Calibrating and validating cellular automata models of urbanization - Urban Remote Sensing: Monitoring, Synthesis and Modeling in the Urban Environment - page 322

city, which loses significance as the city develops but retains a
central position in its metropolitan hierarchy because of inertia
(Hall, 1988). Similar mechanisms are used to calibrate models to
known (historical) conditions. Clarke and colleagues (1997), for
example, used historical maps and other data sources to identify
and place the initial position of settlements in the San Francisco
Bay Area. This information was then used to set seed cells for
a cellular automata simulation of the area's urbanization; in a
sense, it ensured that the right stuff grew in the right places. They
also introduced a layer of road states, employed such that once a
simulation run transitioned through specific temporal markers,
the appropriate road data features were read into the model.
Torrens (2006b) similarly used the initial settlement pattern of
the system of cities around Lake Michigan and known population
totals to establish initial conditions in his model of sprawl
formation in the Midwestern megalopolis. Seed constraints can
also be applied in the opposite direction: the SLEUTH model,
for example, has been run from contemporary seed conditions,
and reversed back in time over a historical period for the Santa
Barbara Region, beginning with conditions in 1998 and running
back to 1929 (Goldstein, Candau and Clarke, 2004).
Exclusion mechanisms can also be used to constrain simula-
tions by withholding certain cells from transition consideration
over a model run, or over a particular time period in a simulation.
White, Engelen, and colleagues, for example, used this procedure
to distinguish between ''fixed'' and ''functional'' cells in their
cellular automata models. ''Fixed'' cells correspond to areas of a
city that remain exempt from urbanization: permanent land-uses
such as rivers, parks, and railways. ''Functional'' cells are consis-
tent with sites that are open to urbanization; they are subject to
the full range of transition rules specified in the model (White and
Engelen, 2000). Clarke and colleagues similarly enjoyed a layer of
''excluded areas'' in their models (Clarke et al ., 2007). This layer
was used to represent cells that are immune to growth processes
in a simulation: ocean, lake, and ''protected areas''. They also
introduced topography constraints that prohibited urbanization
above a given slope threshold. A similar scheme was employed
in the Dynamic Urban Evolution Model (DUEM) developed by
Xie and Batty (Batty, Xie and Sun, 1999). Li and Yeh (2002)
varied this standard approach slightly in their applications: they
associated development with the potential environmental costs
of urban growth, excluding areas of cropland, forest, and wetland
from their model. In a similar exercise, they developed mecha-
nisms to freeze urban growth in environmentally sensitive and
important agricultural areas of their simulated area, relating the
constraint to ideas of sustainability (Li and Yeh, 2000).

Essentially,amodeldesigneroruseractsasanexpertsystem,
adjusting weights and parameter values based on her observation
of model dynamics: ''The eye of the human model developer
is an amazingly powerful map comparison tool, which detects
easily the similarities and dissimilarities that matter, irrespective
of the scale at which they show up. And the model developer,
with all his knowledge of spatial form and spatial interaction pro-
cesses, is a very able (if often unwilling) ''calibration machine''''
(Straatman, White and Engelen, 2004). On other occasions, the
values of calibration parameters have been derived from histor-
ical data sources. Most often, land-use maps are used. White
and colleagues calibrated weights in their model of Cincinnati
against land-use maps dating back to 1970 (White, Engelen and
Uljee, 1997), for example.
Statistics may also be used to calculate parameter values.
Clarke and Gaydos ran descriptive statistical tests to determine
the parameter vales in their models of San Francisco, Wash-
ington DC, and Baltimore (Clarke and Gaydos, 1998). Wu and
Webster (1998) used a series of logistic regressions to calibrate
the probabilities for transition rules in their model of land devel-
opment in Guangzhou, China: the beta-values from a regression
equation were used, directly, as the value for model weights.
Similarly, in his model of polycentric urbanization, Wu (1998)
introduced a transition rule (which he termed as an ''action func-
tion'') that calibrated the model's decision- and preference-based
transition rules. This function was specified using a regression
equation that was itself calculated based on real choice observa-
tion data. Arai and Akiyama (2004) also used regression to derive
transition weights in their model of urbanization in the Tokyo
Metropolitan area.

23.2.5 Coupling automata and
exogenousmodels

Strictly speaking, automata models should be closed systems:
they should not be open to external influence. However, in
some instances (and often born of a necessity to better ally with
the reality that they try to emulate), urban automata models
have been coupled with exogenous simulations: model output,
routines, or equations external to an automata model are used
to influence transition in an automata simulation, either by
initiating state transition directly, or by determining the value
of constraints and weights. There are a few rationales for using
exogenous models in this way. Simple convenience is one reason:
exogenous models can be employed to introduce mechanisms
that may not be treated (or that a model-builder may not
wish to treat because of disjointed time scales, for example).
There are also theoretical justifications. Exogenous models can
be used to represent phenomena that are external to the system
of interest: non-urban subsystems such as climate, hydrology,
geology, or external (but locally relevant) phenomena such as
the operation of cities in a regional system, national boom-and-
bust cycles, and geopolitical dynamics. The MURBANDY model
developed by White, Engelen, and colleagues (Engelen, White
and Uljee, et al ., 2002) used three exogenous models to establish
the level of demand for cell state transition in its automata-based
microsimulation of urbanization. Sea-level rises, as simulated
in a natural environment model, may trigger a conversion in
state variables from active land-use to inactive sea uses at low
elevations, for example. Many top-down systems, such as the

23.2.4 Specifying the value of
calibration parameters

There are a variety of methods by which the empirical value of
calibration parameters such as weights and constraints might be
derived. These methodologies include visual calibration, statis-
tical tests, the use of historical data, and statistically regressing
parameter values. In addition, exogenous models may be used to
supply parameter values. In recent years, several automated
calibration procedures have also been developed for urban

automata models.
Visual calibration involves the manual tweaking of rules
by comparing simulation runs visually (Aerts et al ., 2003).