Page 249 - Soil and water contamination, 2nd edition

236 Soil and Water Contamination

length, profile curvature, and local drainage direction network, i.e. a converging network in
which the grid cells are connected in the direction of steepest downhill slope). The SEDEM
model presented by Van Rompaey et al. (2001) and the WEPP model (USDA, 1995, 2012)
are examples of such a spatially distributed soil erosion and deposition model.

Example 12.4 Soil erosion and deposition
Consider a long, straight slope of 6 percent. Estimate the distance from the divide (slope
length) at which the rill erosion rate equals the interrill erosion rate and the distance at
which the transport capacity is exceeded. Assume a value of f = 170 m and for the other
parameters use the values given in the text above for the loam belt in central Belgium .
Solution
First, calculate the sine of the slope:
s = sin(arctan(0.06)) = 0.0599

Note that for gentle slopes, the sine of the slope approximates the tangent of the slope
(in this example 6 percent = 0.06). Second, use equation (12.28) to calculate the interrill
-3
erosion , which is independent from the slope length (d = 1.1·10 and e = 0.8):
-2
E 1 . 1 10 3 1350 . 0 0599 8 . 0 . 0 156 kg m y -1
ir
For the slope length at which the rill erosion rate equals the interrill erosion rate, the
following applies:

-2
E a s b l c 3 10 4 1350 . 0 0599 . 1 45 l . 0 75 E . 0 156 kg m y -1
r b ir
. 0 0068 l . 0 75 . 0 156
l . 0 75 22 9 .
l 65 m

Thus, at 65 m from the divide, the rill erosion rate has increased to the same value as the
interrill erosion rate. At smaller slope lengths, the interrill erosion dominates the erosion
process, whereas further downslope, rill erosion prevails.

To calculate the slope length at which the transport capacity is exceeded, we must first
calculate the total cumulative erosion as a function of slope length. The total erosion is
simply the sum of rill erosion and interrill erosion:
-2
E E E . 0 0068 l . 0 75 . 0 156 kg m y -1
tot r ir
The total cumulative erosion is the integral of the total erosion with respect to the slope
length:
. 0 0068 1 . 75 . 1 75
0
0
0
E tot dl l . 156 l p . 0039 l . 156 l p
. 1 75
where p = an integration constant. In order to satisfy the boundary condition E = 0 at
tot
l = 0, we must set p = 0. Hence,
E dl . 0 0039 l . 1 75 . 0 156 l
tot

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Soil and Water.indd 248 10/1/2013 6:45:09 PM