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associated with parameters, but it is also done in
a spatial framework allowing for some represen-
tation of the effects of both spatial variability
and the heterogeneity of error to be incorporated
into predictions. The approach of Mokrech (2001)
shows the most promise, as numerous parame-
ters and therefore parameter interactions are con-
sidered in parallel. However, the work is still best
described as forward error or forward uncertainty
analysis as the model predictions are not evalu-
ated against observed data, such that the 'reality'
of the model uncertainty that is presented is not
tested.
parameterization, the effects of which were
assessed against the mean square error of model
output. In this example, results showed that the
model was able to simulate the watershed dynam-
ics well. Thus, these two model evaluations illus-
trate well how subtly different approaches to
uncertainty evaluation can yield very different
results, and that the choice of the uncertainty
analysis technique may be crucial in determining
the degree of confidence that the user may have in
the model. Section 4.6 revisits this issue by sum-
marising a further uncertainty analysis of the
WEPP model (Brazier
et al
., 2000), and demon-
strating a potential way forward for the uncer-
tainty analysis of erosion models.
Recognising the limitations of previous first-
order sensitivity analyses of the USLE (see above),
Hession
et al
. (1996) conducted a two-stage uncer-
tainty analysis of the model. The authors
attempted to address epistemic uncertainty “due
to incomplete understanding or inadequate meas-
urement of system properties” and uncertainty
associated with model stochastic variability
which is “due to random variability of the natu-
ral environment”. It is argued that the former
may be reduced, through better measurement or
constraint of parameter values, but the latter may
always be present in model predictions and can-
not be reduced. Both types of uncertainty were
incorporated into the parameter distributions
that were sampled in a Monte Carlo-based analy-
sis of model performance against observations
made over a 27-year period on an experimental
plot in Guthrie, Oklahoma, US. Figure 4.1 (after
Hession
et al
., 1996) illustrates that confidence
limits based on 10
th
and 90
th
percentiles describ-
ing the uncertainty associated with model pre-
dictions capture some of the observed soil erosion
behaviour over the 27-year period. However, the
model does not do well at predicting the 30% of
events that are small (<ca. 3 kg m
−2
) or the 15%
that are large (>17 kg m
−2
). The authors did not
present data describing the performance of the
model in terms of any objective function against
observations, but the results demonstrate well
that model uncertainty must be assessed in appli-
cations of models such as the USLE, if we are to
4.5.3
Uncertainty analysis of soil
erosion models
The following section describes a range of
approaches to model evaluation that are described
in the literature as 'uncertainty analyses'. As will
be seen, however, very few of these numerical
experiments are actually uncertainty analyses in
the true sense of the term, as they do not evaluate
model performance with respect to observed data.
The results of each approach are therefore pre-
sented alongside a summary of the methods
employed, to demonstrate how robust and mean-
ingful each model evaluation is.
Early approaches to evaluate model uncer-
tainty were conducted on the WEPP model by
Chaves and Nearing (1991) and Tiscareno-Lopez
et al
. (1995). Chaves and Nearing (1991) explored
the effect of 60 scenarios (random parameteriza-
tions across the 28-dimensional parameter space)
on the output of the model - quantified in terms
of the coefficient of variation of peak runoff rate,
soil loss, sediment yield and sediment enrichment
ratio. The authors found that maximum coeffi-
cients of variation for the four outputs were 196,
267, 323, and 47%, respectively, demonstrating a
wide range of uncertainty associated with model
output, but not evaluating this uncertainty against
any observed data. In contrast, Tiscareno-Lopez
et al
. (1995) did employ observed data from the
semi-arid Walnut Gulch Experimental Watershed
to assess model uncertainty. Parameters were var-
ied to reflect the typical variance associated with
