Calibrating and validating cellular automata models of urbanization - Urban Remote Sensing: Monitoring, Synthesis and Modeling in the Urban Environment - page 320

23.1 Introduction

be a thorny issue (Torrens and O'Sullivan, 2001; Batty and
Torrens, 2005; Manson, 2007; Pontius Jr. et al ., 2008).
Nevertheless, work in this area is active and it is advancing.
Much of the current research emphasizes statistical procedures,
which are employed in gauging uncertainty or sensitivity in
empirical analysis, providing formal methodology for analyzing
relationships and the strength of association between simulation
output and data about the system being simulated (Kocabas
and Dragicevi c, 2006; Dragi cevi c and Kocabas, 2007; Pontius Jr.
et al ., 2008). Remotely-sensed imagery has also emerged as an
important source of ''dataware'' for model validation and cali-
bration, feeding models with data and providing the catalyst that
allows model data output to be contextualized into information
(Herold and Clarke, 2002; Torrens, 2006a; Bone et al ., 2007).
Increasingly, model developers are relying on spatial analysis
and image processing techniques that are more usually applied
to the analysis of real cities to analyze patterns and regulari-
ties in simulated cities: to extract features, examine geographic
trends, analyze spatial structures, etc. (Herold, Clouclesi and
Clarke, 2005). Some of the advances in the computer sciences
that enabled the introduction of automata techniques to the geo-
graphical sciences have also been employed in the calibration and
validation of automata models using techniques from artificial
intelligence (AI) (Almeida et al ., 2008).
In his chapter, I review the state of the art in cali-
bration and validation of urban cellular automata models,
with particular emphasis on models tasked with simulating
human - environment interactions through land-use and land
cover change, largely because it is in these application domains
that development of automata models is advancing most rapidly.
The chapter continues in the next sections with discussion
of calibration mechanisms - conditional transition, weighted
transition, and state-based constraints. Discussion of the
derivation of values for calibration parameters follows, with
particular attention to visual calibration, statistical tests, the
use of historical data, regression of parameter values, the use
of exogenous models, and automatic calibration procedures.
The focus of this chapter then moves to consideration of
model validation routines through use of visual inspection,
pixel-matching, feature and pattern recognition, and the analysis
of complexity signatures. Various procedures for sweeping the
parameter space of models are then discussed before the chapter
draws to a close with some concluding discussion.

All models are abstractions of a complicated reality and in simu-
lation there is an imperative to assess the match between modeled
phenomena and the real world. Empirically determining this cor-
respondence is always somewhat of a losing proposition because
of limits to what might be observed, the partiality inherent in
most datasets, discrepancy between modeled spatial and tem-
poral scales and those of natural and social phenomena, and
the non-uniqueness of any hypothesis or assumption (Oreskes,
Shrader-Frechette and Belitz, 1994, Batty and Torrens, 2005).
These problems are exacerbated when models are used to spec-
ulate about futures, about which we can know almost nothing
with certainty and they become especially problematic when we
fashion models of complex systems (Allen and Torrens, 2005).
Regardless of how problematic issues of mismatch might be,
models are nevertheless used as research, experimental, and diag-
nostic tools and so treatment of their ''fit'' to the real world or
to a purpose is significant, particularly when models are tasked
to test theories or to support plans, decisions, or policies. Cal-
ibration and validation exercises are particularly significant in
urban applications of models to human-environment interac-
tions, where there has been a tradition of using computer models
as planning support systems (Brail and Klosterman, 2001), often
for use in determining the potential impact of infrastructure
developments, human activities, and land-uses upon the envi-
ronment, or even for assessing compliance with legislative rulings
relating to transportation efficiency and air emissions standards
(Southworth, 1995).
The terminology surrounding model-matching exercises is
infamously vague and confused (Oreskes, Shrader-Frechette and
Belitz, 1994), but is perhaps best summarized as follows. ''Ver-
ification'' exercises serve to register a model (generally) to a
particular application, system, place, or time, or to fit a particular
purpose (normative modeling, conceptual modeling, decision
support). ''Calibration'' involves (specifically) adjusting model
parameters so that simulations (where simulation is the act of
''running'' a model on data or applying it to a given scenario)
can be performed with a level of fitness or sufficiency for their
intended purpose. ''Validation'' involves assessing the success of
a model or simulation run in achieving its (specific) intended
goals. In all cases, these exercises usually involve comparing the
performance of the model to some properties of the real system
being simulated. In a relative minority of cases, similar schemes
are used to compare models to other models, or individual runs
of a single model in varying places and times (Pontius Jr. et al .,
2008, Wegener, 1994). Comparisons are commonly made against
known or observed conditions.
Urban automata models, usually formed as cellular automata,
individual-based models, agent-based models, or multi-agent
systems (Benenson and Torrens, 2004) have become increasingly
popular in human-environment research, in large part owing
to their flexibility in representing an almost limitless variety of
phenomena and systems. Among their advertised advantages,
automata model-builders often tout the ability of automata to
simulate complex dynamic systems that defy easy analysis by more
traditional forms of modeling (Grimm, 1999; Manson, 2001;
Parker et al ., 2003; Batty, 2005). Verifying the utility of such
models for the systems and uses to which they are applied
in urban and environmental studies has, however, proven to

23.2 Calibration

Cellular automata models are generally calibrated by tailoring the
parameters that control transition rules. In addition, calibration
may be performed on a state-basis or cell-basis, allowing special
conditions by which the normal state transition procedure for
those states or cells might be specially treated. For system prop-
erties that might sit beyond the range of an automata simulation,
external models may be used to calibrate automata parameters.

23.2.1 Conditional transition rules

Conditional transition invokes calibration by determining cir-
cumstances under which transition may or may not take place.
One classic example is a so-called stopping rule, which freezes