An examination of urban form in Halifax-Dartmouth: Alternative approaches in data.
Subject: Urban land use (Research)
Urban geography (Case studies)
Authors: Cuthbert, Angela L.
Anderson, William P.
Pub Date: 12/22/2002
Publication: Name: Canadian Journal of Urban Research Publisher: Institute of Urban Studies Audience: Academic Format: Magazine/Journal Subject: Social sciences Copyright: COPYRIGHT 2002 Institute of Urban Studies ISSN: 1188-3774
Issue: Date: Winter, 2002 Source Volume: 11 Source Issue: 2
Topic: Event Code: 310 Science & research
Geographic: Geographic Scope: Nova Scotia Geographic Name: Halifax, Nova Scotia; Dartmouth, Nova Scotia Geographic Code: 1CNOV Nova Scotia
Accession Number: 98248390
Full Text: Resume

Get article examine le changement de la forme urbaine de la region Halifax-Dartmouth entre 1970 et 1996. Alors que plusieurs etudes empiriques emploient la fonction de densite negative exponentielle pour etudier un tel changement, cette etude analyse les formes spatiales du developpement. En faisant appel a des donnees desagregees a l'echelle de la parcelle, nous avons calculte des estimes de type << Kernel >> pour examiner la decentralisation et 'deconcentration' des terres residentiels et commerciales et la segregation urbaines. Les resultats indiquent que les changements de la forme urbaine d'Halifax-Dartmouth sont du a la fois A l'amenagement des terrains libres, contigue et a un amenagement urbain 'saute-mouton'. II apparait egalement que les terrains residentiels et commerciaux ont differents modes d'amenagement spatial.

Mots clefs: forme urbaine, decentralisation, 'deconcentration', amenagement urbain, gradient de densite, estimates de type "Kernel."


This paper examines the changing urban form of the Halifax-Dartmouth region between 1970 and 1996. While many empirical studies employ the negative exponential density function to study such change, this paper studies urban form by examining the spatial pattern of development. Using disaggregate parcel level data, we compute kernel estimates to investigate the decentralization and deconcentration of residential and commercial land parcels, and to examine the segregation of land uses. The results of the kernel estimates suggest that changes in the urban form of Halifax-Dartmouth were a combined result of infill, contiguous, and leapfrog development. However, it is apparent that residential and commercial land parcels exhibit different spatial patterns of development.

Key words: urban form, decentralization, deconcentration, land development, kernel estimates, density gradients


According to Bourne (1987), urban form is the physical arrangement of activities, households, and institutions in urban space. Over the past several decades, there have been tremendous changes in the form of urban areas. Most notably, many urban areas have transformed from a monocentric to a polycentric urban form. The fundamental transformation of urban form is characterized by three contributing trends: the outward expansion of the urban boundary (decentralization); the general decline in intensity of all forms of land use (deconcentration); and the segregation of residential land use from other land uses.

Many empirical studies commonly describe urban form by the geographical distribution of population and/or employment (For examples see Mieszkowski and Smith 1991; Bourne 1989; Edmonston, Goldberg and Mercer 1985). The results of these studies suggest that population and employment are decentralizing away from the urban core; that is, activity sites are re-locating from the urban core to the periphery. The result is an expanded urban area with low density, peripheral development. The most widely used method in describing these distributions is to employ zonal data in the estimation of the negative exponential density function. Despite the widespread use, zonal data and the density function provide only a limited picture of changes in urban form.

Parcel level data offer a valuable opportunity to explore the changing form of urban areas. Using point data rather than zonal data provides a better basis for examining the physical arrangement of activities, households, and institutions. In particular, the development of new residential land parcels explicitly shows where households are locating. Similarly, the development of new commercial land parcels shows where employment sites are locating. By examining the change in these household and employment locations over time, changes in urban form are apparent. Recent studies of urban structure suggest that urban form evolves through land conversion and land development processes (Wu and Gar-On Yeh 1997). Thus, the analysis of land parcel development is a viable alternative to study changes in urban form.

