A pluralistic approach to defining and measuring urban sprawl - Urban Remote Sensing: Monitoring, Synthesis and Modeling in the Urban Environment - page 163

any aspect of spatial geometry, ecological impact, or land use
composition - all of which are significant elements of sprawl
by all conventional definitions discussed here and elsewhere
(Frenkel and Ashkenazi, 2008b).
Sprawl is generally defined as a condition in which one or more
types of density is relatively low or decreases over a certain time
period. But what constitutes low density? Burchell and colleagues,
among others, make it clear that density a relative value:

The distribution of patches across the landscape are characterized
and quantified with measures including relative abundance,
connectivity and degree of separation between like patches. The
individual patch geometry and the aggregate distribution patterns
of patches is posited to affect ecological function at the landscape
scale (Turner, 1989; Gustafson, 1998). When patch theory is
transferred to the domain of urban spatial analysis, patches are
defined as land use types (e.g. residential, industrial, commercial,
open-natural space, open-agricultural space), and the metrics
transfer as well. Here, the patch geometry and distribution of
urban patches are suggested to have wide ranging implications
for environmental quality, economics, social relations and other
social variables.
Geometric-ecological measures can be grouped into two types
for urban landscape analysis: composition and configuration
(Torrens and Alberti, 2000). Composition refers to how hetero-
geneousanareaiswithregardtoitsmixofpatchtypesand
provides information regarding the relationship between and
among patches in a matrix. Configuration refers to the geometry
of individual land use patches, or how regular or irregular their
shape. Patch circumference, and various descriptors of shape
of the patch and its edge, like circularity (Gibbs, 1961) and
area/edge ratio (McGarigal et al ., 2002), are common measures
for configuration. 5
Fractal dimensions provide a second approach to measuring
sprawl, where fractal measures replace Euclidean geometry (Batty
and Longley, 1994). Fractals are defined as ''objects of any kind
whose spatial form is nowhere smooth, hence termed 'irreg-
ular', and whose irregularity repeats itself geometrically across
many scales'' (Batty and Longley, 1994). Although the measures
are related to configuration, fractals arise from a conceptually
different way of looking at the spatial development of cities.
Research on fractal dimensions has contributed to our under-
standing of urban spatial development and our understanding
of the forces that may shape a city's form (Benguigui et al .,
2000, Benguigui, Blumenfeld-Lieberthal and Czamanski, 2006,
Thomas, Frankhauser and Biernacki, 2008). Torrens (2008) and
Frenkel and Ashkenazi (2008b) integrate fractal variables into a
list of geometric variables with which they characterize sprawl.
The degree of homogeneity/heterogeneity in built land uses
(e.g. residential, commercial, industrial) is measured by compo-
sition variables (Fulton, 1996; Ewing, Pendall and Chen, 2002).
Urban sprawl has been defined as a homogeneous development
pattern, characterized by the absence of mixed land use (in par-
ticular, residential areas separated from trade and services) at
the neighborhood and city scale (Fulton, 1996). Built-up areas
with a high rate of mixed land uses are regarded as compact and
sustainable (Jenks, Burton and Williams, 1996, Burton, 2000),
whereas a high percentage of residential land use is considered
homogenous and non-mixed, and thus, sprawling. Another way
of looking at this aspect is the balance that exists between the
amount of population and the number of jobs (Ewing, Pendall
and Chen, 2002). A non-balanced situation where population is
large relative to jobs in a single geographic unit is considered a
component of sprawl.

Sprawl is not simply development at less-than-maximum
density; rather, it refers to development that, given a national
and regional framework (i.e. suburbs in various locations of
the United States), is at a low relative density, and one that
may be too costly to maintain

(Burchell et al., 1998).

Population density can be calculated in several ways, depending
on the extent of data and knowledge of the urban landscape. These
include gross population density (total population/built area)
(Fulton et al ., 2001; Sutton, 2003), net population density (total
population/built residential area), and population plus expected
population divided by developed plus developable land. Density
gradient analyses consider density as a function of distance from
urban centers or central business districts, where population
per unit area declines with distance from urban centers (Batty
and Longley, 1994; Alperovich, 1995, Jordan, Ross and Usowski,
1998). Researchers point out that during the past few decades
density gradients have been falling (i.e. sprawl is increasing) in
developed as well as developing countries (Ingram, 1998). This,
they suggest, emphasizes the universality of urban sprawl.

12.4.2.2 Relative population
growth rates
If it is possible to differentiate between built land use types and
if municipal scale population data is available, a ''Sprawl Index''
(SI) or ''Sprawl Quotient'' can be estimated. These are defined
as the ratio between the growth rate of built-up areas and the
population growth rate in that area. A quotient higher than one
implies urban sprawl (Weitz, 1999; Hadly, 2000).
Another example applying density measures is the use of the
relative amount of population living in low-density as compared
to high-density census tracts in US metropolitan areas (Lopez
and Hynes, 2003). Similarly, sprawl has also been defined as a
condition in which population growth rates in the suburbs are
higher than inside the central city (Jackson, 1985).

12.4.2.3 Spatial-geometry of built and
open space
Spatial geometry constitutes the largest group of sprawl measures.
These are numerous geometric measures, many of which have
been adopted from ecological research (Irwin and Bockstael,
2008) or from fractal geometry (Torrens and Alberti, 2000;
Herold and Menz, 2001). They have particular relevance to
remote sensing experts and others seeking to quantify spatial
measures of sprawl.
As in the discipline of landscape ecology, the landscape
is considered to be composed of spatially distinct ''patches''
with distinct ecological qualities and parameters including area,
circumference, edge shape, area/circumference ratio and others.

5 For readers interested in the mathematical equations for each of these indicators
derived from landscape ecology, the easily accessible Fragstats Users Guide provides
a comprehensive and detailed overview of each landscape indicator, its equation
and its strengths and weaknesses (McGarigal et al ., 2002); see: http://www.umass.
edu/landeco/research/fragstats/documents/fragstats_documents.html (accessed 15
November 2010).