A local and regional spatial index for measuring three-dimensional urban compactness growth

Abstract

The negative impacts resulting from urban sprawl are recognized as serious issues entailing environmental problems. Urban developments are moving towards a more compact form to mitigate many issues including pollution concerns, land depletion, and population growth demands. Urban compactness has been reported to be a more sustainable form of development that occurs through densification and mixed land use practices through spatial indicators that intensify the landscape. Urban modeling has been used extensively to aid in urban and regional planning as it can forecast possible scenarios of urban growth. The objective of this research is to develop and implement a spatial index for three-dimensional (3D) urban compactness to evaluate potential vertical development growth. The spatial index has two components, local and regional, and it is derived based on parameters accounting for a vertical urban growth suitability analysis, land designation, and average building height. Datasets used for this study were for the Metro Vancouver Region, Canada, a rapidly developing area with plans in place for sustainability and compact growth. The spatial index was derived for the study area for the year 2011 and projected to the year 2041 with a 10-year time interval, accounting for the spatio-temporal land use change. Results indicate concentrations of urban compactness growth near densely populated and transportation-oriented locations and also capture urban leap-frogging processes. The presented research aims to aid local governments in future planning processes related to regional sustainable development growth.

Keywords

Spatial index for 3D urban compactness urban vertical growth 3D GIS land use change urbanization

Introduction

Urban sprawl has been attributed to many negative consequences in environmental (Johnson, 2001), economic (Carruthers and Ulfasson, 2003), health (Ewing et al., 2003), and social (Burton, 2000) sectors. Low-density developments grow horizontally across the landscape and consume valuable lands such as watersheds, forests, and agricultural areas, which encourage residing populations to travel further and longer to gain access to services or to central business districts where many economic opportunities are located. Additionally, the conversion of land negatively affects important and valuable agricultural land reserves, generally by consuming such land into urban land use (Livanis et al., 2006). Globally, there are many cities exemplifying low-density growth but North America contains more cities known for their wide sprawl such as Chicago, Los Angeles, Detroit and Phoenix, USA, which are oriented around automobile and other industry sectors (Brunn et al., 2003). However, cities including Las Vegas, Miami, and Phoenix, USA have experienced severe growth decline during the economic crash in 2008 (Aalbers, 2009), while other cities such as metropolitan regions of Seattle, USA and Vancouver, Canada continue to experience dynamic urban expansion (Fox, 2010). Urban sprawl and land use change processes are recognized as one of the contributors to climate and environmental changes. In general, planning practices should try to mitigate the undesirable results of urban sprawl (Dieleman and Wegener, 2004) as it is an unsustainable form of urban development (Johnson, 2001).

Sustainable development has been defined as meeting current needs through practices that do not endanger natural systems that support life, and therefore, future generation’s ability to meet their own needs (World Commission on Environment and Development, 1987). Population and development densification in urban regions can mitigate many of the concerns attributed to urban sprawl. This form of densification is commonly known as urban compactness or compact cities and has been determined to be a more sustainable form of urban growth (Jenks et al., 1996), though contested by some (Neuman, 2005). Although there is no single consensus on the term urban compactness, it is commonly defined as a variation of a high-density, mixed use, and an intensified city (Burton, 2002). Urban sprawl is seen as a process of development that induces land changes at the periphery of a city (Torrens, 2008). Unlike urban sprawl that tends to grow horizontally across a landscape, urban compactness concentrates urban growth by increased development in the vertical direction, augmenting the population density per amount of land used (Galster et al., 2001). This rapid growth increase in the vertical direction is inherently a three-dimensional (3D) change in the environment and as such, urban growth indices should consider the vertical dimension in the measurement.

Interest in urban compactness development has been concentrated in developed countries such as USA, Japan, and Australia (Burgess and Jenks, 2002), although European cities have been forcing densification for many decades because of limited available land. Due to exceptionally high population growth demands coupled with the depletion of available land, Shanghai and Hong Kong are amongst many Asian cities that are examples of compact cities with high volumes of high-rise buildings (Burgess and Jenks, 2002). Other North American cities such as Seattle (USA), Toronto, or Vancouver (Canada) do not have as demanding population growths as regions in Asia but are growing rapidly, and urban planning is encouraging urban compactness growth to mitigate environmental and social concerns (Herrschel, 2013; Hess and Sorensen, 2015). In theory, urban compactness growth may decrease vehicle dependency as access to services and amenities may become more available (Jenks et al., 1996) and positive correlations have been reported such as an increase of CO₂ efficiency (Liu et al., 2014).

High-density concentrations and mixed land use design are characteristics of urban compactness (Burton, 2002). In this context, density is thought of as both population and built environment, while mixed use suggest land designations supporting residency, facilities, retail, commercial, and other activities. The intensification process enabling the development of density and mixed use has strong relations with demographics such as population density (Burton, 2002) and other socio-economic factors (Koomen et al., 2009). Transportation nodes, including major roads and stations, are networks that also contribute to urban compactness (Abdullahi et al., 2015). Burton (2002) states that mixed land use is important for urban compactness and helps plan and develop the built environment landscaped (Frenkel, 2007). Access to services, recreational amenities, and job centers are also attractive locations for urban compactness development (Abdullahi et al., 2015; Roychansyah et al., 2005). The combinations of these factors that affect urban compactness contribute to optimal locations for future densified growth. Urban compactness may support concerns regarding more sustainable practices, conservation of land, and accommodation of growing populations (Galster et al., 2001). Urban compactness growth encourages higher densification of populations and built environments that typically grow in the vertical direction. For these reasons, there is a need to develop urban compactness analysis methods, spatial metrics, scenario-based models, and tools that are capable to incorporate and measure in three spatial dimensions to aid sustainable urban planning. In the context of Canadian cities, many decisions regarding urban and sustainable growth happen at local municipal-city levels, while the overall landscape changes emerge and have impacts at metropolitan-regional levels (Temenos and McCann, 2012).

Regional and local indices can be used to analyze the interactions of urban processes occurring at various scales. Regional indices such as the Index of Regional Sustainability Spatial Decision Support System (Graymore et al., 2009) and the Regional Environmental Quality Index (Rahman et al., 2014) were developed to identify regional interactions using remote sensing, GIS, and multi-criteria evaluation. However, regional indices are summaries of patterns and interactions that occur at larger scales, omitting the complexities occurring at smaller scales. For this reason, local indices such as the Local Segregation Index (Wong, 2002) have been developed to detect the non-uniformity within the larger region. Additionally, Feitosa et al. (2007) demonstrated the importance of both local and regional (global) indices to show the difference in neighborhood and scales of analysis for urban segregation.

