Geology Reference
In-Depth Information
simultaneously for different erosion/deposition
domains, depending on the relative dominance
of the three processes (Beuselinck
et al
., 1999).
Ideally this will not be restricted to primary
particles, as in Morgan and Duzant (2008) and
Fiener
et al
. (2008), but will cover the sizes of soil
aggregates. In addition, since deposited material
has different strengths to that of the original soil
because cohesion has been lost during detach-
ment and transport, erosion models will need to
distinguish between the two when simulating the
detachment and transport of the sediment (Rose
et al
., 1983).
for the volume or mass of sediment passing a
given point on the land surface at a given time is:
()()
() ()
¶
AC
¶
QC
+
-
ext
,
=
q xt
,
(2.2)
s
¶
t
¶
x
where
A
is the cross-sectional area of the flow,
C
is
the sediment concentration in the flow,
t
is time,
x
is the horizontal distance downslope,
e
is the net
pick-up rate or erosion of sediment on the slope
segment, and
q
s
is the rate of input or extraction of
sediment per unit length of flow from land external
to the segment, for example, from the sides of a
convergent slope surface. On a planar slope,
q
s
=
0,
and the continuity equation can be rewritten as:
2.4 Operating Equations
()()
i
¶
AC
¶
QC
The simplicity and number of operating equa-
tions required to run an erosion model depends
on its type and level of complexity. Since this sec-
tion is descriptive rather than intended for practi-
cal application, the units of the equations are not
given. Readers should consult the original sources
for these details. A simple grey-box model like
the USLE (Wischmeier & Smith, 1978) requires
only one equation which multiplies together six
numbers:
+
=
ee
+
(2.3)
r
¶
t
¶
x
where
e
i
is the net rate of erosion in the inter-rill
area of the slope segment and
e
r
is the net rate of
erosion by rills. This is the form of the continuity
equation used in WEPP (Nearing
et al
., 1989b),
EUROSEM (Morgan
et al
., 1998), LISEM (Jetten
& de Roo, 2001) and many other process-based
models. In GUEST (Rose
et al
., 1983) the equation
takes a slightly different form. In this model,
the soil is described in terms of up to 50 particle-
size classes, determined according to their set-
tling velocity, and, for each particle-size class,
a distinction is made between that eroded from
the original soil and that eroded from previously-
detached and recently deposited sediment; in
addition, deposition is modelled explicitly. The
continuity equation becomes:
ARKLSCP
=´´´´´
(2.1)
where
A
is the mean annual soil loss,
R
is the
rainfall erosivity factor,
K
is the soil erodibility
factor,
S
is the slope steepness factor,
L
is the
slope length factor,
C
is the crop management
factor and
P
is the erosion-control practice factor.
Additional equations are required to determine
the values of the
S
and
L
factors and, as indicated
above, a third equation can be used to estimate
the value of
K
(Wischmeier
et al
., 1971). Graphical
solutions to these additional equations exist in
the form of nomographs.
More complex process-based models use sepa-
rate equations to describe the various processes of
erosion and deposition, and link these together
using continuity equations to ensure conserva-
tion of energy and mass. The continuity equation
()()
¶
AC
¶
QC
j
j
+
=
ee ee d
+
+
+
-
(2.4)
ij
idj
rj
rdj
i
¶
t
¶
x
where
C
j
is the concentration of sediment of par-
ticle size
j
in the flow,
e
ij
is the rate of erosion of
particles of sediment class
j
in the original soil on
the inter-rill area,
e
idj
is the rate of erosion of par-
ticles of sediment class
j
from previously detached
soil on the inter-rill area,
e
rj
is the rate of erosion
of particles of sediment class
j
from the original
