Measuring urban sprawl, coalescence, and dispersal

Environment and Planning B: Planning and Design 2011, volume 38, pages 1085 ^ 1104

doi:10.1068/b36090

Measuring urban sprawl, coalescence, and dispersal: a case study of Pordenone, Italy Federico Martellozzoô

Department of Geography, McGill University, 805 Sherbrooke Street West, Montreal, Quebec H3A 2K6, Canada; e-mail: [email protected]

Keith C Clarke

Department of Geography, 1832 Ellison Hall, University of California Santa Barbara, Santa Barbara, CA 93106-4060, USA; e-mail: [email protected] Received 25 July 2009; in revised form 23 April 2010

Abstract. A critical challenge of global change is managing the uncontrolled spread of cities into their surrounding rural and other land. The phenomenon of urban `sprawl' is well known, but it remains controversial because there are no universal definitions about its etiology, nor of the causes and variables related to it. The goal of this study is to depict the temporal trend of sprawl, so as to identify a `sprawl signature' and its evolution for the Italian Province of Pordenone focusing exclusively on spatial dispersion features. Data were compiled from multitemporal remote sensing and used to delimit urban expansion over time. We aim to describe the spatiotemporal patterns associated with urban sprawl using the perspective of the cyclical urban growth theory and focusing on measures that can detect the degree of spatial dispersion during time related to sprawl both in past and projected urban forms. Exactly how the spatiotemporal patterns of urban growth are identified is crucial for urban planners, as knowledge of them allows more efficient calibration of policies to control land-use change in order to satisfy specific needs of the population and prevent the risks and costs related to sprawl.

Introduction Land-use change and urban sprawl are very much causes of many of the major humaninduced environmental challenges affecting modern society, with most scholarship agreeing that the changes are predominantly harmful to public services (Carruthers and Ulfarsson, 2003), public health (Ewing et al, 2003), and climate (Ewing et al, 2007). Yet exactly what constitutes urban sprawl is highly multidimensional and difficult to quantify (Ewing et al, 2002; Frenkel and Ashkenazi, 2008; Torrens, 2008), especially when all of the causes and impacts are incorporated into the measures (Burchfield et al, 2006; Ewing, 1994). Hasse and Lathrop (2003, page 160) noted that ``The literature on sprawl, with a tinge of irony, is broadly dispersed and multifaceted. A variety of definitions for sprawl have been put forth that describe sprawl.'' There has been considerable debate about the costs and consequences of sprawl, and even whether the net effect is positive or negative (Burchell et al, 1998; Ewing, 1997; Glaeser and Kahn, 2003; Gordon and Wong, 1985; Hasse and Lathrop, 2003). Clearly sprawl is a component of urban expansion and a defining element is low settlement densities (Brueckner, 2002; Peiser, 1989). From the majority of points of view the characteristics of modern urbanization are considered unsustainable; however, new models of sustainable urban development are proposed which should help to mitigate the risks related to sprawl (Ewing, 1994). Starting in the late 1970s, new urban planning theories arose in the US with a background in urban visions and theoretical models inspired by the Èuropean' city ô Current address: Department of Geography and Earth System Science Program, Room 705, 7th Floor, Burnside Hall, McGill University, 805 Sherbrooke Street West, Montreal, Quebec H3A 2K6, Canada; e-mail: [email protected]

