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related to modelling spatial distributions of soil
erosion is relatively large, particularly with the
increasing use of GIS in modelling, but studies
that make any attempt to evaluate the spatial
predictive capability of the models using meas-
ured data are very few.
If we have learned anything over the past two
decades it is that increased model complexity
does not correspond to improved capability to
predict soil erosion rates and sediment yields.
It is important to keep in mind, however,
that improved prediction capability, in terms of
improved ability to quantify erosion rates and
amounts as a function of system properties and
inputs, is not the only goal for the models. Models
also form a structure for integrating our under-
standing of soil erosion processes. Complex mod-
els may also play a role in addressing some
problems that simple models cannot - climate
change, for example. Govers (1996) noted this in
his review paper on soil erosion models, as did
Williams et al . (1996) in discussions of modelling
climate change impacts on soil erosion. Also,
complex models do not necessarily need to remain
complex in the application phase. A good example
of this was the evolution of the Hairsine-Rose
model framework (Hairsine & Rose, 1992a,b) to
that of the GUEST model described in Chapter 11.
Another example was the use of the framework
of the WEPP model (Laflen et al ., 1997) to the
simpler, more targeted-use, and less data- intensive
Rangeland Hydrology and Erosion Model (Wei
et al ., submitted), as well as the web-based WEPP
Climate Assessment Tool (Bayley et al ., in
preparation).
Model complexity can lead to increased pre-
diction uncertainty. Chapter 4 addressed the issue
of model uncertainty in a great deal of detail. The
most mathematically accurate, and hence com-
mon, manner to assess the propagation of input
errors is with the use of Monte Carlo simulations
using distributions of input parameter variation
(e.g. Wei et al ., 2008). Conceptually, however, the
first-order error (FOE) framework (Wu et al ., 2006)
allows one easily to visualize error summation in
the models as a function of complexity. Every
input parameter for a model carries with it some
degree of uncertainty, which can be expressed
using FOE by using a coefficient of variation (CV).
Prediction uncertainty associated with parameter
definition will propagate through all models to
generate some level of uncertainty in the model
response, which within the FOE analysis is
expressed as a CV of the model response. The
degree to which the error propagates is directly
proportional to the sensitivity of the model out-
put to the model input parameter and to the input
uncertainty (CV). First-order errors sum with
each additional input parameter, so the decision
on whether to add an additional input parameter
to a model is whether or not the new process
described by the equations that use the parameter
adds more to prediction capability than is lost
through the additional error propagated due to
the uncertainty in the value of the input param-
eter. This is more or less equivalent to the state-
ment attributed to Govers (1996) above.
Hairsine and Sander (2009) recently provided
a further description of the trade-offs in the devel-
opment of models of soil erosion by water.
Figure 20.1 shows the conceptual trade off
between data availability, model complexity and
model performance as proposed by Grayson and
Bloschl (2000) for hydrological prediction. For any
application with a given level of data available,
there will be an optimum level of model com-
plexity that will allow one to reach optimum pre-
dictive performance (see bold solid line in
Fig. 20.1). In order to move forward with increas-
ing model predictive performance, model com-
plexity must move forward hand-in-hand with
data availability. To make progress, we should be
constantly moving in the direction of the solid
arrow in Fig. 20.1. When one is using a model
that is parameter-rich and informed by a rela-
tively small amount of data, predictive perform-
ance deteriorates due to parameter identifiability
problems because the model is too complex. We
contend that this is the current situation for most
existing models of soil erosion and related sedi-
ment transport in most predictive environments.
Thus these models plot in the bottom right-hand
corner of Fig. 20.1, in which case the path to
greater predictive capability is along the bold
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