This paper employs parcel level data in the computation of kernel estimates. The kernel estimate shows variations in the intensity of land parcel development over space. The kernel estimate reveals a general pattern of land development by smoothing the data and removing extraneous detail. The kernel estimate is a visualization approach rather than an inferential or parametric statistics approach. The mapped results of the kernel estimates provide a visual indication of the most intense land development. A comparison of kernel maps for different time periods and for different land uses indicates changes in urban form. This makes it possible to observe the three contributing trends that lead to the transformation of urban form: decentralization, deconcentration, and the segregation of land uses. The kernel estimate is a valuable tool in that it employs detailed, disaggregate data. Moreover, it is a relatively simple technique that may be easily applied to other urban areas.

The objective of this paper is to investigate the changing urban form of the Halifax-Dartmouth region by examining the spatial pattern of residential and commercial land development. To accomplish this, disaggregate parcel level data are employed instead of zonal densities. The paper also provides an alternative approach to the traditional exponential density function to explore transformations in urban form. Kernel estimates provide a visual, two-dimensional exploration of the spatial pattern of land development.

Using the parcel level data and the results of the kernel estimates, this paper addresses the following research questions. First, what is the spatial pattern of land development and how do infill, contiguous, and leapfrog development contribute to the spatial pattern of development? Second, is there evidence of decentralization; that is, are new parcels locating outside the urban core? Third, is there evidence of deconcentration; that is, has the intensity of land development declined? Finally, is there evidence of segregation of residential land parcels from commercial land parcels?

The remainder of the paper is organized as follows. First, we explain the traditional negative exponential density function and then review several empirical studies that employ the function. Next, we describe the study area. Using census data for the study area, we estimate the negative exponential density function for several census years. We then describe the parcel level data and the kernel estimate. Finally, using the results of the kernel estimates, we address the research questions.

Literature Review

Numerous studies document the changing form of urban areas. While the study areas may vary, the most commonly used method is to estimate the negative exponential density function. The negative exponential density function provides insight into the relationship between population and/or employment density and distance to the centre of the city. The population and/or employment densities are calculated for a sufficiently large number of urban zones over a period of time. The results show how the locational patterns of population and employment change over time. Essentially, the density function attempts to summarize a complex pattern with a single parameter, the density gradient.

Clark (1951) first modeled the density-distance relationship using the following mathematical form:

[D.sub.x] = [D.sub.0][e.sup.-bx] [1]

where D is population or employment density, x is distance from city centre, [D.sub.0] is density at city centre, e is the natural logarithmic base, and b is the slope or density gradient. The density gradient serves as a summary statistic of decentralization. The more uniform density is, as a function of distance from the city centre, the smaller the value of b. Comparing values of b over time provides insight into the decentralization of population and employment. Decreases in b over time indicate increases in the decentralization of urban areas. Clark estimated the model for several cities and concluded that the negative exponential density function is the norm for urban population density patterns.

Since Clark's formulation, the negative exponential density function has been the basis of many empirical analyses that investigate the changing form of urban areas. Edmonston, Goldberg, and Mercer(1985) examine differences in urban form through a comparative investigation of density gradients of residential populations for metropolitan centres in the United States and Canada. The results suggest that urban areas in both countries experienced similar decentralizing trends with central densities on average decreasing by half between 1951 and 1976 (Edmonston, Goldberg and Mercer 1985). However, despite rapid decentralization, central densities in Canadian urban centres are twice as high as their U.S. counterparts. In Canada, b decreased from 0.93 in 1951 to 0.42 in 1976, while in the U.S., b decreased from 0.76 to 0.45 over the same time period. Based on the results, Edmonston, Goldberg and Mercer (1985) suggest that Canadian cities exhibit a more densely settled urban area and a more compact urban form.

In a comparative study of the 27 largest urban areas in Canada, Bourne (1989) examines population and employment data to reveal several trends in urban growth and urban form. Population density gradients indicate that average residential densities have declined and the slopes of the gradients have become much flatter and more convoluted; that is, less smooth because of more variability (Bourne 1989). Bourne (1989) examines the decentralization of employment using journey to work distances and the location of work-trip destinations. The analysis suggests that average commuting distances have decreased for suburban residents and suburban employment locations, but have increased for inner city residents and central employment locations. Bourne (1989) concludes that population and employment have decentralized in Canadian urban areas. Bourne (1989) also calculates a measure of the relative degree of population redistribution to determine how rapidly Canadian urban areas are decentralizing through a combination of suburbanization and inner city decline. Results of a linear regression model in which the rate of population change by census tract is regressed against distances to the central core suggest that all 27 urban areas experienced inner area population decline and overall spatial deconcentration (Bourne 1989). Because of regional variability in the results, Bourne (1989) concludes that the emergence of a new and massively dispersed urban form has not occurred in Canadian urban areas.

