Geology Reference
In-Depth Information
(a)
1 000 000
100 000
10 000
1000
100
10
1 mm particles
0.1 mm particles
0.01 mm particles
1
0.1
0
5
10
15
20
25
Distance (m)
30
35
40
45
50
10
(b)
1
Fig. 6.1
Analytical
model of (a) inter-rill
erosion and (b) rill
erosion as a function
of scale, showing the
relationship between
sediment flux and
distance downslope
on hillslopes of
uniform gradient,
assuming spatially
uniform rainfall and
infiltration, and
unlimited sediment
supply (after Parsons
et al
., 2004).
0.1
0.01
0.001
flux 0.1 mm
flux 1 mm
flux 5 mm
0.0001
0
10
20
30
40
50
Distance (m)
the exact shapes of the curves will vary according
to the distribution function used, Equation (6.5)
predicts scaling characteristics very similar to
those of equations (6.3) and (6.4). The simplest
probability distribution, which is very commonly
used to describe travel distances, is the exponen-
tial distribution. Advantages of this function are
that it has a single parameter, which is easily
measured (as the reciprocal of the mean observed
distance of movement), and that it produces some
