the role of spatial metrics in the analysis
DESCRIPTION
The Role of Spatial Metrics in the Analysis and modeling of urban land use changeTRANSCRIPT
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and modeling of urban land use change
questions for future research are nally put forward to help strengthen the potential of the
Dynamic urban change processes, especially the tremendous worldwide expansion
of urban population and urbanized area, aect natural and human systems at all
geographic scales (Brockhero, 2000; United Nations Population Division, 2000).
Computers, Environment and Urban Systems
29 (2005) 369399* Corresponding author. Tel.: +1-805-893-4196; fax: +1-805-893-3703.proposed framework, especially regarding the further exploration of urban dynamics at dif-
ferent geographic scales.
2003 Elsevier Ltd. All rights reserved.
Keywords: Spatial metrics; Urban growth; IKONOS; Land use change; Urban modeling; Remote sensing
1. IntroductionMartin Herold *, Helen Couclelis, Keith C. Clarke
Department of Geography, University of California Santa Barbara, Ellison Hall, Santa Barbara,
CA 93106, USA
Received 18 February 2003; accepted 3 December 2003
Abstract
The paper explores a framework combining remote sensing and spatial metrics aimed at
improving the analysis and modeling of urban growth and land use change. While remote
sensing data have been used in urban modeling and analysis for some time, the proposed
combination of remote sensing and spatial metrics for that purpose is quite novel. Starting
with a review of recent developments in each of these elds, we show how the systematic,
combined use of these tools can contribute an important new level of information to urban
modeling and urban analysis in general. We claim that the proposed approach leads to an
improved understanding and representation of urban dynamics and helps to develop alter-
native conceptions of urban spatial structure and change. The theoretical argument is then
illustrated with actual examples from the urban area of Santa Barbara, California. SomeThe role of spatial metrics in the analysis
www.elsevier.com/locate/compenvurbsysE-mail address: [email protected] (M. Herold).
0198-9715/$ - see front matter 2003 Elsevier Ltd. All rights reserved.doi:10.1016/j.compenvurbsys.2003.12.001
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Worsening conditions of crowding, housing shortages, and insucient or obsolete
infrastructure, as well as increasing urban climatological and ecological problems
and the issue of urban security underline a greater than ever need for eectivemanagement and planning of urban regions (OMeara, 1999). Recently, innovative
approaches to urban land use planning and management such as sustainable
development and smart growth have been proposed and widely discussed (Kaiser,
Godschalk, & Chapin Jr., 2003; American Planning Association, 2002). However,
their implementation relies strongly upon available information and knowledge
about the causes, chronology, and eects of urban change processes. Despite the
recent proliferation of new sources of data and tools for data processing and anal-
ysis, these have not directly led to an improved understanding of urban phenomena.This paper explores both conceptually and with practical examples how using remote
370 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399sensing technology in combination with spatial metrics can improve the under-
standing of urban spatial structure and change processes, and can support the
modeling of these processes. Fig. 1 illustrates the simple conceptual framework
developed in the paper, consisting of three main components: remote sensing, spatial
metrics and urban modeling, and their interrelations. While the potential direct
contribution of remote sensing to urban modeling is fairly well understood (rela-
tionship 1 in Fig. 1), we argue that the combined use of remote sensing and spatialmetrics will lead to new levels of understanding of how urban areas grow and change
(relationships 2 and 3 in Fig. 1).
In recent years, the use of computer-based models of land use change and urban
growth has greatly increased, and they have the potential to become important tools
in support of urban planning and management. This development was mainly driven
by increased data resources, improved usability of multiple spatial datasets and tools
for their processing, as well as an increased acceptance of models in local collabo-
rative decision making environments (Klosterman, 1999; Sui, 1998; Wegener, 1994).However, the application and performance of urban models strongly depend on the
quality and scope of the data available for parameterization, calibration and vali-
dation, as well as the level of understanding built into the representation of the
processes being modeled (Batty & Howes, 2001; Longley & Mesev, 2000). Remote
sensing data products have often been incorporated into urban modeling applica-
Fig. 1. General framework for analysis and modeling of spatial urban dynamics.
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M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399 371tions as additional sources of spatial data (relationship 1 in Fig. 1), primarily for
historical land use information (Acevedo, Foresman, & Buchanan, 1996; Clarke,
Parks, & Crane, 2002; Meaille & Wald, 1990). Relationship 3 in Fig. 1 correspondsto the use of spatial metrics in urban modeling. This path has been proposed in a few
studies that use spatial metrics to rene and improve remote sensing data for urban
models, for model calibration and validation, or in studies of urban landscape
heterogeneity and dynamic change processes (Alberti & Waddell, 2000; Herold,
Goldstein, & Clarke, 2003; Parker, Evans, & Meretsky, 2001).
Remote sensing represents a major though still under-used source of urban data,
providing spatially consistent coverage of large areas with both high geometric detail
and high temporal frequency, including historical time series. Remote sensingmethods have been widely applied in mapping land surface features in urban areas
(e.g. Haack et al., 1997; Jensen & Cowen, 1999). Several recent developments in
remote sensing have the potential to signicantly improve the mapping of
urban areas. These relate to the availability of data from new remote sensing systems
such as the IKONOS-satellite (Tanaka & Sugimura, 2001), hyper-spectral sen-
sors (Ben-Dor, Levin, & Saaroni, 2001; Herold, Gardner, & Roberts, 2003)
and MODIS (Schneider, McIver, Friedl, & Woodcock, 2001), all of which can
support detailed and accurate urban area mapping at dierent spatio-temporalscales.
Much less widely known than remote sensing, spatial metrics can be a useful tool
for quantifying structure and pattern in thematic maps. Spatial metrics are com-
monly used in landscape ecology, where they are known as landscape metrics
(Gustafson, 1998). Recently there has been an increasing interest in applying spatial
metrics techniques in urban environments because these help bring out the spatial
component in urban structure (both intra- and inter-city) and in the dynamics of
change and growth processes (Alberti & Waddell, 2000; Barnsley & Barr, 1997;Herold, Clarke, & Scepan, 2002). We argue that the combined application of remote
sensing and spatial metrics can provide more spatially consistent and detailed
information on urban structure and change than either of these approaches used
independently. Indeed, coupling these two approaches can improve the thematic
detail and accuracy of remote sensing mapping products and facilitate their analysis
for specic urban applications.
In Sections 24 we review current issues in urban remote sensing, spatial metrics
and urban modeling respectively, discussing the relatively new area of spatial metricsin more detail. We emphasize in particular the combined use of spatial metrics with
remote sensing techniques and their potential contribution to urban modeling (Fig.
1, relationships 23). In Section 5 we illustrate these points with some concrete
examples. Section 5 highlights ve major areas where urban modeling could be
improved using the suggested framework. The examples incorporate the use of
IKONOS satellite data to study spatial urban pattern, specic spatial model appli-
cations, and the analysis of spatio-temporal urban dynamics at dierent scales.
Important areas of future research are outlined along with these examples. Finally,in the concluding Section 6, we summarize what we believe to be the proposed
approachs contribution to urban analysis and modeling.
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372 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 3693992. Remote sensing of urban areas
For decades the visual interpretation of aerial photography of urban areas hasbeen based on the hierarchical relationships of basic image elements. The spatial
arrangement and conguration of the basic elements (tone and color) combine to
give higher order interpretation features of greater complexity such as size, shape
and texture, or pattern and association, that are signicant and characteristic for
urban areas and urban land use (Bowden, 1975; Haack et al., 1997). A number of
urban remote sensing applications to date have shown the potential to map and
monitor urban land use and infrastructure (Barnsley et al., 1993; Jensen & Cowen,
1999) and to help estimate a variety of socio-economic data (Henderson & Xia, 1997;Imho, Lawrence, Stutzer, & Elvidge, 1997). However, much of the expert knowl-
edge of the human image interpreter was lost in the transition from air photo
interpretations to digital analysis of satellite imagery.
