channells of microrills (Moss et al., 1982). In addition to the main flow path downslope, secondary flow paths develop with a lateral component. Where these converge, the increase in discharge intensifies particle movement and small channels or trenches are cut by scouring.
In terms of hydraulic characteristics of flow (Reynolds, and Froude number) the change from interrill overland to rill flow passes through four stages (Merritt, 1984):
* Unconcentrated overland flow,
* Overland flow with concentrated flow paths,
* Microchannels without headcuts,
* Microchannels with headcuts.
At the point of rill initiation, flow conditions change from subcritical to supercritical (Savat, 1979). The overall change in flow conditions through the four stages takes place smoothly as the Froude number F increases from about 0.8 to 1.2, rather than occurring when a distinct threshold value is reached (Torri et al., 1987b; Slattery and Bryan, 1992). For this reason, attempts to explain the onset of rilling through the exceedance of a critical Froude number have not been successful and additional factors - such as particle size of the material (Savat, 1979) and sediment concentration in the flow (Boon and Savat, 1981) have had to be included when defining its value.
Greater success has been achieved relating rill initiation to the exceedance of a critical ratio between hydraulic shear stress $\tau$ exerted by the flow and the shear strength $\tau _{s}$ of the soil. When $\tau /\tau _{s}$ > 0.0001 − 0.0005, rills will form (Torri et al., 1987a).
Using the Darcy-Weisbach uniform flow equation and assuming that discharge varies linearly with the downslope distance $x$, Nearing et al. (1989) describe $\tau$ as function of the specific weight of water $\rho _{w}$, of peak runoff rate $Q_{p}$, of the Chezy discharge coefficient $C$ and of local slope gradient $s$:
$\tau =\rho _{w}{\Bigl{\frac {Q_{p}}{C}}xs{\Bigr )}^{\tfrac {2}{3}}$ (1.23)
where $C$ is related to gravity $g$ and to a total rill friction factor $f_{t}$:
$C={\frac {8g^{\tfrac {1}{2}}}{f_{t}}}$ (1.24)
The critical shear velocity (eqn. 1.10, cf. section → Soil Detachment by Interrill Overland Flow) for rill initiation $u_{*crit}$ is linearly related to the shear strength $\tau _{s}$ of the soil as measured at saturation using a Torvane device (Rauws and Govers, 1988):
$u_{*crit}=0.89+0.56\tau _{s}$ (1.25)
when shear stress or shear velocity is applied wholly to the soil particles, both should strictly be known as grain shear stress or grain shear velocity.
Once rills have formed, their extension upslope occurs by the retreat of the headcut at the top of the channel. The rate of retreat is controlled by the cohesiveness of the soil, the height and angle of the headwall, the discharge and the velocity of the flow (De Ploey, 1989). Downslope extension of the rill is controlled by the shear stress exerted by the flow and the strength of the soil (Savat, 1979).

## Soil Detachment in Rills

Soil detachment in rills occurs when hydraulic shear stress $\tau$ acting on the soil exceeds the critical shear stress $\tau _{c}$ of the soil and when sediment load is less than sediment transport capacity. For the case of rill erosion the detachment rate $D_{f,r}$ is determined by the detachment capacity of flow $D_{c}$, the sediment load of the flow $G$ and the sediment transport capacity in the rill $T_{f}$ (Nearing et al., 1989):
$D_{f,r}=D_{c}{\Bigl1-{\frac {G}{T_{f}}}{\Bigr )}$ (1.26)
Shear stress also determines the detachment capacity of soil particles by flow within a rill (Foster, 1982) as critical shear stress is exceeded:
$D_{c}=K_{r}(\tau -\tau _{c})$ (1.27)
where $K_{r}$ is a measure of the detachability of the soil and $\tau _{c}$ is the critical shear stress of the soil. Rill detachment is considered zero when actual shear is less than critical shear of the soil.