The main objective of this research is to develop a spatial index for measuring urban compactness in 3D that can encompass local-municipal and regional-metropolitan urban landscapes. Hence, the proposed index contains two components, local and regional, for measuring urban compactness in 3D and the spatio-temporal change of urban vertical growth. The urban compactness index consists of the three key parameters combined to characterize 3D urban landscape: (1) suitability analysis; (2) land designation; and (3) average building height. In this research study, the proposed spatial index with two components for 3D urban compactness was applied to datasets at the regional scale for Metro Vancouver, Canada.

Review of compact growth analysis research

Urban compactness has been explored through various analytical and modeling methods using spatial indicators. Chen et al. (2008) compared urban compactness of 45 Chinese cities through the Pearson product–moment correlation coefficient to derive a summarized index to compare the cities. Multiple mid-sized European cities were also measured and compared to identify the significance of the spatial indicators with reasonable results for the given large-scale study (Stathakis and Tsilimigkas, 2015). Frenkel (2007) researched spatial distribution and concentration of vertical developments based on a multi-nominal logit model. The multi-criteria decision making and Bayes theorems approaches were used to measure urban compactness across 18 regional zones in Malaysia. Principal component analysis (PCA) was used to compare various urban compactness indicators by Roychansyah et al. (2005) and Salvati et al. (2013) alongside other statistical methods including descriptive statistics, regression analysis, and supervised classification.

Assessing urban compactness and landscape change over space and time is equally important for the examination of spatial urban morphology. The spatio-temporal aspect of urban land use change has been incorporated with a compactness index, PCA, and entropy measurement (Li and Yeh, 2004). Koomen et al. (2009) present work on an urban-volume indicator that was used to spatio-temporally quantify urban extension and intensification through a self-organizing map approach. Similarly, Min et al. (2010) used various indices to measure urban compactness for spatial carrying capacity, spatial forms, and spatial functions. However, Mubareka et al. (2011) derived a single composite index, from four morphological indicators that determined compactness and sprawl, to demonstrate how an index can be derived and applied to a large urban zone to forecast possible urban scenarios. Also, the cellular automata (CA) method was used to propose and compare various urban density scenarios (Yeh and Li, 2002) and to simulate building height developments (Lin et al., 2014). These research efforts were based on vertical measurements, such as building heights, but did not include representations of the changes in space and time of urban landscapes in 3D.

The urban built environment is inherently 3D and can be represented in such way due to increasing advancements in geospatial information technology (Shiode, 2000). Additionally, 3D urban representation has been reported to improve the quality in decision-making processes and communication between urban professionals (Al-Douri, 2010). Urban compactness growth is typically developed through mid- and high-rise buildings that surpass the surrounding heights of less compact areas. The intrinsic vertical nature of urban compactness needs to be included in modeling to show both where urban compactness may occur and to what vertical extent. Therefore, urban compactness can be measured through the development of indices that capture space in 3D, though not much work has focused on spatial indices with consideration of the third spatial-vertical dimension. Some research efforts have been done to develop spatial indices capable to characterize 3D space using voxels as the smallest spatial units in 3D; however, the application has been developed for ecological and not urban 3D analysis (Jjumba and Dragićević, 2016).

Advancements in remote sensing, especially with LiDAR technologies, have increased the ability to gather appropriate data and measure the built environment in the vertical dimension (Chen et al., 2014). Additionally, remote sensing techniques can provide quantitative measurements for built environments that can better represent the compactness of a region compared to approaches that use parameters such as census tracts, which cover various city blocks (Yoo et al., 2009). Extraction of building volumes was developed using 3D spatial indices based on LiDAR data (Tompalski and Wezyk, 2012). LiDAR data were also used to derive a volumetric density with 3D indicators that were applied to urban compactness modeling (Santos et al., 2013) and on change detection of urban areas in 3D (Stal et al., 2013). In addition, the automatic volumetric change detection for urban land use was developed by Pollard et al. (2010).

A 3D urban expansion measure to evaluate growth efficiency using four indicators accounting for morphology, intensity, and fractal dimension measurements was presented by Qin et al. (2015). The research provided 3D building height models for two time periods to assess the efficiency and intensification of the Chinese city. Magarotto et al. (2016) derived a volumetric index to evaluate building height growth for over 30 years based on remote sensing imagery and GIS data. However, these methods did not provide insight on future urban compactness projection using the derived 3D indices.

There still exists a need to develop 3D urban compactness indices and test them in the context of spatio-temporal changes. The objective of this research study is to develop the 3D urban compactness index for an urban region to evaluate forecasted urban compactness growth. The proposed index includes suitability analysis, land designation, and average building height parameters. The proposed index aims to be used as a tool for planning efforts towards more sustainable and compact urban growth.

Methods

The purpose of the spatial index for 3D urban compactness is to obtain calculated values representing various degrees of urban compactness growth that can be applied to an urban landscape in 3D, reflecting the vertical nature of urban compactness growth. The developed spatial index has a spatio-temporal component that incorporates time intervals to address the changing urban compactness growth across the area. The spatial index of 3D urban compactness calculates regional and local growth values that quantify the change of the urban compactness growth over time.

The spatial index with the two components indicating local and regional urban 3D compactness was developed and applied to datasets from Metro Vancouver to show regional vertical growth change over space and time. Figure 1 presents the overview of the methodology for deriving the spatial index as a product of three parameters: (1) the suitability analysis using the key indicators for urban compactness; (2) the land designation analysis that classifies designations as developable and non-developable for vertical urban growth; and (3) the average building height assignment using sample data sites. In this research study, the term developable means a cadastral lot that has been identified as a suitable location that meets the criteria to have mid- or high-rise buildings constructed. The presented work was operationalized in ESRI’s ArcMap 10.2 and ArcScene 10.2 software (ESRI, 2013).

Figure 1.

The overview of the proposed method for the spatial index for 3D urban compactness.