Mieszkowski and Smith (1991) examine the pattern of population and employment decentralization in Houston. First, the study estimates the negative exponential density function using census tract data. The results reveal that decentralization in Houston involves both absolute decline in inner city population and the infill of existing suburban areas. Next, the study estimates a population density function that employs actual land utilized for residential activity by census tract rather than total land area. The results suggest that much of the decline in density with respect to distance from the centre is attributable to declining rates of land utilization. Declines in aggregate density over time are explained by leapfrog development over large tracts of vacant land rather than by an increase in the amount of land per occupied housing unit (Mieszkowski and Smith 1991).

Barkley, Henry, and Bao (1996) examine patterns of spatial structural change for functional economic areas in North Carolina, South Carolina, and Georgia by estimating population density functions using census tract data. Comparison of population density functions for 1980 and 1990 suggests that population decentralization accompanied metropolitan growth. The results indicate that residential densities declined near the metropolitan core and increased in the suburbs, edge cities and in rural areas proximate to the metropolitan fringe (Barkley, Henry and Bao 1996).

Jordon, Ross, and Usowski (1998) estimate population density functions to analyze differences in rates of suburbanization in U.S. metropolitan areas between 1970 and 1990. The results indicate that while the average rate of suburbanization, that is, the average rate ofchange in the density gradient, did not change significantly over the time period, all metropolitan areas experienced continuing decentralization. The results also show that smaller metropolitan areas have higher values of b and experience greater absolute changes in b than do larger metropolitan areas.

Despite the widespread use of the negative exponential density function, the growth and resultant urban form of contemporary urban areas brings into question the functions' applicability. Several studies suggest that the negative exponential density function is not appropriate for the non-monocentric nature of contemporary cities (Anderson 1985; Crampton 1991; Mieszkowski and Mills 1993). Mieszkowski and Mills (1993) concur that while the exponential density function has been valuable in understanding past trends in decentralization, the emergence of new (polycentric) urban forms makes the function increasingly irrelevant.

In addition to the problems associated with the negative exponential density function, there are several problems in using aggregate zonal data when estimating the function. Because zones are defined for a variety of purposes, actual values for any given variable will vary with the level of aggregation and with the configuration of the zoning system. The zones may not accurately represent the underlying geographical distribution of any particular variable. For example, census tracts are designed primarily for ease of enumeration rather than to represent the underlying geographical distribution of population or employment. This sensitivity of analytical results to the definition of zones for which data are collected is known as the "modifiable area unit problem" (Fotheringham and Wong, 199l; Openshaw, 1984).

Census data may also be problematic when estimating densities because extensive unpopulated areas such as open water, industry, or agriculture are included in the land area measurements of the zone. In particular, peripheral zones are problematic, as they tend to be so spatially extensive that the population physically occupies a small proportion of the land area. Finally, census data are sensitive to demographic trends. For example, declining population densities in older neighbourhoods may be a function of decreasing household size and cannot be interpreted as a change in urban form. Thus, the density gradient will change because of demographic trends, even though urban form does not change.

Several important points emerge from the empirical literature regarding urban form. First, the form of urban areas is changing as a result of the continued decentralization of population and employment. The empirical results indicate that population and employment exhibit different patterns of decentralization; that is, population tends to be more decentralized than employment. Moreover, decentralization may result from different processes such as redistribution of growth from the core to the periphery or new growth in the periphery relative to the core.

Second, many of the empirical studies employ the negative exponential density function in examining changes in urban form. However, there are several problems related to the density function in terms of the functional form and the use of census data. More importantly, the processes that underlie changes in urban form are probably too complex and varied to be captured by a single density gradient parameter. Thus, it is clear that an alternative method that employs less problematic data and takes a more explicitly spatial approach would be valuable in examining the changing form of urban areas.