## Sediment Deposition

Deposition of transported soil particles occurs when sediment load $G$ is greater than the sediment transport capacity $\tau _{f}$. In this case, sediment detachment rate $D_{f,r}$ becomes negative and may be expressed as function of effective settling velocity for the sediment particles $v_{s}$, flow discharge $Q$ per unit width (Nearing et al., 1989):
$D_{f,r}={\frac {v_{s}}{Q}}{\BiglT_{f}-G{\Bigr )}$ (1.28)
The transport capacity of rill flow $\tau _{f}$ is approximately represented by eqns. 1.19, 1.21 or 1.20 (cf. section → Transport of Soil Particles by Flow).
Govers (1992) experimentally related flow velocity in rills is related to the rill flow discharge $Q$:
$v=3.52Q^{0.294}$ (1.29)
which gave better predictions than the Manning equation (eqn. 1.7, cf. section → Soil Detachment by Interrill Overland Flow). This was because over a range from 2 to 8° slope had no effect on flow velocity, neither did the grain roughness or the soil surface form. Govers (1992) therefore modified eqn. 1.21 (cf. Section → Transport of Soil Particles by Flow) by replacing the velocity term in eqn. 1.29:
$C_{max}=a(3.52Q^{0.294}-\omega _{c})Q$ (1.30)
where $a$ is dependent upon the grain size of the sediment and $\omega _{c}$ is the critical value of unit stream power, which amounts at 0.0074. The equation expresses the maximum sediment concentration that can be carried by runoff in a rill.
The actual sediment concentration - and therefore the erosion - may vary considerably from this. This is because the supply of sediment to the rill is not solely dependent upon the detachment of soil particles by the flow. The rill has to adjust continually for pulse influxes of sediment
* due to wash-in from interrill flow,
* due to erosion and collapse of the head wall,
* due to collapse of side walls.
Mass failure of side walls can contribute more than half of the sediment removed in rills (Govers and Poesen, 1988).
Since rill flow is non-selective in particle size it can carry, large grains, and even rock fragments up to 9 cm in diameter (Poesen, 1987), can be moved. Rill erosion accounts for the bulk of the sediment removed from a hillside, depending, besides the soil properties, on the spacing of the rills and the extent of the area affected. Material transported in rills may account for 54-78 % of the total erosion (Govers and Poesen, 1988).
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## Bibliography

* ↑ Moss, A., Green, P., and Hutka, J. (1982). Small channels: their formation, nature and significance. Earth Surface Processes and Landforms, 7:401–415.
* ↑ Merritt, E. (1984). The identification of four stages during microrill development. Earth Surface Processes and Landforms, 9:493–496.
* 1 2 3 Savat, J. (1979). Laboratory experiments on erosion and deposition of loess by laminar sheet flow and turbulent rill flow. In Vogt, H. and Vogt, T., editors, Colloque sur l’erosion agricole des sols en milieu tempere non Mediterraneen, pages 139–143. L’Universite Lois Pasteur, Strasbourg.
* ↑ Torri, D., Sfalanga, M., and Del Sette, M. (1987b). Splash detachment: Runoff depth and soil cohesion. Catena, 14:149–155.
* ↑ Slattery, M. and Bryan, R. (1992). Hydraulic conditions for rill incision under simulated rainfall: a laboratory experiment. Earth Surface Processes and Landforms, 17:127–146.
* ↑ Boon, W. and Savat, J. (1981). A nomogram for the prediction of rill erosion. In Morgan, R., editor, Soil conservation: problems and prospects, pages 303–319. Wiley, Chichester.
* ↑ Torri, D., Sfalanga, M., and Chisci, G. (1987a). Threshold conditions for incipient rilling. Catena Supplement, 8:97–105.
* 1 2 3 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.
* ↑ Rauws, G. and Govers, G. (1988). Hydraulic and soil mechanical aspects of rill generation on agricultural soils. Journal of Soil Science, 39:111–124.
* ↑ De Ploey, J. (1989). A model for headcut retreat in rills and gullies. Catena Supplement, 14:81–86.
* ↑ Foster, G. (1982). Modelling the soil erosion process. In Haan, C., Johnson, H., and Brakensiek, D., editors, Hydrologic modelling of small watersheds, volume 5, pages 940–947. American Society of Agricultural Engineers Monograph.
* 1 2 Govers, G. (1992). Relationship between discharge, velocity and flow area for rills eroding loose, non-layered materials. Earth Surface Processes and Landforms, 17:515–528.
* 1 2 Govers, G. and Poesen, J. (1988). Assessment of the interrill and rill contributions to total soil loss from an upland field plot. Geomorphology, 1:343–354.
* ↑ Poesen, J. (1987). Transport of rock fragments by rill flow: a field study. Catena Supplement, 8:35–54.

