Non-Linear Dynamics, Self-Organization and Cellular Automata Models - Environmental Modelling: Finding Simplicity in Complexity - page 44

70000

WEPP

Key: Guelph USLE - a Basic implementation of the Universal Soil Loss Equation
(Wischmeier and Smith, 1978) programmed by D.J. Cook of the University of Guelph; only
the CALSL module is considered here. EPIC - programmed in Fortran and is USLE-based,
but includes a crop growth submodel and a weather generator; Williams et al. (1983).
GLEAMS - also in Fortran with some C; Leonard et al. (1987). WEPP - in Fortran,
combines hillslope and watershed versions, includes a crop submodel; Nearing et a. (1989).

60000

50000

40000

30000

20000

EPIC

GLEAMS

10000

Guelph
USLE

0
1975 1980 1985 1990

Year

Figure 4.1 An estimate of the complexity of some North American field-scale erosion models using the number of lines of
programming source code. The date given is of a 'representative' publication and not the release analysed here. Redrawn from data in
Favis-Mortlock et al . (2001).

4.1.1 Theever-decreasingsimplicityofmodels? and if it has its parameters and variables defined by

means of equations that are at least partly based on the
physics of the problem, such as Darcy's law and the
Richards equation (Kirkby et al ., 1992; but see discussion
by Wainwright and Bracken, 2011). The presumed uni-
versal applicability of the laws of physics is the reason
for preferring physically based models. Thus the more
a model is rooted in these laws (and, conversely, the
less it depends upon empirically derived relationships),
the more widely applicable - i.e. less location specific - it
is assumed to be. By contrast, the second criterion is
pragmatic: how well the model does when model results
are compared against measured values. For hydrological
models, a time series of simulated discharges might be
compared with an observed time series (see Chapters 3,
7, 10 and 11), or for erosion models simulated soil
loss compared with measured values (e.g. Favis-Mortlock
et al ., 1996; Favis-Mortlock, 1998a) (see also Chapters 15
and 23). The inevitable differences between computed
and observed time series are usually attributed to the
model's failure to adequately describe some aspect of
the real world. Thus in an evaluation of catchment-scale
soil-erosion models (Jetten et al ., 1999), the models were
largely able to predict sediment delivery correctly at the
catchment outlet but were much less successful at identi-
fying the erosional 'hot spots' within the catchment that
supplied this sediment. The failure was in part attributed

Models used by geographers have steadily become more
and more complex, from the 'quantitative revolution' in
geography in the 1960s (e.g. Harvey, 1969) when models
first began to be used widely, to the present. This is a trend
that looks set to continue. Figure 4.1 uses the number
of lines of programming code as a surrogate for model
complexity 1 for a selection of computer implementations
of US-written field-scale models of soil erosion by water.
Model complexity in this particular domain has clearly
increased in a somewhat nonlinear way.

4.1.1.1 The quest for 'better' models
The reason for this increased complexity is, of course,
the desire for 'better' models. Although environmen-
tal models differ widely, two general criteria have come
to dominate in assessment of any model's 'success' (or
otherwise). 2 First, the model is usually ranked more
highly if it is physically based, i.e. if it is founded on the
laws of conservation of energy, momentum and mass,

1 Cf. Chaitin's (1999) notion of 'algorithmic complexity'.
2 This is particularly the case in practical applications where the
main aim is a successful replication of measured values, perhaps
with the subsequent aim of estimating unmeasurable values, for
example under some hypothetical conditions of climate or land use.