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F Martellozzo, K C Clarke

proposed by architect Leon Krier, and the `pattern language' theories of Christopher Alexander. The origins of these approaches lie in European city elements as solutions to North American urban problems of sprawl. Ironically, the case study we present in this research concerns an area in northeastern Italy, considered by the European Community to be one of the most explicative examples of modern urban sprawl, even though it is not a big metropolis (Krier and Thadani, 2009). The new philosophy, later called New Urbanism, grew in the early 1980s as a reaction to the negative environmental and human consequences of sprawl. The goal was to use sustainable planning and architectural principles functioning together in order to create human-scale, walkable communities. The planned growth vision of New Urbanism takes into account issues such as sustainable development, reduced traffic congestion, public transportation, and access to parks and green areas, in contrast to the continuous outward expansion and development of urban areas with their constantly increasing need for automobile transportation capacity. Instead, the role of quality of life became central. The monitoring of land-cover transitions related to urban development over time is usually to find out the amount and location of land-use change for planning purposes. Nevertheless, the ability to anticipate a trend in urban sprawl behavior for a specific region would give planners a useful tool to understand sprawl's long-term impact on a region, or even to take steps to prevent or retard it. Although various studies have been dedicated to the measurement and monitoring of urban growth, they have limitations in providing generalizations of the characteristics of urban sprawl. In this study, we choose to define urban sprawl purely cartometrically, that is by quantifying the shape, distribution, and spatial extent of built-up areas. Our approach follows Batty's concept of form as a result of function (Batty and Kim, 1992), but instead of focusing on theories of density and settlement size (Batty, 2002; 2008; Batty and Longley, 1994) or on demographic structure (Brueckner, 2002; Lowry, 1990), we focus on urban spatial form alone. Advantages of this approach are that it avoids the complexity of the sprawl definitions, works across spatial scales, and is approachable with data from maps and geographic information systems. Disadvantages are that it negates social and economic factors, and ignores the body of theory on urban density and rank-size structure. Our work is influenced by the general principles set forth by Dietzel et al (2005a; 2005b) that urban sprawl is a phenomenon highly correlated to time, in that the growth of urban areas oscillates between coalescence and diffusion processes with sprawl growth behavior concentrated in the former. Thus, a priori, we expect both sprawl and regular urban expansion to be present in space and over time. This is in contrast to the view that sprawl represents continued and sustained fragmentation (Irwin and Bockstael, 2007). The measure we chose to follow is spatial entropy, a quantity that has long been associated with the dissipative property of systems, including urban areas and systems (Batty, 1974; Batty and Longley, 1994; Herold et al, 2002; Yeh and Li, 2001). Entropy is apparently the only almost-universally shared spatial measurement concept concerning urban sprawl (Torrens, 2008). We aim to depict the evolution of the spatial patterns of sprawl over time in order to identify a `sprawl evolution signature' for the region of interest, similar to Silva's concept of urban DNA (Silva and Clarke, 2005). The goals of this study were to: (1) map the dynamics of land-use change in a known European sprawling metropolis over time; (2) quantify the spatial form using measures able to detect spatial dispersion, in order to test for evidence of the oscillation between coalescence and diffusion processes in urban growth, and so to test the hypothesis that sprawl is contained in the latter phase only; and (3) to use a land-use-change model and the same measures to test whether it is possible to use these measures prescriptively

Measuring urban sprawl, coalescence, and dispersal

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to forecast sprawl, with the intent of possibly equipping planners with a further tool to support growth management strategies. Urban sprawl as spatial dispersion To be useful, a measure of sprawl must consider it a matter of degree. For instance, scattered development and polycentric or multinucleated urban development are very similar; hence the distinction between these two different trends of growth is elusive and leads us to consider sprawl as a matter of resolution as well as scale (Batty, 2008). `Àt what number of centers polycentrism ceases and sprawl begins is not clear'' (Gordon and Wong, 1985, page 662). Sprawl can also be analyzed across all its dimensions: density, land use, and time (Ewing, 1994; Pesier, 1989). In addition, sprawl measures should permit cross-comparison between cities, and so should avoid dataspecific or reduction techniques, such as multiple regression (Frenkel and Ashkenazi, 2008). Nevertheless, we chose to focus on the entropy of spatial form and its evolution over time. The concept of entropy, based in information theory, has been used to describe the complexity of sprawl patterns through space and time (Yeh and Li, 2001). Entropy has origins in thermodynamics, but is more broadly considered to be the level of disorganization of a system and hence also the amount of energy needed to reorganize the system. Since its formalization by Shannon (1948) as information theory, it has been applied in many different fields including physics, remote sensing, computer science, cartography, mathematics, and geography. Entropy measures for the analysis of spatial distributions have been related to distances and density metrics, depending on the nature of the phenomenon (Novelli and Occelli, 1999). One of the most effective synthetic indices to describe entropy is Shannon's logarithmic function which has been applied widely in urban geography because it is considered to be a robust metric for detecting dispersion when applied with density measures (Peiser, 1989; Yeh and Li, 2001). Batty (1974) defined the concept of spatial entropy and discovered the necessity of a coherent zoning system when analyzing spatial distribution and entropy over space. Entropy is still of interest beyond specific case studies in urban growth detection. It is used in modeling and classification techniques (Li and Huang, 2002) from a more theoretical point of view. Some studies convey modification and correction of the entropy formula in order to obtain a more meaningful tool to compare dispersion and coalescence of spatial phenomena through space and time (Heikkila and Hu, 2006). Entropy has been addressed as fundamental in studies of spatial pattern; hence it is a very good means for the investigation of diffusion or dispersal. The entropy measure is most likely to be affected by the oscillatory behavior between diffusion and coalescence anticipated in the work by Dietzel et al (2005a; 2005b). The fact that entropy can be considered from both a relative and an absolute perspective, and the fact that it can be corrected for biases induced by scale, resolution, or the zoning system, also makes it a useful tool to investigate the diffusive and coalescent phases of urban growth. In phased oscillation theory, urban growth over time follows a process in which dispersed or isolated clusters form due to the influence of core areas (characterized by higher density) on regions of lower density; this is followed by a coalescence phase, with a tendency for the clusters to grow together, clump, and form single entities. In urban growth scenarios no movement of clusters is possible, a cell once urban tends to remain urban, so it is important to observe trends in the distribution of new clusters over time (Dietzel et al, 2005a). In many cases, the scatter and further growth of sprawled zones takes place over long time spans, and so we seek to assimilate both historical data and modeled future trends.