The great strength of remote sensing is that it can provide spatially consistent data
sets that cover large areas with both high detail and high temporal frequency,
including historical time series. Mapping of urban areas has been accomplished at
dierent spatial scales, e.g. with dierent spatial resolutions, varying coverage or
extent of mapping area and varying denitions of thematic mapping objects. Globaland regional scale studies are often focused on mapping just the extent of urban
areas (e.g. Meaille & Wald, 1990; Schneider et al., 2001). A basic diculty these
eorts encounter relates to the indistinct demarcation between urban and rural areas
on the edges of cities. Remote sensing provides an additional source of information
that more closely respects the actual physical extent of a city based on land cover
characteristics (Weber, 2001). However, the denition of urban extent still remains
problematic and individual studies must determine their own rules for dierentiating
urban from rural land (Herold, Goldstein & Clarke, 2003).Most local scale remote sensing applications require intra-urban discrimination of
land cover and land use types. Considering the land cover heterogeneity of the urban
environment several studies have shown that a spatial sensor resolution of at least 5
m is necessary to accurately acquire the land cover objects (especially the built
structures) in urban areas (Welch, 1982; Woodcock & Strahler, 1987). Since 2000,
data from new, very high spatial resolution space borne satellite systems have been
commercially available. For example, IKONOS and QUICKBIRD may be con-
sidered the beginning of a new era of civilian space borne remote sensing withparticular potential for application in the study of urban areas (Ridley, Atkinson,
Aplin, Muller, & Dowman, 1997; Tanaka & Sugimura, 2001).
Investigations in local scale mapping of urban land use have shown that analysis
on a per-pixel basis provides only urban land cover characterization rather than
urban land use information (Gong, Marceau, & Howarth, 1992; Steinnocher, 1996).
Based on the experience with visual air photo interpretation (Haack et al., 1997) it is
known that the most important information for a more detailed mapping of urban
land use and socioeconomic characteristics may be derived from image context,pattern and texture, also described as urban morphology (Barnsley et al., 1993;
Mesev, Batty, Longley, & Xie, 1995). There are several versatile approaches for
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M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399 373including structural, textural and contextual image information in land use mapping.
Some studies have used textural measures derived from spectral images to include
this information in the classication process (Baraldi & Parmiggiani, 1990; Forster,1993; Gong & Howarth, 1990; Gong et al., 1992). Others have applied spatial post-
classication to estimate urban land use information from remote- sensing derived
land cover maps (Barnsley et al., 1993; Steinnocher, 1996). A few studies have used
remote- sensing derived discrete land cover objects or segments and described their
morphology and spatial relationships in a detailed mapping of urban areas (Barnsley
et al., 1993; Mehldau & Schowengerdt, 1990; Moller-Jensen, 1990). Barnsley and
Barr (1997) further developed these ideas and presented a complex GIS-based sys-
tem for detailed contextual urban mapping on an illustrative dataset. Manyresearchers believe that detailed spatial and contextual characterization of urban
land cover has high potential to result in detailed and accurate mappings of urban
land uses and socioeconomic characteristics (Barr & Barnsley, 1997; Herold et al.,
2002).
An emerging agenda in urban applications of remote sensing calls for a new
orientation in related research (Longley, Barnsley, & Donnay, 2001). The traditional
remote sensing objectives emphasizing the technical aspects of data assembly
and physical image classication should be augmented by more inter-disciplinaryand application-oriented approaches. Research should focus on the description and
analysis of spatial and temporal distributions and dynamics of urban phenomena, in
particular urban land use changes. However, there is still a lot of resistance, espe-
cially among social scientists, against using remote sensing techniques in urban
studies. Rindfuss and Stern (1998) mention several reasons. First, there is a general
concern about pixelizing the social environment, i.e., focusing too much on thephysical aspects of urban areas at the expense of social issues. Indeed, the socio-
economic variables of interest are usually not directly visible from measurementstaken from remote sensing observations. Secondly, the social sciences outside of
geography and planning are generally more concerned with why things happen ra-
ther than where they happen, and accordingly, most social scientists tend to
underestimate the value of the detailed spatial data that remote sensing provides. It is
not yet widely appreciated that remote sensing can provide useful additional data
and information for social science oriented studies, e.g., by quantifying the spatial
context of social phenomena and by measuring socially induced spatial phenomena
as these evolve over time. For example, by helping make connections across levels ofanalysis and between dierent spatial and temporal scales, remote sensing has the
potential to provide additional levels of information about the links between land
use and infrastructure change and a variety of social, economic and demographic
processes (Rindfuss & Stern, 1998). In terms of analyzing urban growth patterns,
Batty and Howes (2001) believe that remote sensing technology, especially consid-
ering the recent improvements mentioned above, can provide a unique perspective
on growth and land use change processes. Datasets obtained through remote sensing
are consistent over great areas and over time, and provide information at a greatvariety of geographic scales. The information derived from remote sensing can help
describe and model the urban environment, leading to an improved understanding
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scale, determined by the spatial resolution, the extent of spatial domain, and the
374 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399thematic denition of the map categories at a given point in time. When applied to
multi-scale or multi-temporal datasets, spatial metrics can be used to analyze and
describe change in the degree of spatial heterogeneity (Dunn, Sharpe, Guntensber-that benets applied urban planning and management (Banister, Watson, & Wood,
1997; Longley & Mesev, 2000; Longley et al., 2001).
3. Spatial metrics
The analysis of spatial structures and patterns are central to geographic research.Spatial primitives such as location, distance, direction, orientation, linkage, and
pattern have been discussed as general spatial concepts in geography (Golledge,
1995). In geography these concepts have been implemented in a variety of dierent
ways. Here these basic spatial concepts and the analysis of spatial structure and
pattern will be approached from the perspective of spatial metrics.
Under the name of landscape metrics, spatial metrics are already commonly used
to quantify the shape and pattern of vegetation in natural landscapes (Gustafson,
1998; Hargis, Bissonette, & David, 1998; McGarigal, Cushman, & Neel, 2002;ONeill et al., 1988). Landscape metrics were developed in the late 1980s and
incorporated measures from both information theory and fractal geometry (Man-
delbrot, 1983; Shannon & Weaver, 1964) based on a categorical, patch-based rep-
resentation of a landscape. Patches are dened as homogenous regions for a specic
landscape property of interest, such as industrial land, park or high-density
residential zone. There is no inherent spatial scale to a patch, nor is there an
inherent level of classication such as an Anderson level (Anderson, Hardy, Roach,
& Witmer, 1976). The landscape perspective usually assumes abrupt transitionsbetween individual patches that result in distinct polygons, as opposed to the con-
tinuous eld perspective. Patches are therefore maximally externally and mini-
mally internally variable. Landscape metrics are used to quantify the spatial
heterogeneity of individual patches, of all patches belonging to a common class, and
of the landscape as a collection of patches. The metrics can be spatially non-explicit,
aggregate measures but still reect important spatial properties. Spatially explicit
metrics can be computed as patch-based indices (e.g. size, shape, edge length, patch
density, fractal dimension) or as pixel-based indices (e.g. contagion, lacunarity)computed for all pixels in a patch (Gustafson, 1998).