# Sediment Continuity

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# Sediment Continuity

Overall net erosion along a hillslope as function of downslope distance $x$ may be calculated by solving a
steady state sediment continuity equation (Nearing et al., 1989):
${\frac {dG}{dx}}=D_{f,r}+D_{f,i}$ (1.31)
whereby interrill erosion $D_{f,i}$is considered to be independent of $x$. Rill erosion $D_{f,r}$is positive for detachment (eqn 1.26, cf. section → Rill Erosion) and negative for deposition (eqn 1.28).
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## Bibliography

* ↑ 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.

# Further Reading

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# Further reading
## en

* Morgan, R.P.C (2005). Soil Erosion and Conservation. 3rd ed., Blackwell, Oxford.
* Lal, R. (1994). Soil Erosion Research Methods. 2nd ed., Soil and Water Conservation Society, Ankeny, IA.
* Harmon, R.S., and Doe Ill, W.W. (2001). Landscape Erosion and Evolution Modelling. Kluver Academic/Plenum Publishers, New York
* Toy, T.J., Foster, G.R., and Renard, K.G. (2002). Soil Erosion: Processes, Prediction, Measurement, and Control. Wiley & Sons, New York

## de

* Morgan, R.P.C (1999). Bodenerosion und Bodenerhaltung. Thieme, Stuttgart.
* Richter, G. (1998). Bodenerosion: Analyse und Bilanz eines Umweltproblems. Wissenschaftliche Buchgesellschaft, Darmstadt
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# Strategies

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# Soil Conserving Strategies

According to the driving processes and mechanics of the detachment and transport of soil particles by rainsplash and runoff (cf. chapter 1), basic strategies for soil conservation must be based on:
* Covering the soil to protect it from raindrop impact,
* Increasing the infiltration capacity of the soil to reduce runoff,
* Improving the aggregate stability of the soil,
* Increasing surface roughness to reduce the velocity of runoff.
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## Bibliography
# Techniques

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# Techniques in Soil Conservation

The various conservation techniques can be described under the below headings:

## Agronomic measures:

Utilize the role of vegetation to protect the soil against erosion.
* Crop rotation
    Limiting longterm erosion rates by eliminating perennial monoculture and reducing the share of erosion promoting crop types, such as row crops, within crop rotation.
* Cover crops
    Planting quickly growing crops, which establish an early canopy cover, are aggressive to suppress weeds, and possess a deep root system to improve the macroporosity of the soil as a conservation measure during the off season or as ground protection under trees.
* Strip-cropping
    Growing of row crops and protection-effective crops such as leguminous or grass in alternating strips aligned on the contour or perpendicular to the wind in order to limit erosion to the row-crop strips and to trap the soil removed from these within the downslope, or downwind strip.
* Multiple cropping
    Increasing the production from the land while providing protection from erosion by sequential cropping, growing two or more crops involving protection-effective ones a year in sequence, or intercropping, growing two or more crops on the same piece of land at the same time.
* High density planting
    Increasing plant density of row crops and modifying the plant arrangements effect in a protection soil by an incsreased canopy cover.
* Mulching
    Covering of the soil with crop residues such as straw, maize stalks, palm fronds or standing stubble (direct seeding) to protect it from raindrop impact and to reduce the velocity of runoff and wind.
* Re-vegetation
    Rapidly reconditioning vegetation plays a major role in the process of erosion control on gullied areas, landslides, sand dunes, road embarkments, construction sites, mine spoils or pipeline corridors, and is also necessary for replanting forest in areas cleared by patch-cutting or for covering land cleared of forest in favour of agriculture.
* Agroforestry
    Incorporating trees within a farming system by planting them on land that is not suitable for crop production where trees help to preserve the fertility of the soil through the return of organic matter and the fixation of nitrogen, improve the soil’s structure, and help to maintain high infiltration rates and greater water-holding capacity.

