Non-Linear Dynamics, Self-Organization and Cellular Automata Models - Environmental Modelling: Finding Simplicity in Complexity - page 61

(a) (b)

Figure 4.8 3D views of the soil's surface in the Leicester flume, showing X13 with 10 ◦ slope. (a) experiment (b) simulated by
RillGrow 2 (Reproduced with permission from Favis-Mortlock et al .).

far as to state that 'verification and validation of numerical
models of natural systems is impossible' and argued that
'the primary value of models is heuristic.' Following their
argument, mere resemblance between model output and
reality is no test of a model.
Finally, an important point is necessary regarding dis-
cretization. Wolfram (2002: 327) notes that many systems
in nature appear smooth or continuous, yet CA models
involve only discrete elements. How can such models
ever hope to reproduce what we see in nature? The crucial
point here is that even though the individual elements
of a system may be discrete, the average behaviour seen
when looking at a large number of these components
may well be continuous. The question then becomes, 'Are
there a sufficient number of CA elements for their average
behaviour to approximate the average behaviour of the
real system?'
The mounting weight of model-based evidence,
together with field- and laboratory-based studies not
discussed here, tends to confirm the assumption that
self-organization is a real feature of the real world. If
this is so, then one implication is a message of hope for
environmental modellers. We are not doomed to ever
more complex models!
While it may seem perverse that the study of complex-
ity can lead us to simplicity, ground-breaking research
on self-organization during the late 1980s and 1990s

appears to have been a fresh wind, doing away with the
tired idea of fitting the results of data-hungry models
to sparse, observed data. Instead of the cumbersome
drudgery of varying a large number of parameters and
variables to obtain a better fit between the computed and
observed data, models may again be used to generate
new and exiting ideas, and to help solve the looming and
difficult environmental problems which humanity must
successfully tackle if it is to survive.

4.6 Acknowledgements

There is some overlap between this chapter and Favis-
Mortlock and De Boer (2003) and between this chapter
and Favis-Mortlock (in press).

References

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Anderson, R.S. and Haff, P.K. (1988) Simulation of eolian saltation.
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Andrle, R. (1996) The west coast of Britain: statistical self-similarity
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Aristotle (c. 330 BCE), Metaphysica 10f-1045a.