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of parameters, some erosion models, e.g. WEPP
(Nearing et al ., 1989), do incorporate vegetation-
growth models). However, over longer time-peri-
ods important landscape feed backs may necessitate
considering process feedbacks with the changes
to such static variables that may have been driven
by increased erosion (see Wainwright, 2006, for a
dynamic model of interactions between climate,
vegetation, erosion and slope-channel coupling).
For example, over a single event, it may be argued
that a hillslope has not evolved 'enough' to repre-
sent those changes in an altered digital elevation
model (DEM) of that hillslope as the starting
point for the next event. However, over time,
after several erosion events have occurred, the
hillslope will clearly have evolved even to the
naked eye, so surely a representation of this evo-
lution is necessary and an updated DEM should
be used. At the other end of the spectrum are
landscape-evolution models that dynamically
update the DEM, but which often have a poor
process representation of hillslope changes (e.g.
typically assuming all erosion is diffusive in
nature: see Coulthard (2001) for a review of such
models).
2006a; Brazier et al ., 2007), 11 observed erosion
events occurred at plots sited within a 0.5 km 2
catchment - however, only three of these events
occurred over all eight of the plots being moni-
tored. Furthermore, none of the rainfall events
(durations, intensities) were identical between
each plot, illustrating that rainfall/runoff and
therefore erosion events are often highly unique,
even when observed on plots that may be adjacent
to each other and would be expected to respond in
a very similar manner. This finding is supported
by the work of Nearing (2000) who demonstrated
that even 'replicated' hillslope plots subject to the
same rainfall conditions were poor predictors of
each other and were subject to high levels of vari-
ability in erosion rates. Therefore, the assumption
that time and space parameters in models can be
represented homogeneously, across all but the
smallest grid cells, is questionable, particularly if
the goal of the modelling exercise is to identify
important sources of sediment within the hills-
lope or catchment, and indicate the potential
impacts of important land-use or climatic changes
on erosion rates. Conceptually, as well as practi-
cally, erosion models need to describe the wide
ranges of variability that are associated with our
understanding of erosion processes and that occur
in the real world, in order to provide meaningful
model structures with which to predict erosion.
At present, as most erosion models are in some
way based on previously collected plot data, they
are unlikely to describe the variability associated
with the larger fields or catchments that they are
then applied to.
There is an additional problem in scaling
erosion predictions - that of spatial equifinality.
Erosion rates may be predicted at larger scales,
due to a misrepresentation of the dominant proc-
esses, or the patterns of those processes, as the
system becomes inherently more complex with
increasing scale (see Chapter 4 for a full explana-
tion of the equifinality problem). The implica-
tions of equifinality are all too common in the
erosion model evaluation literature that has
grown in recent years. Model testing, post-
calibration, to demonstrate that adequate predic-
tions can be made of erosion rates, without any
6.7
Discussion - the Research Frontier
in Scaling Erosion Models
In the soil-erosion literature there is often a lack
of reporting of the time and the precise space over
which soil-erosion rates or sediment yields are
measured or modelled. However, Lu et al . (2005)
illustrated that the spatial variation of erosion
and the consequent sediment yield from a catch-
ment is strongly controlled by storm durations
and the residence times of sediment on hillslopes
or in channels. Thus, good erosion science requires
explicit descriptions of spatial and temporal
dynamics that can be used to test the quality of
erosion model predictions. Averaging (over time
or space) may hide important variability in sedi-
ment production both within events and between
events (Nichols, 2006). For example, during a
three-year monitoring period at the Walnut
Gulch Experimental Watershed (Parsons et al .,
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