## Soil management:

Is concerned with ways of preparing the soil to improve its structure so that it is more resistant to erosion and to promote plant growth.
* Organic content
    Applying organic matter as a way of achieving and maintaining soil fertility which effects an improved the cohesiveness of the soil, an increased water retention capacity and a stable aggregate structure.
* Tillage practices
    Preventing or reducing soil compaction and increasing the residue cover by reducing intensity and frequency of soil management operations and introducing conservation, contour, strip, mulch, or minimum tillage.
* Drainage
    Reducing soil moisture content, runoff and therefore erosion on heavy clay soils by means of subsurface mole or pipe drainage and subsoiling.
* Soil stabilizers
    Improving soil structure by applying soil conditioners which may take the form of polyvalent salts such as gypsum, which bring about flocculation of clay particles, organic by-products or synthetic polymers, which both bind the soil particles into aggregates.

## Mechanical methods:

Depend on manipulating the surface topography to control the flow of water and air and often involve engineering structures.
* Contour bunds
    Building earth banks of 1.5-2 m width, thrown across the slope to act as a barrier to runoff, to form a water storage area on their upslope side and to break up a slope into segments shorter in length than is required to generate overland flow.
* Terraces
    Installing earth embankments constructed across the slope to intercept surface runoff (retention terraces), convey it to a stable outlet an a non-erosive velocity and shorten slope length (diversion and bench terraces).
* Waterways
    Conveying runoff at a non-erosive velocity to a suitable disposal point by means of a system of diversion channels, terrace channels or grass waterways, which all have to be carefully dimensioned in order to provide sufficient capacity to convey the peak runoff from a storm with at least a ten-year return period.
* Temporary measures
    Installing silt fences, burlap rolls, straw bales and sedimentation ponds as temporary measures for erosion control required on construction sites, road banks and pipeline corridors until a soil protecting vegetation cover has been established.
* Stabilization structures
    Controlling erosion on steep slopes such as gully sidewalls, embarkments and cuttings using bioengineering techniques like brush layering and wattling, which use live cuttings of quick-rooting plat species, usually willow, to give an immediate reinforcement of the soil and to provide the basis for long-term slope stability as the cuttings take root and vegetation grows.
* Geotextiles
    Controlling soil detachment by raindrop inpact with the help of surface-laid mats made of natural fibres which provide effective surface cover, high water absorption, interception of splashed particles from their point of ejection, and ponding water in a rough surface; geotextile products range from open-weave testile meshes made from polypropylene, coir or jute, to blankets, containing natural or synthetic fibres that are woven, glued or structurally bound with nets or meshes.
* Brush matting
    Using bush mats as an alternative to geotextiles to provide an immediate cover to the slope and prevent surface erosion and complementarily providing the basis for a long-term vegetation cover, they are only suitable where the used species is appropriate as the final land cover.
* Gully control
    Installing stabilization structures such as small dams made from locally available materials such as earth, wooden planks, brushwood or lose rock and built across bullies to trap sediment and thereby reduce channel depth and slope; the structures have a high risk of failure but provide temporary stability and are used in association with agronomic soil conservation treatment of the surrounding land.
* Footpaths
    Constructing paths with a camber or a cross-fall and providing them with revetments, surfaced side and cut-off drains where stabilization structures are needed in the construction and maintenance of footpaths, especially in recreational areas on sloping land.
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# Exercise A

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# Exercise A

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# Exercise B

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