Applied to elds of research outside landscape ecology and across dierent kinds
of environments (in particular, urban areas), the approaches and assumptions of
landscape metrics may be more generally referred to as spatial metrics. In general,
spatial metrics can be dened as measurements derived from the digital analysis of
thematic-categorical maps exhibiting spatial heterogeneity at a specic scale and
resolution. This denition emphasizes the quantitative and aggregate nature of the
metrics, since they provide global summary descriptors of individual measured ormapped features of the landscape (patches, patch classes, or the whole map). Fur-
thermore, the metrics always represent spatial heterogeneity at a specic spatial
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In summary, the application of spatial metrics for both mapping and modeling
M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399 375the urban environment is just beginning, but has already focused on a variety ofdierent applications. Most case studies point out the importance of these methods
in urban analysis and urge further systematic investigations in this area (Barr &
Barnsley, 1997; Geoghegan et al., 1997; Parker et al., 2001). An important, thus far
little explored potential lies in the combined application of remote sensing and
spatial metrics. Indeed, remote sensing can provide the spatially consistent,gen, Stearns, & Yang, 1991; Wu, Jelinski, Luck, & Tueller, 2000). Based on the work
of ONeill et al. (1988), sets of dierent metrics have been developed, modied and
tested (Hargis et al., 1998; McGarigal et al., 2002; Ritters et al., 1995). Many of thesequantitative measures are implemented in the public domain statistical package
FRAGSTATS (McGarigal et al., 2002).
3.1. Research on urban analysis using spatial metrics
Interest in using spatial metric concepts for the analysis of urban environments is
starting to grow. Based on the few studies published so far, Parker et al. (2001)
summarize the usefulness of spatial metrics with respect to a variety of urban models
and argue for the contribution of spatial metrics in helping link economic processes
and patterns of land use. They investigate their hypothesis using an agent-based
model of economic land use decision-making resulting in specic theoretical land use
patterns. They conclude that urban landscape composition and pattern, as quantiedwith spatial metrics, are critical independent measures of the economic landscape
function and can be used for an improved representation of spatial urban charac-
teristics and for the interpretation and evaluation of modeling results. Alberti and
Waddell (2000) substantiate the importance of spatial metrics in urban modeling.
They proposed specic spatial metrics to model the eects of the complex spatial
pattern of urban land use and cover on social and ecological processes. These metrics
allow for an improved representation of the heterogeneous characteristics of urban
areas, and of the impacts of urban development on the surrounding environment.Geoghegan, Wainger, and Bockstael (1997) explored spatial metrics in modeling
land and housing values. They show that . . . the nature and pattern of land usessurrounding a parcel have an inuence on the price, implying that people care very
much about the patterns of landscapes around them . . ., and recommend the use oflandscape metrics to describe such relationships (urban landscape composition).
Earlier, Batty and Longley (1994) systematically investigated the role of fractals in
representing urban structure, including urban land use morphology. Barr and
Barnsley (1997) explored concepts of graph theory in mapping and representingurban land use structures. Their approach used spatial primitives such as location
and area and spatial relationships such as adjacency, distance, orientation and
containment. They implemented and applied a framework called XRAG, designed
to describe graph relations and characteristics of urban land cover objects
(graphtown) based on digital line vector datasets (Barnsley & Barr, 1997) and
remote sensing data analysis (Barnsley & Barr, 2000).
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376 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399high-resolution datasets that are required for the analysis of spatial structure and
pattern through spatial metrics.
3.2. Problems in the application of spatial metrics
The development and evaluation of a framework for spatial metrics analysis of
datasets derived from urban remote sensing must deal with both theoretical and
methodological problems. These relate to issues of scale in the selection and analysis
of appropriate remote sensing data and in the application of the metrics, and to the
selection of the appropriate spatial metrics themselves.
3.2.1. Spatial accuracy
An important consideration is the spatial accuracy and/or spatial resolution of the
remote sensing data used as inputs to the spatial metrics analysis. Data accuracy andresolution directly aect landscape heterogeneity as represented in the mapping
product and determine the appropriate spatial scale of the investigation. This issue is
central to all remote sensing data analysis and has been recognized in related re-
search (Woodcock & Strahler, 1987). The lower the spatial resolution, the more
generalized the structure of the mapped features (e.g. urban land cover objects) and
their spatial heterogeneity will be in both the image data and the metrics. At too low
a spatial resolution, individual objects may appear articially compact or they may
get merged together. The spatial measures are then dominated more by the rectan-gular shape of the pixels than by the actual object patterns of interest (Krummel,
Gardner, Sugihara, ONeill, & Coleman, 1987; Milne, 1991). Furthermore, specic
kinds of structures, especially linear features, may not be represented at all, thus
leading to an overestimation of landscape homogeneity. In some cases it may be
useful to include ancillary digital data, e.g. relating to linear landscape elements, to
improve the remote sensing data product and have these features included in the
spatial metrics analysis (Lausch & Menz, 1999).
3.2.2. Thematic accuracy
The thematic accuracy of the remote sensing data product relates to the denition
of the thematic mapping classes and the classication accuracy. Thematic accuracy
obviously directly inuences the further analysis of the map with spatial metrics
(Barnsley & Barr, 2000). The thematic mapping capabilities of remote sensing data
mainly depend on the spectral contrast between the classes of interest and the
spectral resolution of the sensor. The lower the spectral separability of mapping
categories, the less accurately the land cover characteristics of an area can be
mapped. An overall classication accuracy of 85% is commonly considered sucientfor a remote sensing data product (Anderson et al., 1976). However, the denition of
the classes should represent all thematic objects and structures in the landscape that
are of interest in a specic investigation. A generalized class denition may result in a
representation of the landscape that is too homogenous, and as a result important
structural features may not be detectable with spatial metrics. On the other hand, if
the landscape classication is too detailed, relevant structures may get lost in a highly
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yields a higher fractal dimension.
M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399 377Before any kind of application, these metrics have to be interpreted, analyzed and
evaluated as to their ability to capture the thematic information of interest (Gus-
tafson, 1998). The few studies published so far on spatial metrics analysis in urban
areas have applied and suggested dierent sets of metrics. Geoghegan et al. (1997),
Alberti and Waddell (2000), Parker et al. (2001) and Herold, Liu, and Clarke (2003)
suggest and compare a wide variety of dierent metrics. Their results show the role
each of these plays in representing the composition, spatial conguration and spatialneighborhood of the urban landscape as represented in urban models. These studies
were especially interested in analyzing land cover/land use pattern and economic
landscape function (Parker et al., 2001) and in explaining land values (Geoghegan
et al., 1997). So far, there is no standard set of metrics best suited for use in urban
environments as the signicance of specic metrics varies with the objective of theheterogeneous pattern. Furthermore, the classication accuracy of the remote
sensing data usually decreases as more classes are derived. Accordingly, the thematic
denition of the classes should consider both the spectral mapping capabilities of thesensor and the user requirements concerning thematic map accuracy for spatial
metrics analysis. The analysis of urban land cover and land use must consider at the
very least the two main land cover categories built up (buildings and transportation
surfaces) and non-built up (vegetation, bare soil, water). A renement of this clas-
sication, e.g. the discrimination of dierent built up and land use categories, may be
useful in an analysis of spatial urban structure but should take into account the
separability of land cover mapping categories and related quality characteristics of
the land cover map.
3.2.3. Selection of metrics
A number of dierent approaches in representing spatial concepts have resulted in
the development of various spatial metrics or metric categories as descriptive sta-tistical measurements of spatial structures and patterns. Commonly applied metrics
are patch size, dominance, number of patches and density, edge length and density,
nearest neighbor distance, fractal dimension, contagion, lacunarity, etc. (see
McGarigal et al., 2002). Some of these names are self-explanatory. The contagion
index measures the probability of neighborhood pixels being of the same class and
describes to what extent landscapes are aggregated or clumped (ONeill et al., 1988).
Landscapes consisting of patches of relatively large, contiguous landscape classes are
described by a high contagion index. If a landscape is dominated by a relativelygreater number of small or highly fragmented patches, the contagion index is low.
