Modelling and Model Building - Environmental Modelling: Finding Simplicity in Complexity - page 22

The quantitative evaluation of uncertainty has been
discussed above in detail. Error-propagation techniques
can be used in relatively simple models (or their sub-
components) to evaluate the impact of an input error
(measurement uncertainty) on the outcome. In more
complex scenarios, Monte Carlo analysis is almost cer-
tainly necessary. If sufficient runs are performed, then
probability estimates can be made about the outputs.
Carrying out this approach on a model with a large num-
ber of parameters is a nontrivial exercise, and requires the
development of appropriate sampling designs (Parysow
et al ., 2000). The use of sensitivity analysis can also be
used to optimize this process (Klepper, 1997, Barlund
and Tattari, 2001). Hall and Anderson (2002) note that
some applications may involve so much uncertainty that
it is better to talk about possible outcomes rather than
give specific probabilities. Future scenarios of climate
change evaluated using General Circulation Models (see
Chapters 9 and 18) is a specific case in point here. Another
approach that can be used to evaluate the uncertainty in
outcome as a function of uncertain input data is fuzzy set
theory. Torri et al . (1997) applied this approach to the esti-
mation of soil erodibility in a global dataset and Ozelkan
and Duckstein (2001) have applied it to rainfall-runoff
modelling. Because all measurements are uncertain, the
data used for model testing will also include errors. It
is important to beware of rejecting models because the
evaluation data are not sufficiently strong to test it. Monte
et al . (1996) presented a technique for incorporating such
uncertainty into the model-evaluation process.
Distributed models may require sophisticated visu-
alization techniques to evaluate the uncertainty of
the spatial data used as input (Wingle et al ., 1999).
An important consideration is the development of
appropriate spatial and spatio-temporal indices for
model evaluation, based on the fact that spatial data
and their associated errors will have autocorrelation
structures to a greater or lesser extent. Autocorrelation of
errors can introduce significant nonlinear effects on the
model uncertainty (Henebry, 1995).
Certain systems may be much more sensitive to the
impacts of uncertainty. Tainaka (1996) discusses the
problem of spatially distributed predator-prey systems,
where there is a phase transition between the occurrence
of both predator and prey, and the extinction of the
predator species. Such transitions can occur paradoxically
when there is a rapid increase in the number of the prey
species triggered by instability in nutrient availability, for
example. Because the phase transition represents a large
(catastrophic) change, the model will be very sensitive to

uncertainty in the local region of the parameter space,
and it can thus become difficult or impossible to interpret
the cause of the change.

2.5.3 Comingtotermswitherror

Error is an important part of the modelling process (as
with any scientific endeavour). It must therefore be incor-
porated within the framework of any approach taken, and
any corresponding uncertainty evaluated as far as pos-
sible. A realistic approach and a healthy scepticism to
model results are fundamental. It is at best misleading
to present results without corresponding uncertainties.
Such uncertainties have significant impacts on model
applications, particularly the use of models in decision
making. Large uncertainties inevitably lead to the rejec-
tion of modelling as an appropriate technique in this
context (Beck, 1987). Recent debates on possible future
climate change reinforce this conclusion (see the excellent
discussion in Rayner and Malone, 1998).
In terms of modelling practice, it is here that we come
full circle. The implication of error and uncertainty is that
we need to improve the basic inputs into our models. As
we have seen, this improvement does not necessarily just
mean collecting more data. It may mean that it is better
to collect fewer samples, but with better control. Alter-
natively, it may be necessary to collect the same number
of samples, but with a more appropriate spatial and/or
temporal distribution. Ultimately, the iterations involved
in modelling should not just be within computer code,
but also between field and model application and testing.

2.6 Conclusions

Modelling provides a variety of tools with which we can
increase our understanding of environmental systems. In
many cases, this understanding is then practically applied
to real-world problems. It is thus a powerful tool for
tackling scientific questions and answering (green!) engi-
neering problems. But its practice is also something of an
art, which requires intuition and imagination to achieve
appropriate levels of abstraction from the real world to
our ability to represent it in practical terms. As a research
tool, it provides an important link between theory and
observation, and provides a means of testing our ideas
of how the world works. This link is important in that
environmental scientists generally deal with temporal and
spatial scales that are well beyond the limits of observation