Urban sprawl in Canada and America:
just how dissimilar?
John R. Miron*
Professor of Geography and Planning.
University of Toronto at Scarborough
1265 Military Trail, Toronto, Canada M1C 1A4
Phone 416 287 7311
Fax 416 287 7283
E-mail [email protected]
http://pc218.cus.utoronto.ca
Abstract
In the 1950s and 1960s, gross urban population density across Canada and America fell quickly and a new
phrase, "urban sprawl", was coined to describe the phenomenon. This phrase meant different things to
planners, to residents, and to scholars. Popular concern over urban sprawl continues to the present day.
However, in the 1970s, 1980s, and 1990s, new development in the form of clustered housing, in-fill,
redevelopment, and conversions helped raise densities in parts of some urban regions. Oftentimes with
the approval and encouragement of local governments, cooperation was promoted by land-use planners
who saw such development as the cure for sprawl. In Canada, where land-use regulation is thought to have
been more extensive, it might be argued that population density should therefore now be correspondingly
higher. At the same time, residents typically think of urban sprawl as loss of open space, increasing
homogeneity, and built-form clutter. Many political battles have been fought by residents working to
prevent planners from enacting exactly the kind of higher densities that planners thought would curb
sprawl. Making novel use of data for block groups for the entire United States and corresponding
dissemination areas in Canada, this paper explores the variation in, within, and among American and
Canadian urban regions for evidence of changes in urban sprawl. For each urban region, the paper
presents a pair of new measures, average local density (LDr) and its standard deviation (Sr), that help to
characterize urban form and that allow us to categorize urban regions by their reactions to different
notions of sprawl.
*
The financial support of the Social Sciences and Humanities Research Council of Canada (grant 410-00-0769) is
gratefully acknowledged.
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In the cacophony of voices within the social sciences and city planning literature on the subject, "urban
sprawl" often is an epithet hurled at a pattern or process that an author finds distasteful.1 Like the proud
but apprehensive parent finding the gangling adolescent in soiled clothes draped over the family's new
sofa, the author might admire the vitality, but be overwhelmed by the physical changes that have
occurred, the waning of a more-innocent time, and a heightened sense of complexities and costs in today's
world. It is similarly difficult to maintain objectivity in the swirl of emotions in which we observe and
critique urban sprawl; caught as we are between our disciplinary and professional lenses and our
aesthetic, social, and environmental sensibilities. As Myers and Kitsuse (1999, 2) argue:
We find all of the literature on this topic is very subjective, no matter how many objective facts are
introduced into the debate … As we will show, one man's sprawl is another one's compact development
… At root, evaluations of development density patterns and presumptions of desirable changes appear to
be heavily flavored by preconceptions and unstated values. There can be little hope of progress toward
resolving the impasse reached in this debate until these preconceptions have been brought to the
surface.
Even worse, some authors equate the term with a specific urban region, often Los Angeles, that is offered
as a stereotypical villain.2 The confusion and intellectual quagmire that has resulted is unfortunate.
Proponents of planning innovations through the years—e.g., planned unit development, growth
management, transit-supportive development, smart growth, new urbanist, compact cities, and
sustainable cities—are each quick to point out how we might cure sprawl by application of their ideas. At
the same time, their critics point out the fuzziness in thinking, the rationalizations, and the evident
failures in past attempts to "correct" sprawl.3 Now, perhaps more than ever, scholars, planners, activists,
communities, and governments alike, albeit in different ways, express the view that current patterns of
urban development create worrisome social, economic and environmental problems. To clarify this
debate, we need a better conceptualization, better definitions and better supporting data. Fortunately,
with the proliferation in recent years of massive amounts of geo-referenced small-area data, and the
technology to analyze them, we are now able to take a fresh look at the topic of urban sprawl.
This paper presents a measure of sprawl that I call "Local Density". I use this measure to characterize
sprawl across a sample of urban regions. It is helpful here if the sample of urban regions is sufficiently
similar in some respects, but different in others, in ways that can then be related to sprawl. Here, I
compare Canadian and American urban regions. In many ways, urban development in Canada and America
are driven by similar institutions and market forces. However, Canada's institutions differ in two important
respects. First, there is no constitutional protection for municipal government in Canada; municipalities
are enabled by the provinces, and the provinces can and do restructure them at will. This should mean
that provincial governments in Canada have been better able than state governments in America to
reorganize urban regions and their planning to deal with sprawl at a metropolitan/regional level. Second,
1 Donaldson (1969) considers at length the vilification of suburbs and sprawl in the popular and scholarly press.
2
See, for example, Ewing (1997) and Burchell et all (2000).
3
See, for example, Gordon and Richardson (1997b).
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because Canada does not guarantee property rights in its constitution, planners there have more leeway to
manage or control land use and thus the spatial pattern of growth in urban areas. Consequently, planning
regulation in Canada, particularly with respect to zoning and land subdivision, is arguably stronger. At the
same time, the American experience is different also because of federal legislation, such as the Clean Air
Act, Clean Water Act, Endangered Species Act, and Intermodal Surface Transportation Efficiency Act,
whose provisions have no direct equivalent in Canada. These provisions enable regulation of suburban
development at a regional scale, and hence can be used to control sprawl. Have these planning
instruments made a difference on net? Are the effects comparable across the two nations? It is now almost
two decades since the Goldberg and Mercer (1986) comparison of Canadian and American Cities: much has
happened since then, and it is fair to ask just how much different is urban sprawl among urban regions in
the two nations today.
Why is sprawl an issue?
In the contemporary social science and planning literature, there appear to be essentially three distinct
discourses (sets of voices) in thinking about urban sprawl as a problem. One discourse, as residents might,
is as a problem experienced. The second discourse, as planners and other advocates might, is as a problem
to be solved. The third discourse, as an economist or other social scientist might, is to interpret the
problem of sprawl in terms of implications arising from a particular theoretical framework. Let me
illustrate starting from early writers in the field.
Whyte (1958) is an early statement on urban sprawl as a problem experienced. Born in West Chester,
Pennsylvania, near Philadelphia, in 1917, Whyte was a journalist with Fortune magazine who went on to a
second career as a scholar of urban sprawl and revitalization. Whyte characterized sprawl in terms of its
adverse environmental impacts, and gave it a personal and polemical twist:
Already huge patches of once green countryside have been turned into vast smog-filled deserts… On the
outer edge of the present Philadelphia, some of the loveliest countryside in the world is being
irretrievably fouled…
Whyte (1958, 103)
Arguably, Whyte is ideologically conservative, bordering on NIMBYism. He had seen his beloved West
Chester as the rolling farmland it had been, and rued the change wrought by urbanization. However,
accepting that urbanization was unstoppable, he then refocused the problem that he saw as urban sprawl:
Because of the leapfrog nature of urban growth, even within the limits of most big cities there is to this
day a surprising amount of empty land. But it is scattered; a vacant lot here, a dump there—no one
parcel big enough to be of much use.
Whyte (1958, 103)
This refocusing brings Whyte to his principal solution:
Reserve open space while there is still some left—land for parks, for landscaped industrial districts, and
for just plain scenery and breathing space… There are many local efforts by private and public groups to
control sprawl and save open space. But, each group is going at the problem from its special point of
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view, indeed without even finding out what the other groups are up to. Watershed groups, for example,
have not made common cause with the recreation people or utilities; farmers and urban planners have a
joint interest in open space but act more as antagonists than as allies—and all go down to piecemeal
defeat.
Whyte (1958, 104)
Whyte proposed the establishment of land banks and land trusts to acquire and manage significant pieces
of open space. How does the acquisition of open space ameliorate the smog-filled deserts to which Whyte
initially refers? At one level, Whyte might simply be trying to save vestiges of his West Chester for future
generations. At another level, one can argue that the new suburbanites would benefit from having places
to walk their dogs, to hike, or simply to relax and enjoy the scenery.