For example if an urbanized area is represented by one large compact blob the
contagion index will be high. The more heterogeneous the urbanized area becomes as
a result of higher fragmentation or a larger number of individual urban units, the
lower the contagion index will be. The fractal dimension describes the complexity and
fragmentation of a patch as a perimeter-to-area ratio. Low values are derived when a
patch has a compact rectangular form with a relatively small perimeter relative to the
area. If the patches are more complex and fragmented, the perimeter increases and
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378 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399study and the characteristics of the urban landscape under investigation (Parker
et al., 2001).
3.2.4. Denition of the spatial domain
A basic problem in the application of spatial metrics is the denition and spatial
discrimination of spatial entities for metrics calculation. In general, metrics can
characterize structures or features of an individual patch as a spatially and themat-ically consistent area representing an elementary landscape element (McGarigal
et al., 2002). Metrics can also describe properties of patch classes (e.g. as sums or
mean values of individual patch metrics), and some (e.g. the contagion metric) can
summarize properties of the entire landscape or spatial domain of the analysis. It is
always important to dene the spatial domain of the study as it directly inuences
the spatial metrics. In some studies the extent of the study area will determine the
spatial domain. For other investigations, in particular in the comparative evaluation
of intra-urban structures, it is essential to decompose the urban environment intorelatively homogenous units that will serve as the spatial domains of the metric
analysis.
The spatial discrimination and thematic denition of the spatial units must con-
sider the characteristics of the landscape, the objectives of the study, and the use of
the metrics in further analysis that may require a specic spatial subdivision of the
urban area. There are many dierent ways of spatially subdividing an urban region
based on administrative boundaries, remote sensing and/or map analysis, or on
urban modeling considerations. Another common way is through the use of a reg-ular grid as used in many urban models (Landis & Zhang, 1998; Pijankowski, Long,
Gage, & Cooper, 1997). A similar concept in remote sensing data analysis is the
quadratic window or kernel used to analyze features in the neighborhood of a pixel.
The neighborhood is determined by the size of the moving kernel and its spectral or
thematic characteristics are derived statistically. Barnsley and Barr (2000) discuss
several problems related to kernel-based approaches in urban area analysis. For
example: grid-based approaches tend to smooth the boundaries between discrete
land cover/land use parcels; it is dicult to determine a priori the optimum kernelsize; and, a rectangular window represents an articial area that does not conform to
real parcels or land use units, which tend to have irregular shapes and their own
distinct spatial boundaries. In contrast, region-based approaches allow the discrete
characterization of thematically and functionally dened areas that are generally
irregularly shaped (Barnsley & Barr, 2000; Barr & Barnsley, 1997; Gong et al., 1992).
Regional subdivisions of urban space vary extensively in size, shape and purpose.
Governmental and planning organizations use systems such as census tracts and
blocks or zoning districts, based on the characteristics of the built environment,socioeconomic variables, administrative boundaries and other considerations (Knox,
1994). Urban models have also used a wide variety of spatial units, including indi-
vidual parcels associated with key human agents such as landowners participating in
micro-economic processes (Irwin & Geoghegan, 2001; Waddell, 1998), and uniform
analysis zones dened by the multiple intersections of polygons on dierent data
layers representing natural and socioeconomic variables of interest (Klosterman,
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region-based methods are likely to provide a better segmentation of urban space for
M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399 379most applications.
Besides spatial resolution, the internal discrimination or subdivision of the study
area is one of the central issues of spatial scale in metric analysis. The available
approaches can overcome the averaging nature of metrics over an entire study area
that may lead to incorrect interpretations of the dynamics in the region. For
example, changes reected in the metrics cannot usually be related to specic loca-tions within the urban area without visual spatial interpretation or some more de-
tailed analysis at the patch level. Furthermore, temporal variations in the spatial
metrics may result from the aggregate or cumulative eects of dierent dynamic
processes. Spatial disaggregation allows the study area to be considered as a set of
smaller individual landscapes and regionalizes the metric analysis to an appropri-
ate scale. Even so, it may be impossible to directly relate the metric changes to
specic urban change processes. For studies of urban land cover and land use
structure change, a denition of more or less homogenous urban land use unitswill usually have to be developed before the analysis can begin. These have to
be dened and spatially dierentiated using the available data sources (e.g.
remote sensing or/and census data) and any other relevant information and local
knowledge.
4. Models of urban growth and land use change
Socioeconomic, natural, and technological processes both drive and are pro-
foundly aected by the evolving urban spatial structures within which they operate.
Research into understanding, representing and modeling urban systems has a long
tradition in geography and planning (Batty, 1994; Knox, 1994). In recent years,models of land use change and urban growth have become important tools for city
planners, economists, ecologists and resource managers (Agarwal, Green, Grove,
Evans, & Schweik, 2000; EPA, 2000; Klosterman, 1999; Wegener, 1994). This
development was mainly driven by an increased availability and usability of multiple
spatial datasets and tools for their processing (e.g. GIS). Community-based col-
laborative planning and consensus-building eorts in urban development have also1999). The denition of regions based on remote sensing uses automated, semi-
automated or supervised approaches. Automated techniques are usually based on
pattern recognition or image segmentation that result in areas with similar spectraland textural pattern. A traditional approach in region-based remote sensing analysis
is the concept of photomorphic region developed for aerial photographic interpre-
tation (Peplies, 1974). Photomorphic regions are dened as image segments with
similar properties of size, shape, tone/color, texture and pattern. Barr and Barnsley
(1997) following Barnsley, Barr, and Sadler (1995) discuss a combined remote
sensing and GIS approach for deriving urban morphological zones that describes the
physical extent of the built up area based on remote sensing data, modied by cri-
teria of minimum size and spatial contiguity based on GIS data. In general, all theseapproaches are appropriate for spatial metrics analysis in urban environments, but
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380 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399been strengthened by the new data and tools at the local level (Klosterman, 1999;
Sui, 1998; Wegener, 1994).
Several problems have been identied in building, calibrating and applyingmodels of urban growth and urban land use change. These relate to the issues of
data availability and to the need for improved methods and theory in modeling
urban dynamics (Irwin & Geoghegan, 2001; Longley & Mesev, 2000; Wegener,
1994). In general, the quality of modeling results strongly depends on the quality
and scope of the data used for parameterization, calibration and validation (Batty
& Howes, 2001; Longley & Mesev, 2000). Since many land use change models
simulate both human and environmental systems, the requirements placed on the
data are fairly complex and range from natural and ecological variables tosocioeconomic information and detailed land use/cover data with appropriate
spatial and temporal accuracy. Important socioeconomic data sources include
census and various other types of governmental data as well as data that are
routinely collected by local planning and administrative agencies (Fagan, Meir,
Carroll, & Wo, 2001; Foresman, Pickett, & Zipperer, 1997; Wegener, 1994).
However, these data sources are generally limited in their temporal accuracy and
consistency, in their inclusion of important urban variables, and in their avail-
ability for dierent areas, especially outside the developed countries. Accordingly, anumber of studies have explored alternative sources of data for urban land use
change modeling, in particular data from remote sensing (Acevedo et al., 1996;
Clarke et al., 2002; Meaille & Wald, 1990). These investigations capitalize on the
fact that, as discussed above, remote-sensing techniques can provide spatially
consistent datasets that cover large areas with both high detail and high temporal
frequency, including historical time series. In particular, remotely sensed data can
represent urban characteristics such as spatial extent, pattern and land cover, often
also land use and urban infrastructure, and indirectly, a variety of socioeconomicpatterns (Usher, 2000).