Study area and datasets

The Metro Vancouver Region is a rapidly growing area with populations expected to grow to 3.2 million people by 2040, adding an approximate 570,000 new dwelling units (Metro Vancouver, 2016). This region, encompassing 21 municipalities, covers approximately 2800 km² of land area (Statistics Canada, 2012). However, the region’s urban area is further restricted by the surrounding natural geography including water bodies and mountains, and an administrative urban land containment boundary that includes agricultural land and forest reserves. The Metro Vancouver Region also experienced rapid urban sprawl with low-density residential developments, while concurrently experiencing compact growth with increased high-rise building developments. The study area for this research on measures of urban compactness in 3D is therefore confined to the developable regions within the Metro Vancouver urban containment boundary. The City of Surrey, District of North Vancouver, and City of Vancouver, are municipalities within the Metro Vancouver Region and were used as samples for average building height data given that they are known for various compact urban growth and that they have rich geospatial datasets widely available. These municipalities were selected also because of their difference in total population size and building heights to provide a more representative sample of the region.

The Metro Vancouver Region is governed by the political body called Metro Vancouver and has been developing sustainable growth plans for the past years. In 1997, Metro Vancouver developed the Livable Region Strategic Plan (LRSP) concerned with protecting green zones, building complete communities, achieving a compact metropolitan region, and increasing transportation options (Holden, 2006). The LRPS was replaced by the Sustainable Region Initiative (SRI), a framework, vision, and action plan that encourages economic growth, community development, and environmental responsibility (Holden, 2006). Since the introduction of the SRI, Metro Vancouver has been responsible for core services, political forums, and policy through a sustainability assessment using metrics, targets, and deliverables (Metro Vancouver, 2010). Metro Vancouver has presented five goals, it aims to achieve by 2040 as follows: (1) to create an urban compact area; (2) to support a sustainable economy; (3) to protect the environment and respond to clime change impacts; (4) to develop complete communities; and 5) to support sustainable transportation practices. The sustainability-driven planning is also prevalent in residing municipalities through initiatives like the City of Vancouver’s Greenest City Action Plan and the City of Surrey’s 40-year Sustainability Charter. In whole, Metro Vancouver’s urban planning and development have much consideration for sustainable and compact growth, which is a key reason for this research study.

The required data for this research included regional spatial datasets satisfying the urban compactness indicators and municipal building heights. Data satisfying the suitability analysis indicators are categorized into factors that include: roads, bus and rapid rail stations, hazardous and restricted land, schools, walking and biking routes, community centers, hospitals, water bodies, and central business districts (obtained from DataBC, 2015; GeoBC, 2015; Metro Vancouver Open Data, 2015). Population densities were calculated at the Dissemination Area level from 2011 census population total (Statistics Canada, 2011). Slope was derived from the 10 meters resolution Digital Elevation Model dataset (GeoGratis, 2015) with a selected degree of 0 to 40 that are assigned as most adequate slopes for building constriction (Hatch et al., 2014). The land use designation spatial dataset was obtained for the Metro Vancouver region, essential for the suitability analysis, land designation, and average building height parameters.

The data required for the average building height parameter included building footprints and heights for the City of Surrey, District of North Vancouver, and City of Vancouver municipalities obtained from: District of North Vancouver GEOweb (2015a), Surrey Open Data (2015), and the City of Vancouver Open Data Catalogue (2015). These municipalities were selected because they represent very high (City of Vancouver), medium (City of Surrey), and low (District of North Vancouver) high-rise buildings in the region. The City of Vancouver building footprint data contained the height values for each establishment current to the year 2009. The obtained building footprint data for the City of Surrey, first published in 2014 and updated monthly, was joined with the available 2013 LiDAR dataset to derive approximate building height values. The District of North Vancouver building footprint data did not contain a building height field but provided building storey counts. The District of North Vancouver municipality building requirements state that no residential buildings can have storeys higher than 2 meters, but this does not account for the structural material between each storey (District of North Vancouver, 2015b). Given this, a value of 3 meters for a single storey was deemed suitable and multiplied by the total amount of storeys to obtain an approximate height. Additionally, a value of 3 meters for each storey was used by Magarotto et al. (2016) and Santos et al. (2013) in their research when calculating the height of each building floor.

Spatial index of 3D urban compactness

The spatial index calculates values for urban compactness to forecast locations of higher densification of the built environment and population derived from the suitability analysis, land designation, and average building height parameters. Locations that have suitable land with consideration of the factors contributing to urban compactness and appropriate land use designation may develop in a more compact form and, therefore, with higher buildings in the vertical dimension. The spatial index of 3D urban compactness 3DI_Ti at time Ti is composed of the suitability analysis P1, land designation P2, and average building height P3 parameters and can be calculated as follows:

3 {DI}_{Ti} = P 1 \cdot P 2 \cdot P 3

where Ti represents iterations at time i denoting values as initial, 1, 2, and 3.

The spatial index of 3DI for urban compactness was derived for the study area, and each raster cell was assigned a value representing building height in meters. The suitability analysis and land designation parameters were updated for each time iteration, while the average building height remains a constant. The index was updated for each iteration to project vertical growth in the study area. The values were extruded in 3D by the calculated height value to present an alternative perspective of the projected vertical urban landscape growth.

The local and regional component of the spatial index were developed to calculate quantifiable growth values to provide a measureable understanding of compactness growth across the area. The local and regional components calculate values to compare changes occurring at different scales, smaller (local) and larger (regional), to identify “hot-spots” of growth. The local component of the spatial index represents the measure of the averaged difference of the height between each time iteration and for each raster cell. The regional component of the spatial index of 3D urban compactness was derived by calculating the average height for the entire region for each time iteration. The details regarding each parameter and implementation of land use spatio-temporal changes are presented in the next three subsections.

Suitability analysis parameter

The suitability analysis parameter P1 was developed to weigh the various spatial indicators to identify suitable locations for urban compactness for this particular study. Based on the literature, the indicators selected to represent urban compactness in this study are presented in Table 1 and are subdivided into the more detailed factors comprising transportation, environment, land use, services and amenities, population density, recreation and community, and job opportunity. To satisfy these factors, the data obtained for this study include: roads, bus and rapid rail stations, slope, land use designations, schools, population census, walking and biking routes, community centers, and central business district, as few examples. Once obtained, the spatial datasets were converted to grid format, necessary to perform the suitability analysis.

Table 1.

Urban compactness indicators, intensification process, and literature sources.

