# Soil Erosion by Water/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 correction 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.