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Pordenone as a sprawling metropolis Changing dynamics are particularly relevant to describe the modern Italian urban system. Pordenone falls within an Open Specialized System; or more generally the northeastern Italian region can be characterized by dense and articulated settlement patterns (Dematteis, 1997). In Italy, as in many European countries, the concept of a Metropolitan Area is specific and ``refers more to the urban concentration of the sixties that to the current phase of selective polarization, more to the old form of compact agglomeration and suburbanization than to the new networked regional structures, no longer based on continuous settlement expansion'' (Dematteis, 1997, page 337). In 2006 the European Environment Agency (2006) portrayed the Pordenone area as one of the most explicative examples of urban sprawl in eastern and central Europe. This led us to choose the region for a study of sprawl, its development over time, and likely development in the future. We adopted a methodology that integrated satellite imagery with land-cover cartographic data [Corine Land Cover, 2000 (CLC 2000)] (http://www.eea. europa.eu/data-and-maps/data/Corine-land-cover-2000.clc2000-seamless-vector), topographic map data at a scale of 1:25 000 of the Friuli Venezia Giulia province, in situ data collection, and an orthophotoimage from 2003. The time span considered was 1985 ^ 2005, requiring the merging of data across different sensors and resolutions. This also required the homogenization of the land classification so as to permit temporal comparison and involved data fusion across different spatial and radiometric resolutions. The area of study is bounded by the trapezoid shown in figure 1, and includes the municipalities of Fontanafredda, Roveredo in Piano, San Quirino, Porcia, Pordenone, and Cordenons, all part of the Pordenone metropolitan area. Much land-use-change research uses satellite imagery classified with relatively low or even unknown levels of accuracy. We sought more accurate data, since changes from image to image should be due to actual change on the ground and not to errors of automated classification procedures. The methodology used in this research was based on a new method of classification of satellite imagery to allow more accurate analysis of urban growth from 1985 to the most recent image. The data were also used as the input to a cellular automata modeling methodology for the prediction of future urban extents, specifically the SLEUTH (http://www.ncgia.ucsb.edu/projects/gig) landuse-change model. Four summer (leaf-on) satellite images were classified to extract land use, including urban land. These images were, in chronological order, Landsat Thematic Mapper (http://www.landsat.gsfc.nasa.gov/) data from 18 October 1985 and 18 August 1992, a Landsat 7 Enhanced Thematic mapper image from 3 August 2001, and an image from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) dated 29 July 2005. All data were supplied by NASA (http:// www.nasa.gov/). Classification methodology and land-use-class schema

Operations to homogenize the imagery were performed, including georeferencing, orthorectification, and adjusting the spatial resolution to a common 15 m for all the images by resampling. The classification technique involved comparing the accuracy assessment values of different classification methods applied to each image with the goal of selecting the most accurate classification. Each automated classification procedure groups all the pixels into homogeneous classes in order to portray the coverage and the spatial distribution of different features detected by the sensor. The choice of the methodology depends on both the way of sampling pixels and the a priori analyst's knowledge of the scene object of study (Favretto, 2006). The standard supervised and unsupervised classification methods were compared in an innovative way with machine learning algorithms released with the image analyst module within Erdas Imagine


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Figure 1. [In color online.] Area of interest with the name of the municipalities of the Pordenone metropolitan area and geographic coordinates of the trapezoid that frames the area of interest. Source: false color image, ASTER 29 July 2005 (Advanced Spaceborne Thermal Emission and Reflection Radiometer database, http://asterweb.jpl.nasa.gov/).

software (http://www.erdas.com). The method looks at a pixel and determines the rules of classification not only on the base of spectral properties of pixels but also on the context, the positional relation with neighboring pixels. For an accuracy assessment, the image chosen for comparing the different classifications results was the Landsat image from 2001; this image was classified using all three methods (supervised, unsupervised, and machine learning). The classification scheme chosen used a reduction of the CLC 2000 scheme into seven relevant classes (tables 1 and 2) (Favretto and Martellozzo, 2008). The unsupervised classification was performed first; this method was very useful for exploratory analysis. Furthermore it helped us to understand the spectral differentiation within classes, even if the use of ground truth was minimal (Jensen, 1996). The output was thematic maps where the number of classes is known but their meaning needs to be interpreted. This method was applied several times before reduction into the seven CLC 2000 classes, in order to understand the land cover and to better define a significant classification scheme. The algorithm used for the unsupervised classification was ISODATA (iterative self-organizing data analysis technique). The second methodology applied was supervised classification; generally speaking this automatic procedure is more accurate than the unsupervised. In spite of this, it requires more analyst effort and a sufficient knowledge of the area of study. It requires the analyst

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Table 1. Land-cover classes as a reduction of Corine Land Cover 2000 scheme into the seven-class scheme used in this study (see table 2). Corine Land Cover 2000

Subclass description

Class

Built-up areas

Urban and residential areas Commercial and industrial sites and infrastructures Abandoned areas, mining zones, dump sites, construction Green urban areas, sport and leisure facilities