The Study Area

The Halifax Regional Municipality covers an area of 6200 square kilometres along the south shore of Nova Scotia. The municipality consists of the cities of Halifax and Dartmouth, the town of Bedford, and the remaining rural periphery. Because urban land development is of interest, we define a functional urban area within the administrative region. While the eastern half of the region is primarily sparse rural development, the western half holds the majority of the land parcels and corresponds roughly to the Halifax Census Metropolitan Area (CMA). For the purposes of this paper, we only employ parcel level data for the western half of the Halifax Regional Municipality to examine the spatial pattern of land development. We refer to this sub-region as the Halifax-Dartmouth region. Figure 1 provides a map of the study area with various points of interest that we highlight later in the discussion.

To effectively evaluate the viability of an alternative method and type of data to investigate urban form, it is necessary to provide results from the traditional method. We estimate the negative exponential density function using census tract data for the Halifax-Dartmouth region for the years 1971, 1976, 1981, 1986, 1991, and 1996. We define the centre ([D.sub.0]) as the Halifax census tract that contains the central business district. Table 1 provides the results.

Over the time period, the density gradient became slightly flatter. Compared to the density declines documented in the literature (particularly Edmonston, Goldberg and Mercer 1985), these results suggest that the urban form of the Halifax-Dartmouth region did not experience significant change. Despite the lack of change, a scatter plot of population density and distance in Figure 2 reveals significant variability around the spatial trend. It is evident that there is much more going on than the density gradients indicate. The central densities fluctuate over the time period but indicate a decentralizing trend. The disaggregate parcel level data and the kernel estimates will provide additional insights into the changing urban form of the Halifax-Dartmouth region.

The Data Set

Parcel level data offer an excellent opportunity to examine the pattern of urban land development at a detailed spatial and temporal scale. For each year, the parcel level data indicate precisely where land is being developed. Through time, it is the development of individual land parcels that lead to the pattern of urban growth and the subsequent urban form. Wu and Gar-On Yeh (1997) assert that the change in the location of land development can reflect more readily the transformation of the urban spatial structure whereas the redistribution of population and changing land prices are results of land development. Thus, analysing the development of land parcels provides the opportunity to begin to understand the process that creates urban form.

Parcel level data are available from Service Nova Scotia and Municipal Relations (SNSMR). (1) SNSMR maintains a Property Records Database that includes a Property Information Report for every land parcel in the province. For each land parcel, the Property Information Report provides the UTM coordinate location, the year of parcel creation, and the land use type (i.e. residential or commercial (2). In 1996, the Halifax-Dartmouth region contained approximately 90 000 developed land parcels. Of those 90 000 parcels, 54 773 parcels were developed between 1970 and 1996. One variable that would be useful is the size or land area of each parcel. The lack of area data is unfortunate because the size of the establishment is unknown. Thus, a given commercial land parcel could be the site of a large factory or a convenience store while a given residential land parcel could be a single family home or an apartment building.

In order to examine changes in urban form, particularly decentralization, an urban core must be defined. The urban core, as defined by the 1971 Census of Canada (3) for the Halifax Census Metropolitan Area, is used as the urban core for this paper. The urban core includes the cities of Halifax and Dartmouth. The remaining part of the region is considered the periphery. Figure 1 shows the extent of the urban core and the periphery in the Halifax-Dartmouth region.

Table 2 summarizes the number of commercial and residential land parcels created in the urban core and the periphery in each time period. (4) The aggregate data clearly shows that the majority of the residential land parcels are located in the periphery. Alternatively, the majority of the commercial land parcels are located in the urban core. Between 1970 and 1978, 80 percent of all residential land parcels were developed in the periphery. This proportion decreased slightly between 1979 and 1987 when 71 percent of the residential land parcels were developed in the periphery. The periphery increased its share of parcels between 1988 and 1996 with the development of 76 percent of the residential land parcels.

Commercial land parcels exhibit a much different pattern of development. Between 1970 and 1978, the development of commercial land parcels was almost evenly split between the urban core (55 percent) and periphery (45 percent). Over the period 1979 to 1987, the urban core's share of new commercial land parcel development increased slightly to 59 percent. Finally, between 1988 and 1996, the core captured 61 percent of all new commercial land parcel development. Rather than decentralizing, these data suggest that commercial land parcel development has become more centralized. It should be noted, however, that given the lack of area data, parcels developed in the periphery may be larger than those developed closer to the core.

To begin to visualize the spatial pattern of development, we plot the land parcels using Arc View geographical information software. The land parcel data are divided into four cumulative time periods: those land parcels created prior to 1970, those created prior to 1979, those created prior to 1988, and those created prior to 1997. Each period represents a snapshot of the physical arrangement of residential and commercial land parcels that existed at that time.

