Geology Reference
In-Depth Information
in the physics or the parameters. This may be
important in the event of political and/or manage-
rial resistance to acceptance of the LEM results.
To do the calibration above we need to do the
simulations on some kind of landform. The sim-
plest way to calibrate LEMs to an existing model
is to create a series of synthetic hillslopes of dif-
ferent length/area and slope and run the existing
model on them, outputting the erosion rate for
each slope. The fluvial transport equation is nor-
mally expressed in the form
upward concavity (Fig. 18.6). If a key part of the
landform design process is to design the concav-
ity of the slope, then some caution is needed in
calibration of the LEM to an existing traditional
erosion model.
The user must therefore feel confident that the
area and slope dependencies of the traditional
erosion model are correctly calibrated, otherwise
any inaccuracy in the traditional model will be
simply transferred to the LEM through the cali-
bration. A subtle difference in the area-slope
dependency can make non-trivial differences in
landform evolution. In a comparison study of two
LEMs, SIBERIA and CAESAR, Hancock
et al
.
(2010) showed that slight differences in this
aspect of the two models resulted in subtle but
noticeable differences in their long-term sedi-
ment transport predictions.
Given the concavity/area-slope dependence of
the physics of landform evolution, the best data
source for calibrating an LEM is field erosion plot
data collected at the site for the soils of interest,
where the areas and slopes of the experimental
plots encompass the range of areas and slopes
expected in the final landform to be assessed by
the LEM. It is important to have a range of areas
and slopes so that
m
and
n
can be calibrated from
the data. Given the simplicity of Equation (18.3) it
is generally sufficient to do a multiple regression
with area and slope as the independent variables
and sediment load as the dependent variable.
As part of a project to develop a general LEM
for the Queensland Coal Industry (Bell
et al
.,
1993), an easy graphical interface for the first
author's SIBERIA model and associated engi-
neering tools were developed, called EAMS-
SIBERIA, and a database of parameters for
unvegetated spoils and soils found in the Bowen
Basin Coal Province in Queensland was derived.
While generality of the parameters in the Bowen
Basin database for other areas has never been
fully tested, a number of studies has shown
that the database is quite robust if soil texture
properties are known (Hancock
et al
., 2008a,b).
The location and rate of erosion is well mod-
elled with EAMS-SIBERIA when using the
Bowen Basin database. The only deviation from
ˆ
ˆ
(18.3)
mn mn
s
QKQS KAS
=
=
where it is normally assumed that discharge is pro-
portional to the catchment area so that
m
mˆ
..
The key components of the calibration of
Equation (18.3) are (a) the area and slope depend-
ence of the fluvial erosion process, (b) any mini-
mum shear stress threshold on transport, and
(c) any upper bound threshold on slope stability.
For simplicity, Equation (18.3) reflects only the first
of these three sets of parameters. Either by multi-
ple regressions on area and slope, or by hand-fitting
the LEM directly to erosion plot data (either field-
based or computer-generated), these parameters of
the erosion model in the LEM can be calibrated.
The main difficulty with this approach is that
the ratio
a
of the area and slope exponents in
Equation (18.3) (i.e.
a
=
(
m
− 1)/
n
; see Willgoose
et al
. (1991b) and Willgoose (1994) for further
explanation) that is calibrated will be a function
of the traditional model used. For natural catch-
ments
a
is about 0.5, while for traditional models
a
ranges between 0 and 1 (Willgoose & Gyasi-
Agyei, 1995). To place the
a
range of 0-1 implied
by traditional models in context with respect to
the evolution of natural slopes:
●
=
0 means that rilling cannot occur
and that the long profile of the final equilibrium
slope is a flat plane (see Fig. 18.6 and Example
18.3.3 for an explanation of how
a
controls the
concavity of the slope that the landform will
evolve to in the LEM); while
●
a value of
a
=
1 indicates a slope that will rill quite
strongly and will generate a slope with a strong
a
=