7 6 6 3

Agricultural areas

Arable Vineyards, fruit trees, and berry plantations Pastures Agroforestry areas

4 4 4 4

Forests and seminatural environments

Forests Moors and heath lands, transitional woodland ± shrub Open fields with little or no sparse vegetation

2 3 5

Humid areas

Inland marshes and peat bogs Salt marshes

2 na

Water bodies

Continental water Maritime water

1 na

Table 2. The land-cover classes identified with seven-class scheme used in this study. Class Description

1 Water

2 Forest

3 Shrubs

4 Arable

5 Bare ground

6 Periurban

7 Urban

to define training areas that allow an algorithm to analyze and group pixels on the basis of spectral similarities (Jensen, 1996). The supervised algorithm used maximum likelihood, where a statistical procedure assigns each pixel to the class that shows most spectral similarity. Ground-truth data came from field visits to the zones in question. The third classification method applied was the machine learning (ML) approach. This method was inspired by a computing philosophy that develops algorithms that are adaptive to the data. A classification is applied, and then adjusted to maximize a preestablished performance criterion (Huang and Jensen, 1997). Successive adjustments improve the overall classification accuracy. The ML algorithm learns each time it receives feedback and then modifies a set of weights in order to achieve the best results. This methodology generally gives improved results, but it is also time consuming and still requires more work to be done by analysts. The step-by-step procedure starts with preliminary information given to the algorithm that refines itself with subsequent corrections; actually ML methodologies produce a large amount of data but only the final results are useful (Huang and Jensen, 1997). In our case the ML functionalities distributed with the Image Analyst module within Erdas Imagine were used. The accuracy for each classification method was assessed taking as a reference a mosaic of an Orthoimage from 2003 and a Landsat image from 2002. Accuracy assessment defines the degree of coherence of the classified image with the ground truth. A large number of pixels are taken from the thematic image and compared with a reference map of higher authority to see which and how many pixels were classified correctly (Jensen, 1996). An error or confusion matrix is built for this comparison; the sampling strategy used to select pixels was stratified random sampling. The kappa statistic, a measure of overall accuracy, ranges from 0 to 1, where values >0.7 are considered good to optimum correlation between the classified image and the ground truth (Jensen, 1996) while values 4 0.4 identify a very low correlation.


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A comparison of the accuracy assessment from the Landsat 2001 image classified with the three different classification methods (table 3) showed that the classification most suitable for the area of interest was the ML procedure, since both the kappa index and overall accuracy show that ML classification is significantly better than the supervised and unsupervised methods. The superior accuracy of the ML method is also easy to see by visual inspection of the image (see figure 2). Following comparison of the different classification methods based on the 2001 Landsat image, the ML procedure was selected and applied to each image in the dataset as follows. First, training areas for each class were identified and from these Table 3. Accuracy assessment for each classification method applied to the Landsat image from 2001. Reference map

Classification

Producer's accuracy (%)

User's accuracy (%)

Overall classification accuracy (%)

Kappa index

Orthophoto 2003 Landsat 2002

Unsupervised ISODATA

71.43

55.56

60.00

0.5277


Supervised maximum likelihood

68.63

55.32

63.33

0.5706


machine learning

81.85

76.87

76.67

0.7246

Administrative boundaries Water Forest Shrubs Arable Bare ground Periurban Urban

(a)

(b)

(c)

(d)

Figure 2. [In color online.] Detail of the Landsat 2001 image classified with the (a) unsupervised, (b) supervised, and (c) machine-learning methods; (d) shows the same portion of the image as it appears in the orthophoto image used as reference map for the accuracy assessment.

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the ML algorithm classified the whole image, and then it was trained with multiple refinements for each class. Only when a sufficient accuracy in each class was reached did the algorithm reclassify the whole image on the basis of all the refinements. For these images the accuracy and kappa index were computed by the procedure previously described. In addition, with the Aster 2005 image used as reference data, a set of ground control points were collected with a hand-held GPS receiver in the summer of 2006. Literature suggests using as a reference map a different image or data from that from which the classification is derived, because it could introduce bias that might overestimate or underestimate the classification accuracy (Foody, 2002). As no better source for comparison was available, pixels used as training areas for the classification phase were excluded from the pixels used to build the confusion matrix and to assess accuracy (Favretto and Martellozzo, 2008) (see table 4). Table 4. Accuracy assessment report of the machine learning classification for dataset images. Reference map

Image

Classification

Overall classification accuracy (%)

