Environmental Engineering Reference
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historical growth, and realistic urban extents. They also looked
at the plausibility of area, edge, and cluster attributes in the
simulation output.
One might opt, alternatively, to have a computer inspect the
visual match between a model's output and a real-world pattern.
This is usually done by pixel matching or by pattern recogni-
tion. Pattern recognition implies a targeted search - analysis to
determine the presence of specific features, artifacts, or config-
urations that are known or spelled-out apriori . Pixel-matching,
by contrast, is a more mechanical approach, involving the anal-
ysis of the composition of a particular scene and usually this
involves matching the pixel images generated by a model to
those in a digitized map or remotely sensed image, but - and this
is important - ignoring the configurations of those elements in
relation to each other (Torrens, 2006a). Pixels (picture elements)
in one scene are simply registered to another scene and the level
of coincidence between the two is gauged.
The most straightforward approach to pixel matching is to
fashion an inventory of pixel attributes within a simulated scene
and to compare the results to corresponding attributes in a
remotely sensed image. In analyzing output from their models,
Clarke and colleagues (1997) collated information regarding the
total number of urban pixels (urban extent), the number of edge
pixels on the boundary of a simulated landscape, and the amount
of pixel clusters at various stages in the course of a simulation
run. They then performed a validation exercise by determining
the correlation between those results and observed ''knowns''
from historical maps of the area. Pixel matching can also be
performed on a pixel-by-pixel basis. These techniques originate
in image processing, where they are used to evaluate classification
accuracy. Coincidence matrices are commonly used to register
cell-by-cell comparisons between simulated and remotely sensed
scenes: pixels are evaluated to determine whether they are identi-
cal on both scenes, in terms of states. In some instances, error data
is also calculated. Mismatches may be recorded, and moving fil-
ters can be used to discern displacement in the mismatch. There is
a problem, however, with spatial autocorrelation (Moran, 1950),
that weakens the reliability of correlation statistics of this form
when applied over geographically-coincident pixels, and with
serial autocorrelation when matching is performed between tem-
poral snapshots (Berry, 1993). Similarly, results at one scale of
observation or matching may not hold at other scales (Qi and
Wu, 1996).
The kappa-statistic is commonly used in conjunction with
pixel matching coincidence matrices. Low values of kappa indi-
cate conditions in which there is little correspondence between
observed and expected scenes; high values indicate a ''good''
match between the two. The kappa-statistic has been used in
these contexts in a number of urban cellular automata models
(White, Engelen and Uljee, et al ., 997; Wu, 1998), but there are
some important complications associated with the technique. The
statistic is almost unsuitably sensitive. If a simulated scene is sim-
ilar to an observed scene, but the correspondence is mismatched
by just one pixel in a few places, the overall accuracy of the match
may suffer considerably (Wu, 1998). Dislocation of this vari-
ety may be particularly problematic in sparsely-populated areas
of a scene (Wu and Webster, 1998). Correspondence between
observed and expected results may be highly susceptible to vari-
ation when different resolutions are used. Coarse resolutions
essentially ''average out'' disagreement between scenes. In the
context of urban models, there may be difficulties associated with
particular state variables. States designed to represent transport
infrastructure are an excellent example. White and colleagues
(1997) noted a displacement - of one cell in value - owing to
the rasterization of road and rail in their model. This may seem
minor, but it ended up becoming (statistically) significant in
the context of coincidence matrices. Moreover, the problem, in
this example, was transport-specific, and therefore introduced
error to a significant feature of the simulation by misrepresenting
transport land-use specifically.
23.3.2 Feature and pattern
recognition
Recognition exercises focus on identifying particular (and the-
oretically well-understood and/or significant) features and pat-
terns within model output. An advantage of pattern generation
in urban simulations is that the patterns to be sought are often
robust to changes in rules and parameter values (Andersson et al .,
2002). Whereas pixel-matching techniques deal with relatively
simple compositional correspondence between scenes, pattern
recognition techniques are used to measure specific (space -time)
structures in model output.
For example, edge detection may be used to measure the
morphology of urban boundaries: the perimeter of an entire
city, or the boundary of zones of activity within a city, or well-
understood morphologies such as downtown, suburbs, exurbs,
and urban - rural fringe (Torrens, 2008). Fractal analysis (Batty
and Longley, 1994) can be employed in determining space-filling
of urban (or landscape) processes and this has the advantage of
being quantifiable across model variables and can help in avoid-
ing thorny scale issues. Cluster-frequency spectra may be used
to compare hierarchies in urban clustering, to look at central-
place structures, for example. White and colleagues (1997) have
performed extensive analysis of their models using these tech-
niques, as have Batty and Xie (Xie, 1996). A similar approach
is employed by Torrens (2006b) in modeling suburbanization
within the American midwestern megalopolis, where clustering-
frequency is used to distinguish between the varying growth
trajectories of cities within that urban system.
Another approach to pattern-based validation is to study
urban ''patchiness.'' In landscape ecology (Forman and Gor-
don, 1986), a patch is representative of a spatial object (with
homogenous characteristics or states) situated within a broader
landscape, e.g., the coverage of a particular vegetative type within
a larger forest composed of several vegetative species. One can
easily see how this concept might be related to urban contexts: we
could distinguish clusters of retail activity amidst a sea of urban
development, ''ecologically,'' for example. There is a variety of
spatial analysis techniques associated with landscape ecology,
each designed to support the quantification of composition and
configuration properties of patches in landscapes (Gustafson,
1998). Several such landscape metrics have been used to validate
urban automata models. Goldstein and colleagues (2004), for
example, have calculated a variety of spatial metrics to explore
the robustness of their SLEUTH simulation of the Santa Barbara
region. These metrics are also employed by Torrens in explor-
ing the results of his automata simulations (Torrens, 2006b), as
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