The dot maps in Figures 3a-d illustrate the location of new land parcels during the four time periods. By comparing the dot maps, particularly Figure 3a and 3d, it is evident that the Halifax urban edge expanded slightly outward over the time period, while the Dartmouth urban edge expanded more significantly. Several finger-like axes of development along important regional roads formed early in the time period and continued to expand. Significant development also occurred in the periphery.

While the dot maps provide some insights into the pattern of urban growth, the precise spatial pattern of land development is complicated and difficult to interpret. When dealing with approximately 90 000 land parcels, it is not surprising that interpretation is difficult. What is required is a way to simplify the development pattern. To accomplish this, kernel estimates are computed. The resultant kernel maps reveal a more general structure in the spatial pattern of development.

Kernel Estimates

The kernel estimate is a spatial statistical technique that measures the variation in the mean value or intensity of a process in space. Essentially, the kernel estimate is a measure of the number of observed events per unit area. In this paper, we use the kernel estimate to measure the intensity of land parcel development. By mapping the kernel estimates, we can evaluate variations in the intensity of land development both spatially and temporally. For a complete derivation of the kernel estimate, refer to the Appendix.

The shading (gray scale) of the kernel maps corresponds to the intensity of land development where black is the highest intensity and white is the lowest. Because the kernel estimate smoothes the data, white does not necessarily imply that no development exists. The intensity of development, i.e. number of parcels, may just be so low relative to other areas that the value of intensity does not fall in the range of the gray scale. Because the level of commercial development is so small compared to residential development, the gray scales have different maximum values. Given this, we cannot directly compare the actual value of intensity represented by the shade of gray in the commercial and residential kernel maps. However, we can compare the spatial pattern of development and the location of the most intense areas of development.

We compute separate kernel estimates for both residential and commercial land parcels. As with the dot maps, we estimate cumulative time periods for land parcels created prior to 1970, parcels created prior to 1979, parcels created prior to 1988, and parcels created prior to 1997. The cumulative kernel maps illustrate the existing urban form in each time period, in terms of the physical arrangement or location of developed residential and commercial land parcels. We also compute kernel estimates for incremental time periods, 1970-1978, 1979-1987, and 1988-1996, to illustrate the areas of new residential and commercial land development.

Addressing the Research Questions

Based on the results of the kernel estimates, we address the following research questions. First, 'what is the spatial pattern of land development and how do infill, contiguous, and leapfrog development contribute to the spatial pattern of development?'. Analyses of the cumulative kernel maps, Figures 4a-d and 5a-d, suggest that growth in the Halifax-Dartmouth region was a combined result of infill, contiguous, and leapfrog development. We characterize infill development as the creation of new parcels within areas of existing development. Contiguous development is development that occurs adjacent to existing development. Leapfrog development is development that ignores vacant land closer to the urban core while land at further distances is developed instead.

Comparing the four time periods in Figures 4a-d and 5a-d, the spatial pattern of land development is apparent. Initially, the urban core was the most intensely developed with a combination of infill and contiguous development. The urban core promoted the form and pattern of growth by establishing a pattern from which subsequent growth followed. As development consumed land within the core, clusters of development evolved outside the core. Subsequently, infill and contiguous development of these clusters occurred.

The development of finger-like axes along regional roads is also a common pattern of development. The initial finger-like pattern expanded with a combination of infill and contiguous development along these axes. Scattered development is also apparent in the peripheral areas. Such scattered development was isolated initially, but in some instances eventually developed into a larger cluster when subsequent contiguous development occurred. The result is an intensely developed urban core with several smaller clusters of development in the periphery.

Results from the incremental kernel estimates address the research question 'is there evidence of decentralization?'. Decentralization results from the creation of new parcels outside the urban core. Leapfrog development clearly contributes to decentralization. Development that is contiguous to the urban core may also result in decentralization, as the urban core itself may become decentralized. However, leapfrog development and contiguous development have different scales of influence on decentralization. Leapfrog development, at a considerable distance from the urban core, may result in rapid decentralization, while development that is contiguous to the urban core may result in gradual decentralization. The result in both cases is land development that has decentralized from the original urban core.