Kappa index

Aster 2005

Ground control point (GPS survey)

machine learning

78.00

0.7408

Landsat 1992

Landsat 1992

machine learning

78.57

0.7500

Landsat 1985

Landsat 1985

machine learning

77.14

0.7284

Land-use-change modeling

Modeling plays a fundamental role in explaining the spatiotemporal dynamics of urban growth and land-use change (Petrov et al, 2009). Yet, although a model has been successfully applied in one particular geographical area and outcomes are found to be valid, this does not automatically mean it can be profitably used in another environment. Even so, this study aims to investigate patterns of urbanization that can be applied widely and used to fit a more general theory. Our goal was to examine the trends in spatial form metrics (including entropy) both in the past and the future, with the goal of assessing the value and consistency of the predictive measures. The thematic maps obtained from the classifications produced enough useful data for the creation of future urban scenarios. For modeling we used the SLEUTH landuse-change model due to the fact that it has been shown to produce realistic, valid, and statistically robust results and has been applied extensively for urban-growth planning and prediction for more than one hundred cities around the world (Clarke et al, 2007; Dietzel and Clarke, 2007). Many prior studies that have used SLEUTH give thorough descriptions of its performance and structure, while more recent research has experimented with SLEUTH on patterns and theories of complex future urban forms (Candau, 2003; Dietzel et al, 2005b; Silva and Clarke, 2002). SLEUTH is a cellular automaton model that uses four spatial-behavior types to forecast land-use change and urban growth. SLEUTH is an acronym that covers the six types of spatial input layers required by the models: slope, land use, exclusion, urban extent, transportation network, and a hill-shaded background. The topographic data required by the model are in the form of percentage slope and hill-shaded maps, the latter are used only as a background to visualize urban growth and land-use-change results in animations, and do not affect the behavior of the model. For calibration purposes and to implement the Deltatron land-use submodel, a consistent land-use classification for two time periods is required. The exclusion layer introduces areal limitations to growth by excluding from the computation areas


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where urban growth is not possible, for example, water bodies. The user can also use a weights layer in order to establish a certain degree of `resistance' (Clarke, 2008) against growth, in an attempt to reduce or modify the urbanization rate due to legal restriction, zoning, or differential suitability. SLEUTH is based on a tight coupling of two cellular automata models: the urban growth model and the Deltatron land-use-change model (Clarke, 2008). The basic growth procedure in SLEUTH is a cellular automaton in which urban expansion is modeled in a spatial two-dimensional grid. The activities of the cellular automaton are controlled by five parameters: diffusion, breed, spread, slope, and road-dependency coefficients; through these four different types of growth behavior are possible: spontaneous, diffusive, organic, and road-influenced (Clarke, 2008). The model modifies its own control parameters during a simulation run using aggregate rules which control the growth parameters when growth rates are exceeded, so that the model's behavior includes feedbacks (Clarke et al, 1997). Hence, the model is designed to mimic urban expansion and, furthermore, it is scalable and so far almost universally applicable. The temporal dependency and sensitivity of SLEUTH have been investigated (Candau, 2003) and the results show that the model performs better using recent data for short term forecasts rather than using long-term historical data for either short-term or long-term forecasts. Therefore, our prediction has been based on data restricted to a twenty-year time window (1985 ^ 2005) and forecast up to 2030. Calibration uses computational brute force methods (Silva and Clarke, 2002). Initially the calibration ensures that the whole five-dimensional control parameter space is covered, but only coarsely. Ideally the incremental calibration process aims to reduce the step value (1 is the optimum) for each of the five growth parameters (diffusion, breed, spread, slope, road-dependency) in order to isolate the best values that are then used in the prediction process. (See table 5.) Just how to reach an optimum SLEUTH calibration has been widely investigated; so far, many calibration approaches for SLEUTH have been tried and several rules have been suggested for application within the brute force procedure in order to handle problems of tractability. Even so, most of these leave out many of the possible parameter combinations (Dietzel and Clarke, 2007). In order to isolate the best parameter sets a methodology using the optimum SLEUTH metric (OSM) has been adopted (Dietzel and Clarke, 2007). The OSM measure combines seven of the measures used in SLEUTH, eight if land use is modeled. Furthermore it is the recommended method to best calibrate SLEUTH and is a way to eliminate biases due to different calibration procedures. This use of OSM is also relevant for achieving better comparability within SLEUTH applications, and to give superior modeling and forecasting results (Dietzel and Clarke, 2007). After the operation described, SLEUTH prediction was performed in order to obtain maps of possible future scenarios of urban spatial extent up to 2030; those Table 5. Sleuth calibration parameters obtained with the optimum SLEUTH metric methodology and used in the three different calibration steps. Coarse

Diffusion Breed Spread Slope Road

Fine

Final

start

step

stop

start

step

stop

start

step

stop

0 0 0 0 0

20 20 20 20 20

100 100 100 100 100

0 0 10 0 0

5 10 5 20 20

20 100 30 100 100

1 50 25 20 20

1 5 2 10 10

5 100 35 100 100

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results were then used with the classified historical maps to observe spatial form and entropy trends in urban patterns from 1985 to 2030 for a time span of almost half a century. The model was capable of creating annual projections, unlike the data from past years where only four time slices were available. Entropy