Since Whyte, numerous authors have written on sprawl as a problem experienced.1 Notable here are the
three laments about suburbia in Carver (1962: 12-22); the lament about muddle, the lament about
uniformity, and the lament about what is not there. More recently, Danielson et al (1999, 517) argue
similarly that the Los Angeles basin is sprawl, despite its density, because it is huge, is an unrelieved
fabric of developed land, contains little open space, and has an over-abundance of low-quality commercial
space. While there are evident differences in perspective here, what these have in common is that Whyte,
Carver, and Danielson et al equate sprawl with both the loss of something (e.g., open space, clean air,
aesthetics), tied to increased density and the spread of an unrelieved, muddled, or uniform urban fabric.
Bauer (1956) exemplifies the second approach: urban sprawl as a problem to be solved. In her case, the
perspective is that of a planner.
The wartime boom in babies caught us unaware, but we thought it would be temporary… Here we are,
focused on old central areas, with a tremendous kit of tools for reconstruction, while the vast flood of
new urban development flows beyond our view, all around our chosen island. The wave mounts and
mounts.
Bauer (1956: 106)
Why is sprawl a problem? Presumably for dramatic effect, Bauer makes the following polemical prediction
about urban sprawl (in her words, "rurbanization")
If the next several million people [in the LA basin] are scattered even more widely than the last wave,
won't everyone … spend all day driving from one place to another …? All our present overwhelming
problems of servicing such areas will be multiplied tenfold, and the countryside, that vague ideal for
which we have sacrificed all else, will have moved out into another state. Against this, we would have
none of the traditional urban virtues to console us. For rurbanization is the kiss of death for city and
country alike, as anyone who has been in California recently can attest. Although the goal is personal
and family freedom, cum natura, it doesn't quite work out that way.
Bauer (1956: 109)
Bauer, at the time a professor at the University of California at Berkeley, personalized sprawl much as
Whyte did above. However, her practitioner's sensibilities were different. In sprawl, she saw problems of
slow and lengthy trips, the costliness of lot servicing, and the loss of both countryside and urban benefits.
However, note that the loss of open space, so dear to Whyte, is not central here.
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For Bauer, the solution to urban sprawl was strong metropolitan governance (she saw Toronto as an
early example of what could be done here). She argues (p 112) polemically that this can help "re-establish
some of the traditional cosmopolitan virtues of urban life which are now lost in the stupid village ideology
and class-race exclusionism practiced in suburbia". Her disdain for features of suburbs that some residents
find attractive indicates that she is not looking at urban sprawl simply as a problem experienced. She
concludes that:
The concept of city planning, effectuated by zoning, subdivision control, and the careful location of
public works and community services, is fully accepted almost everywhere. It would simply have to be
applied at a much broader regional level and be geared to bold and positive criteria for future
metropolitan structure.
Bauer (1956: 112)
Bauer does not clarify here what she means by 'bold and positive criteria". She ends her essay with a
question that exemplifies the gap between those who see urban sprawl as a problem experienced and
those who see it as a problem to be solved.4
Perhaps then, the biggest potential obstacle is neither political nor economic, but mainly cultural. Do
we want real cities and real country—or do we actually prefer the rurban sprawl?
Bauer (1956: 112).
Of course, Bauer is just one selection from the extensive planning literature on urban sprawl as a
problem to be solved. Another notable early study is Lower Mainland Regional Planning Board of British
Columbia (1956). This Report (p. 8) is specific about how to measure sprawl:5
Sprawl takes many forms, but all forms have one common characteristic—low population density…
Sprawl is a stage of transition between true agricultural development, which has a density less than 0.3
people per acre, and suburban residential development, with a density greater than 3.5 people per
acre.
The Report argued that sprawl areas, being costly for governments to service relative to the property tax
revenue they generated, were thus fiscal "deficit areas". Given this approach to the delineation of sprawl,
the obvious solution might have been to impose exaction fees (also known as development charges or lot
levies) that make each new property owner bear the full marginal costs of servicing, and thus eliminate
the fiscal deficit. Also interesting is that the Report did not suggest that municipalities practise fiscal
neutrality by sharply reducing property taxes for farms and other land uses that generate a fiscal surplus.
4
Rome (2001, 270) makes a similar point. He argues that, despite the in-roads made by environmentalist thought,
consumers still want "a house with adequate and aesthetically satisfying space in a pleasant neighborhood, in a good
school district, with bearable taxes and with a good chance of appreciating in value. That list of essential attributes
does not reflect a deep sense of our dependence on the larger living world of plants and animals and microbes, of soil
and water and air."
5
In the empirical literature on sprawl, there is a debate about whether to measure sprawl using the density of
population or the density of dwellings. Advocates of the dwellings approach argue that, with the decline in average
household size in the last century, the same stock of dwellings contains fewer people with the passing of time. Thus,
built form of the city may remain unchanged, yet population density declines. While this is undoubtedly true, this
paper uses population density measures throughout in keeping with the majority of the literature. However, the
reader should be mindful of the "drift" in average population density that is possible over time because of a shrinking
household size.
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Instead, the Board made the following recommendations to solve the sprawl (deficit area) problem. First,
designate a five-year urban growth boundary so that residential land uses are encouraged inside, and rural
land uses outside. Second, in the rural zone outside, do not permit subdivision that reduces lot size to
under one acre. Third, keep servicing to a minimum in the rural zone. Fourth, protect large farms in
designated farm districts within the rural zone with modest property tax abatements.
In the ensuing years, proponents continued to argue the idea of sprawl as a problem to be solved.
Notable here is Downs (1994) who argues that the typical American consumer wants to own a car and a
detached house in the suburbs with yard space and clean air, in an environment free from poverty. The
consumer also wants a quick commute to a low-rise worksite in a park-like setting and a responsive local
government. This has resulted in sprawl—"unlimited low density growth" in Downs' words—that raises issues
of excessive travel, traffic congestion, air pollution, water and waste disposal problems, and disappearance of open (vacant) space. As a result, local governments in fast-growing metropolitan regions
have individually enacted growth management and control practices that have made them exclusionary
and inequitable and have dumped the problems of growth on other local governments nearby. To Downs,
the policy prescription is a region-wide approach to planning controls. In Downs' view, the simplest way to
think about sprawl is to equate it with low-density[sub]urban development. Other critics ague that
broader measures of sprawl are needed. Ewing (1997) summarizes the sprawl literature and argues that
there are three more characteristics of sprawl, in addition to Down's low-density development; these are
strip development, scattered development, and leapfrog development. Calthorpe and Fulton (2001)
similarly argue the importance of the region-wide approach to sprawl. They see inequity and
environmental degradation as two major policy issues arising from sprawl. They see sprawl as the failure
to plan the metropolitan region as networks of communities, of open spaces, of economic systems, and of
cultures; they emphasize, as the antithesis to sprawl, a diversity of communities, variety of connections,
and clearly-defined common ground (open space system, cultural diversity, physical history, and economic
character).
From urban sprawl as a problem experienced and as a problem to be solved, we see diverse
conceptualizations of the problem and its solution. Even though it is not the only way to think about
sprawl, population density is at the heart of many of these conceptualizations. Further, much of the
debate about sprawl focuses on the extent of variation in density across an urban region. Further, there is
a fundamental conflict here in the interpretation of a change in density and its spatial variation. To those
who see sprawl as a problem to be solved, an increase in density (a more compact urban region) and a
reduction in its variation is often seen to be good. To those who see sprawl as a problem experienced, an
increase in density—whether through intensification, in-filling, or reduction in open space—and a reduced
variability may well be seen as bad.
