Geology Reference
In-Depth Information
national scale, for the relatively densely popu-
lated areas in Australia, covering some 1.7 mil-
lion km
2
. This methodology was used because of
the complexity of the relationship between gully
density and environmental factors. Their final
model included land use, geology, texture, rain-
fall and other climate indices and topographical
attributes.
critical runoff slope (m m
−1
) and
t
c
is the critical
flow shear stress (N m
−2
).
Nachtergaele
et al
. (2001a,b) were among the
first to thoroughly test the model's performance
against field data on ephemeral gullies formed in
stony soils (Mediterranean environment) and in
loess-derived soils (temperate maritime climate).
In spite of the fact that both gully length and
maximum depth were input parameters, they
showed that EGEM was not capable of predicting
measured ephemeral gully volumes satisfactorily.
Pooling all data from 112 ephemeral gullies, they
observed a strong relationship between gully vol-
ume (
V
, m
3
) and gully length (
L
, m):
V
(ii) Modelling soil losses by (ephemeral) gully ero-
sion
One of the first models for simulating soil
loss by ephemeral gully erosion that was accessi-
ble to field practitioners was the Ephemeral Gully
Erosion Model (EGEM), developed by scientists
from USDA-NCRS (Merkel
et al
., 1988; Woodward,
1999). The main limitation of EGEM is that the
length and topographic location of the gullies
need to be known exactly. Gully evolution in the
model is therefore limited to incision and widen-
ing, neglecting its lengthwise growth. The chan-
nel erosion routines are a slightly modified version
of those used in the CREAMS model, and also
used in WEPP (Foster, 1986). Soil detachment rate
is dependent upon the difference between actual
sediment load and maximum sediment load in
the flow according to the following equation:
0.048
L
1.29
with an R
2
of 0.91. Capra
et al
. (2005) confirmed
the conclusions of Nachtergaele
et al
. and also
observed a significant relationship between
V
and
L
for 92 ephemeral gullies formed in clayey soils
(Sicily):
V
=
0.0082
L
1.42
with an R
2
of 0.64.
Recently, Zhang
et al
. (2007) reported the follow-
ing relation for 21 ephemeral gullies formed in
clay loam soils in northeast China:
V
=
0.015
L
1.43
with an R
2
of 0.67. These findings imply that
predicting ephemeral gully length is a valuable
alternative for the prediction of ephemeral gully
volume. Nachtergaele
et al
. (2001a, b) also pre-
sented a simple procedure based on topographic
thresholds to predict ephemeral gully length. The
empirical
V
-
L
relations can also be used to convert
ephemeral gully length data extracted from, say,
aerial photographs into ephemeral gully volumes.
Apart from the static gully length that was
needed
a priori
, several other drawbacks of EGEM
were reported. Nachtergaele
et al
. (2001a,b)
pointed to the practical problems associated with
field determination of parameters for Equation
(19.2), such as
n
and
t
c
. Furthermore, runoff dis-
charge and channel width vary distinctly in time
and space over the gully's length, which are not
taken into account. Instead, concentrated flow
discharge was assumed constant in time over the
entire length of the runoff event. Calculations
according to equations (19.1) and (19.2) were per-
formed at the gully mouth. In space, some con-
stants were then used to scale gully width and
transport capacity, calculated at the gully mouth,
over the rest of the gully channel. One of the
=
D
=
KC
(
t
-
t
c
)
(19.1)
where
D
is the detachment rate (g m
−2
s
−1
),
KC
the
channel erodibility,
τ
the average flow shear stress
τ
c
the critical shear stress for particle
entrainment (N m
−2
).
In order to satisfy Equation (19.1), gullies are
first deepened (maintaining the initial width)
until they reach a less erodible soil layer, typi-
cally the tillage depth or topsoil depth, and then
widened until they reach the estimated maxi-
mum width. Since the maximum depth is also
user-defined, this maximum width is a critical
variable. This width (
W
max
) was calculated using
the following regression equation:
(N m
−2
) and
W
max
=
179
Q
0.552
n
0.556
S
0.199
t
c
−0.476
(19.2)
where
Q
is the peak runoff rate (m
3
s
−1
),
n
is
Manning's roughness coefficient (m
−1/3
s),
S
is
