Geology Reference
In-Depth Information
validation, and then went on to assume that large-
scale model estimates can be validated against
average values for areas, without any considera-
tion of scale dependency of either the model esti-
mates or the observed values. Until there are
accepted standards and appropriate measurements
for testing erosion models at different scales, all
erosion predictions should be treated with
extreme caution.
neglects to consider the influence that the meas-
urement scale may have on the performance of
the model. It may well be the case that the high-
est resolution data provide the best results at the
plot scale, but not at the catchment scale, as top-
ographic characteristics may scale in a non-linear
fashion (Zhang
et al
., 2002: see below). Clearly,
when applying models over larger spatial scales,
for computational reasons it is often necessary to
reduce the spatial resolution of the model, that is,
increase the cell size over which process repre-
sentations are applied. Applying models at differ-
ent cell sizes assumes that process descriptions
are not affected by a change in resolution, and
does not consider how this change may influence
the output from the model (see also Section 2.5).
Increasing the cell size assumes that a larger area
may be represented in a homogeneous manner.
This approach may be flawed (unless some sto-
chastic representation of the within-cell proper-
ties is included). For example, Kalin
et al
. (2003)
showed that as overland flow routing is often
derived from surface slope (approximating energy
slope), which in turn is extracted from topogra-
phy, different cell resolutions will produce differ-
ent model results. In addition, for similar reasons
Brazier
et al
. (2005) demonstrated that the resolu-
tion of DEM that is employed exerts a strong con-
trol over the quality of the predictions that are
made in modelling sediment and phosphorus
delivery at increasingly coarse scales. Thus, when
process descriptions are dependent upon the reso-
lution of the data used to parameterize the model,
explicit consideration of the appropriate scale of
data required to represent the dominant processes
is needed
a priori
and is often not available with-
out further work.
Zhang
et al
. (2002) investigated the scaling
characteristics of a simple erosion model in a
range of conditions. They evaluated the Musgrave-
type erosion model as developed by Thornes
(1985) for variable vegetation conditions, focus-
ing on a series of parameters that could be
obtained from a range of data sources, with
extents up to continental. As pixel size increased,
they found that mean estimated erosion rates
decreased. Sensitivity analyses demonstrated that
6.4 Combined Scaling Approaches
and More Complex Conditions
Most hillslopes are more variable than the uni-
form, planar slopes that have been largely covered
above. As the extent of a study area increases, the
likelihood that conditions are spatially variable
increases, and variability in topography, soils and
rainfall are all significant factors in further com-
plicating the evaluation of erosion rates at dif-
ferent scales. When modelling environmental
systems and interpreting model results, explicit
consideration must be given to the validity of
process descriptions and their influence on model
output. Process representation should be evalu-
ated in light of the purpose of the model appli-
cation and against all available data - both
qualitative and quantitative and, ideally, spatially
explicit data (see above and also Chapter 4 where
the impacts on model uncertainty are discussed).
The first methodological problem that soil-
erosion modellers may encounter is that of scale-
appropriate parameterization. In order to measure
(or more likely estimate) a parameter for input to
a model, a measurement scale has to be chosen.
Some thought may be given to the scale at which
each parameter is represented, but more often,
the modeller is constrained by available data and
so chooses the 'best available' or 'cheapest avail-
able' data with which to parameterize the model.
As an example, the use of a digital elevation
model (DEM) is common in many soil erosion
model applications, but the choice about the res-
olution of DEM is often arbitrary or simply
reflects the highest resolution of data that are
available. Such a choice is pragmatic, but it also