Finally, let us consider sprawl as an intellectual concept. In a seminal paper that does not even mention
"urban sprawl" as such, Clark (1951) used a density gradient model to help understand and predict the
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variation in population density across the urban region and its changes over time. He used data at the
level of Census Tracts for large, growing urban regions in North America, Europe, and Australia from 1801
to 1947 to draw two generalizations:
1 In every large city, excluding the central business zone, which has few resident inhabitants, we have
districts of dense population in the interior, with density falling off progressively as we proceed to
the outer suburbs.
2 In most (but not all) cities, as time goes on, density tends to fall in the most populous inner suburbs,
and to rise in the outer suburbs, and the whole city tends to 'spread itself out'.
Clark (1951: 490)
The first generalization suggests the presence of sprawl, in the sense that newer (outer) suburbs are less
densely populated than older (inner) suburbs. In Table 1, I show the gross population density predicted by
Clark's density gradient model for selected urban regions in the 1930s and 1940s. These predictions
indicate that population density in a suburb 10 km from the city center was only about one-half the
density at a suburb 5 km from the city center.
The second generalization suggests that, with time, low-density suburbs become more densely populated.
Put differently, in-filling and intensification slowly raise density in the outer suburbs. It might seem that
Clark is simply describing a process of in-filling that over time gradually causes outer suburbs to approach
the same density as inner suburbs. However, this is not exactly true. Clark explains his results as follows.
If a metropolitan area is to have a high total population, it must either put up with a considerable
degree of overcrowding in the inner suburbs, or it must spread itself out … Spreading out is only possible
where transport costs are low in relation to the citizen's income.
Clark (1951: 495).
So, it is the combination of city size and the cost of transportation relative to income that drives the
density gradient. Flattening of a city's gradient over time leads to a spreading urban region (sprawl), and
the cause is the increasing affluence of households.
Since Clark's pioneering work, much has been written on the application of density gradient mdels.
These have included great names in quantitative human geography (Berry, Casetti, Dacey, Edmonston,
Griffith, Haynes, Mercer, Morrill, Papageorgiou, Yeates) and urban economics (Alonso, Beckmann,
Brueckner, Kain, Kau, McDonald, Mills, Muth, Niedercorn, Pines, Richardson, Straszheim). Much of this
literature focused on the economic argument as laid out by Clark above and elaborated in the AlonsoMuth-Mills approach to urban spatial structure.6 Others saw density-gradient models arising because of
other processes. Bussière and Snickars (1970) saw density gradients as the outcome of entropy
maximization. Guest (1973), Harrison and Kain (1974), and Brueckner (1980) attributed the density
gradient to the historical pattern of urban development.
6
As Alonso (1964) would later elaborate, Clark's argument is that a higher income lessens the impact of commuting
costs on housing consumption and well-being. A different argument is that higher income also changes consumption of
goods in favour of those that are income elastic. To the extent that higher income therefore favours independent
living arrangements and a larger home/lot, it may also help explain the decline in population density.
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Clark's empirical analysis rasises the question of local geographic scale. Clark arrayed Census Tracts by
distance from downtown, and then fitted a density gradient model to these data.7 In so doing, an effort
was made to exclude land used for nonresidential purposes (e.g., industrial, commercial, or park lands). In
this way, Clark was measuring a kind of "net" density for each census tract; one that measures persons per
unit of land used for housing, local roads, and presumably some residual ancillary land uses.
Definition and measurement of sprawl
To this point, I have argued that there are different ways of conceptualizing sprawl. In many (but not
all) of these ways, population density is indicative of sprawl: lower density implying greater sprawl. At the
same time, this is chiefly the view of a planner (sprawl as problem to be solved). From the perspective of
the resident (sprawl as problem experienced), the loss of open space and increased homogeneity that
typically accompanies increased population density itself is sprawl; hence, higher and more uniform
density implies sprawl. Therefore, if we want to use population density as an indicator of sprawl, we need
to be able to detect how it varies across the urban region as well as how it is changing over time.
To begin thinking about the definition and measurement of sprawl, consider the following preliminary
question. Which is more densely inhabited: Canada or America? At the nationwide level, this is easily
answered. Excluding freshwater surfaces, the two nations are similar in land area; Canada at 9.0 million
km2, and America at 9.2 million km2. However, in 2001, Canada's population was just over 30 million
persons, compared to 281 million in America in 2000. Therefore, the ratio of these two — nationwide
average (gross) population density — was much lower in Canada (3 persons per km2) than in America (31
persons per km2). However, comparison of such nationwide gross densities is often not helpful in thinking
about the extent of urban sprawl. Nationwide gross density is too crude. Presumably, we want to exclude
wilderness, rural, and other areas that are sparsely populated. It is sometimes said that Canada is a small
nation inside a big country. Much of its population clusters in a narrow band near the U.S. border.
Therefore, local population density, measured as the average number of people living nearby, might well
be higher in much of Canada compared to America even though nationwide gross population density is
much lower. Put differently, an average density measured locally can differ substantially from a
nationwide gross density.
It is not just nationwide averages that are problematic here. Even at the level of CMSAs, metropolitanwide gross density measures are misleading. Consider the data in Table 2 showing population density by
size of metropolitan region for America in 2000 and Canada in 2001. The New York CMSA tops the list of
7
Mills (1972) is famous for a shortcut method in which just two data points are used; the first point being the land
area and population of the central city, and the second point being the land area and population of the entire
metropolitan area. From these two points, it is possible to estimate the parameters of the density gradient model.
Mills' sample, which consisted of 18 larger American cities in the period from 1948 to 1963, showed evidence of
ongoing urban sprawl. Edmonston and Guterbock (1984) use the same method to look at American cities from 1950 to
1975 and conclude that there was no slackening in the rate of suburbanization (deconcentration) during 1970-75
compared to the earlier time period.
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large American urban regions at 783 persons per km2 while the Los Angeles CMSA is at the bottom (186
persons per km2).8 Such density values only weakly evidence the spike in population density that one might
expect to find in the largest urban regions. Interestingly, among Canadian areas of the same size (except
"rural and small urban"), area-wide density is higher than the corresponding American urban regions.9
Nonetheless, at both the nationwide and area-wide level, the problem with these gross density measures
is that they include all land within a given jurisdiction even though much of that land might well be
unoccupied or unoccupiable. Such land deflates the average population density as seen by residents who
typically must interact within, and navigate through, the built-up areas. Further, such measures provide
no information about the variability of density across an urban region.
Area-wide versus local density
This paper explores an alternative measure of population density; one that emphasizes the typical
exposure of a person to other people resident nearby. It is like a net density in that it ignores areas in
which no one lives; however, unlike a traditional net density measure, the analyst need not explicitly
identify parcels of land to be excluded. This paper presents a rationale for the measure, and then
implements it using comparable data from the 2000 and 1990 US Censuses and the 2001 and 1996 Canadian
censuses.
It is often argued that an important goal of land use planning in both America and Canada is to
discourage "urban sprawl", which I take here to mean low-density, scattered, residential development.
Part of the planning solution is to encourage in-filling, conversions, and other forms of residential
intensification. Presumably, this serves to increase the overall mean density of population in the urban
region and to reduce its variability from one neighbourhood to the next within the urban region. Suppose
that we obtain a pair of estimates for each urban region under study: (i) the mean local population density
and (ii) the variability of local density across that urban region. We could then plot each urban region as a
point on a scatter plot as shown in Figure 1. Clark and his intellectual heirs would argue that the land
market would tend toward higher average densities and a greater dispersion in density across the urban
region as city size increases. Therefore, we would expect both average density and its variation to
increase with the size (population) of the urban region.
From this diagram, we could identify "best practice" urban regions as seen by planners: that is, urban
regions that, for their size, combine a high mean local density with a low spatial variation. Best-practice
8
These are calculated as persons per square kilometer of land area, and include both urbanized and non-urbanized
land areas. It is possible to separate urbanized and non-urbanized areas in the 1990 U.S. census, but data for 2000
were not available at time of writing. Using persons per square kilometer of urbanized areas would give modestly
higher densities. Gordon and Richardson (1997) report markedly higher urbanized population densities for 1990, but I
have been unable to reproduce these from published U.S. census data.