Data issues also underlie, at least in part, the second major problem in urban land
use change modeling, the need for better methods and theory. Longley and Mesev
(2000) argue that our understanding of physical and socioeconomic patterns and
processes through urban modeling is largely limited by the available data. They also
refer to remote sensing as an important and insuciently exploited source of data to
aid not only applications but also theoretical understanding. In the same vein Batty
and Howes (2001) argue that remote sensing data provide a unique view on spatialand temporal urban change patterns and should be further investigated to improve
our understanding and modeling of those processes. Remote sensing may also
contribute to better representations of the spatial heterogeneity of urban land use
structure, landscape features and socioeconomic phenomena, improving on the
traditional models that often tend to reduce urban space to a uni-dimensional
measure of distance (Irwin & Geoghegan, 2001). However, the potential of the
combined application of remote sensing techniques and urban modeling has yet to be
fully explored and evaluated (Batty & Howes, 2001; Longley & Mesev, 2000;Longley et al., 2001).
-
M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399 3815. Improving urban modeling with remote sensing and spatial metrics: some case studies
Thus far we presented several arguments for combining remote sensing andspatial metrics to support and improve urban modeling and ultimately, urban
management and planning. In this section we further extend and rene these ideas
and present illustrative case studies based on actual data. We address (1) basic
mapping and data support, (2) model calibration and validation, (3) the interpre-
tation, analysis and presentation of model results, (4) the representation of spatial
heterogeneity in urban areas, and (5) the analysis of spatio-temporal urban growth
pattern. The rst three of these ve points are known and fairly well understood in
current urban modeling. They are included here for completeness as we discuss thenew possibilities resulting from the application of the framework presented in this
paper. The remaining two points are novel and address the core of our argument,
highlighting the potential for improving not only the representation of urban
dynamics but also the theoretical background of urban modeling.
5.1. Basic mapping and data support
Current spatial urban models have specic requirements in terms of data for
parameterization, e.g. data on urban extent, topography, land use, or transportation
networks (Agarwal et al., 2000; EPA, 2000). Remote sensing products are widely
used to provide these datasets or to improve existing databases in terms of spatial
accuracy and temporal consistency (relation 2 in Fig. 1). Researchers must of courseconsider the ever-improving capabilities of sensor systems to provide more detailed
and accurate remote sensing data products. In particular, the land cover hetero-
geneity of urban environments requires special attention in selecting a sensor with
appropriate spatial and spectral characteristics. Next to a more focused sensor
selection, an important potential improvement of current methods relates to the use
of spatial metrics in remote sensing data analysis. For example, the problem of land
cover versus land use in urban areas, as discussed in Section 2, can often be solved by
including a contextual component in the image analysis, which could be providedthrough spatial metrics.
The following example illustrates the application of spatial metrics in the analysis
of urban characteristics, using an IKONOS image mosaic of the Santa Barbara
South Coast region. The IKONOS image analysis includes a land cover classication
(3 classes: buildings, vegetation and rest) using the eCognition software, which
segments the image and allows for the incorporation of spatial and contextual
information of object features in the image classication process (Baatz et al., 2001;
Herold, Liu & Clarke, 2003). The spatial metrics for each land use region (derivedfrom remote sensing data interpretations) were derived using the public domain
program Fragstats (McGarigal et al., 2002). Given a land cover discrimination of
the urban environment in the three main classes: buildings, vegetation, and the rest
(soil, water, and transportation areas) the question becomes: What characterizes the
spatial land cover heterogeneity of urban areas and how can it be described with
metrics? For example, the heterogeneity of the class buildings can be related to the
-
size of structures (small versus large buildings), their shape (compact versus complex
and fragmented), and the spatial conguration (regular versus irregular). Size is
measured by the mean patch size; the variation in size by the patch size standarddeviation metric. Shape can be quantied by the fractal dimension metric, an
area/perimeter ratio that increases as spatial forms get more complex, and by the
number of edges or edge length of a patch. Spatial building patterns are described by
the mean nearest neighbor distance and the nearest neighbor distance standard
deviation metrics, with the latter metric increasing as the spatial pattern of build-
ings gets more irregular. Similar measures can be applied to explore the heteroge-
neity of the vegetation class.
Characteristic examples of metrics calculations for regions that encompass dis-tinct urban land uses are shown in Fig. 2. The contagion is lowest for single unit
high-density residential, multi-unit residential and commercial/industrial areas.
These land uses represent the most heterogeneous, fragmented type of urban land-
scape. High contagion is found for forest, wetlands, agriculture, and rangelands.
These natural or non-urban environments are clearly identied as such by the
landscape contagion metric. Furthermore, a distinct residential gradient exists, with
lower contagion for higher residential density. The fractal dimension of the vege-
382 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399Fig. 2. Density graphs of four spatial metrics for nine types of land uses found within urban areas from
IKONOS data. The metrics represent dierent spatial features noted on top of each graph, e.g. contagion
describes the whole land use region, the fractal dimension all vegetation patches within each area, the
patch density and nearest neighbor standard deviation the building pattern.
-
M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399 383tation areas reects high fragmentation for all residential land uses, that is, resi-
dential development results in characteristic disperse vegetation structures. Although
having less vegetation coverage overall, urban land uses like commercial or publicinstitutions show more compact vegetated areas, e.g. urban parks or ornamental
landscaping. The high values of the patch density metric reect the diverse patterns
of high and medium density residential land uses with high numbers of individual
buildings per area unit. The open space and rural land uses show low values. The
nearest neighbor standard deviation describes the regularity of the building pattern.
The values for forest, wetlands, agriculture, recreational and open spaces are
indistinct as these kinds of areas have no inherent spatial regularities. By contrast,
the actual urban land uses reect the characteristic human ngerprint of a regularspatial conguration. High-density single unit residential areas have the most dis-
tinct spatially ordered building pattern. Commercial/industrial, multi-unit residen-
tial, and medium density single unit residential also indicate a high degree of
regularity. The building congurations in low-density residential area are signi-
cantly less regular.
This thematic exploration of commonly applied spatial metrics emphasizes that
most metrics are in themselves fairly simple statistical measurements. They require,
however, a comprehensive interpretation and translation from the language oflandscape ecology, their domain of origin, to the concepts describing intra-urban
environments. For the purposes of urban model parameterization and remote
sensing data analysis, the metrics provide valuable second-order image information
to help distinguish and map dierent types of urban land use (Herold, Liu & Clarke,
2003). Hence, the combined use of remote sensing and spatial metrics can improve
the data products used to parameterize current models of urban growth and land use
change.
5.2. Model calibration and validation
Model calibration and validation are possibly the most challenging of the prac-
tical aspects of urban modeling. In dynamic models historical datasets of urbandevelopment usually form the empirical basis of these steps. Spatial metrics have
been used to evaluate and assess the local, small-scale performance of models in
addition to the summary statistics addressing total amounts of change or growth.
These metrics help assess the goodness of t in terms of spatial structure and
highlight specic problems, uncertainties or limitations of the model results (Can-
dau, 2002; Clarke, Hoppen, & Gaydos, 1996; Herold, Goldstein & Clarke, 2003;
Manson, 2000; Messina, Crews-Meyer, & Walsh, 2000). The type and number of
metrics used vary among studies, and dierent metrics have been found useful indescribing dierent characteristics of model performance and results.