Demographics	Population density	Abdullahi et al. (2015); Burton (2002); Koomen et al. (2009); Lin et al. (2014); Min et al. (2010); Roychansyah et al. (2005); Stathakis and Tsilimigkas (2015)
Transportation	Major roads, public transportation	Abdullahi et al. (2015); Burton (2002); Koomen et al. (2009); Lin et al. (2014); Min et al. (2010); Roychansyah et al., (2005)
Environment	Slope, undevelopable land	NA
Land use	Zoning, land use designations	Abdullahi et al. (2015); Burton (2002); Frenkel (2007); Koomen et al. (2009); Min et al. (2010); Roychansyah et al. (2005); Stathakis and Tsilimigkas (2015)
Services and amenities	Schools, hospitals, shopping centres	Abdullahi et al. (2015); Roychansyah et al. (2005)
Recreation and community	Walking and biking routes, parks, fields, recreation and community centres, library	Abdullahi et al. (2015); Burton (2002); Roychansyah et al. (2005)
Access to job opportunity	Central business districts, urban centres	Abdullahi et al. (2015); Burton (2002); Frenkel (2007); Roychansyah et al. (2005)

In the past, various multi-criteria evaluation (MCE) methods were used for land use suitability analysis to rank spatial data layers to determine optimal locations (Malczewski, 2004). MCE methods have been used for different land designations (Jankowski, 1995), have incorporated fuzzy membership approaches (Jiang and Eastman, 2000), and have been used on regional sustainability assessments (Kropp and Lein, 2012). The GIS-based MCE approaches that have been typically used are analytical hierarchy process (AHP), ordered weighted average (OWA), simple additive scoring (SAS), weighted linear combinations (WLC), and more recently the logic scoring or preference (LSP) method (Hatch et al., 2014; Montgomery and Dragićević, 2016).

The suitability analysis parameter was calculated using a GIS-based MCE method with AHP for weighing the spatial datasets. Suitability functions were developed for all factors composing the indicator. Table 2 presents information for describing each indicator used to build the compactness index, corresponding weights, and suitability function break points. Suitability values ranging from 0 to 1, where 0 represented unsuitable locations and 1 represented highly suitable locations for vertical urban growth.

Table 2.

Suitability analysis indicators, factors, weights, and functions with breakpoints.

Drivers	Factors	Weights within indicators (%)		Total Weights (%)		Suitability Functions Breaking Points (m) Criteria(attribute) = {(value1, suitability1),…, (value n, suitability n)}
Demographics	Population density	NA		15	100	NA
Transportation	Rapid rail stations (public)	20	100	35		Crit(Rapid rail stations) = {(400,1), (6000,0)}
	Frequent bus stations (public)	20				Crit(Frequent bus stops) = {(400,1), (6000,0)}
	Rail stations (public)	20				Crit(Rail stations) = {(400,1), (6000,0)}
	Rail	10				Crit (Rail stations) = {(40,0), (100,1)}
	Highway	20				Crit (Highway) = {(200,0), (600,1), (800,1), (3000,0)}
	Arterial	10				Crit(Arterial) = {(100,0), (300,1), (500,1), (3000,0)}
Environment	Slope	50	100	10		Crit(Slope) = {(20,1), (40,0)}
Environment	Local hazards (flood, landslide, etc.)	50	100	10		Crit(Hazard) = {(10,0), (50,1)}
Land use	Zoning, land use designations	NA		15		NA
Services and amenities	Urban centres	45	100	10		Crit(Urban centres) = {(800,1), (4000,0)}
Services and amenities	Schools	55	100	10		Crit(Schools) = {(800,1), (4000,0)}
Recreation and community	All forms of routes (walking, greenways)	30	100	5		Crit(Routes) = {(600,1), (4000,0)} Crit(Parks and centres) = {(800,1), (3000,0)}
Recreation and community	Parks and recreation centres	70	100	5
Access to job opportunity	Urban centres	50	100	10		Crit(Urban centres) = {(800,1), (4000,0)}
	Commercial regions	35				Crit(Commercial centres) = {(800,1), (4000,0)}
	Industrial regions	25				Crit(Industrial) = {(50,0), (150,1)}

Transportation values were assigned from recommendations of the regional public transportation authority (Translink, 2011) and other literature reports this factor as highly influential for urban compactness (Burton, 2002; Frenkel, 2007). Literature also reports that population demographics and land use designations are highly influential indicators of urban compactness (Burton, 2002; Frenkel, 2007); therefore, in this study, these indicators were weighted the highest (Table 2). These indicators are also highly regarded in the Metro Vancouver Region’s urban growth goals for 2040. Values obtained for the factors representing access to services and job opportunities, community and recreational services, and environmental assessments were determined by regional (Metro Vancouver, 2016), municipal (City of Surrey, 2014), and other literature (Abdullahi et al., 2015; Hatch et al., 2014). For indicators that had no values provided, Google Earth imagery was referenced to measure average distance from the indicator to the nearest residential development. Land use and population density were not assigned suitability functions but were reclassified into 0 to 1 values as the other indicators. Land use designations that were not suitable for urban compactness growth (e.g. airports and cemetery) were assigned a value of 0, where designations suitable for urban compactness (e.g. residential high-rise apartments) were assigned a value of 1. Population demographics were classified into 10 categories, determined by the Jenks natural breaks in ArcMap (ESRI, 2013) and assigned values from 0 to 1 increasing by equal increments.

The suitability analysis parameter P1 required an update to depict land use change over space and time. The first derived suitability analysis map represented the initial land suitability for the year 2011, the same year of the Canada census data. Suitable locations determined from the first suitability analysis were used as a new input for following iterations but were re-calculated for the next time interval to depict changes.

Land designation parameter

The land use designations for parameter P2 were used because their boundaries are stable and less likely to change in shorter time period, unlike zoning boundaries that change very often. In this respect, land designations are more appropriate for spatio-temporal modeling of urban vertical growth because of the boundary stability over the time iterations. Although each municipality has its own detailed land use designation, a region-wide land use designation was used for this research to have a consistent land classification representation and extent. From multiple available land designations, only six were found acceptable for development of mid- and high-rise buildings. Their specific designations are: residential-townhouses, residential-low-rise apartment buildings, mixed residential commercial-low-rise apartment buildings, residential-high-rise apartment buildings, commercial, and mixed residential commercial-high-rise apartment buildings. These specific land use designations appropriate for vertical urban growth were assigned a value of 1, while other designations were assigned 0.