9
The U.S. Census typically uses larger geographic areas to represent urban regions than does the Canadian Census. For
example, the south shore of Lake Ontario (U.S.) is largely partitioned into just three urban regions (Buffalo-Niagara
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urban regions would form a lower envelope in this diagram, and are here denoted in black. Following the
argument of Clark above, I conjecture that this envelope, a planning "efficiency frontier", is an increasing
function of average density. I presume here that a low-density area contains primarily single detached
housing with little variation in density throughout. In contrast, in larger urban regions, where high central
city rents impel consumers to opt for high densities, we observe a wide range of housing densities across
the urban region, and thus more variability. This planning efficiency frontier is a political battlefield. Over
time, planners work to move their urban region closer to the frontier. At the same time, groups opposed
to intensification (including, but not limited to, residents) work to resist such shifts, or even to reduce
density still further. As a prelude to understanding the outcomes, it is therefore interesting to know which
urban regions have moved away from the planning efficiency frontier and which have moved closer.
Method
To illustrate the approach of this paper, consider the hypothetical area depicted on the left side of
Figure 2. Suppose that the area is 8 km wide by 10 km high, and contains 1,000 residents in total. The
area-wide average population density is 1000/80 = 12.5 persons/km2. Further, let me assume that 50
persons live at each of the 20 dots shown in Figure 2. Each dot is therefore a geographic cluster of
population. The dots form a rectangular grid with a 2 km spacing. For each dot, I now sum the number of
persons who live within r=2 km, which therefore includes those at the dot itself plus those at the dots to
either side or immediately above or below. These summed counts are shown on the right hand side of
Figure 2. They total 150 persons at the corner dots, 200 persons at other edge dots, and 250 persons at
non-edge dots. The weighted average dot count (weighted by the number of persons living at the dot, in
this case the same for each dot) is 205 persons. Because we calculate this average using all dots within 2
km of a given dot, that is like drawing circles of radius 2 km. Therefore my density measure divides
weighted average dot count (205) by the area over which it is calculated: namely πr2. This yields a Local
Density (LDr) equal to 205/(4π) or 16.31 persons/km2 which is the measure that I employ in the remainder
of this paper.
For the purpose of comparison, consider the area depicted on the left-hand side of Figure 3. Here again
are 20 dots of 50 persons each: now spread across an area that is 10 km by 14 km. Again, for simplicity,
assume that dots, where found, are 2 km apart both horizontally and vertically. The area-wide average
population density is 1000/140 = 7.1 persons/km2, or about 57% of the corresponding value in Figure 2. For
each dot, now calculate the number of persons who live within r=2 km. These counts are shown on the
right hand side of Figure 3. The weighted average dot count (weighted by the number of persons living at
the dot) is 175 persons. This yields a Local Density (LD2) equal to 175/(4π) or 13.93 persons/km2. Note that
LD2 here is about 85% of the LD2 calculated above for Figure 2. In other words, the gap between the values
Falls, Rochester, and Syracuse) whereas the north shore (Canada) includes 8 urban regions (St Catharines-Niagara,
Hamilton, Toronto, Oshawa, Port Hope, Cobourg, Belleville, and Kingston), plus a substantial nonurban region.
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for LD2 in the two figures is much smaller than the gap between the two area-wide average population
densities. If we seek a measure of density that reflects the typical experience of a resident, LD2 is useful.
We can now set out the method formally in the case where an area consists of n dots, and where dot "i",
among these, has pi residents, and where the distance (km) between dots i and j is dij. Let r be the
maximum radius (km) within which neighbors are to be summed in calculating local density.
LDr = (Âi piVi )/ (Âi pi)
where
Vi = (Âj ∂ijpj)/(πr2)
∂ij = 1 if dij≤r, 0 otherwise.
To measure the variability in LDr, we also calculate its weighted standard deviation, Sr, as follows
Sr = ÷[(Âi pi{Vi-LDr}2)/(Âi pi)]
To operationalize the calculation of LDr, we need counts of population spatially disaggregated for n dots.
Since the method assumes that everyone assigned to a dot lives there (and not simply somewhere nearby),
a large n (more disaggregated) is better than small n (less disaggregated). For each dot, the method
requires the count of persons and the spatial coordinates (e.g., longitude and latitude) for each dot.
Coordinate pairs can then be used to calculated distance (spherical or Cartesian) between each pair of
dots. As well, the method requires that we specify a given distance threshold (r).
In the empirical case study presented here, the finest geographic scale at which comparable Census
population counts are available for Canada and America are the Dissemination/Enumeration Area (Canada)
and Block Group (America). These data give population counts and centroid location for dots of typically
200 to 400 households. There were 52,993 dots in the Canadian census in 2001, averaging 566 persons per
dot, and 333,098 dots in the American census in 2000, averaging 845 persons. In addition to having a larger
population on average, American Block Groups are also more varied than Canadian Dissemination Areas;
see Figure 4. There are relatively more Block Groups with a small population, as well as relatively more
with a large population; in contrast, Dissemination Areas are more similar in size.
To calculate LDr, I use r=2 km. I choose this radius so that I can approximate the notion of a "district". In
contrast, a neighborhood is sometimes thought to be an area with a radius of about 5 minutes walk, or
about 400 meters. I use a 2 km radius instead, because I want to approximate the area within which a
person might expect to drive to do local shopping, go to school, or visit a doctor or dentist.
In choosing a radius, we must be mindful of the fact that the Dissemination/Enumeration Area or Block
Group is properly a polygon on a map, not simply a dot as represented by its centroid. Inaccuracy arises
when part of a polygon lies (1) outside the r km circle even though the centroid is inside, or (2) inside the
r km circle but the centroid itself is outside. This problem means that we prefer to enumerate dots at the
20 March 2003
Urban sprawl in Canada and America: just how dissimilar?
Page 11
finest geographic scale possible. At the same time, it also means that we need to measure density at a
similar scale in the two countries; using different scales introduces the possibility of systematic
differences in our estimates. In this respect, we need to assure ourselves that the sets of curves for
Canada and America in Figure 4 are sufficiently similar.
Note also that, in the absence of complete street network data for Canada, my measure of distance is
as-crow-flies. I therefore ignore coastlines and other impediments to travel in straight line. In a similar
manner, the calculation of LDr employs a circle of radius r wherein no account is taken of surface areas
covered by water or that are otherwise uninhabitable.
Findings
On average, Canadians live at higher local densities than do Americans.10 From Dissemination Area data,
the average Canadian in 2001 had 22,871 neighbors within 2 km; from Block Group data, the average
American in 2000 had only 20,656 neighbors. This gives LD2 = 1,820 persons per km2 for Canada versus
1,644 persons per km2 for America. Thus, measured locally, density is higher in Canada than in America.
At the same time, there is considerable variability here. The S2 for Canada in 2001 was 2,016, and for
America in 2000 was even larger at 2,920. These standard deviations for LD2 are so large that they appear
to swamp the differences in national means. This should not be surprising. After all, the "district" covered
by this measure can range from a dense urban high-rise neighborhood to a remote hamlet. We might
therefore expect to see less variability once we restrict our attention to a specific urban region.
