Calibrating and validating cellular automata models of urbanization - Urban Remote Sensing: Monitoring, Synthesis and Modeling in the Urban Environment - page 321

state transition to prevent a simulation from evolving beyond
a particular time-step, over a geographical boundary, or out-
side specified state parameters. Stopping rules do have some
theoretical basis. For example, in urban applications they are
synonymous with holding capacity for built infrastructure or
the environment; they may be associated with the notion that
cities can accommodate people, vehicles, only up until a certain
point or up to a particular threshold of sustainability. The actual
stopping procedure can be introduced, apriori ,oritcanbe
context-specific, subject to evolving conditions in a simulation.
In their model of urbanization in Dongguan, China, for example,
Yeh and Li (2002) used population totals as a stopping rule for
simulation runs. A simulation is halted when the total target
(''known'') population for a simulation run is reached. Alterna-
tively, Ward, Murray and Phinn (2000a) used geographical extent
as the basis for a stopping rule in their models of urbanization;
once a simulation reaches a target area, urbanization ceased to
proceed further.
Thresholds are another example of conditional calibration,
used to establish the lower- and upper-limits for certain proper-
ties or events in a simulation run. Often, attainment of a threshold
value stimulates a particular action in a simulation (a particu-
lar state transition, introduction of a new rule, initiation of a
feedback loop). Transition thresholds have strong analogies with
properties of real urban systems (trip-making is often governed
by capacity thresholds, for example). White, Engelen and Uljee
(1997) used thresholds to specify a quota of total cell transitions
in their simulations of urbanization. Their models were run as
normal, transitioning between states on a cell-by-cell basis, until
the threshold quota is reached. At that point, transition was
constrained by setting the transition potential of all cells in the
model to zero.
The use of transition hierarchies is another way to calibrate a
model. Often, the sequence of urbanization adheres to a particular
formal sequence. Vacant lots, for example, have the potential to
be used for any activity; a site that was previously occupied by a
heavy chemical industry, on the other hand, has limited potential
for re-development because of the considerable effort required to
''reclaim'' it. Hierarchies are generally implemented as rankings
on state transition potentials in urban models. This process
operates as follows. Particular uses are rank-ordered: states that
are observed in great abundance in the system (residential land-
use, for example) may be ranked on one (higher) extremity of
a scale. States that feature less frequently (some form of locally
unwanted land-use such as waste disposal, for example) will be
ranked on another (lower) extremity of that scale. State transition
can then be specified in such a way that states may only transition
to other states with higher rankings . White and Engelen (1993)
used this approach to condition land-use transition in their
models. In their examples, a vacant cell may transition to any
other use (housing, industry, commerce). A cell with a housing
land-use can transition either to industrial or commercial uses.
An industrial cell may transition only to a commercial state. The
use of hierarchies thereby establishes a mechanism for plausible
urban momentum.

processes by determining the likelihood of an event occurring
in a simulation run, or the intensity of its influence. Weights
are commonly specified as transition potentials, controlling the
likelihood of transition to a particular state. Often, the influ-
ence of several such potentials can be combined, as a weighted
sum . Transition weights have analogies in real urban systems.
Agglomeration effects are the most obvious example: colocation
of particular land uses (car dealerships, for example) may estab-
lish mutual further potential for additional collocation of the
same activity, say, through economies of scale, for example. The
phenomenon also works inversely; certain activities act with a
repellant influence: power plants, hazardous industries, disposal
facilities are rarely collocated with residential land-uses (they
have a negative elasticity).
Weights are particularly useful for calibrating rates of change
and transition potentials for automata (Xie, 1996; Batty and
Xie, 1997). Static weights remain constant over the course of
a simulation run. Dynamic weights, on the other hand, may
change in influence as a simulation run evolves. The most com-
mon exemplar in automata modeling is the use of growth rates.
By weighting growth (or decline), the speed of evolution in a
model run can be hastened, placed in relative stasis, or slowed.
In a sense, growth rates set the overall metabolism for a simu-
lation. In their model of urbanization in Cincinnati, OH, White
and colleagues (1997) introduced a static, universal growth rate,
which held constant over a simulation. In the SLEUTH models
developed by Clarke and colleagues (Clarke, 1997; Clarke, Hop-
pen and Gaydos, 1997; Clarke and Gaydos, 1998; Clarke et al .,
2007), the rate of urbanization in their simulations is linked,
dynamically, to the (evolving) size (area extent) of the simu-
lated city. As the city grows, its rate of development accelerates.
As growth slows toward a standstill, the growth rate is damp-
ened. Weighting by distance is a related approach. White and
colleagues (1997) made use of a distance-dependent weight on
state transition in their cellular automata models. Transition is
weighted more heavily - specifically, it has a higher probability
of successful transition - for cells that are closer to a specific cell.
Essentially, this establishes a mechanism to temper transition by
distance-decay. Elsewhere, White and colleagues (1997) intro-
duced weights designed to mimic the attraction-repulsion effects
of various land-uses on one another, designing weights to mimic
agglomeration and nuisance effects and the distance-decay of
those influences. Weights can also be used to introduce stochas-
tic perturbation to model dynamics, as a proxy for unexplained
(or uncertain) factors in a model. For example, White and Enge-
len (1993) used a weighting parameter to control the overall level
of perturbation in their models. They found that their simulation
runs were highly sensitive to the perturbation parameter, con-
cludingthatitwasanimportantfactorincalibratingamodelto
real applications. Yeh and Li (2002) used a random variable for
stochastic perturbation, scaling (weighting, really) it to restrict it
within a ''normal range of fluctuation'' (plus or minus 10%).

23.2.3 Seeding and initial conditions

Urbanization often exhibits trends of path dependence around
a particular condition or event. Once this pattern is ''locked-
in'' (Arthur, 1990), it becomes relatively difficult to change
the trajectory of the system to a new phase. The canonical
example in urban studies is the initial settlement site for a given

23.2.2 Weighted transition rules

Weights are used to calibrate automata models by ''elasticiz-
ing'' transition rules; this allows models to amplify or dampen