Non-Linear Dynamics, Self-Organization and Cellular Automata Models - Environmental Modelling: Finding Simplicity in Complexity - page 45

to deficiencies in modelling within-catchment flow paths.
The standard remedy for such shortcomings is the addi-
tion of detail, preferably physics-based, to the model or
its successors. Thus the empirical Universal Soil Loss
Equation (USLE: Wischmeier and Smith, 1978) made no
distinction between rainsplash-dominated interrill soil
loss, and flow-dominated rill erosion, whereas these pro-
cesses are separately modelled, in a more physically based
way, in two subsequent models: the Water Erosion Pre-
diction Project (WEPP: Nearing et al ., 1989) model and
the European Soil Erosion Model (EUROSEM: Mor-
gan et al ., 1998). This strategy is often - though not
always - successful; however it inevitably leads to an
explosion in model complexity (cf. Figure 4.1) and data
requirements (Favis-Mortlock et al ., 2001).
Despite great strides, our still-incomplete knowledge
of the physics of several environmental processes (e.g.
for soil erosion, the details of soil-surface crusting) gives
rise to an associated modelling problem. These poorly
understood processes can only be described in current
models in a more-or-less empirical way, which means
that some model parameters essentially fulfil the function
of curve-fitting parameters, adjusted to provide a match
between the observed and computed time series rather
than measured independently. This inclusion of empirical
elements in otherwise physics-based models is to the
dismay of authors such as Klemes, who wrote: 'For a good
mathematical model it is not enough to work well. It must
work well for the right reasons. It must reflect, even if only
in a simplified form, the essential features of the physical
prototype' (Klemes, 1986: 178S). Model parameterization
under such conditions becomes more and more a curve-
fitting exercise (Kirchner et al ., 1996). As an example, an
evaluation of field-scale erosion models (Favis-Mortlock,
1998a) found calibration to be essential for almost all
models involved, despite the supposed physical basis of
the models.
Additionally, results from a more complex model
may not necessarily improve upon those of a simpler
model if interactions between processes are inadequately
represented within the model (Mark Nearing, personal
communication 1992; Beven, 1996). The addition of
more model parameters increases the number of degrees
of freedom for the model, so adding extra free parameters
to a model means that changes in the value of one input
parameter may be compensated by changes in the value of
another. Therefore unrealistic values for individual input
parameters may still produce realistic results (in the sense
of a close match between the observed and computed time
series). The model is 'unidentified' with its parent theory

(see Section 4.3.5) in the sense of Harvey (1969: 159),
and results from the model may be 'right for the wrong
reasons' (Favis-Mortlock et al ., 2001). To illustrate this
point, Jakeman and Hornberger (1993) found that com-
monly used rainfall-runoff data contains only enough
information to constrain a simple hydrological model
with a maximum of four free parameters. This problem
ultimately leads to Beven's 'model equifinality' (the con-
cept of equifinality is originally due to Von Bertalanffy,
1950), whereby entirely different sets of input parameters
all produce similar model outputs (Beven, 1993).
The result of the pressures upon model development
described above is a vicious circle, whereby a 'better'
environmental model inexorably has to describe more
processes, or existing processes in more detail. Doing so:

• Will probably increase the model's predictive power in
a specific domain, but may cause it to fail unexpectedly
elsewhere (because it is giving 'the right answer for the
wrong reasons' in the original domain).
• Requires more data, and so in practical terms narrows
the circumstances in which the model may be used.
• May well make the model less comprehensible.

Is there any way out of this vicious circle?

4.2 Self-organization in complex
systems

The foregoing suggests that, if an environmental model is
to be considered 'better', it has to describe the environ-
ment in greater physically based detail. Does this greater
detail necessarily imply a more complex model? Put more
generally: does real-world complexity inevitably imply
an equivalent complexity of the underlying generative
process?

4.2.1 Nonlineardynamics: chaosandfractals

Since scientific research is the 'art of the soluble' (see
the second quote which began this chapter), the focus of
science at any period of history has, at least in part, been
dependent on the tools available for solving the problems
which arise from this focus. Prior to the 1960s, the tools
available for quantitative research often limited scientists
to rather simple analyses (by present standards). These
often involved linear (i.e. straight-line) approximation.
Along with much other change, the 1960s saw the
widespread adoption of electronic computers in all