The incremental kernel maps, Figures 6a-c and 7a-c, illustrate the location of new land development. By comparing the maps from the three time periods, it can be determined whether the areas of new land development are in peripheral locations. Continual development in the periphery suggests that development is decentralizing overtime. Figures 6a-c indicate that the majority of residential development occurred in the periphery, particularly in the area east of Dartmouth and in Lower Sackville. Commercial land parcel development, as illustrated in Figures 7a-c, is highly centralized. The urban core experienced most of the commercial development in terms of the number of developed land parcels, but some smaller clusters of commercial development did appear in peripheral areas. During the period 1988-1996, commercial development contiguous to these peripheral clusters resulted in the coalescing of commercial development.

We examine deconcentration -- the decline in intensity of land use -- by examining the variation of the intensity of land parcel development over the study area. In particular, we ask 'does the intensity of land development decline with distance from the urban core?'. Because the kernel estimate is essentially the number of parcels per unit area, declining intensity suggests fewer parcels per unit of land - deconcentration. Referring to Figures 6a-c, it is apparent that residential development is most intense in the core and diminishes with distance from the core. Intense development in the core is represented by the darkest colour of the gray scale, which becomes increasingly lighter with distance from the core. Between 1970 and 1996, there is substantial residential development in the periphery with several intense clusters of development. While these clusters intensify over time, the overall intensity of residential development continues to diminish with distance from the urban core. Peripheral residential development is less intense than residential development in the urban core. Figures 7a-c indicate that commercial development is also most intense in the urban core and the intensity decreases with distance. This pattern is consistent over time as there is little change in the intensity of commercial land development over the entire time period.

The final research question asks 'is there evidence of segregation of residential land parcels from commercial land parcels?'. From the cumulative kernel maps in Figures 4a-d and Figures 5a-d, it is evident that commercial land development is more centralized than residential land development in terms of intensity of land parcels. Residential land development exhibits a very different pattern of growth. Specifically, Halifax experienced contiguous growth resulting in a slightly expanded urban edge whereas in Dartmouth, extensive residential land development pushed the urban edge further and further into the rural periphery. Even more significant is the residential development in the Sackville area. From the initial development of a few clusters, intense contiguous and infill development caused the clusters to coalesce into a continuous mass of residential development.

While the traditional negative exponential density function suggests that the Halifax-Dartmouth region experienced little change in urban form, the kernel estimates provide more detailed insight. The results of the kernel estimates suggest that the urban form of the Halifax-Dartmouth region is a combined result of decentralization, deconcentration and land use segregation. However, there are differences in terms of residential and commercial land development. Residential land parcels exhibited decentralization and deconcentration. Commercial land parcels remained centralized within the urban core but the intensity of development did decrease with distance from the core. It is apparent that residential and commercial land parcels exhibit different spatial patterns of development.


Numerous empirical studies have been conducted for a variety of urban centres to examine changes in urban form. The common result of these studies is that population and employment are decentralizing. The results of this study for the Halifax-Dartmouth region concur that population is decentralizing in the fact that residential land parcels are decentralizing. However, commercial land parcels have not decentralized to the same extent. Several factors may help to explain these spatial patterns of land development in the Halifax-Dartmouth region. These factors also provide insight into the process of land development.

The spatial pattern of land development is partly explained by the heterogeneity of the land. Land development in the Halifax-Dartmouth region is constrained by several factors including the government ownership of land and the presence of numerous lakes. Figures 8a-b illustrate these constraints. Federal government holdings, located mainly in the Halifax-Dartmouth core, consist of Department of National Defence lands. The larger tracts of land in the periphery correspond to provincially owned crown land and parkland. The smaller tracts of land within the urban core are mostly municipal land holdings corresponding to local parks. The Halifax-Dartmouth region is also dotted with numerous lakes, which also constrain land development. In terms of the pattern of land development, such constraints may have contributed to the leapfrog development and subsequent infill and contiguous development in the region.

The role of planning in the Halifax-Dartmouth region also helps to explain the development patterns. The Halifax-Dartmouth Regional Development Plan was introduced in 1975 with the objective of directing growth to the Bedford-Sackville area, yet retaining a strong, viable core. The regional plan defined an urban development boundary and established a framework for municipal planning. The results of the kernel maps suggest that the regional plan was successful in directing growth to Bedford and Sackville. Despite this apparent success, interviews with Halifax Regional Municipality planners suggest that planning controls in the region have been permissive. Thus, a lack of planning control in other areas of the region may have contributed to the leapfrog development and subsequent contiguous and infill development.

