The role of spatial metrics in the analysis and modeling of urban land use change

Computers, Environment and Urban Systems 29 (2005) 369 399 www.elsevier.com/locate/compenvurbsys The role of spatial metrics in the analysis and modeling of urban land use change Martin 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 fields, 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 alternative conceptions of urban spatial structure and change. The theoretical argument is then illustrated with actual examples from the urban area of Santa Barbara, California. Some questions for future research are finally put forward to help strengthen the potential of the proposed framework, especially regarding the further exploration of urban dynamics at different geographic scales. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Spatial metrics; Urban growth; IKONOS; Land use change; Urban modeling; Remote sensing 1. Introduction Dynamic urban change processes, especially the tremendous worldwide expansion of urban population and urbanized area, affect natural and human systems at all geographic scales (Brockheroff, 2000; United Nations Population Division, 2000). * Corresponding author. Tel.: +1-805-893-4196; fax: +1-805-893-3703. E-mail address: martin@geog.ucsb.edu (M. Herold). 0198-9715/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.compenvurbsys.2003.12.001

370 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369 399 Worsening conditions of crowding, housing shortages, and insufficient 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 effective management and planning of urban regions (O Meara, 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 effects of urban change processes. Despite the recent proliferation of new sources of data and tools for data processing and analysis, these have not directly led to an improved understanding of urban phenomena. This paper explores both conceptually and with practical examples how using remote sensing technology in combination with spatial metrics can improve the understanding 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 (relationship 1 in Fig. 1), we argue that the combined use of remote sensing and spatial metrics 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 collaborative 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 validation, 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.

M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369 399 371 tions 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 corresponds to the use of spatial metrics in urban modeling. This path has been proposed in a few studies that use spatial metrics to refine 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 sensing methods 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 significantly 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 sensors (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 different spatio-temporal scales. 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 commonly 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 specific urban applications. In Sections 2 4 we review current issues in urban remote sensing, spatial metrics and urban modeling respectively, discussing the relatively new area of spatial metrics in 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 2 3). In Section 5 we illustrate these points with some concrete examples. Section 5 highlights five 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, specific spatial model applications, and the analysis of spatio-temporal urban dynamics at different 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 approach s contribution to urban analysis and modeling.

372 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369 399 2. Remote sensing of urban areas For decades the visual interpretation of aerial photography of urban areas has been based on the hierarchical relationships of basic image elements. The spatial arrangement and configuration 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 significant 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; Imhoff, Lawrence, Stutzer, & Elvidge, 1997). However, much of the expert knowledge 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 different spatial scales, e.g. with different spatial resolutions, varying coverage or extent of mapping area and varying definitions of thematic mapping objects. Global and 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 difficulty these efforts 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 definition of urban extent still remains problematic and individual studies must determine their own rules for differentiating 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 considered the beginning of a new era of civilian space borne remote sensing with particular 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

M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369 399 373 including 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 classification process (Baraldi & Parmiggiani, 1990; Forster, 1993; Gong & Howarth, 1990; Gong et al., 1992). Others have applied spatial postclassification 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 system for detailed contextual urban mapping on an illustrative dataset. Many researchers 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 classification should be augmented by more inter-disciplinary and 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, especially 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 Ôpixelizing the social environment, i.e., focusing too much on the physical aspects of urban areas at the expense of social issues. Indeed, the socioeconomic variables of interest are usually not directly visible from measurements taken from remote sensing observations. Secondly, the social sciences outside of geography and planning are generally more concerned with why things happen rather 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 of analysis and between different 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 considering 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 great variety of geographic scales. The information derived from remote sensing can help describe and model the urban environment, leading to an improved understanding

374 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369 399 that benefits 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 different 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; O Neill et al., 1988). Landscape metrics were developed in the late 1980s and incorporated measures from both information theory and fractal geometry (Mandelbrot, 1983; Shannon & Weaver, 1964) based on a categorical, patch-based representation of a landscape. Patches are defined as homogenous regions for a specific 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 classification such as an Anderson level (Anderson, Hardy, Roach, & Witmer, 1976). The landscape perspective usually assumes abrupt transitions between individual patches that result in distinct polygons, as opposed to the continuous field perspective. Patches are therefore maximally externally and minimally 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 reflect 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 fields of research outside landscape ecology and across different 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 defined as measurements derived from the digital analysis of thematic-categorical maps exhibiting spatial heterogeneity at a specific scale and resolution. This definition emphasizes the quantitative and aggregate nature of the metrics, since they provide global summary descriptors of individual measured or mapped features of the landscape (patches, patch classes, or the whole map). Furthermore, the metrics always represent spatial heterogeneity at a specific spatial scale, determined by the spatial resolution, the extent of spatial domain, and the thematic definition 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-