Further insights are gained by looking at the cumulative distribution for LD2 in the two nations. See
Table 3 and Figure 5. Evident here are two important national-level distinctions between Canada and
America. First, in Canada, a higher proportion of the population lives at low LD2—roughly up to about 80
persons per km2. This corresponds roughly to rural and remote Canada. In America, the proportion at
these low densities is lower. In part, however, this appears to be because of the way that the Block Group
is defined.11 Second, in Canada, a higher proportion of the population lives at high LD2. LD2 exceeds 1,280
persons per km2 for 50% of Canadians in 2001, compared to only 36% of Americans in 2000. This is all the
more surprising since, as will be seen below, no Canadian urban region has the very high density
associated with New York urban region,
A breakdown of these national averages by size of urban area is instructive. See Table 4. The means for
the size categories vary substantially in each country. Not surprisingly, density is highest on average in
large urban regions, and declines as city size shrinks. Further, there is an important difference in average
density between the two countries after controlling for size class. In the two intermediate size categories
10
Edmonston, Goldberg, and Mercer (1985) come to a similar conclusion by looking at density gradient model
estimates for Canadian and U.S. cities.
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Urban sprawl in Canada and America: just how dissimilar?
Page 12
(100,000 - 999,999 persons, and 1,000,000 - 3,999,999 persons), Canadian urban regions are about twice
the density of their American peers. In fact, I argue below that Canada is exceptional also in the largest
size class (4 million persons or more) after taking into account New York urban region.
Let us now turn our attention to the largest urban regions individually in the two nations. Table 5
presents comparative results for the 10 largest American urban regions and the 10 largest (albeit much
smaller) in Canada. For comparison purposes, area-wide population density is calculated as well as the
local density (LD2) that is emphasized here. Urban regions are listed in Table 5 in order of declining LD2 as
of the latest census. What is immediately striking here is that this is much different from a list ordered by
area-wide average population density; e.g., Los Angeles, which would have been near the bottom, is now
near the top of this list. Among the twenty areas, the New York urban region has, by far, the highest local
density. This should not be surprising. After all, a history of urban development predating automobileoriented development in the 20th century, a constraining topography (i.e., coastline) and a large
metropolitan population help put pressure on central area rents and land prices, and thereby made
necessary a high local density. What is perhaps more surprising is that other large older American urban
regions with topographical constraints of their own do not also show substantial local densities. Despite
their large sizes, the Philadelphia CMSA ranks only 9th, Boston CMSA is 13th, and the Washington MSA is
15th in the list in Table 5. Moving westward and southward across America brings us to younger urban
regions with less history of intensive development before the 20th century. For such urban regions, we
might well expect lower local densities. Indeed, in the Midwest, Chicago comes 5th in the list, but Detroit
is a lowly 18th. In the Southwest, Dallas and Houston are at the bottom of the list as one might expect,
but much-larger Los Angeles ranks fully 4th. What is also surprising here are the relative positions of the
Canadian urban regions. Toronto and Montreal stand 2nd and 3rd among all the urban regions in Table 5.
Vancouver has only one-third of the population of San Francisco, and yet has a comparable local density.
Comparison of the latest and previous census is also telling. A word of caution is in order here. The data
in Table 5 are for urban regions as they existed at the time of a census: no attempt is made here to adjust
for changes in the boundary of the urban region from one census to the next. In eight of the urban regions,
LD2 rose by more than 50 persons/km2: Dallas, Houston, Los Angeles, New York, and San Francisco in
America, and Vancouver, Ottawa-Hull, and Edmonton in Canada. In five of the urban regions, LD2 fell by
more than 50 persons/km2: Boston, Detroit, Philadelphia, and Washington in America and London in
Canada. While this provides some evidence that local density overall has been increasing over time, there
are clearly many urban regions that are exceptions to this.
Consider now the measure of variability (S2) presented in Table 5. First, note that the urban region
variances are generally less than the national values (2,920 for America, 2,016 for Canada in the latest
11
Practice here appears to differ from one state to the next. Northern Pennsylvania, for example, has numerous block
groups where LD2 is under 80 persons per km2; there, block groups look like Canadian Enumeration Areas. In contrast,
neighboring Southwestern New York State has no block groups this small.
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Urban sprawl in Canada and America: just how dissimilar?
Page 13
census) in Table 4: only in New York, Toronto, and Montreal does the urban region variation exceed the
respective national variation. Further, S2 is now typically smaller than LD2 in each urban region.
The following conclusions can now be drawn from comparisons of these 20 urban regions. First, not
surprisingly, large urban regions have higher local densities than do smaller urban regions; local density is
also more variable across the urban region as city size increases. Second, in general, Canadian urban
regions have higher local densities than American urban regions. Third, variability in local density within
individual urban regions is still substantial. Fourth, while there is some evidence that local density is rising
over time, there are also numerous urban regions where local density has declined.
Let us turn our attention to the full set of urban regions across America, and their Canadian
counterparts. Do the findings for our 10 top urban regions hold up for urban regions as small as 100,000
persons? Figure 6 plots average local density against size for the 247 smaller American and Canadian urban
regions (100,000 to 999,999 persons). Figure 7 shows the same information for larger urban regions (1
million population or more). Figure 6 and Figure 7 show a pronounced trend; the larger the urban region,
the more densely it is populated. At the bottom end among smaller urban regions (under about 125
thousand population), Canadian and American urban regions of the same size typically have about the
same density. It is only at the top end among small urban regions, above 125,000 population, that
Canadian urban regions tend to be relatively more densely populated than their American peers. Also,
Figure 7 shows that larger Canadian urban regions are almost always denser than their American peers.
Across Canada and America, which urban regions are the leaders (high mean Local Density for their size)
and which are the laggards (low mean Local Density for their size)? To answer this question, I combine and
array by size all American and Canadian urban regions of 100,000 persons or more as of the latest census.
There are 290 urban regions altogether here. From this, I then find the subset of these urban regions such
that there is no smaller urban region with a higher mean Local Density. This subset contains the 11 urban
regions shown in Table 6. Since this subset, by definition, always includes the urban region with the lowest
population, I ignore the smallest region (Kokomo). To the remaining 10 regions, I then fit a model of the
form:
LD2*=(a+bP)c
using least squares to obtain a=2741830, b=13712, c=0.33. Then, I use this formulate to predict the
"potential density", LD2*, for each of the 290 urban regions in the full sample. The discrepancy between a
region's LD2* and the local density it actually achieves is a measure of the laggard-ness of the region.
Now we are ready to look at the efficiency frontier. In Figure 8, consider first the case of the smaller
urban regions: those with a population of from 100,000 to 1,000,000 persons. Figure 9 presents the same
kind of data for larger urban regions: those of 1,000,000 population or more. In both figures, we see that
S2 is positively correlated with LD2. At lower levels of LD2 in Figure 8, under about 800 persons per km2,
smaller Canadian and American urban regions appear to have a similar variability (S2). It is only at higher
20 March 2003
Urban sprawl in Canada and America: just how dissimilar?
Page 14
levels of LD2 that one finds that smaller Canadian urban regions have typically lower S2. In Figure 9, larger
Canadian urban regions generally also have a lower S2 than do their American counterparts. I also show, in
Figure 8 and Figure 9, a possible planning efficiency frontier. This frontier shows a "minimum" level of S2,
here denoted S2*., for each level of LD2. I chose the intercept to correspond to the lowest S2 observed
among our urban regions, and then chose the exponent to undercut the vast majority of urban regions in
the sample (here including larger urban regions as well as smaller). The estimated equation is as follows.
0.2454
S2* = 200+exp(LD2
)
In Figure 8 and Figure 9, there are 11 urban regions whose S2 lies below the efficiency frontier: even if
only by the smallest of amounts. The most extreme case is Anniston AL for which S2=196 and S2*=258. I
could have chosen a smaller exponent to ensure that even urban regions like Anniston did not lie under
the efficiency frontier, but I prefer to think of the frontier as an achievable standard that has already
been reached in some municipalities.