Many studies in geography, economics, or other social sciences have used the concept of entropy to describe the dispersal of activities or phenomena in spatial settings (Hekkila and Hu, 2006). To state that a relation or a phenomenon shows spatial variability implies that the observations are not spatially stationary at all times (Novelli and Occelli, 1999), hence spatiotemporal investigation of urban sprawl is justified. One way to look at urban sprawl is to consider the urban extent as a phenomenon spatially dispersed across the territory or spatial extent and considered as the density of urban land with respect to the total land area available, yielding a fundamental measure of urban density: fi

Diact , k X act Di

(1)

i act i

where D , the density of land development in the ith zone [equal to the amount of actual land developed (built-up land)], is divided by the amount of land that is available for development (ie, excluding water bodies or nonconvertible land uses) for a total of k zones. 1985

(b) 1992

(c)

(a) administrative boundary class 1Ðwater class 2Ðriparial trees class 3Ðlow vegetation class 4Ðcrops class 5Ðbare ground class 6Ðperiurban class 7Ðurban

2001

(d)

2005

(e)

Figure 3. [In color online.] (a) Municipal boundaries of the study area used for the entropy zoning scheme, and (b) classified land cover for 1985; (c) 1992; (d) 2001, and (e) 2005.


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The general entropy function is believed to have some limitations because it contains bias when used for a wider period of time or for different areas. Even though our study focused only on a single area, we calculated Batty's entropy H because it is widely considered to be more spatially oriented ``though Batty had clearly space in mind when he introduced equation (2)'' (Hekkila and Hu, 2006, page 853). k X fi H ÿ , (2) ln D i i where Di represents the discrete extent of the feature analyzed for the ith category, and, as before, fi is urban density. Given that entropy can be usefully applied to investigate the spatial spread of geographical phenomena, we examined the differences among entropy at different times (Ht1 ÿ Ht ), as this change might indicate a change in the degree of dispersion of land (urban) development or urban sprawl (Yeh and Li, 2001). While looking at entropy the choice of an informative zoning system is very important. The zones should not be too numerous because this would overestimate the level of entropy (Hekkila and Hu, 2006), and entropy must be sufficiently accurate to convey the information on sprawl that we seek. We chose to use the municipal boundaries to divide the Pordenone metropolitan area into six zones (figure 3). Results and discussion SLEUTH was calibrated for Pordenone and used to forecast urban expansion and land-use transitions up to 2050. The forecast period is probably too large, because it is well known that prediction results are more reliable when the forecast time span is as wide as or smaller than the time span of the input data used for calibration (Dietzel and Clarke, 2007). However, the calibration achieved OSM values close to 0.3. OSM is a composite of eight measures of goodness of fit from 0 to 1, multiplied together. These values were considered sufficient, and the values of coefficients used for the calibration and their related OSMs are shown in table 6. These values were used in the final calibration to derive coefficient values to use for prediction (table 7). We found that using standard SLEUTH forecasting parameters results in an overestimate of growth. While SLEUTH applications usually assume that all areas that urbanized in 90% of the Monte Carlo simulations are likely to become urban, instead we used 99%, a much higher level of confidence, and so fewer forecast urban areas. We noticed that land-use transitions and urban extents from the two confidence rates are almost identical up to 2037 but, as might be expected, notable differences show up beyond that time. Consequently, we used the more conservative definition of forecast growth. Table 6. Ten best OSM results and coefficients. Optimum SLEUTH metric

Coefficient diffusion

breed

spread

slope

road

0.30 0.28 0.27 0.27 0.27 0.26 0.26 0.26 0.26

10 8 11 11 11 10 11 11 11

83 83 83 83 83 83 83 83 83

86 86 86 86 86 86 86 86 86

44 44 42 44 44 44 44 42 43

55 57 54 57 57 54 53 57 55

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Table 7. Coefficient change due to SLEUTH self-modification. The 2005 coefficients (rounded to integers) were used for the prediction process. Forecast set was {12,100,100,5,59}. Year

1992 2001 2005

Coefficient diffusion

breed

spread

slope

road

10.62 11.61 12.08

88.11 96.36 100

91.29 99.84 100

35.75 15.29 4.77

55.83 57.87 58.92

Results show urban expansion in the area considered up to 2050 of more than 90% compared with 2005, implying that the urban area will double in less than half a century (figure 4). The period 1985 ^ 2005 is known to have been characterized by increasing sprawl. With geostatistical analysis and by visual inspection, we noticed that the period 2005 ^ 20 is when most new urban clusters are generated, while 2020 ^ 50 shows a predominance of coalescence between the clusters. Therefore, we expected an increase in entropy around 2010 and a drop in entropy values while approaching 2050 (figure 5). Even so, the entropy trend shows that there is a break point between 2005 and 2010 in which the slope of the curve changes dramatically, but the drop that we expected was not found. This is the point when past data yield to model forecasts, so the change may be more abrupt than actual, yet the overall slow down is apparent. This might be because the entropy value is strictly related to the total area of land available and depends on the zoning scheme chosen, or likewise because spatial entropy applied to spatially distributed data might be independent of how those geographical data are arranged in space. We note that `Àn entropy function can be applied to spatial data, but the entropy as such may be completely aspatial'' (Karlstro«m and Ceccato, 2000, page 5). The two-phase urban growth theory can help us to understand the entropy curve we computed. In fact, the oscillation from a growth pushed by sprawl to a form of growth influenced by coalescence it is not immediate but needs time to gradually shift from one form to the other. Hence, we have to seek measures that can observe either the level of dispersion or the degree of cohesion. Therefore, from this perspective, 2005

