Geology Reference
In-Depth Information
soil by rills,
e
rdj
is the rate of erosion of particles
of sediment class
j
from previously detached soil
by rills, and
d
j
is the rate of deposition of particles
in sediment class
j
.
Even where models use the same form of the
continuity equation, they differ in the operating
functions used to describe erosion and deposition.
The user therefore has the possibility of selecting
a model according to which functions best describe
the way that erosion occurs in a particular study
area or which functions are theoretically more
satisfying. As an illustration, the way
e
i
and
e
r
are
described in WEPP and EUROSEM are compared.
In WEPP (Nearing
et al
., 1989b), the inter-rill ero-
sion rate (per unit rill width) is given by:
In EUROSEM (Morgan
et al
., 1998) a single
equation is used to describe the erosion rate by
soil particle detachment by raindrop impact and
runoff, i.e.
e
i
e
. The equation can be applied
to unchannelled inter-rill flow or to runoff in
rills. Where rills are present, these need to be
defined in terms of their number, depth and
width. The model initially places all the runoff in
the rills and then uses a unified rill model to
describe the hydraulic conditions of the flow as
the runoff overflows the rills and spreads out over
the inter-rill area. The single equation is:
+
e
r
=
é
(
)
1.0
ù
e
=
k KE
+
KE
e
-
2
h
ë
û
DT
LD
{
}
(2.8)
(
)
é
ù
(
)
b
+
h
wv
a
w w
-
-
C
ê
ú
(
)
s
ë
c
û
(
)
2
0.34
PH
-
2.5
G
eKI
=
1
-
F
e
RW
/
(2.5)
i
i
s
where
K
i
is the inter-rill erodibility of the soil,
I
is the intensity of the rainfall,
F
is the fraction
of the soil protected by the plant canopy,
PH
is
the height of the plant canopy,
G
is the fraction
of the soil covered by ground vegetation or crop
residue,
R
s
is the spacing of the rills and
W
is the
width of the rill computed as a function of the
flow discharge. The rate of rill erosion is calcu-
lated from:
where
k
is the detachability of the soil by
raindrop impact,
KE
is the kinetic energy of the
rainfall which is divided into direct throughfall
(
DT
) and that falling from the plant canopy as
leaf drainage (
LD
),
h
the depth of surface water,
h
is an expression of the efficiency of soil parti-
cle detachment by flow which is a function of
soil cohesion,
w
is the width of flow,
v
s
is the
settling velocity of the particles in the flow,
w
is
the unit stream power of the flow (the product of
slope and flow velocity),
w
c
is the critical value
of unit stream power for sediment transport,
a
and
b
are coefficients related to sediment parti-
cle size, and
C
is the sediment concentration in
the flow.
The user therefore has a choice between a
model that simulates the detachment of soil par-
ticles by raindrop impact as a function of rainfall
intensity, and one that uses the kinetic energy of
the rain. WEPP allows for the effect of the plant
cover by assuming that ground-level vegetation
protects the soil completely and that the plant
canopy provides some protection dependent upon
its height above the ground surface. In EUROSEM,
the proportion of the soil surface covered by veg-
etation is used to split the rainfall into direct
throughfall and leaf drainage. The kinetic energy
of the leaf drainage is calculated as a function of
=
(
)
(
)
é
3/2
ù
eK
=
tt
-
1/
-
Ck
t
(2.6)
ë
û
r
r
c
t
where
K
r
is the rill erodibility of the soil,
t
is the
flow shear stress acting on the soil,
t
c
is the criti-
cal flow shear stress for detachment to take place,
C
is the sediment load in the flow, and
k
t
is a sedi-
ment transport coefficient. This equation only
operates when the sediment load in the flow is
less than the sediment transport capacity of the
flow. When the sediment load exceeds the trans-
port capacity, the equation becomes:
{
}
(
)
(
)
é
3/2
ù
eK
=
tt
-
vqk
/
t
-
C
(2.7)
ë
û
r
r
c
s
t
where
v
s
is the particle settling velocity and
q
is
the flow discharge per unit width.