As urban compactness develops across the region, land use designations bordering the perimeter of suitable locations can evolve to accommodate mid- and high-rise developments. This study incorporated the land use update for each temporal iteration to accommodate this growth. Residential-single-detached designations within 50 meters of the initial developable land use designations were re-assigned to residential low-rise apartment. Only residential-single-detached designations were considered because other designations were not fit to develop. As the time iterations progressed, more residential-single-detached designations within the neighbourhood were added to the developable land classifications. The land designation parameter was thus developed to allow more growth to occur in the horizontal direction by incorporating neighbouring land use designations.

Average building height parameter

The average building height parameter P3 was derived as a GIS spatial layer that contains information on height values for each developable land use designation. To derive values of building heights for the entire region, three different municipalities were used as sample areas to average the building height values. Building heights, in meters, were filtered and extracted from the City of Vancouver, the City of Surrey, and the District of North Vancouver building dataset. Next, the highest building within each land use designation was extracted for all three municipalities and averaged to get the mean building height value. As the focus of this study is on urban compactness through vertical developments, land use designations that typically do not contain mid- and high-rise developments were assigned 0 as a building height value. All remaining land use designations were assigned the average maximum building height value determined for each designation.

Spatio-temporal change

The spatio-temporal change for the suitability analysis and land use designation parameters was incorporated for the years 2011, 2021, 2031, and 2041 with a 10-year temporal resolution, denoted as T_initial, T₁, T₂, and T₃. The initial year began at 2011 because this is the year of the Canadian census data for total population obtained for the study area. The selection of the year 2041 as the final year was due to the closeness of the year 2040 for which most of the regional and municipal urban growth plans are projected. The spatio-temporal changes are accounted when calculating the suitability analysis and land designation parameters. Suitable locations of vertical urban growth were identified for the year 2011 as the initial time T_initial for suitability analysis parameter P1. These identified suitable locations for urban compactness were extracted and added to the next time iteration as a new indicator. The land designation parameter also incorporated a spatio-temporal component by updating more cadastral lots to become developable for time iterations T₁, T₂, and T₃ for the years 2021, 2031, and 2041, respectively.

The parameter P3 was combined with the parameter P2 by matching designations. As the parameter P2 updated newly available land suitable for development, the parameter P3 updated the corresponding building heights. Each time iteration incrementally advanced the assigned building heights of the land use designations to the next highest building average height.

Results and discussion

The spatial index for 3D urban compactness was derived for the Metro Vancouver Region using 10 meters spatial resolution raster GIS data and with a 10-year temporal resolution for years 2011, 2021, 2031, and 2041. The index for 3D urban compactness was calculated for each raster cell to identify developable land for vertical urban growth within the urban containment boundary identified by Metro Vancouver.

Parameter values for the Metro Vancouver Region

The calculated values for parameter P1 were obtained for the Metro Vancouver Region study area for the years 2011, 2021, 2031, and 2041 (Figure 2). Locations identified as most suitable for urban compactness (values closer to 1) are presented in red and locations unsuitable (values closer to 0) are in blue. Locations with the highest values of suitability are closer to transportation nodes and higher population densities as these are key indicators affecting urban compactness.

Figure 2.

Values obtained for the suitability analysis parameter P1 for the Metro Vancouver Region.

The obtained values for the parameter P1 were compared to Google Earth’s imagery and 3D building model. Google Earth’s model for mid- and high-rise buildings reside within areas identified as most suitable locations for urban compactness, which confirms that the calculated suitability values of parameter P1 are in accordance to reality. Figure 3 presents selected areas of urban compactness with highest obtained values for P1 and also known areas where urban densification exhibit dynamic changes in the past decade: (a) Downtown Core, City of Vancouver; (b) Metrotown Centre, City of Burnaby; (c) Coquitlam Centre, City of Coquitlam; and (d) Brentwood Centre, City of Burnaby. Figure 3 depicts values for P1 combined with Google Earth’s model (on the left) and compared to reality (on the right) as seen for year 2016.

Figure 3.

Selected areas in the Metro Vancouver Region with the obtained suitability map overlaid with Google Earth 3D model (left) and the images of real high-rise building locations (right).

The parameter P2 was calculated for the Metro Vancouver Region land use dataset. Figure 4 shows a composite of all land use evaluation iterations, symbolized to show the spatio-temporal growth. Darker red areas shown are land use designations acceptable to have urban compactness development in the initial iteration T_initial. The other colors represent the following iterations and the new land that becomes acceptable to be developable for mid- and high-rise buildings.

Figure 4.

Values obtained for the land designation parameter P2 for the Metro Vancouver Region depicting changes of available developable land over time for T_initial, T₁, T₂, and T₃ representing the years 2011, 2021, 2031, and 2041, respectively.

The parameter P3 for the Metro Vancouver Region was derived from the sample municipalities of City of Surrey, District of North Vancouver, and City of Vancouver’s building average height for each suitable land designation. The derived average building heights were assigned to the six land use designations for the Metro Vancouver Region that were acceptable for development. Low building height averages were calculated for land use designations with townhouse and low-rise apartment buildings, while higher building averages were calculated for land use designations with high-rise apartment and commercial building. Figure 5 presents the spatial distribution of the parameter P3 for the Metro Vancouver region for the year 2011 as T_initial.

Figure 5.

Values obtained for the average building height parameter P3 for the Metro Vancouver Region for year 2011 and with focus on smaller areas with concentrations of tall buildings.

Spatial index values for the local and regional components

The generated parameters were combined to derive the spatial index of 3D urban compactness for the Metro Vancouver Region and to demonstrate land densification change over time. The height values calculated by the 3D urban compactness index were extruded for the 2011, 2021, 2031, and 2041 years. Moreover, the spatial index for 3D urban compactness was recalculated for each time iteration. The local component of the index also indicated vertical growth for individual lots with an average growth of 2.9, 3.7, and 4.6 meters for the years 2021, 2031, and 2041, respectively. The total average cell growth over all iterations was 11.2 meters, and the vertical growth is evident. Individual lots indicating smaller heights rose in the following iterations, decreasing the mid-height gap. The regional component of the index was calculated to determine overall lot heights of 17.04, 21.74, 24.51, and 28.81 meters for the Metro Vancouver Region for the years 2011, 2021, 2031, and 2041, respectively. This is in accordance with the overall trend in the forecast of increasing urban compactness growth across the region.