Using these two criteria, leader-laggard status and proximity to PEF, which are the best performing
urban regions. Panel (a) of Table 7 lists five of the best performers in the latest census from among the
290 urban regions examined; Panel (b) lists five of the worst. The best performers consist of New York plus
four Canadian urban regions. In each case, planners might well be proud that these urban regions have a
high LD2 given their population size and also have an S2 near the planning efficiency frontier. The worst
performers include five American urban regions: all in the Northeast. Presumably, planners generally
would not be proud of any of these poor performers; all have a low LD2 for their population size and all
have an S2 far away from the planning efficiency frontier.
Which cities have moved closer to the planning efficiency frontier: that is, where has LD2 increased
and S2 decreased from previous to latest census. In this analysis, I control for boundary changes between
censuses. I overlay digital boundary files for each urban region from the latest census on the block group
or enumeration area centroids from the previous census. This permits me to assign each block group or
enumeration area from the previous census to the urban regions in the latest census, and therefore to
recalculate local density and its variability in America in 1990 using 2000 urban region boundaries; and in
Canada in 1996 using 2001 boundaries. I then calculate the change in LD2 and the change in S2 for each
"constant boundary" urban region between the previous and latest census. See Figure 10 wherein, once
again, each urban region is represented as a point. The horizontal axis there measures the change in mean
Local Density in each "constant boundary" urban region from previous to latest census (negative if LD2
declined). The vertical axis measures the corresponding change in S2. In terms of the planning efficiency
frontier, the best-performing urban regions are those that in the lower right quadrant.
The lower right quadrant includes 46 urban regions. The 46 are listed in Table 8. I have broken them
up into 4 panels depending on how close their mean LD2 is to LD2*. Panel (a), which includes only
Honolulu, is the set of leaders. Panel (b), "near leaders", includes urban regions wherein LD2 is within 500
20 March 2003
Urban sprawl in Canada and America: just how dissimilar?
Page 15
persons/km2 of LD2*. The largest urban regions in panel (b) are Stockton and Modesto. Panel (c), "near
laggards" includes urban regions wherein LD2 is within 500-1000 persons/km2 of LD2*. The largest urban
regions here are Fresno and Omaha. Finally, Panel (d), "laggards", includes urban regions wherein LD2 is
more than 1000 persons/km2 below LD2*. The largest urban regions in panel (d) are Portland and Nashville.
None of the 46 urban regions are Canadian. So, although local density tends to be higher on average for
Canadian urban regions, the evidence suggests that some American urban regions have begun the process
of trying to catch up.
It is interesting that none of the largest urban regions in either Canada or America moved closer to the
Planning Efficiency Frontier. To me, this result is surprising. The planning literature contains much praise
and enthusiasm for just the kind of infilling and intensification that would presumably lead to a higher LD2
and a lower S2. What are the possible explanations for this anomaly? One possibility is that planners are
unable to achieve what they want because of political opposition by residents or others. It is difficult for
me to assess the validity of this argument because I have no systematic source of information on political
involvement across Canada and America. A second explanation might be that planners are responsible for
a single jurisdiction (e.g., a municipal government) within the urban region and therefore are unable to
control sprawl over the larger urban region area that we are studying here. This is a question that I can
explore further because it is possible to measure local density and its variation within individual
municipalities across the two nations.
Conclusions
Local Density (LD2) is a valuable tool in the assessment of urban sprawl. Given the improved ease with
which large quantities of geo-referenced small-area data can now be accessed and manipulated, LD2 is
simple to implement and makes possible interesting comparisons of density among urban regions. My
measure of local density is not constrained by the well-known problems with area-wide gross population
density measures and is easier to calculate than conventional net population density measures. At the
same time, the variation (S2) in local density gives us a useful description of heterogeneity of density
across the urban region. This variation in density is also relatively simple to calculate. I have argued here
that planners and residents may well see the issue of sprawl quite differently, but that this pair of values
(LD2 and S2) is relevant to both groups.
References
Alonso, W. 1964. Location and Land Use. Cambridge, Mass.: Harvard University Press.
Bauer, C. 1956. First job: control new-city sprawl. Architectural Forum, 105, September 1956, 104-112.
Brueckner, J.K. 1980. A vintage model of urban growth. Journal of Urban Economics, 8, 389-402.
Burchell, R.W., Lostokin, D., Galley, C.C. 2000. Smart growth: more than a ghost of urban policy past, less
than a bold new horizon. Housing Policy Debate, 11(4), 821-879.
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Urban sprawl in Canada and America: just how dissimilar?
Page 16
Bussière, R., and Snickars, F. 1970. Derivation of the negative exponential model by an entropy
maximising method. Environment and Planning A, 2, 295-301.
Calthorpe, P., and Fulton, W. 2001. The Regional City: Planning for the End of Sprawl. Washington, D.C.:
Island Press.
Carver, H. 1962. Cities in the Suburbs. Toronto: University of Toronto Press.
Clark, C. 1951. Urban Population Densities. Journal of the Royal Statistical Society, Series A, 114, 490496.
Donaldson, D, 1969. The Suburbasn Myth. New York: Columbia University Press.
Downs, A. 1994. New Visions for Metropolitan America. Washington, D.C.: The Brookings Institution.
Danielson, K.A., et al. 1999. Retracting suburbia: smart growth and the future of housing. Housing Policy
Debate, 10(3), 513-40.
Edmonston, B., and Guterbock, T.M. 1984. Is suburbanization slowing down? Recent trends in population
deconcentration in U.S. metropolitan areas. Social Forces, 62(4), 925.
Edmonston, B., Goldberg, M.A., and Mercer, J. 1985. Urban form in Canada and the United States: an
examination of urban density gradients. Urban Studies, 22, 209-217.
Ewing, R. 1997. Is Los Angeles-style sprawl desirable? American Planning Association Journal, 63(1), 107126.
Goldberg, M.A., and Mercer, J. 1986. The Myth of the North American City: Continentalism Challenged.
Vancouver: University of British Columbia Press.
Gordon, P., and Richardson, H.W. 1997. Where's the sprawl. American Planning Association Journal, 63(2),
275-278.
Gordon, P., and Richardson, H.W. 1997b. Are compact cities a desirable planning goal? American Planning
Association Journal, 63(1), 95-106.
Guest, A.M. 1973. Urban growth and population densities. Demography, 10(1), 53-69.
Harrison, D., and Kain, J. 1974. Cumulative urban growth and urban density functions. Journal of Urban
Economics, 1, 61-98.
Lower Mainland Regional Planning Board of B.C. 1956. Economic Aspects of Urban Sprawl: A Technical
Report. New Westminster, B.C: The Board. 45 p.
Mills, E.S. 1972. Studies in the Structure of the Urban Economy. Baltimore: Johns Hopkins University
Press.
Myers, D., & Kitsuse, K. 1999. The Debate Over Future Density of Development: An Interpretive Review.
Working Paper WP99DM1. Washington, D.C.: Lincoln Institute of Land Policy.
Rome, A. 2001. The Bulldozer in the Countryside. Cambridge: Cambridge University Press.
Whyte, W.H. 1958. Urban Sprawl. Fortune, January 1958, p. 103.
20 March 2003
Urban sprawl in Canada and America: just how dissimilar?
Local Variation in Density
Figure 1 Mean versus variation in local population density.
Local Mean Population Density
Source
See text.
20 March 2003
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Urban sprawl in Canada and America: just how dissimilar?
Page 18
Figure 2 Uniformly populated dots with regular 2 km spacing, showing count of neighbors
within 2 km.
Source
50
50
50
50
150
200
200
150
50
50
50
50
200
250
250
200
50
50
50
50
200
250
250
200
50
50
50
50
200
250
250
200
50
50
50
50
150
200
200
150
See text.
20 March 2003
Urban sprawl in Canada and America: just how dissimilar?
Page 19
Figure 3 Uniformly populated dots with irregular 2 km spacing, showing count of neighbors
within 2 km.
