Geology Reference
In-Depth Information
error structure (effectively by definition!). The
same is not necessarily the case for epistemic
uncertainties, which represent all the different
factors affecting the accuracy and uncertainty
with which we can make predictions, but about
which we cannot make very strong statements.
Epistemic uncertainties (in respect of model
structures, effective parameter variables, input
data and boundary conditions) will be important
in real applications.
Unfortunately, there is no equivalent theory
for the information content of data in the face of
epistemic uncertainties. If we choose to represent
epistemic uncertainties in terms of probabilities
and formal likelihoods, we will necessarily be
making an approximation. In some cases this
approximation might be useful in compensating
for unknown sources of uncertainty (for example
in the data assimilation strategies for real-time
forecasting), while in others it might lead to mis-
leading estimates of parameters and predictions
(and the choice of an over-strong formal likeli-
hood might then be
incoherent
(Beven
et al
.,
2008)). We should also recognise that we might
need to expect the unexpected: the result of
unknown unknowns that we do not yet recog-
nise, and will not recognise until something
unexpected is observed (and model predictions
fail). There is no real way to allow for the unex-
pected, of course, but we might learn more about
our science from studying model failures than
simply compensating for them with a statistical
error model.
The limits of acceptability approach discussed
above offer some interesting possibilities in this
respect. If we think about the value of observa-
tions in conditioning models as multiple hypoth-
eses, then those observations that allow the
maximum differentiation between hypotheses
(the greatest rejection of models) will be the most
informative (as long as there is no evidence that
those observations might themselves be mislead-
ing). Thus, periods of observations that are simi-
lar to types of response seen previously will have
little marginal information content (note that
this is not the case under statistical assumptions;
additional measurements are always assumed to
add information multiplicatively within the
Bayes framework). Periods of observations that
are quite different to the types of response seen
previously, on the other hand, would have much
greater information content in differentiating
between different models as hypotheses. Much
more research is required on appropriate methods
for evaluating models as hypotheses, given obser-
vations in future.
4.5
Review of Uncertainty Analysis of Soil
Erosion Models
Although uncertainty analysis and even robust
examples of more traditional evaluations of soil
erosion models are rare, there are some examples
from the literature where attempts have been
made to understand the quality of soil erosion
predictions or the components within erosion
models to which predictions are most sensitive.
This assessment of uncertainty in soil erosion
models is in its infancy, unlike in the parallel
field of hydrological modelling, but nonetheless a
review is warranted, as already the approaches
employed exhibit quite different interpretations
of how to assess model performance and there-
fore demonstrate how valid model predictions
are. Broadly speaking, the approaches taken can
be described as 'sensitivity analyses', 'forward
error analyses' or 'uncertainty analyses'. The fol-
lowing section provides a discussion of the cur-
rent state-of-the-art in assessing the quality of
erosion predictions, and begins with the earliest
work first in an attempt to trace the chronologi-
cal progression of uncertainty analysis of erosion
models.
4.5.1
Sensitivity analysis of erosion models
By far the most common form of model explora-
tion employed in the soil erosion modelling
literature is that of sensitivity analysis. The fol-
lowing section summarises the development of
this technique and how it has been used to
improve understanding of soil erosion models
and how (in a direct sense) input parameters affect
model output, but also (indirectly) how model