Figure 6 (on the left) presents the obtained values for the local spatial index for the Metro Vancouver Region in a series of maps for each year 2011, 2021, 2031, and 2041. On the right side of Figure 6, smaller areas are presented with lots extruded into 3D based on the calculated index height. The figure depicts the cities of New Westminster and Burnaby with the perspective area identified by the view-cone on the top Metro Vancouver map. This area is another dynamic corridor for urban densification with noticeable development of subcenters and the leap-frogging effect in 2011 and 2021. From the obtained results, it can be seen that in 2031 and 2041 the mid- and high-rise buildings will cover much larger surfaces, if not the entire city of New Westminster.

Figure 6.

The spatial index for urban compactness for the Metro Vancouver Region (left) and the smaller sub-region of the City of New Westminster (right) for the years 2011, 2021, 2031, and 2041.

The Metro Vancouver region is an example of an urban landscape that is already experiencing urban compactness growth with encouragement of sustainable development from the regional and municipal governments. The highest values of the local spatial index of 3D urban compactness for the region were obtained for well-known urban centers such as Downtown Vancouver, Metrotown Centre, Coquitlam Centre, Richmond and Surrey Centre, where high building densification has occurred in the past decade.

Downtown Vancouver has the tallest and greatest quantity of high-rise buildings in the entire Metro Vancouver Region. It is the largest Central Business District in the region with many employment opportunities and is a very livable center. The high-rise buildings within Downtown Vancouver are a mix of commercial and residential developments. Downtown Vancouver has a well-developed public transportation system including frequent buses, rapid rail, and water ferries. The proposed spatial index was calculated for the Downtown Vancouver region to derive local component values of 77.6, 72.0, and 67.8 meters for the years 2021, 2031, and 2041 demonstrating a decrease in the building height range and an increase of building height difference over time. The regional component values of the spatial index were calculated as 68.0, 70.0, and 70.1 meters for the same years as the local component, demonstrating a less aggressive height growth for the region that can be explained by the already highly built up core downtown of the Metro Vancouver region.

Metrotown Centre resides within the City of Burnaby municipality and has the largest shopping center in the entire Province of British Columbia. It also has a large park and many walking trails in close proximity. The center has a rapid rail and bus network that connects residents to Downtown Vancouver in approximately 30 minutes. Most of the mid- and high-rise developments in the area are residential, with a few commercial buildings. The spatial index was calculated for the Metrotown Centre core and local component values were calculated as 78.7, 73.0, and 69.2 meters for the years 2021, 2031, and 2041 also showing a decreasing gap in building height difference as increased number of buildings in the region gain height over time. The regional component values were calculated as 43.1, 44.6, and 47.6 meters following the same years as the local component, which also demonstrates an averaged regional growth for this area.

Similarly, the City of Surrey is also connected to the same rapid rail line that connects to Downtown Vancouver. Unlike Metrotown, Surrey Center is located close to a major highway enabling faster travel to Downtown Vancouver and other parts of the region. The City of Surrey is experiencing great population growth and is projected to be one of the fastest growing cities in the region. With plans to develop a strong Central Business District and transportation extension, Surrey Centre may rapidly develop a more compact center. The calculated values of the local component of the spatial index are 78.7, 73.5, and 68.8 meters for the years 2021, 2031, and 2041 demonstrating a decreasing gap in building height difference and an overall building height increase over time. The regional component values were calculated as 40.2, 42.0, and 44.0 meters for the same years as the local component, which show an average of building height growth over the Surrey Centre region.

Coquitlam Centre has less mid- and high-rise buildings than the other three centers. However, the high-rise developments occurring next to the shopping and large transportation hub have been under development in recent years. Although not currently connected to the rapid rail network, the development of such connection is expected to be completed by the year 2017 and this may be a strong indicator as to why these buildings have more recently developed at this location. The local component of the spatial index was calculated for the Coquitlam Centre region with values recorded as 78.5, 73.7, and 70.1 meters for the years 2021, 2031, and 2041, which again shows the decreasing gap between building heights as the building grow in height over time. The regional component of the index was calculated for the same years with values shown as 42.3, 43.3, and 45.0 meters demonstrating the areas average building height growth over time.

As presented in this research study, the developed urban compactness index with the local and regional components presented through the developed equation has properly identified and calculated locations for urban compactness growth. The obtained results demonstrate that urban compactness is closely linked to major transportation networks and more specifically to the rapid rail stations in Metro Vancouver, which is documented in regional urban growth literature. As the rapid rail transportation continues to branch out, alongside other services, more subcenters of urban compactness can be expected to be developed in the Metro Vancouver region. The presented spatial index with the local and regional components can be applied to future growth scenarios, such as proposed transportation expansions, to aid in regional planning.

Conclusions

The presented research proposed the spatial index of 3D urban compactness with two components used for local and regional representation of urban vertical growth over space and time. The spatial index was derived from three parameters, a suitability analysis, land designation, and average building height. The parameters were combined to produce an urban compactness index that was applied to the Metro Vancouver Region for the years 2011 to 2041. The results present locations deemed suitable for urban compactness and provide a vertical height growth over time. The spatial index calculates local values to demonstrate a decreasing building height difference and regional values to show the increasing average building heights, both calculated over time. The local and regional component values were calculated for the entire Metro Vancouver region and individual smaller urban centers with results all demonstrating a decreasing of building height difference and average building height increase over time. The 3D extrusion of the vertical heights presented a perspective view on the regional spatial distribution of urban compactness. As discussed, the urban compactness index identified centers within Metro Vancouver that are already experiencing vertical growth through mid- and high-rise building developments.

The presented work has potential to aid in municipal and regional urban and sustainable planning to achieve sustainable urban growth. The 3D urban compactness index was based on a multi-criteria decision-making method that identified suitable locations for vertical growth determined by spatial indicators. This decision-making method can be used as a tool to identify locations of changing vertical growth by incorporate recommendations and providing indicator weights directly from city stakeholders such as planners, buyers, developers, and others. Specifically, the urban compactness projections can provide insights on urban compactness “hot-spots”, important for planning scenarios such as transportation, view-obstruction, energy efficiency, and pollution concentrations, as few examples. Planning for such demands can ultimately aid in designing a more sustainable and efficient built environment. Additionally, the presented 3D urban compactness index can be refined to municipal level scales that can utilize their own data, such as building height and land use designation, for more detailed study. Conversely, the methods presented can be applied to other growing regions with few refinements unique to each geographic locations.