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
Source
50
50
100
200
200
200
150
150
250
250
200
150
250
200
150
200
50
150
50
150
50
100
See text.
20 March 2003
150
150
150
Urban sprawl in Canada and America: just how dissimilar?
Page 20
Figure 4 Cumulative proportion of dots (Block Groups, Dissemination Areas, or Enumeration
Areas) by population resident in dot.
1.00
0.90
Cumulative proportion of BGs, DAs, or EAs
0.80
0.70
0.60
US BG (091) 2000
Canada DA 2001
US BG (090) 1990
Canada EA 1996
0.50
0.40
0.30
0.20
0.10
0.00
0
500
1000
1500
2000
2500
3000
3500
Population in Block Group, Dissemination Area, or Enumeration Area
Source
U.S. data calculated from 2000 Census of Population and Housing Summary File 1
using summary level 091 block groups and 1990 Census STF3a using summary level
090 block groups. Canadian data calculated from the 2001 Census Geosuite database
and the 1996 Census GEOREF database. Calculations by the author.
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Urban sprawl in Canada and America: just how dissimilar?
Page 21
Figure 5 Cumulative proportion of population by local density (LD2).
1.00
0.90
Cumulative proportion of population
0.80
0.70
0.60
US BG (091) 2000
Canada DA 2001
US BG (090) 1990
Canada EA 1996
0.50
0.40
0.30
0.20
0.10
0.00
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
10,000
LD2 Local density (persons per square kilometer)
Note
LD2 is weighted average local density measured at 2 km. radius.
Source
U.S. data calculated from 2000 Census of Population and Housing Summary File 1
using summary level 091 block groups and 1990 Census STF3a using summary level
090 block groups. Canadian data calculated from the 2001 Census Geosuite database
and the 1996 Census GEOREF database. Calculations by the author.
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Urban sprawl in Canada and America: just how dissimilar?
Page 22
Figure 6 Average local density (LD2) by size of metropolitan area for comparable smaller
American urban regions in 2000 and smaller Canadian urban regions, 2001.
2,500
Local Density (LD2)
2,000
1,500
America 2000
Canada 2001
1,000
500
0
0
200,000
400,000
600,000
800,000
1,000,000
Population
Note
LD2 is weighted average local density measured at 2 km. radius.
Source
U.S. data calculated from 2000 Census of Population and Housing Summary File 1
using summary level 091 block groups. Canadian data calculated from the 2001
Census Geosuite database. Calculations by the author.
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Urban sprawl in Canada and America: just how dissimilar?
Page 23
Figure 7 Average local density (LD2) by size of metropolitan area for comparable large urban
regions: America 1990 and Canada 1996.
8,000
7,000
Local Density (LD2)
6,000
5,000
America 2000
Canada 2001
4,000
3,000
2,000
1,000
0
0
5,000,000
10,000,000
15,000,000
20,000,000
25,000,000
Population
Note
LD2 is weighted average local density measured at 2 km. radius.
Source
U.S. data calculated from 2000 Census of Population and Housing Summary File 1
using summary level 091 block groups. Canadian data calculated from the 2001
Census Geosuite database. Calculations by the author.
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Urban sprawl in Canada and America: just how dissimilar?
Page 24
Figure 8 Efficiency frontier (S2 versus LD2) for comparable smaller urban regions: America
2000 and Canada 2001.
2,000
1,800
Standard Deviation of LD2 (S2)
1,600
1,400
1,200
America 2000
Canada 2001
Planning efficiency frontier
1,000
800
600
400
200
0
0
500
1,000
1,500
2,000
2,500
Local Density (LD2)
Note
LD2 is weighted average local density measured at 2 km. radius. S2 is the weighted
standard deviation of local density within 2 km. radius. PEF is S2 predicted by
planning efficiency frontier at observed LD2.
Source
U.S. data calculated from 2000 Census of Population and Housing Summary File 1
using summary level 091 block groups. Canadian data calculated from the 2001
Census Geosuite database. Calculations by the author.
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Urban sprawl in Canada and America: just how dissimilar?
Page 25
Figure 9 Efficiency frontier (S2 versus LD2) for comparable larger urban regions: America 2000
and Canada 2001.
8,000
7,000
Standard Deviation of LD2 (S2)
6,000
5,000
America 2000
Canada 2001
Planning efficiency frontier
4,000
3,000
2,000
1,000
0
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
Local Density (LD2)
Note
LD2 is weighted average local density measured at 2 km. radius. S2 is the weighted
standard deviation of local density within 2 km. radius. PEF is S2 predicted by
planning efficiency frontier at observed LD2.
Source
U.S. data calculated from 2000 Census of Population and Housing Summary File 1
using summary level 091 block groups. Canadian data calculated from the 2001
Census Geosuite database. Calculations by the author.
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Urban sprawl in Canada and America: just how dissimilar?
Page 26
Figure 10 Change in LD2 and S2: America urban regions from 1990 to 2000, and Canadian urban
regions from 1996 to 2001.
500
Change in S2 from preceding census
400
300
200
America
Canada
100
0
-300
-200
-100
0
100
200
300
400
500
600
-100
-200
-300
Change in LD2 from preceding cenus
Note
LD2 is weighted average local density measured at 2 km. radius. S2 is the weighted
standard deviation of local density within 2 km. radius.
Source
U.S. data calculated from 2000 Census of Population and Housing Summary File 1 using
summary level 091 block groups. Canadian data calculated from the 2001 Census Geosuite
database. Calculations by the author.
20 March 2003
Urban sprawl in Canada and America: just how dissimilar?
Table 1
Predicted gross population density in suburb: Clark's density gradient model estimates.
City, Year
New York, 1940
London, 1939
Boston, 1940
Manchester, 1931
Sydney, 1947
Los Angeles, 1940
5 km from
city center
(persons/km2)
10 km from
city center
(persons/km2)
25,090
16,727
7,649
7,154
5,365
5,365
13,430
8,953
2,995
3,275
2,456
2,456
Source: Clark (1951: 492-493). Calculations by author.
20 March 2003
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Urban sprawl in Canada and America: just how dissimilar?
Table 2
Page 28
Population, land area, and area-wide population density by size of urban region, America
(2000) and Canada (2001).
Population Land area
Persons
(000s)
(km2)
per km2
America, 2000
281,422 9,161,927
4,000,000 persons or more
92,846
283,181
New York--Northern New Jersey--Long Island, NY--NJ--CT, CMSA 21,200
27,065
Los Angeles--Riverside--Orange County, CA, CMSA
16,374
87,944
Chicago--Gary--Kenosha, IL--IN--WI, CMSA
9,158
17,941
Washington--Baltimore, DC--MD--VA--WV, CMSA
7,608
24,803
San Francisco--Oakland--San Jose, CA, CMSA
7,039
19,083
Philadelphia--Wilmington--Atlantic City, PA--NJ--DE--MD, CMSA 6,188
15,372
Boston--Worcester--Lawrence, MA--NH--ME--CT, CMSA
5,819
14,574
Detroit--Ann Arbor--Flint, MI, CMSA
5,456
17,004
Dallas--Fort Worth, TX, CMSA
5,222
23,579
Houston--Galveston--Brazoria, TX, CMSA
4,670
19,956
Atlanta, GA, MSA
4,112
15,861
1,000,000 to 3,999,999 persons
68,672
486,166
100,000 to 999,999 persons
62,758
977,622
Rural or small urban (under 100,000 persons)
57,145 7,414,958
31
328
783
186
510
307
369
403
399
321
221
234
259
141
64
8
Canada, 2001
4,000,000 persons or more
Toronto
1,000,000-3,999,999
100,000-999,999
Rural or small urban (under 100,000 persons)
3
793
793
529
122
1
Source
30,007 9,012,112
4,683
5,903
4,683
5,903
6,477
12,244
8,988
73,485
9,859 8,920,481
ICPSR series 3194. Census of Population and Housing, 2000 [United States]: Summary File 1,
States. Calculations based on aggregation from SUMLEV 091 (block group) by the author.