M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369 399 375 gen, Stearns, & Yang, 1991; Wu, Jelinski, Luck, & Tueller, 2000). Based on the work of O Neill et al. (1988), sets of different metrics have been developed, modified and tested (Hargis et al., 1998; McGarigal et al., 2002; Ritters et al., 1995). Many of these quantitative 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 specific theoretical land use patterns. They conclude that urban landscape composition and pattern, as quantified with spatial metrics, are critical independent measures of the economic landscape function and can be used for an improved representation of spatial urban characteristics and for the interpretation and evaluation of modeling results. Alberti and Waddell (2000) substantiate the importance of spatial metrics in urban modeling. They proposed specific spatial metrics to model the effects 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 uses surrounding a parcel have an influence on the price, implying that people care very much about the patterns of landscapes around them..., and recommend the use of landscape 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 representing urban 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). In summary, the application of spatial metrics for both mapping and modeling the urban environment is just beginning, but has already focused on a variety of different 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,

376 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369 399 high-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 and resolution directly affect 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 research (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 artificially compact or they may get merged together. The spatial measures are then dominated more by the rectangular shape of the pixels than by the actual object patterns of interest (Krummel, Gardner, Sugihara, O Neill, & Coleman, 1987; Milne, 1991). Furthermore, specific 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 definition of the thematic mapping classes and the classification accuracy. Thematic accuracy obviously directly influences 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 classification accuracy of 85% is commonly considered sufficient for a remote sensing data product (Anderson et al., 1976). However, the definition of the classes should represent all thematic objects and structures in the landscape that are of interest in a specific investigation. A generalized class definition 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 classification is too detailed, relevant structures may get lost in a highly

M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369 399 377 heterogeneous pattern. Furthermore, the classification accuracy of the remote sensing data usually decreases as more classes are derived. Accordingly, the thematic definition of the classes should consider both the spectral mapping capabilities of the sensor 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 refinement of this classification, e.g. the discrimination of different 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 different approaches in representing spatial concepts have resulted in the development of various spatial metrics or metric categories as descriptive statistical 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 (O Neill 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 relatively greater 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 yields a higher fractal dimension. Before any kind of application, these metrics have to be interpreted, analyzed and evaluated as to their ability to capture the thematic information of interest (Gustafson, 1998). The few studies published so far on spatial metrics analysis in urban areas have applied and suggested different 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 different metrics. Their results show the role each of these plays in representing the composition, spatial configuration and spatial neighborhood 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 significance of specific metrics varies with the objective of the

378 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369 399 study and the characteristics of the urban landscape under investigation (Parker et al., 2001). 3.2.4. Definition of the spatial domain A basic problem in the application of spatial metrics is the definition 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 thematically 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 define the spatial domain of the study as it directly influences 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 into relatively homogenous units that will serve as the spatial domains of the metric analysis. The spatial discrimination and thematic definition of the spatial units must consider the characteristics of the landscape, the objectives of the study, and the use of the metrics in further analysis that may require a specific spatial subdivision of the urban area. There are many different 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 regular 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 difficult to determine a priori the optimum kernel size; and, a rectangular window represents an artificial 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 defined 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 individual parcels associated with key human agents such as landowners participating in micro-economic processes (Irwin & Geoghegan, 2001; Waddell, 1998), and uniform analysis zones defined by the multiple intersections of polygons on different data layers representing natural and socioeconomic variables of interest (Klosterman,

M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369 399 379 1999). The definition of regions based on remote sensing uses automated, semiautomated or supervised approaches. Automated techniques are usually based on pattern recognition or image segmentation that result in areas with similar spectral and textural pattern. A traditional approach in region-based remote sensing analysis is the concept of photomorphic region developed for aerial photographic interpretation (Peplies, 1974). Photomorphic regions are defined 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, modified by criteria of minimum size and spatial contiguity based on GIS data. In general, all these approaches are appropriate for spatial metrics analysis in urban environments, but region-based methods are likely to provide a better segmentation of urban space for most 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 reflected in the metrics cannot usually be related to specific locations within the urban area without visual spatial interpretation or some more detailed analysis at the patch level. Furthermore, temporal variations in the spatial metrics may result from the aggregate or cumulative effects of different 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 appropriate scale. Even so, it may be impossible to directly relate the metric changes to specific urban change processes. For studies of urban land cover and land use structure change, a definition of more or less homogenous urban land use units will usually have to be developed before the analysis can begin. These have to be defined and spatially differentiated 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 profoundly affected 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 collaborative planning and consensus-building efforts in urban development have also