Footnotes

Acknowledgements

Authors are thankful for valuable feedback from two anonymous referees and the journal Editor.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was funded by the Natural Sciences and Engineering Research Council (NSERC) of Canada Discovery Grant (No. 328224-2012) awarded to the second author.

Olympia Koziatek completed her Masters of Science degree in the Spatial Analysis and Modeling (SAM) Research Laboratory at Department of Geography, Simon Fraser University, Canada. Her research focus is on three-dimensional analysis, modeling and visualization related to urban growth and the spatial factors that affect land-use change. Specifically, she is interested in modeling high-density urban growth for regional and local scales. She is currently lecturing courses in the department of geography focusing on spatial information sciences.

Suzana Dragićević is a Professor in the Department of Geography and director of the Spatial Analysis and Modeling (SAM) Research Laboratory, Simon Fraser University, Canada. Her main research work deals with the integration of GIS, complexity science and computational intelligence for the analysis and modeling of complex dynamic geographical systems. Application areas include land-use/land-cover change, urban growth, forestry and landscape ecology. Dr. Dragićević is co-editor of the Springer book series on ‘Advances in Geographic Information Science’; associate editor for the ‘Computers, Environment and Urban Systems’, ‘Geomatica’ and ‘Earth Science Informatics’ journals and member of several international journal editorial boards.

References

Aalbers

(2009) Geographies of the financial crisis. Area 41(1): 34–42.

Abdullahi

Pradhan

Jebur

(2015) GIS-based sustainable city compactness assessment using integration of MCDM, Bayes theorem and RADAR technology. Geocarto International 30(4): 365–387.

Al-Douri

(2010) The impact of 3D modeling function usage on the design content of urban design plans in US cities. Environment and Planning B: Planning and Design 37(1): 75–98.

Brunn

Williams

Zeigler

(2003) Cities of the World: World Regional Urban Development, Lanham: Rowman & Littlefield.

Burgess R and Jenks M (eds) (2002) Compact Cities: Sustainable Urban Forms for Developing Countries (1). London: Routledge. Available at: www.ebrary.com.proxy.lib.sfu.ca (accessed 29 March 2017).

Burton

(2000) The compact city: Just or just compact? A preliminary analysis. Urban Studies 37(11): 1969–2006.

Burton

(2002) Measuring urban compactness in UK towns and cities. Environment and Planning B 29(2): 219–250.

Carruthers

Ulfarsson

(2003) Urban sprawl and the cost of public services. Environment and Planning B: Planning and Design 30(4): 503–522.

Chen

Jia

Lau

SSY

(2008) Sustainable urban form for Chinese compact cities: Challenges of a rapid urbanized economy. Habitat International 32(1): 28–40.

10.

Chen

Devereux

(2014) Urban landscape pattern analysis based on 3D landscape models. Applied Geography 55: 82–91.

11.

City of Surrey (2014) Official community plan. Bylaw No 18020. Planning and Development, Surrey, Canada. Available at: www.surrey.ca (accessed 27 April 2015).

12.

DataBC [computer file]. Government of British Columbia, 2016. Available at: www.catalogue.data.gov.bc.ca (accessed 2 October 2015).

13.

Dieleman

Wegener

(2004) Compact city and urban sprawl. Built Environment 30(4): 308–323.

14.

District of North Vancouver (2015b) Size, location, and dimensions of building on you lot. Zoning guides, multiple. Available at: from: www.dnv.org (accessed 3 May 2016).

15.

ESRI (2013) ArcGIS desktop version 10.2, Redlands, CA: Author.

16.

Ewing R, Schmid T, Killingsworth R, et al. (2003) Relationship between urban sprawl and physical activity, obesity, and morbidity. American Journal of Health Promotion 18(1): 47–57.

17.

Feitosa

Camara

Monteiro

AMV

et al. (2007) Global and local spatial indices of urban segregation. International Journal of Geographical Information Science 21(3): 299–323.

18.

Fox

(2010) Halting urban sprawl: Smart growth in Vancouver and Seattle. Boston College International and Comparative Law Review 33(1): 43–60.

19.

Frenkel

(2007) Spatial distribution of high-rise buildings within urban areas: The case of the Tel-Aviv metropolitan region. Urban Studies 44(10): 1973–1996.

20.

Galster

Hanson

Ratcliffe

et al. (2001) Wrestling sprawl to the ground: Defining and measuring an elusive concept. Housing Policy Debate 12(4): 681–717.

21.

GeoBC (2015) Government of British Columbia. Available at: www.geobc.gov.bc.ca (2015, accessed 29 March 2017).

22.

GeoGratis (2015) Natural resources Canada. Available at: www.nrcan.gc.ca (2015, accessed 29 March 2017).

23.

Geoweb Open Data (2015a) [computer file]. District of North Vancouver. Available at: www.geoweb.dnv.org/data (accessed 2 October 2015).

24.

Graymore

Wallis

Richards

(2009) An index of regional sustainability: A GIS-based multiple criteria analysis decision support system for progressing sustainability. Ecological Complexity 6(4): 453–462.

25.

Hatch

Dragicevic

Dujmović

(2014) Logic scoring of preference and spatial multicriteria evaluation for urban residential land use analysis. Lecture Notes in Computer Science 8728: 64–80.

26.

Herrschel

(2013) Competitiveness and sustainability: Can ‘Smart city regionalism’ square the circle? Urban Studies 50(11): 2332–2348.

27.

Hess

Sorensen

(2015) Compact, concurrent, and contiguous: Smart growth and 50 years of residential planning in the Toronto region. Urban Geography 36(1): 127.

28.

Holden

(2006) Urban indicators and the integrative ideals of cities. Cities 23(3): 170–183.

29.

Jankowski

(1995) Integrating geographical information systems and multiple criteria decision-making methods. International Journal of Geographical Information Systems 9(3): 251–273.

30.

Jenks

Burton

Williams

(1996) The Compact City: A Sustainable Urban Form?, London: E., & F. N. Spon.

31.

Jiang

Eastman

(2000) Application of fuzzy measures in multi-criteria evaluation in GIS. International Journal of Geographical Information Science 14(2): 173–184.

32.

Jjumba

Dragićević

(2016) Spatial indices for measuring three-dimensional patterns in a voxel-based space. Journal of Geographical Systems 18(3): 183–204.

33.

Johnson

(2001) Environmental impacts of urban sprawl: A survey of the literature and proposed research agenda. Environment and Planning A 33(4): 717–735.

34.

