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Interestingly, predictive uncertainty increased
with the magnitude of erosion predictions (as
seen in Fig. 4.6), whereas variability of observed
erosion was greatest for smaller storms described
in the Nearing
et al
. (1999) dataset.
Using these results, Wei
et al
. (2008) argue that
it is useful to transfer the uncertainty associated
with predictions to sites where observed data are
not available, and where it might be most useful to
know about the uncertainty surrounding model
predictions to guide decision-making. Philosophi-
cally, this approach is similar to that of Brazier
et al
.
(2001) who mapped the uncertainty associated with
predictions from the WEPP model on to the wider
landscape to illustrate the implications of model
uncertainty for the spatial prediction of erosion. In
the Wei
et al
. (2008) example, regression equations
are used to describe the confidence limits (analo-
gous to the uncertainty bounds of Brazier
et al
.,
2000), in relation to two input parameters - rainfall
amount and saturated hydraulic conductivity -
and two outputs - soil loss and runoff depth. It is
argued that these regression equations can then be
used to transfer the description of model uncer-
tainty to wider predictions, without recourse to fur-
ther Monte Carlo model runs.
The approach has some merit, and indeed dem-
onstrates a potential way forward that model
users may take in order to illustrate how good
model predictions may be. However, it is likely
that confidence limits would be different if model
uncertainty was assessed specifically at each site
(through Monte Carlo simulations), so it is not
yet clear how meaningful such transferral of
uncertainty bounds actually is, without support-
ing data (and model evaluation) to test the assump-
tion that predictive uncertainty is transferable. It
might be argued that model predictions are not
transferable (without validation), so perhaps this
approach needs further evaluation before it is
widely used. A further point to consider is that
Wei
et al
. (2008) do not try to assess the full range
of uncertainty associated with model predictions;
some consideration of model structural uncer-
tainty and uncertainty associated with observa-
tions
alongside
the assessment of parameter
uncertainty presented here would be very useful.
Solid line: measured data
(Nearing
et al.
,1999)
10
1
0.1
1 E-6
1 E-5
1 E-4
1 E-3
0.01
0.1
1
10
Mean soil loss value (kg/m
2
)
Fig. 4.5
Coefficient of variation (
CV
) for measured soil
loss from the output distribution at a point against the
expected predicted soil loss value. The corresponding
relationship developed from measured data (Nearing
et al
., 1999) is also shown as a single log-log line
(after Wei
et al
., 2008).
uncertainty associated with the soil erosion pre-
dictions is high, particularly where observed ero-
sion rates were low (or observed as deposition),
and small changes in sediment transport param-
eters led to large differences in erosion/deposition
rate predictions. It is suggested that this finding is
a general problem for spatially distributed erosion
models, as appropriate definition of sediment
transport parameters (which may be highly vari-
able in time and space) is exceedingly difficult.
The final example of uncertainty analysis that
will be reviewed here is that of Wei
et al
. (2008)
who employed a “dual-Monte Carlo approach to
estimate model uncertainty” associated with pre-
dictions from the Rangeland Hydrology and
Erosion Model (RHEM). Model predictions are
evaluated against event-based observations of
three storms using a two-stage Monte Carlo proce-
dure to explore the implications of parameter
uncertainty on model predictive uncertainty.
Results demonstrate that predictive uncertainty is
significant and realistic when compared to the
coefficient of variation around mean soil loss
observations described by Nearing
et al
. (1999), as
is shown in Fig. 4.5.
