Geology Reference
In-Depth Information
relationship between
L
and
A
. Respectively,
P
values of 0.2 (
n
é
5/3
ù
æ
ö
L
=
67) and 0.6 (
n
=
49) were
ê
j
ú
A
=-
ç
1
÷
(19.4)
ç
÷
j
L
ê
ú
è
ø
obtained.
In order to determine shear stresses exerted
by the flow on the gully walls, gully width is a
critical parameter to calculate flow velocity from
discharge. Gully width (
W
) is now determined
directly from flow discharge (
Q
) through the
regression equations in the form of:
ë
max
û
Equation (19.4) results from the simplified repre-
sentation of the drainage area as a right-angled
triangle. For the same reason,
L
max
is not directly
available from the real path of the concentrated
flow.
L
max
is defined as a function of the given
drainage area
A
d
(ha) of each gully. In the present
model, it is calculated by an empirical function
fitted by Leopold
et al
. (1964).
b
WaQ
=
(19.6)
where the values of the coefficients reported by
Nachtergaele
et al
. (2002a) and Torri
et al
. (2006)
are used:
a
L
=
80.3
A
0.6
(19.5)
max
d
0.412. Torri
et al
. (2006)
observed that the exponent
b
varies continuously
with channel width, indicating that more research
is needed to improve the predictive capacity of this
equation. The Manning equation is then applied,
with Manning's
n
as a user-defined input parame-
ter, to derive flow depth and velocity iteratively so
that flow shear stresses can be calculated.
Sediment detachment rate is calculated
according to Equation (19.1). The critical flow
shear stress
t
c
in Equation (19.3) is further
adapted according to tillage practices. Soil erod-
ibility
KC
is determined from
t
c
according to the
relation:
=
2.51 and
b
=
This equation was originally fitted for rivers,
with considerably larger dimensions and drainage
areas than ephemeral gullies.
The consideration of gully headcut migration
is one of the main changes with respect to EGEM.
The fact that gully length is no longer a static
variable is a big step forward, although it still
has to be assessed how the model performs in
heterogeneous material (e.g. in the presence of a
resisting soil layer). The underlying plunge-pool
erosion and headcut migration model of Alonso
et al
. (2002) has been validated by Bennett (1999),
Bennett
et al
. (2000) and Bennett and Casalí
(2001), who conducted their experimental meas-
urements in homogeneous material. Although
Gordon
et al
. (2007) reported that gullies did not
reach maximum length in their simulations, for
longer simulations, where the gullies might
reach maximum length, this length fully depends
on the gully initiation point defined by the user
and the maximum gully length as derived from
Equation (19.5). Since Nachtergaele
et al
.
(2001a,b) identified gully length as the single
most important parameter controlling ephem-
eral gully soil loss, it seems critical to evaluate
the performance of this empirical equation in
different environments. Available datasets for
ephemeral gullies in the Belgian and Chinese
loess belt do not seem to corroborate this simpli-
fied approach. Gully length (
L
)-drainage area (
A
)
relations from Nachtergaele
et al
. (2001a,b) and
Cheng
et al
. (2006) did not yield any statistical
-
0.5
(19.7)
KC
=
100
c
t
Although Gordon
et al
. (2007) recognized that at
present, no comprehensive field dataset is avail-
able that would allow a full validation of REGEM,
they tested the model's performance against data
from four field sites in central Mississippi (Smith,
1992). Detailed measurements across multiple
cross-sections were available for four gullies.
They reported that simulated gully lengths and
channel widths approximated reasonably well
to the observations (RMSE of 31% and 52%
respectively).
In the light of these results it is clear that
although REGEM conceptually tackles some of
the limitations of EGEM, at present, no extensive
validation of REGEM has been performed.
Nevertheless, REGEM is conceptually a very