380 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369 399 been strengthened by the new data and tools at the local level (Klosterman, 1999; Sui, 1998; Wegener, 1994). Several problems have been identified in building, calibrating and applying models 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 to socioeconomic 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 availability for different areas, especially outside the developed countries. Accordingly, a number 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 socioeconomic patterns (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 insufficiently 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 spatial and 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) 369 399 381 5. Improving urban modeling with remote sensing and spatial metrics: some case studies Thus far we presented several arguments for combining remote sensing and spatial metrics to support and improve urban modeling and ultimately, urban management and planning. In this section we further extend and refine 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 interpretation, 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 first three of these five points are known and fairly well understood in current urban modeling. They are included here for completeness as we discuss the new 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 specific 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 course consider the ever-improving capabilities of sensor systems to provide more detailed and accurate remote sensing data products. In particular, the land cover heterogeneity 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 provided through 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 classification (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 classification process (Baatz et al., 2001; Herold, Liu & Clarke, 2003). The spatial metrics for each land use region (derived from 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

382 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369 399 size of structures (small versus large buildings), their shape (compact versus complex and fragmented), and the spatial configuration (regular versus irregular). Size is measured by the mean patch size ; the variation in size by the patch size standard deviation metric. Shape can be quantified 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 buildings gets more irregular. Similar measures can be applied to explore the heterogeneity of the vegetation class. Characteristic examples of metrics calculations for regions that encompass distinct 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 landscape. High contagion is found for forest, wetlands, agriculture, and rangelands. These natural or non-urban environments are clearly identified 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- Fig. 2. Density graphs of four spatial metrics for nine types of land uses found within urban areas from IKONOS data. The metrics represent different 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) 369 399 383 tation areas reflects high fragmentation for all residential land uses, that is, residential development results in characteristic disperse vegetation structures. Although having less vegetation coverage overall, urban land uses like commercial or public institutions show more compact vegetated areas, e.g. urban parks or ornamental landscaping. The high values of the patch density metric reflect 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 reflect the characteristic human fingerprint of a regular spatial configuration. High-density single unit residential areas have the most distinct spatially ordered building pattern. Commercial/industrial, multi-unit residential, and medium density single unit residential also indicate a high degree of regularity. The building configurations in low-density residential area are significantly 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 of landscape 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 different 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 practical aspects of urban modeling. In dynamic models historical datasets of urban development 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 fit in terms of spatial structure and highlight specific problems, uncertainties or limitations of the model results (Candau, 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 different metrics have been found useful in describing different characteristics of model performance and results. An example of the use of spatial metrics in the evaluation of a dynamic model s 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 km 2 to more