The Regional Development Plan may have also succeeded in maintaining a strong, viable urban core. In terms of the number of land parcels, the data suggest that commercial development has actually become more centralized over time. For waterfront cities like Halifax-Dartmouth such a trend is unusual. According to Bourne (1987), waterfront cities tend to have higher land and congestion costs and as a result, the degree of employment and population decentralization is more pronounced. This decentralization reflects the reduced centrality of the waterfront downtown core. Despite the peninsula topography of Halifax-Dartmouth, the urban core maintains a strong presence in the region.

The Halifax-Dartmouth region may have retained a strong urban core for other reasons as well. The twin city configuration of Halifax-Dartmouth contributes to the strength of the urban core. The cities have also invested in revitalizing the urban core. A revitalized waterfront and historic district, particularly in Halifax, helps to counterbalance the trend to decentralization and deconcentration. The fact that Halifax serves as a provincial and regional capital, and a regional service centre also contributes to the strength of the urban core. The Halifax central business district is the largest single employment centre in Atlantic Canada (Millward and Bunting 1999). Located within the urban core are a Naval Dockyard, two large medical centres and two academic institutions. Thus, the urban core holds agglomerative power, which has led to greater centrality.

Transportation infrastructure development has also played a vital role in maintaining the centrality of the urban core. The construction of two bridges that connect Halifax and Dartmouth have improved the accessibility of the urban core. High accessibility at the intersections of important regional roads has encouraged the development of several industrial parks in the region. Many of the peripheral clusters of commercial development evident in the kernel maps correspond to industrial parks at these highly accessible locations.

Several important factors have played a role in the pattern of land development in the Halifax-Dartmouth region. Heterogeneity of the land influences the pattern of development in terms of limiting what land can and cannot be developed. The presence of lakes also influences the spatial pattern of land development. Planning controls have influenced the pattern of growth by directing development to certain areas. Finally, transportation infrastructure development has improved the accessibility of certain locations, thereby increasing the attractiveness of these locations for development.


Empirical studies suggest that many urban centres are experiencing a decentralization of both employment and population. Many studies, including those reviewed in this paper, evaluate these trends using aggregate measures of employment and population, specifically the negative exponential density function. Using parcel level data, this paper employs kernel estimates to examine the spatial pattern of land development. The resultant kernel maps allow for an explicit examination of the land development process, which leads to the pattern of urban growth and the subsequent urban form. Because the kernel estimate is a visualization approach rather than a parametric approach, the maps reveal both quantitative and qualitative changes in urban form that cannot be inferred from the changes in the gradient of the negative exponential density function. Additionally, kernel estimates are simple to compute and may easily be applied to any urban area for which point data are available.

Changes in urban form are characterized by three contributing trends: decentralization, deconcentration, and segregation of land uses. We used the results of the kernel estimates to determine if these trends are occurring in the Halifax-Dartmouth region. The kernel maps indicate significant residential land parcel development in the peripheral areas of the region. However, a corresponding pattern of commercial land parcel development is not evident. The kernel maps suggest that residential land parcel development experienced decentralization and deconcentration while commercial development did not. While the results of the kernel maps are robust, area data for the land parcels would provide additional insight into the decentralization/centralization of population and employment.

Using parcel level data, this paper explores the changing urban form of Halifax-Dartmouth by examining the spatial pattern of residential and commercial land parcel development. Although changes in urban form are apparent in the kernel maps, there are a number of factors that influence the specific spatial pattern of land development that must be considered more explicitly. Such factors include the availability of developable land, planning controls, and the development and location of transportation infrastructure. Of course, numerous other factors also influence development. To further our understanding of the process that leads to changes in urban form, additional analyses that explore the causal mechanism underlying urban growth and land development are required.