An example of the use of spatial metrics in the evaluation of a dynamic models
performance is shown in Fig. 3. The model used is the SLEUTH Cellular Automaton
urban growth model (Clarke, Hoppen, & Gaydos, 1997) applied to the Goleta, CA
urban area. The Goleta urban area has experienced intensive urbanization since the
1960s as indicated by the growth in total urban area increasing from 0.6 km2 to more
-
384 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399than 50 km2 by 2000 (Fig. 3(a)). Interesting features in the diagrams are the sig-
nicant jumps in the metrics graphs for the calibration years, reecting the dis-
crepancies between the independent remote sensing validation measurements and the
SLEUTH model results (annual). The model generally represents well the total
amount of growth (total urban area metric) despite a tendency to underpredict. Thecontagion and fractal dimension metrics also indicate good model performance in
terms of the general spatial form of urban development. Most substantial dis-
Fig. 3. Five spatial metrics are used to evaluate SLEUTHs performance in reproducing urban devel-
opment patterns in the Goleta area. The model calibration and metrics calculation years from remote
sensing data are 1929, 1943, 1954, 1967, 1976, 1986, 1998 and 2001. The jumps in the metric graphs that
appear for the calibration years highlight the disagreements between model and observations as reected
in the metrics.agreements are recorded for the calibration year 1967. That period is associated with
signicant urban sprawl rst appearing in the area and representing a new form of
growth that causes some problems in the models performance. That is, the model
produces less accurate results as the urbanization pattern shows signicant changes
relative to the historical calibration time frame.
The metrics shown in Fig. 3(b) together provide an evaluation of a dierent aspectof the models performance. The metric describing the number of individual urban
patches shows quite signicant discrepancies between the measured and modeled
data. Although the model produces broadly correct results in simulating the amount
and spatial form of urban development, it tends to systematically underestimate the
number of individual urban patches. The model may err either by not generating
enough individual new areas of development (urban diusion) or by not retaining
existing disconnected urban areas. Both these errors would decrease the predicted
number of urban patches. However, the metric describing the percentage of urbanarea in the largest urban patch only marginally reects the major jumps in the
number of individual patches. This observation leads to the conclusion that the
discrepancies are due pre-dominantly to the insucient generation of new devel-
opment units and not to the spatial aggregation and connection of individual urban
patches to the urban core.
-
M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399 385This detailed exploration and discussion of problems in the models performance
helps suggest possible improvements. In the case presented here dierent reasons
were identied for the observed disagreements between metric measurements andmodel results. These relate to the general nature of the modeling approaches using
cellular automata, the SLEUTH models calibration method, and the specic
threshold values models that were used in the Monte Carlo simulations to decide
whether a grid cell will be considered urbanized or not. These thresholds were
eective in getting the model to simulate fairly accurately the growth of existing
urban areas but less so when it came to the allocation of new individual areas of
urban development (Herold, Goldstein & Clarke, 2003). It seems indeed that the
spatial metrics, individually or in combination, do reect the multiple facets of theSLEUTH models performance. These results suggest that it would be useful to
explore and evaluate systematically the use of dierent types of metrics in order to
develop more standardized, transparent and ecient model calibration and valida-
tion procedures.
5.3. Interpretation, analysis and presentation of model results
The results of spatial modeling need to be thoroughly interpreted and assessed in
order to derive useful information for specic applications. Remote sensing imagery
can greatly enhance the interpretation, visualization and presentation of model
outcomes, e.g., by providing a recognizable background to the spatial patterns
produced by the model. Realistic visualization is of special importance if the resultsare to be presented to the public. Further renement of the model results and
assessment of the impacts of urban development can be supported by spatial metrics
analysis (Alberti & Waddell, 2000). Berry, Flamm, Hazen, and MacIntyre (1996) use
landscape metrics in their LUCAS model to assess the impact of urban expansion on
the surrounding natural areas. Generally, this approach can be applied in a variety
of investigations relating to urban dynamics and the resulting spatial structures. For
example, spatial metrics can be used to interpret the localized implications of dif-
ferent model scenarios. They can provide a better understanding of how dierentpolicies or weightings of growth factors might impact dierent parts of the urban or
natural areas. Metrics can also be used to dene, rather than just interpret growth
scenarios, as they can help represent locally detailed alternative spatial congura-
tions.
Fig. 4 shows the results of a case study evaluating and assessing a set of alternative
paths of future urban growth. The comparative analysis and assessment of dierent
possible urban growth trajectories is one of the most important purposes of mod-
eling in connection with urban management and planning (Xiang & Clarke, 2003).The application of the SLEUTH urban growth model (Clarke et al., 1997) to the
Santa Barbara urban region focuses on ve dierent sets of assumptions corre-
sponding to alternative growth trajectories over the next 30 years (Candau &
Goldstein, 2002). The rst of these (MSQ) assumes that the status quo will be
maintained, and future growth will be allowed to continue in a manner similar to
what had occurred in the past. The second alternative (ER) uses the same
-
386 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399assumptions as MSQ but includes an expanded road network. The third alternative
(EEP) reects maximum protection of environmentally sensitive lands, while the
fourth (MEP) reects a lesser degree of environmental protection. Finally, the fth
alternative (UB) uses an urban boundary to dene and constrain the maximum
extent of urban growth.
The graphs in Fig. 4 compare the ve growth alternatives using four dierent
spatial metrics. The changes in total urban area, length of urban boundary, numberof urban patches, and degree of contagion are for the year 2030 relative to 2001, with
the year 2001 being the last calibration year that was derived from IKONOS satellite
remote sensing data. The metrics analysis shows very similar results for the MSQ and
ER cases. The most urban growth appears for MSQ (continuation of current trends)
and ER (expanded road network), the least for maximum environmental protection
(EEP). The number of individual urban patches signicantly decreases for MSQ and
ER as a result of the large expansion in urbanized area within the physically con-
strained South Coast region, a narrow plain lying between the ocean and a steep
Fig. 4. Spatial metric comparison of ve dierent growth scenarios for the Santa Barbara South Coast
region forecasted for the year 2030 using the SLEUTH urban growth model.coastal range. These patterns reect the build-out of the limited amounts of existing
intra-urban vacant land and the general loss of open space and natural corridors. In
the cases of maximum environmental protection (EEP) and the enforcement of an
urban growth boundary (UB), the decrease in the number of individual urban pat-
ches is signicantly lower due to the spatially regulated and lower total amount of
growth. Both alternatives maintain similar, comparatively high degrees of spatial
landscape homogeneity as indicated by the contagion metric. An interesting dier-
ence between the EEP and UB alternatives is summarized in the change in urbanboundary length that reects the complexity of the urban/rural interface. The EEP
case shows an increase in total boundary length due to the need to avoid ecologically
sensitive areas and retain natural corridors, open spaces and specic habitats. The
UB alternative on the other hand, as would be expected, represents the most com-
pact growth pattern. Finally, the MEP case shows intermediate values for all metrics
with distinct dierences with the EEP case (extreme environmental protection). This
alternative compromises between environmental considerations and the pressures for
-
M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399 387further urban development, as reected in its intermediate position on all four
metrics. These examples illustrate the value of metrics in providing additional
information for the interpretation, analysis and presentation of model results.However, further research is needed in order to understand more systematically the
role that particular metrics and combinations of metrics can play in this complex
task.
5.4. Representation of spatial heterogeneity in urban areas
Urban spatial form, especially at the local scale, poses major challenges for urban
modeling. Its correct representation, let alone prediction, are very dicult yet nec-
essary for understanding and managing urban function (Alberti, 1999; Geoghegan
et al., 1997; Irwin & Geoghegan, 2001). Urban form is the focus of urban mor-
phology, described as . . . a specic branch of urban geography (. . . with) its own,largely descriptive, language of discourse. It attempts to nd more precise mathe-matical descriptions of cities or parts of cities. (Webster, 1995). There is potential
for new ways of representing urban form and structure through a combined appli-
cation of remote sensing and spatial metrics. This could lead to much improved
modeling of the spatial heterogeneity of urban form and land use. The structures and
patterns identied with spatial metrics may constitute critical independent measures
of the urban socioeconomic landscape and can be used for an improved represen-
tation of a variety of urban spatial characteristics (Geoghegan et al., 1997; Parker
et al., 2001). Beyond socioeconomic functions, spatial metrics can also help highlightthe relationships between urban spatial form (including its three-dimensional
building structure: Adolphe, 2001), and various dimensions of urban environmental
quality and performance (Alberti, 1999).