2010

2020

2030

2040

2050

Figure 4. Output maps of SLEUTH forecast of urban area expansion up to 2050 (likelihood 99%).


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2.4 2.2

Batty's spatial entropy

2.0 1.8 1.6 1.4 1.2 1.0 0.8

1985 1995 2005 2015 2025 2035 2045 1990 2000 2010 2020 2030 2040 2050

Figure 5. Batty's spatial entropy for 1985 ^ 2050.

in order to investigate the distribution of urban spread, spatial autocorrelation must be reflected in the measure. Spatial autocorrelation is basically a comparison of two sets of similarities; similarities that can belong to either the attribute or the location (Goodchild, 1986). A measure of spatial autocorrelation can be intended as a descriptive index, focusing on patterns drawn by the way phenomena are spatially distributed. Even so `àt the same time the measure can be a causal process, measuring the degree of influence exerted by something over its neighbors'' (Karlstro«m and Ceccato, 2000, page 6). The main aim of this study is to investigate urban sprawl and to suggest a simpler and easier means of observing its trend over time. We note that the most shared concept about urban sprawl is that it involves the spread of urban areas into the surrounding landscape. This concept is closely associated with the number of distinct and separate clusters in the study area and the average size of the clusters. It is reasonable to imagine a sprawled area as characterized by a large number of small disconnected urban land parcels (or pixels), while on the other hand an urban form characterized by a small number of urban cells that is large and connected leads to an urban growth pattern that follows cohesion principles. In other words, the degree to which an urban system is previously clustered represents an initial condition that propagates into future patterns. Consequently, we calculated both the average cluster (of urban cells) size and the number of clusters and then normalized these measures over the time span in order to have more comparable values (figure 6). These data reveal a situation in which urban extent is continuously and gradually growing and the average cluster size also gradually grows. Yet the number of clusters initially increases and then falls, curiously at almost the same time that Batty's entropy trend shows a change in slope (figure 5), in about 2009. These observations lead us to believe that the time of maximum sprawl in the Pordenone region is when the distance between curves 2 and 3 in figure 6 is largest; while when they cross, in about 2034, is when sprawl will eventually end in favor of the increased coalescence of urban areas. To better observe and depict the Pordenone urban growth trend we computed an index that summarizes the results and dynamics conveyed by the number of clusters and the

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1.2

1. Growth trend (normalized) 2. Number of clusters (normalized) 3. Average cluster size (normalized)

1.0

0.8

0.6

0.4

0.0

1985 2001 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 2026 2028 2030 2032 2034 2036 2038 2040 2042 2044 2046 2048 2050

0.2

Figure 6. Trends of the number of clusters, average cluster size, and urban extent over the time considered.

average cluster size, and that might be generally applied to any other region and be equivalent for other urban areas. We saw in the normalized difference ratio of the values of number of clusters and average cluster size (figure 6) a useful normalized difference ratio; in the form: nc ÿ na , nc na

(3)

where nc is the normalized value of the number of clusters at a specific time, and na is the normalized average cluster area at the same time (figure 7). 1.2

1. Growth trend (normalized) 2. Normalized difference ratio

1.0 A

0.8 0.6 0.4

H

0.2 L

0.0 ÿ0.2 ÿ0.4

85

19

B

06 010 014 018 022 026 030 034 038 042 046 050 2 2 2 2 2 2 2 2 2 2 2

20

C

ÿ0.6 ÿ0.8

Figure 7. Normalized difference ratio of number of clusters and average cluster size (series 2); growth trend (series 1).


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So far this curve assumes positive values when the nc parameter affects the growth trend more than the na parameter, hence when it is above the x-axis urban growth is more influenced by the number of separate clusters rather than the average size of the clusters; in other words, positive values indicate growth characterized by sprawl rather than coalescence. The peak sprawl is signified by the maximum distance of the curve above the x-axis (in 2009) that conveys the largest number of urbanized clusters during the period investigated. Since this number is relative, not absolute, this curve can be applied across cities and regions. Such comparison may be of great use in understanding urbanization and sprawl in different urban systems. Urban growth is visibly a process that alternates periods of coalescence with periods of sprawl, but the shift of the growing predominant modality is not immediate but a smooth process (Dietzel et al, 2005a). When the curve intercepts the x-axis reflects the time at which growth is equally determined by sprawl as by coalescence (year 2034). After that point the plot shows future growth dominated by coalescence as all land available for urbanization is consumed. Where the curve has its minimum is the moment at which urban growth registers its largest geographical extent (figure 8). 2005

(a) 2034

(c)

2009

(b) 2050

(d)

Figure 8. Modeled urban extent of the Pordenone urban area in (a) 2005; (b) 2009; (c) 2034; and (d) 2050.