Derivation of the Kernel Estimate:

At a general location in the study area, s, the intensity of developed land parcels (events) is calculated. Following the notation of Bailey and Gatrell (1995), the intensity, [lambda](s), ats is estimated by:

[[lambda].sub.[iota]](s) = 1/[[delta].sub.[iota]](s) [summation over (n/i=1)] 1/[[iota].sup.2] k((s - [s.sub.i])/[iota]) [1]

wherek() is a bivariate probability density function or the kernel

[s.sub.i] is the location of observed event i

[lambda] is the bandwidth

[[delta].sub.[iota]](S) is an edge correction

Bailey and Gatrell (1995) describe the bandwidth, [iota], as the radius of a disc centred on s within which points [s.sub.i], will contribute significantly to the intensity at s. The value of [iota] is determined through experimentation. The effect of increasing [iota] is to increase the radius around s within which the observed events influence the intensity estimate at s. A large value of [iota] will cause the kernel map to appear smooth and local details will be lost, while a small value of [iota] will result in a kernel map with a collection of spikes centred on [s.sub.i].

In conducting the kernel analysis, several values of [iota] were tested. Using intervals of 500 metres, values of [iota] ranging from 500 metres to 5 000 metres were tested. Because [iota] determines the amount of smoothing, the kernel estimates that employed higher values of [iota] (2 000 [less than or equal to] [iota] [less than or equal to] 5 000) were too smooth and obscured the local detail. Alternatively, lower values of [iota] produced kernel maps that were too spikey to reveal general patterns. The most appropriate value of [iota] was 1500 metres, which allowed for the visualization of development in both the urban core and the periphery.

The most common choice of functional form for the kernel, k( ), and the one employed in the following estimations is the quartic kernel of the form:

k(u) = {3/[pi] 0 [(1-[u.sup.T] u).sup.2] for [u.sup.T]u[less than or equal to] 1

otherwise [2]

According to Bailey and Gatrell (1995), the quartic kernel is a radially symmetric probability density function, which is centred on the location sand scaled up by a factor [tau] of to provide a weighting applied to observed events around s. At locations (distance of zero), the weight is 3/[pi][[tau].sup.2] and it drops smoothly to a value of zero at distance [tau] Bailey and Gatrell 1995). Using the quartic kernel, the equation for intensity, [lambda](s), at s then becomes:

[[lambda].sub.[tau]](S) = 1/[[delta].sub.[tau]](S) [summation over ([h.sub.i][less than or equal to][tau] 3/[pi][[tau].sup.2] 1 - [([h.sup.2.sub.i]/[[tau].sup.2]).sup.2] [3]

where is the distance between the point s and the observed event location [s.sub.i]. It is important to note that the summation is only over values of [h.sub.i], that do not exceed [tau], thus an event outside the region of influence is not considered (Bailey and Gatrell 1995).

We compute the kernel estimates using the Splancs software package operating in the S-Plus programming environment. Splancs interfaces with S-Plus to display and analyze spatial point pattern data. Splancs employs a formulation for the kernel estimate that was proposed by Diggle (1985) and Berman and Diggle (1989).



The authors would like to thank the School of Geography and Geology at McMaster University where the work for this paper was completed.


(1.) Service Nova Scotia and Municipal Relations was formerly the Nova Scotia Department of Housing and Municipal Affairs.

(2.) Commercial parcels include all secondary, tertiary, quaternary, and quinary activities.

(3.) The urban core is a large urban area around which a CMA (census metropolitan area)

(3.) The urban core must have a population of at least 100 000.

(4.) The choice of these time periods corresponds to the incremental time periods used later in the kernel analysis. The incremental time periods 1970-1978, 1979-1987, 1988-1996 divides the entire time period into an approximately equal number of years. Several other variations of time periods were tested and the results were robust.


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Table 1

Density Gradients for the Halifax-Dartmouth Region 1970-1996

      N   [D.sub.0]    b    R-square

1971  46    3164     -0.19    0.49
1976  55    1997     -0.16    0.69
1981  61    2200     -0.16    0.69
1986  73    2086     -0.15    0.62
1991  73    2695     -0.15    0.64
1996  73    2377     -0.14    0.62

Table 2

Number of Commercial and Residential Land Parcels Developed in the
Halifax-Dartmouth Region, 1970-1996

                 1970-1978            1979-1987          1988-1996
             Core     Periphery  Core     Periphery  Core     Periphery

Residential  3236       12712    5058     12356      3909       12469
             (20%)      (80%)    (29%)    (71%)      (24%)      (76%)

Commercial    375        309      475      333        546        345
             (55%)      (45%)    (59%)    (41%)      (61%)      (39%)
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