384 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369 399 Fig. 3. Five spatial metrics are used to evaluate SLEUTH s performance in reproducing urban development 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 reflected in the metrics. than 50 km 2 by 2000 (Fig. 3(a)). Interesting features in the diagrams are the significant jumps in the metrics graphs for the calibration years, reflecting the discrepancies 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. The contagion and fractal dimension metrics also indicate good model performance in terms of the general spatial form of urban development. Most substantial disagreements are recorded for the calibration year 1967. That period is associated with significant urban sprawl first appearing in the area and representing a new form of growth that causes some problems in the model s performance. That is, the model produces less accurate results as the urbanization pattern shows significant changes relative to the historical calibration time frame. The metrics shown in Fig. 3(b) together provide an evaluation of a different aspect of the model s performance. The metric describing the number of individual urban patches shows quite significant 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 diffusion) 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 urban area in the largest urban patch only marginally reflects the major jumps in the number of individual patches. This observation leads to the conclusion that the discrepancies are due pre-dominantly to the insufficient generation of new development 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) 369 399 385 This detailed exploration and discussion of problems in the model s performance helps suggest possible improvements. In the case presented here different reasons were identified for the observed disagreements between metric measurements and model results. These relate to the general nature of the modeling approaches using cellular automata, the SLEUTH model s calibration method, and the specific 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 effective 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 reflect the multiple facets of the SLEUTH model s performance. These results suggest that it would be useful to explore and evaluate systematically the use of different types of metrics in order to develop more standardized, transparent and efficient model calibration and validation 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 specific 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 results are to be presented to the public. Further refinement 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 different model scenarios. They can provide a better understanding of how different policies or weightings of growth factors might impact different parts of the urban or natural areas. Metrics can also be used to define, rather than just interpret growth scenarios, as they can help represent locally detailed alternative spatial configurations. 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 different possible urban growth trajectories is one of the most important purposes of modeling 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 five different sets of assumptions corresponding to alternative growth trajectories over the next 30 years (Candau & Goldstein, 2002). The first 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) 369 399 Fig. 4. Spatial metric comparison of five different growth scenarios for the Santa Barbara South Coast region forecasted for the year 2030 using the SLEUTH urban growth model. assumptions as MSQ but includes an expanded road network. The third alternative (EEP) reflects maximum protection of environmentally sensitive lands, while the fourth (MEP) reflects a lesser degree of environmental protection. Finally, the fifth alternative (UB) uses an urban boundary to define and constrain the maximum extent of urban growth. The graphs in Fig. 4 compare the five growth alternatives using four different spatial metrics. The changes in total urban area, length of urban boundary, number of 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 significantly decreases for MSQ and ER as a result of the large expansion in urbanized area within the physically constrained South Coast region, a narrow plain lying between the ocean and a steep coastal range. These patterns reflect 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 patches is significantly 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 difference between the EEP and UB alternatives is summarized in the change in urban boundary length that reflects 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 specific habitats. The UB alternative on the other hand, as would be expected, represents the most compact growth pattern. Finally, the MEP case shows intermediate values for all metrics with distinct differences 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) 369 399 387 further urban development, as reflected 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 difficult yet necessary for understanding and managing urban function (Alberti, 1999; Geoghegan et al., 1997; Irwin & Geoghegan, 2001). Urban form is the focus of urban morphology, described as... a specific branch of urban geography (... with) its own, largely descriptive, language of discourse. It attempts to find more precise mathematical descriptions of cities or parts of cities. (Webster, 1995). There is potential for new ways of representing urban form and structure through a combined application 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 identified with spatial metrics may constitute critical independent measures of the urban socioeconomic landscape and can be used for an improved representation of a variety of urban spatial characteristics (Geoghegan et al., 1997; Parker et al., 2001). Beyond socioeconomic functions, spatial metrics can also help highlight the 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 specifically, it has been shown that fairly reliable relationships exist between the spatial configuration 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 fingerprints of different types of urban land use and their representation in different metrics. To further explore these differences, the corresponding intra-urban patterns of the Santa Barbara South Coast region are shown in Fig. 5. The land use characteristics reflect the three urban cores and a nearly concentric 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 reflects both the level of human impact or urbanization and the environmental and ecological significance of these areas. The vegetation fragmentation metrics yield high values for residential areas, in particular for areas surrounding the central urban cores. The cores themselves are characterized by lower values since the vegetation is confined to a few small compact patches (e.g. parks). The fragmentation of vegetation decreases near the rural/urban interface, reflecting 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) 369 399 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 classification. 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. relationships 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 density reflects 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 specific socioeconomic characteristics in urban areas with the metrics. The work of Liu (2003) has

M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369 399 389 Fig. 6. Spatial urban characteristics of population density from CENSUS data (people per mile 2 ) 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 different spatial domains they are based on (a case of the modifiable area unit problem). indicated 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 sufficient 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 (for example, 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 reflect combinations of different 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 configurations reflecting socio-economic characteristics as well as a variety of other factors influencing growth (e.g. topography, road networks, planning efforts).

390 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369 399 In 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 first categorize urban space into land use classes in order to derive specific spatial 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 appropriate 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 specifically tailored to urban space. This should lead to a special set of urban metrics capturing important urban characteristics. 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 different 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 classification 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 urban development 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 different 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 reflects 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 patterns will 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 finer architectural and design scales of 3-dimensional, internal and external building structures (Steadman et al., 2000), or on the much coarser scales served by spatially aggregated

M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369 399 391 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 spatial metrics can provide a unique source of information on how various spatial characteristics 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 different metrics are calculated for each point in the time series, yielding corresponding 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 air photos in the Santa Barbara, CA region 1929 1997 (Note: %LAND ¼ percent of landscape (built up), PSSD ¼ patch size standard deviation, CONTAG ¼ contagion index, PD ¼ patch density, ED ¼ edge density, AWMPFD ¼ area weighted mean patch fractal dimension).

392 M. Herold et al. / Comput., Environ. and Urban Systems 29 (2005) 369 399 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 significant growth in the total urbanized area (urban sprawl). 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 affected 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 nearestneighbour distance, indicating the loss of open space between the urbanized patches. The continuous growth in total area occurs through new development in surrounding 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, considering both urban and rural land. With high spatial resolution remote sensing data urban dynamics can also been studied at the intra-urban scale. The example in Fig. 8 shows the evolution of six different spatial metrics indicating the change in urban structure over a 10-year period. The metrics represent the changing spatial heterogeneity of the actual built-up areas as mapped from historical air photos. The La Cumbre neighborhood, only marginally developed in 1978, experiences new residential 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 significantly, 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 ¼ percent of landscape (built up), PSSD ¼ patch size standard deviation, CONTAG ¼ contagion index, PD ¼ patch density, ED ¼ edge density, AW- MPFD ¼ area weighted mean patch fractal dimension).