Observing figure 7, we already argued that at point A the normalized difference ratio registered its peak because it included the largest number of pixels, so it was the moment of highest sprawl. Similarly, we can also say that the intensity of sprawl is determined by the distance (H) between A and the x-axis; we also consider that L represents the period during which sprawl occurs. At point B we have the inversion of the growth mode, from this point forward coalescence will predominantly affect subsequent urban growth, and when the curve reaches C, (as far as we know, prediction stops in 2050) the minimum of the curve reflects the largest extent of urban area and the maximum coalescence. These results refer to the case of constant and relatively gradual growth. We are also interested in possible future conditions in which urban land reverts to other uses, as has happened following natural disasters (eg, in New Orleans), economic depressions (eg, in Detroit), and due to depopulation (eg, the nearby former major Roman city of Aquileia, now a village). We pursued this idea of eventual convergence as a hypothetical argument. We used the normalized difference measure to test a fictional dataset built from the real data

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1.0


Growth

Degrowth

growth trend normalized difference ratio

0.8 0.6 0.4 0.2 0.0 ÿ0.2 ÿ0.4 ÿ0.6

85 95 05 25 35 45 55 65 75 85 95 05 19 19 20 20 20 20 20 20 20 20 20 21

Figure 9. Growth trend and normalized difference ratio built up on a fictional dataset created from real data.

in order to represent a situation of oscillatory behavior of growth and degrowth (figure 9). In this dataset, we speculate that the urban extent of Pordenone between 2050 and 2100 will simply reverse the growth experienced during 1985 ^ 2005 and modeled from 2005 to 2050, that is, we reflected the data along the x-axis. Figure 9 shows behavior that matches our expectations from the two-phase urban theory. It is reasonable to speculate that degrowth, if constant over time, might be affected by sprawl and coalescence, as remote sites are systematically abandoned in favor of a central cluster. Also, in this case the positive value shows a predominance of sprawl rather than compactness in both the growth and the degrowth phases. Theoretically, the ratio should trace a regular curve, a harmonic wave (figure 10), but this is highly unlikely in the real world. These behaviors are captured in a small set of values: H reflects the intensity of sprawl, L shows the intensity of coalescence; M is the period between maximum sprawl 0.22

Growth

Degrowth

normalized difference ratio growth trend

0.44

0.22 H M 0.00

L l

ÿ0.22

Figure 10. Ideal situation of oscillatory behavior between growth and degrowth with sprawl and coalescence.


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and highest compactness, and l determines the period during which the urban area passes from its largest extent to its smallest. Using the results presented allows us to describe the behavior of urban expansion over time and to focus on defining whether growth (or degrowth) will eventually be affected by coalescence rather than spread. Both the growth trend and the normalized difference ratio can be used to classify growth in the two phases. To define further whether an urban area is passing through a coalescence phase rather than sprawling we computed the simple ratio between the number of clusters and average cluster size (figure 11). From the results obtained by measurement and with SLEUTH, the Pordenone urban area faces the greatest amount of sprawl somewhere between 2005 and 2010 (probably in 2009), after which the growth mode shifts from sprawl to coalescence somewhere around 2034. The simple ratio in 2034 is forecast to be 7.81, which suggests that anything below that value would be indicative of coalescence, while on the other hand everything above 7.81 should reflect sprawl. These assertions must be tested against known historical data, since the data for Pordenone cannot clarify completely the relation between the number of clusters and average cluster size. 80 simple ratio 70

nc na

60 50 40 30 20

0

1985 2001 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 2026 2028 2030 2032 2034 2036 2038 2040 2042 2044 2046 2048 2050

10

Figure 11. Simple ratio of number of clusters and average cluster size.

Conclusion So far the observations we have made allow understanding of what kind of landcover transitions occurred in the past and toward which future forms they could lead. Similarly the forecast modeling provides a longer time span on which to compare and analyze the modifications of the spatial form of the urban environment. From the Italian Urban System Dynamics (Dematteis, 1997) we found evidence of the tendency of an urban node to first sprawl and then start cohesion in order to gain more importance in the network. Hence, our investigation conducted with the aim of detecting the spatial dispersion of the system through entropy, which proved unsatisfactory as an aggregate measure of sprawl, led us to develop an approach based on the same principles supported by evidence of the oscillatory behavior of urban growth set forth by Dietzel et al (2005a). We also tested the index with a hypothetical growth/ degrowth trend. The authors are aware that a single case study cannot prove a theoretical framework; nevertheless, we believe the methodology and measures presented are useful tools for urban planners and policy makers. In future research we

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