Page 248 - Soil and water contamination, 2nd edition

Sediment transport and deposition 235

and transport capacity , respectively. The processes of splash transport and detachment by
runoff are ignored. An overview of the operating functions of this model and typical values
for the input parameters is given by Morgan (2001).
A common shortcoming of the above described long-term soil erosion models is that
they ignore sediment deposition. Govers et al. (1993) have proposed an alternative one-
dimensional model for erosion on a slope, which also includes sediment deposition. In
addition, the model accounts for soil redistribution due to splash erosion, soil creep, and
tillage . Because overland flow concentrates in rills, i.e. small channels where the water flows
faster and is deeper, the model makes a distinction between rill erosion and interrill erosion,
i.e. erosion on the land between the rills. The erosion rate is modelled as a function of slope
gradient and length:
E a s b l c (12.27)
r b
-1
-2
where E = the rill erosion rate per unit area per unit time (kg m y ), ρ = the dry bulk
r b
-3
density of the soil (kg m ), s = the sine of the slope, l = slope length (m), a, b, c are empirical
constants. From a field study of rill erosion in the loam belt in central Belgium , the mean
-4
values of a, b, and c were found to be 3⋅10 , 1.45 and 0.75 respectively (Govers et al., 1993).
-3
For the dry bulk density a mean value of 1350 kg m can be assumed. The interrill erosion
rate is assumed to depend only on the local slope:
E d s e (12.28)
ir b
-3
where d and e are empirical constants, for which values of 1.1⋅10 and 0.8 can be assumed
(Govers et al., 1993). The transport capacity is considered to be directly proportional to the
potential for rill erosion :
T c f E r (12.29)

-1
-1
where T = transport capacity (kg m y ), and f = an empirical constant (m). In the
c
model, the eroded sediment is routed downslope until the transport capacity is reached. If
the accumulated erosion exceeds the transport capacity, the excess sediment is deposited.
Accordingly, a sediment mass balance for each location along the slope is formulated, taking
into account the supply of sediment from upslope areas, the local soil erosion and deposition,
and the losses to the downslope areas.
The diffusion process as a consequence of splash erosion , soil creep, and tillage operations
is modelled by assuming that the resultant soil movement is proportional to the sine of the
slope angle:
s
E d g (12.30)
x
-2
where E = the erosion rate per unit area attributable to diffusion processes (kg m ), x = the
d
-1
distance from the divide (m), and g = a coefficient (kg m ). For small slope angles, the sine
of the slope angle s is approximately equal to the tangent of the slope angle (the difference for
slopes up to 14 percent (≈ 8°) is less than 1 percent), so ∂s/∂x is approximately equal to the
profile curvature (i.e. the concavity/convexity in the direction of the slope).
The governing equations of the above long-term soil erosion model can be implemented
in a raster GIS relatively easily in order to calculate the spatial distribution of soil erosion and
deposition. The advantage of a GIS implementation of the model is that the GIS can also be
used to derive the model input parameters related to the topography from a gridded digital
elevation model (DEM) (see Burrough and McDonnell, 1998) (e.g. slope gradient, slope

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Soil and Water.indd 247
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