Koomen

Rietveld

Bacao

(2009) The third dimension in urban geography: The urban-volume approach. Environment and Planning B, Planning & Design 36(6): 1008.

35.

Kropp

Lein

(2012) Assessing the geographic expression of urban sustainability: A scenario based approach incorporating spatial multicriteria decision analysis. Sustainability 4(9): 2348–2365.

36.

Yeh

(2004) Analyzing spatial restructuring of land use patterns in a fast growing region using remote sensing and GIS. Landscape and Urban Planning 69(4): 335–354.

37.

Lin

Huang

Chen

et al. (2014) Modeling urban vertical growth using cellular automata – Guangzhou as a case study. Applied Geography 53: 172–186.

38.

Liu

Song

(2014) An empirical study on the relationship between urban compactness and CO₂ efficiency in China. Habitat International 41: 92–98.

39.

Livanis

Moss

Breneman

et al. (2006) Urban sprawl and farmland prices. American Journal of Agricultural Economics 88(4): 915–929.

40.

Magarotto

da Costa

Tenedório

et al. (2015) Vertical growth in a coastal city: An analysis of Boa Viagem (Recife, Brazil). Journal of Coastal Conservation 20(1): 31–42.

41.

Malczewski

(2004) GIS-based land-use suitability analysis: A critical overview. Progress in Planning 62(1): 3–65.

42.

Metro Vancouver (2010) Metro Vancouver sustainability framework. Available at: www.metrovancouver.org (accessed 29 March 2017).

43.

Metro Vancouver (2016) Regional growth strategy. Available at: www.metrovancouver.org (accessed 29 March 2017).

44.

Min

Fengjun

Fath

(2010) Measurement and spatial distribution of urban land use compactness in Chaoyang district of Beijing, China. Chinese Journal of Population Resources and Environment 8(4): 3–9.

45.

Montgomery

Dragicevic

(2016) Comparison of GIS based logic scoring of preference and multi-criteria evaluation methods: Urban land use suitability. Geographical Analysis 48: 427–447.

46.

Mubareka

Koomen

Estreguil

et al. (2011) Development of a composite index of urban compactness for land use modelling applications. Landscape and Urban Planning 103(3): 303–317.

47.

Neuman

(2005) The compact city fallacy. Journal of Planning Education and Research 25(1): 11–26.

48.

Open Data Catalogue (computer file). City of Vancouver, 2016. Available at: www.data.vancouver.ca (accessed 2 October 2015).

49.

Open Data Catalogue (computer file). Metro Vancouver, 2016. Available at: www.metrovancouver.org/data (accessed 2 October 2015).

50.

Pollard

Eden

Mundy

et al. (2010) A volumetric approach to change detection in satellite images. Photogrammetric Engineering & Remote Sensing 76(7): 817–831.

51.

Qin

Fang

Wang

et al. (2015) Evaluation of three-dimensional urban expansion: A case study of Yangzhou city, Jiangsu province, China. Chinese Geographical Science 25(2): 224–236.

52.

Rahman

Shi

Chongfa

(2014) Assessing regional environmental quality by integrated use of remote sensing, GIS, and spatial multi-criteria evaluation for prioritization of environmental restoration. Environmental Monitoring and Assessment 186(11): 6993–7009.

53.

Sani Roychansyah

Ishizaka

Omi

(2005) Considerations of regional characteristics for delivering city compactness: Case of studies of cities in the greater Tokyo area and Tohoku region, Japan. Journal of Asian Architecture and Building Engineering 4(2): 339–346.

54.

Salvati

Zitti

Sateriano

(2013) Changes in city vertical profile as an indicator of sprawl: Evidence from a Mediterranean urban region. Habitat International 38: 119–125.

55.

Santos

Rodrigues

Tenedório

(2013) Characterizing urban volumetry using LIDAR data. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-4/W1: 71–75.

56.

Shiode

(2000) 3D urban models: Recent developments in the digital modelling of urban environments in three-dimensions. GeoJournal 52(3): 263–269.

57.

Stathakis

Tsilimigkas

(2015) Measuring the compactness of European medium-sized cities by spatial metrics based on fused data sets. International Journal of Image and Data Fusion 6(1): 42–64.

58.

Stal

Tack

De Maeyer

et al. (2013) Airborne photogrammetry and LIDAR for DSM extraction and 3D change detection over an urban area – A comparative study. International Journal of Remote Sensing 34(4): 1087–1110.

59.

Statistics Canada (2011) Census. Faculty of Arts & Sciences, University of Toronto, 2016. CHASS Data Centre, Canadian Census Analyzer. Available at: http://datacentre.chass.utoronto.ca.proxy.lib.sfu.ca/census/ (accessed 14 September 2015).

60.

Statistics Canada (2012) Greater Vancouver, British Columbia (Code 5915) and British Columbia (Code 59) (table). Census Profile. 2011 Census. Statistics Canada Catalogue no. 98-316-XWE. Ottawa. Available at: www12.statcan.gc.ca/census-recensement/2011/dp-pd/prof/index.cfm?Lang=E (2012, accessed 30 May 2016).

61.

Surrey Open Data (computer file). City of Surrey: GIS section, 2016. Available at: www.data.surrey.ca (accessed 2 October 2015).

62.

Temenos

McCann

(2012) The local politics of policy mobility: Learning, persuasion, and the production of a municipal sustainability fix. Environment & Planning A 44(6): 1389–1406.

63.

Tompalski

Wezyk

(2012) LiDAR and VHRS data for assessing living quality in cities – An approach based on 3D spatial indices. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences 39: B6.

64.

Torrens

(2008) A toolkit for measuring sprawl. Journal of Applied Spatial Analysis 1: 5–36.

65.

Translink (2011) Transit-oriented communities: A primer on key concepts. Available at: www.translink.ca (accessed 29 March 2017).

66.

Wong

(2002) Modeling local segregation: A spatial interaction approach. Geographical and Environmental Modelling 6(1): 81–97.

67.

World Commission on Environment and Development (1987) Our Common Future, Suffolk, EN: Oxford University Press.

68.

Yeh

(2002) A cellular automata model to simulate development density for urban planning. Environment and Planning B: Planning and Design 29(3): 431–450.

69.

Yoo

Lee

Kwon

(2009) Quantitative indices based on 3D discrete wavelet transform for urban complexity estimation using remotely sensed imagery. International Journal of Remote Sensing 30(23): 6219–6239.