More specically, it has been shown that fairly reliable relationships exist between
the spatial conguration of build up areas, as mapped with the help of remote
sensing and spatial metrics, and land use and socioeconomic characteristics (Barr &
Barnsley, 1997; Herold et al., 2002; Liu, 2003). For example, the metric information
in Fig. 2 shows the spatial ngerprints of dierent types of urban land use and theirrepresentation in dierent metrics. To further explore these dierences, the corre-
sponding intra-urban patterns of the Santa Barbara South Coast region are shown in
Fig. 5. The land use characteristics reect the three urban cores and a nearly con-
centric pattern of decreasing residential density away from these. The contagion
metric follows the concentric pattern with heterogeneous urban environments near
the central urban (low contagion) and a gradient of increasing contagion towards the
peripheral rural areas. Contagion reects both the level of human impact or
urbanization and the environmental and ecological signicance of these areas. Thevegetation fragmentation metrics yield high values for residential areas, in particular
for areas surrounding the central urban cores. The cores themselves are character-
ized by lower values since the vegetation is conned to a few small compact patches
(e.g. parks). The fragmentation of vegetation decreases near the rural/urban inter-
face, reecting the more natural character and higher ecological value of these
areas. This example emphasizes the potential of spatial metrics to highlight the
-
388 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399relationships between urban spatial form and various dimensions of urbanization
and environmental quality (Alberti, 1999).
In Fig. 6, a comparison of the spatial distribution of patch density and nearest
neighbor distance standard deviation with the distribution of population densityreects their similar pattern. Higher population density corresponds to areas of
higher patch density. The relationship is intuitive: if you have more houses per unit
area you expect to have more people living there. The similarity in spatial pattern
between the nearest neighbor distance and the population density is not quite as
obvious but still clear. High-density residential areas are characterized by more
regular building patterns, hence lower nearest neighbor standard deviation measures
(see also Fig. 2). These examples show the potential of representing specic socio-
economic characteristics in urban areas with the metrics. The work of Liu (2003) has
Fig. 5. Spatial urban characteristics of land use and two spatial metrics in the Santa Barbara South Coast
urban area derived from IKONOS data. The land use distribution was derived from spatial metric/texture
based classication. The metrics describe the spatial heterogeneity for each land use region (see Herold,
Liu & Clarke, 2003). The land use map highlights the three urban core areas in the region of Santa
Barbara, Goleta, and Carpinteria.
-
M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399 389indicated a direct relationship between IKONOS derived texture measures and
spatial metrics on the one hand, and census population data on the other. The
quality of the correlation, however, was not sucient to use spatial metrics as a
direct predictor of urban population densities. A very close relationship was not
expected since urban spatial patterns are not uniquely associated with land uses (forexample, commercial buildings are hard to distinguish from residences in the patch
density metric though they do not contribute to the urban population count).
Generally the metrics reect combinations of dierent spatial characteristics. From
an urban modeling perspective, it is more important to think about urban land cover
pattern (and consequently related spatial metrics) as the cumulative outcome of
urban development processes. An evolving urban environment will result in distinct
spatial congurations reecting socio-economic characteristics as well as a variety of
other factors inuencing growth (e.g. topography, road networks, planning eorts).
Fig. 6. Spatial urban characteristics of population density from CENSUS data (people per mile2) and two
spatial metrics in the Santa Barbara South Coast urban area derived from IKONOS data. The spatial
distributions can only be compared qualitatively due to the dierent spatial domains they are based on
(a case of the modiable area unit problem).
-
390 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399In this context, spatial metrics can be used to explore alternative representations of
the urban environment in urban models (Parker et al., 2001). While many urban
models rst categorize urban space into land use classes in order to derive specicspatial characteristics of interest, spatial metrics can provide a more continuous
representation of land use and socioeconomic and demographic characteristics based
on actual, detailed land cover structure.
One of the central research questions certainly concerns the selection of appro-
priate metrics. The metrics used so far are directly adopted from landscape ecology.
Future research should explore the potential roles of individual metrics in urban
analysis and the development of new metrics specically tailored to urban space.
This should lead to a special set of urban metrics capturing important urban char-acteristics. These are likely to contribute towards much improved and detailed
representations of urban form, function and functionality. Urban metrics should be
transferable and comparable among dierent urban areas. The dynamic range and
statistical characteristics of the metric values should be considered in adjusting for
possible data skewness in the further analysis (e.g. urban land use classication based
on the metrics). Clearly, the development of urban metrics should focus on
describing the spatial characteristics of the built environment and the patterns
formed by the buildings in particular. These are the obvious components of urbandevelopment and urban form. It is important however to also consider the vegetation
and its spatial characteristics, as previous studies have shown. Vegetation can
present an inverse pattern to building heterogeneity if no other land cover classes are
present (such as transportation areas, soil surfaces, water etc.). This is usually not the
case. A separability study of urban land use categories shows that vegetation-based
metrics contribute more information than building-based metrics (Herold, Liu &
Clarke, 2003). One reason is the unique spectral characteristic of vegetation that
usually result in higher mapping accuracy than for built-up land cover types (Herold,Gardner & Roberts, 2003; Sadler, Barnsley, & Barr, 1991). A second reason relates
to the distinct spatial characteristics of vegetation that reveal dierent information
than building patterns. For example, Fig. 2 shows a clear distinction between urban
and rural land uses based on the fragmentation of the vegetated areas. Vegetation
reects important urban and socio-economic characteristics almost as much as the
building patterns do because vegetation patches in urban areas are usually there as a
result of human design, (e.g. gardens, front yards, parks, open spaces, golf courses,
recreational areas or protected urban habitats). Of course, urban vegetation patternswill play a critical role if the metrics are used primarily for environmental and
ecological purposes (Alberti, 1999).
In summary, remote sensing and spatial metrics combined provide an exiting new
source of information and an innovative way to study and represent spatial urban
characteristics in considerable detail. Central to this development are the high spatial
resolution satellite systems such as IKONOS that provide data at a new spatial scale
that is of particular relevance to the study of urban form and morphology. Nearly all
previous work on urban morphology has focused on either the ner architecturaland design scales of 3-dimensional, internal and external building structures
(Steadman et al., 2000), or on the much coarser scales served by spatially aggregated
-
census data or remote sensing data in coarser spatial resolution (Foresman et al.,
1997; Mesev et al., 1995).
5.5. Analysis of spatio-temporal urban growth pattern
One major advantage of remote sensing data is their availability and consistency
in terms of historic time series. These datasets used in combination with spatialmetrics can provide a unique source of information on how various spatial char-
acteristics of cities change over time. This allows important insight into urban spatial
structure changes and the evolving urban growth dynamics. An example of the
analysis of urban change in the Santa Barbara, CA region is shown in Fig. 7. The
changes in urban structure were mapped from historical air photos. The values of six
dierent metrics are calculated for each point in the time series, yielding corre-
sponding spatial metric growth signatures (Herold, Goldstein & Clarke, 2003).
The growth of Santa Barbara develops outward from the original downtown core.While the largest growth rates occur in the 1960s and 1970, the rapid growth phase
started in the 1940s and 1950s with the appearance of small individual developments
around the core area. These caused a peak in urban patch density, an increase in the
number of urban patches, and a decreasing proportion of the total area being
Fig. 7. Spatial metrics describing the spatial and temporal growth dynamics mapped from multi-temporal
M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399 391air photos in the Santa Barbara, CA region 19291997 (Note: %LAND percent of landscape (built up),PSSD patch size standard deviation, CONTAG contagion index, PDpatch density, ED edgedensity, AWMPFD area weighted mean patch fractal dimension).
