Introduction - Environmental Modelling: Finding Simplicity in Complexity - page 3

pages of text). The library is a model of the universe - but
is it a useful one? Borges describes the endless searches
for the topic that might be the 'catalogue of catalogues'!
Are our attempts to model the environment a similarly
fruitless endeavour?
Compare the definition by Grand (2000: 140): 'Some-
thing is complex if it contains a great deal of information
that has a high utility, while something that contains a lot
of useless or meaningless information is simply compli-
cated.' The environment, by this definition, is something
that may initially appear complicated. Our aim is to ren-
der it merely complex! Any explanation, whether it be a
qualitative description or a numerical simulation, is an
attempt to use a model to achieve this aim. Although
we will focus almost exclusively on numerical models,
these models are themselves based on conceptual models
that may be more-or-less complex (see discussions in
Chapters 2 and 17). One of the main issues underlying
this topic is whether simple models are adequate explana-
tions of complex phenomena. Can (or should) we include
Ockham's razor as one of the principal elements in our
modeller's toolkit?
Bar-Yam (1997) points out that a dictionary definition
of complex suggests that it means 'consisting of inter-
connected or interwoven parts'. 'Loosely speaking, the
complexity of a system is the amount of information
needed in order to describe it' (p. 12). The most com-
plex systems are totally random, in that they cannot be
described in shorter terms than by representing the sys-
tem itself (Casti, 1994) - for this reason, Borges' 'Library
of Babel' is not a good model of the universe, unless it is
assumed that the universe is totally random (or alterna-
tively that the library is the universe). Complex systems
will also exhibit emergent behaviour (Bar-Yam, 1997), in
that characteristics of the whole are developed (emerge)
from interactions of their components in a non-apparent
way. For example, the properties of water are not obvious
from those of its constituent components, hydrogen and
oxygen molecules. Rivers emerge from the interaction of
discrete quantities of water (ultimately from raindrops)
and oceans from the interaction of rivers, so emergent
phenomena may operate on a number of scales.
A number of types of model complexity can be defined:

(c) Temporal complexity - the temporal horizon and
resolution and the extent of representation of system
dynamics.
(d) Inclusivity - the number of processes included.
(e) Integration - the extent to which the important feed-
back loops are closed.

Researchers have tended to concentrate on (a) whereas
(b)-(e) are probably more important in natural systems.
The optimal model is one that contains sufficient
complexity to explain phenomena, but no more. This
statement can be thought of as an information-theory
rewording of Ockham's razor. Because there is a definite
cost to obtaining information about a system, for example
by collecting field data (see discussion in Chapter 2 and
elsewhere), there is a cost benefit to developing such an
optimal model. In research terms there is a clear benefit
because the simplest model will not require the clutter
of complications that make it difficult to work with,
and often difficult to evaluate (see the discussion of the
Davisian cycle by Bishop 1975 for a geomorphological
example).
Opinions differ, however, on how to achieve this
optimal model. The traditional view is essentially a reduc-
tionist one. The elements of the system are analysed and
only those that are thought to be important in explain-
ing the observed phenomena are retained within the
model. Often this approach leads to increasingly complex
(or possibly even complicated) models where additional
process descriptions and corresponding parameters and
variables are added. Generally the law of diminishing
returns applies to the extra benefit of additional variables
in explaining observed variance. The modelling approach
in this case is one of deciding what level of simplicity in
model structure is required relative to the overall costs
and the explanation or understanding achieved.
By contrast, a more holistic viewpoint is emerging. Its
proponents suggest that the repetition of simple sets of
rules or local interactions canproduce the features of com-
plex systems. Bak (1997), for example, demonstrates how
simple models of sand piles can explain the size of occur-
rence of avalanches on the pile, and how this approach
relates to a series of other phenomena (see Chapter 16).
Bar-Yam (1997) provides a thorough overview of tech-
niques that can be used in this way to investigate complex
systems. The limits of these approaches have tended to be
related to computing power, as applications to real-world
systems require the repetition of very large numbers of
calculations. A possible advantage of this sort of approach

(a) Process complexity (complication) - the sophistica-
tion and detail of the description of processes (see
Section 2.2.4).
(b) Spatial complexity - the spatial extent and grain of
variation (and lateral flows) represented.