-
covered by the largest urban patch (the downtown core area). Through 1967 more
individual urban development patches are formed, causing a peak in the number of
individual urban patches and a signicant growth in the total urbanized area (urbansprawl). In the following years the decreasing patch density, the lower proportion of
urban area in the largest urban patches, and the smaller mean nearest neighbour
distance all indicate a much larger area aected by urbanization than in previous
years and the beginning of spatial coalescence of the individual development units.
By 1976 many individual urban patches have grown together, forming larger
urbanized areas with higher fragmentation, as shown by the fractal dimension. This
trend continues to date with decreasing fragmentation and fairly low mean nearest-
neighbour distance, indicating the loss of open space between the urbanized patches.The continuous growth in total area occurs through new development in sur-
rounding rural areas as well as through the expansion of the existing urban area, as
shown by the fairly stable number of both individual patches and the percentage
of urban land in the urban core area.
The example in Fig. 7 analyses urban growth patterns at a regional scale, con-
sidering both urban and rural land. With high spatial resolution remote sensing data
392 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399urban dynamics can also been studied at the intra-urban scale. The example in Fig. 8
shows the evolution of six dierent spatial metrics indicating the change in urbanstructure over a 10-year period. The metrics represent the changing spatial hetero-
geneity of the actual built-up areas as mapped from historical air photos. The La
Cumbre neighborhood, only marginally developed in 1978, experiences new resi-
dential development in all parts of the area. This process is marked by a decrease in
individual built-up patch density, hence a higher level of spatial aggregation of the
built up areas with higher variance in patch size. The complexity of the landscape
increases signicantly, as shown in the decreased contagion and the higher edge
density metrics. The evolution of the fractal dimension metric indicates the larger
Fig. 8. Local scale changes in spatial urban structure mapped from multi-temporal air photos two areas of
the Santa Barbara, CA urban region (Note: %LAND percent of landscape (built up), PSSDpatch sizestandard deviation, CONTAG contagion index, PD patch density, ED edge density, AW-MPFD area weighted mean patch fractal dimension).
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vegetated areas within the urban fabric and the dominance of the built-up class,
M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399 393including the spatial fusion of the built-up areas. Going one step further, one mightventure the educated guess (correct in this case) that average household incomes are
lower in Isla Vista that in the La Cumbre neighborhood, thus linking urban form
and socioeconomic characteristics.
These two case studies illustrate the contribution that remote sensing and spatial
metrics can make to the detailed analysis of urban growth and land use change
patterns. These examples show how dierent patterns of growth are observable at
dierent scales. Individual metrics help track specic spatial and temporal dynamics,
for example, the impact of urban sprawl on landscape structure. Changes in themetrics over time could be read as urban development signatures representing spe-
cic processes of urban growth and land use change, and the impacts of these
processes on large-scale and small-scale urban spatial structure. Although the
examples here represent descriptive analyses of urban growth patterns, this method
could most likely go beyond this descriptive use. Future research needs to explore
how dierent spatial metrics evolve in relation to a variety of spatial and temporal
change patterns and identify the spatial metrics signatures of particular kinds of
processes at dierent geographic scales. More detailed analysis of spatio-temporalgrowth dynamics should reveal both recurring regularities and distinct dierences in
dynamic growth patterns among dierent urban regions. The dierences in spatial
growth patterns should reect local and regional growth characteristics that may be
linked to specic processes and factors of urban development. Associating the
measured spatio-temporal growth patterns with underlying socioeconomic and other
processes will link the empirical metrics observations to urban and regional theory
and modeling.
6. Conclusions
The framework outlined in this paper represents a somewhat dierent philo-sophical approach to the study of urban spatial structure and dynamics than the
ones usually followed. Indeed, most dynamic urban studies adopt a deductive per-
spective, deriving urban structures as the spatial outcomes of pre-specied processes
of urban change (from process to structure). The approach based on a combination
of remote sensing and spatial metrics reverses the procedure by measuring actual
spatial structures in great spatial and temporal detail and linking their changes overspatial complexity of the built up areas as a function of their growth and increasing
spatial aggregation. Over the same period, the Isla Vista neighborhood also shows
signicant change in urban structure caused by further residential inll development.Here the residential land use is signicantly denser than in the La Cumbre neigh-
borhood. The growth patterns show similar trends in the rst three metrics for both
areas. However, the contagion, edge density and fractal dimension metrics indicate
signicant dierences in the impact of continued urban development on the spatial
structure of the two neighborhoods. In Isla Vista, the complexity of the landscape
and the fragmentation of built-up patches decrease due to the disappearance of
-
394 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369399time to specic hypotheses about the processes at work (from structure to process).
Certainly, the patterns obtained from remote sensing data usually represent the
complex aggregate outcomes of many dierent individual processes, making it verydicult to disentangle the eects of the dierent variables and trends of interest. It
seems that both the deductive and inductive approach could benet by being used in
combination, with the deductive perspective helping to narrow down the possibilities
suggested by the detailed analysis of changing urban form.
At a more technical level, the study of urban growth and land use change at all
geographic scales requires detailed and accurate datasets and appropriate methods
for their analysis, modeling and interpretation. The availability of remote sensing
data suitable for urban analysis has signicantly increased in the past few years. Suchdata can provide unique views of urban change dynamics in terms of spatial and
temporal resolution based on highly detailed, consistent mapping products over
large areas and long time periods. This can now be done at all relevant geographic
scales, provided that the appropriate sensors are selected wisely based on their
spatial and spectral characteristics. More generally, the recent developments in re-
mote sensing and in the digital analysis of thematic data layers with spatial metrics,
as well as the increased opportunities for applying urban modeling techniques in
planning and management, invite a systematic evaluation of the potential of com-bining the strengths of these techniques.
We believe that spatial metrics denitely deserve a place in the urban dynamics
research agenda. They can be used for the detailed mapping of urban land use
change at dierent geographic scales and can help infer a number of socioeconomic
characteristics from remote sensing data. Spatial metrics provide sophisticated de-
scriptors of urban spatial heterogeneity based on the distribution of built-up struc-
tures and open areas. Individual metrics reect specic variables of urban land use,
function, and change, and can form the basis for alternative representations of thesefactors in urban models. The analysis of temporal change in urban spatial structure
based on remote sensing and spatial metrics also encourages a new perspective on
these issues. Temporal change signatures that can be related to specic dynamic
processes should be identiable in urban spatial structure. These dierent improved
levels of description and analysis contribute to a better understanding and repre-
sentation of spatial urban structure and change. Thus, quantitative information
derived from spatial metrics can assist all phases of modeling for a wide variety of
urban models. Indeed, spatial metrics can support model parameterization, cali-bration and validation, as well as the analysis, interpretation and presentation of the
model results.
In conclusion, the methodological framework consisting of the combined appli-
cation of remote sensing, spatial metrics and urban modeling promises to support
the analysis of urban growth and land use change in a variety of dierent ways.
However, the research is still at an early stage and relies heavily on metrics and
assumptions originating in landscape ecology. The derivation of a set of urban
metrics tailored to the needs of urban analysis at dierent scales, the study of spatialmetrics signatures corresponding to specic urban processes, as well as the further
improvement of remote sensing mapping products, are the main research issues
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Acknowledgements
This work was conducted with support from the National Science Foundationunder UCSBs Urban Research Initiatives project UCIME (Award NSF-9817761).
We would like to acknowledge Jeannette Candau, Noah Goldstein, Melissa Kelly,
and Ryan Aubry at the University of California Santa Barbara for their support of
this research.
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