Statistics Canada. 2001 Geosuite CD-ROM. Calculations by the author.
20 March 2003
Urban sprawl in Canada and America: just how dissimilar?
Table 3
Cumulative proportion of population by LD2 in Canada, 1996 and 2001, and America, 1990
and 2000.
Local density (LD2)
Under
Under
Under
Under
Under
Under
Under
Under
Under
Under
Under
10 persons/km2
20 persons/km2
40 persons/km2
80 persons/km2
160 persons/km2
320 persons/km2
640 persons/km2
1,280 persons/km2
2,560 persons/km2
5,120 persons/km2
10,240 persons/km2
Cumulative proportion of population
America
Canada
BG
BG
EA
DA
1990
2000
1996
2001
0.01
0.01
0.01
0.01
0.02
0.01
0.03
0.02
0.04
0.03
0.07
0.07
0.12
0.09
0.17
0.17
0.22
0.19
0.22
0.23
0.32
0.29
0.28
0.29
0.45
0.43
0.37
0.37
0.65
0.64
0.51
0.50
0.85
0.85
0.76
0.75
0.94
0.94
0.93
0.92
0.98
0.98
1.00
1.00
Note
LD2 is weighted average local density measured at 2 km. radius.
Source
U.S. data calculated from 2000 Census of Population and Housing Summary File 1 using
summary level 091 block groups and 1990 Census STF3a using summary level 090 block groups.
Canadian data calculated from the 2001 Census Geosuite database and the 1996 Census
GEOREF database. Calculations by the author.
20 March 2003
Page 29
Urban sprawl in Canada and America: just how dissimilar?
Table 4
Page 30
Local density and variation in Canada, 1996 and 2001, and in America, 1990 and 2000, by size
of urban agglomeration.
Population
(000s)
LD2
S2
America, 2000
4,000,000 persons or more
1,000,000 to 3,999,999 persons
100,000 to 999,999 persons
Rural or small urban (under 100,000 persons)
281,422
92,846
68,672
62,759
57,145
1,644
3,304
1,300
801
285
2,920
4,500
988
723
328
America, 1990
4,000,000 persons or more
1,000,000 to 3,999,999 persons
100,000 to 999,999 persons
Rural or small urban (under 100,000 persons)
248,710
61,674
63,102
65,837
58,097
1,584
3,846
1,377
825
270
2,810
4,742
1,109
743
329
Canada, 2001
4,000,000 persons or more
1,000,000-3,999,999
100,000-999,999
Rural or small urban (under 100,000 persons)
30,007
4,683
6,477
8,988
9,859
1,820
3,681
3,102
1,560
331
2,016
2,274
2,370
1,065
432
Canada, 1996
4,000,000 persons or more
1,000,000-3,999,999
100,000-999,999
Rural or small urban (under 100,000 persons)
28,847
4,264
6,169
8,505
9,910
1,780
3,635
3,046
1,579
367
1,960
2,243
2,322
1,048
456
Note
LD2 is weighted average local density measured at 2 km. radius. S2 is the weighted standard
deviation of local density within 2 km. radius.
Source
U.S. data calculated from 2000 Census of Population and Housing Summary File 1 using
summary level 091 block groups and 1990 Census STF3a using summary level 090 block groups.
Canadian data calculated from the 2001 Census Geosuite database and the 1996 Census
GEOREF database. Calculations by the author.
20 March 2003
Urban sprawl in Canada and America: just how dissimilar?
Table 5
Page 31
Population density in the ten largest urban regions in Canada, 2001, and America, 2000,
showing comparable density in previous census.
Urban Region
New York CMSA
Toronto CMA
Montreal CMA
Los Angeles CMSA
Chicago CMSA
San Francisco CMSA
Vancouver CMA
Hamilton CMA
Philadelphia CMSA
Winnipeg CMA
Calgary CMA
Ottawa - Hull CMA
Boston CMSA
Quebec CMA
Washington MSA
Edmonton CMA
London CMA
Detroit CMSA
Houston CMSA
Dallas CMSA
Population
(000s)
18,087
4,264
3,327
14,532
8,066
6,253
1,832
624
5,899
667
822
1,010
4,172
672
3,924
863
399
4,665
3,711
3,885
Previous Census
Land
AD
LD2
area
(sq km)
20,192 896 6,787
11,707 364 3,635
7,990 416 3,634
87,972 165 3,012
14,553 554 2,904
19,084 328 2,602
5,630 325 2,638
2,718 230 2,266
13,845 426 2,498
8,165
82 2,157
10,203
81 2,030
11,347
89 1,845
8,043 519 2,087
6,292 107 1,775
10,274 382 1,880
19,047
45 1,605
4,191
95 1,686
13,405 348 1,614
18,408 202 1,216
18,046 215 1,186
S2
Population
7,192
2,243
2,715
2,252
2,506
2,246
1,536
1,372
2,609
1,198
948
1,223
2,146
1,299
1,604
857
817
1,098
782
700
(000s)
21,200
4,683
3,426
16,374
9,158
7,039
1,987
662
6,188
671
951
1,064
5,819
683
7,608
938
432
5,456
4,670
5,222
Latest Census
Land
AD
LD2
area
(sq km)
27,065 783 6,855
5,903 793 3,681
4,047 847 3,632
87,944 186 3,200
17,941 510 2,892
19,083 369 2,872
2,879 690 2,826
1,372 483 2,246
15,372 403 2,231
4,151 162 2,123
5,083 187 2,032
5,318 200 1,908
14,574 399 1,840
3,154 216 1,747
24,803 307 1,733
9,419 100 1,672
2,333 185 1,635
17,004 321 1,404
19,956 234 1,397
23,579 221 1,333
S2
7,552
2,274
2,776
2,323
2,583
2,365
1,684
1,382
2,394
1,176
951
1,271
2,038
1,339
1,517
918
850
994
940
831
Note
AD is area-wide density (persons per square kilometer). LD2 is weighted average local density
measured at 2 km. radius. S2 is the weighted standard deviation of local density within 2 km.
radius.
Source
U.S. data calculated from 2000 Census of Population and Housing Summary File 1 using
summary level 091 block groups and 1990 Census STF3a using summary level 090 block groups.
Canadian data calculated from the 2001 Census Geosuite database and the 1996 Census
GEOREF database. Calculations by the author.
20 March 2003
Urban sprawl in Canada and America: just how dissimilar?
Table 6
Leaders in Local Density for their size: Canada, 2001, and America, 2000.
Urban Region
Population
LD2
New York CMSA
Toronto CMA
Montréal CMA
Vancouver CMA
Honolulu MSA
HamiltonCMA
Laredo MSA
Regina CMA
Guelph CMA
Peterborough CMA
Kokomo MSA
21,199,865
4,682,897
3,426,350
1,986,965
876,156
662,401
193,117
192,800
117,344
102,423
101,541
6,855
3,681
3,632
2,826
2,324
2,246
1,739
1,586
1,486
1,001
621
Note
LD2 is weighted average local density measured at 2 km. radius. Selection of "leaders" is from
among 290 urban regions in Canada and America that have populations of 100,000 persons or
more. Method is described in text. In this method, the smallest urban region (Kokomo) in the
combined sample is always labeled a leader by this method.
Source
U.S. data calculated from 2000 Census of Population and Housing Summary File 1 using
summary level 091 block groups and 1990 Census STF3a using summary level 090 block groups.
Canadian data calculated from the 2001 Census Geosuite database and the 1996 Census
GEOREF database.
20 March 2003
Page 32
Urban sprawl in Canada and America: just how dissimilar?
Table 7
Page 33
Good performers and poor performers in Canada, 2001, and America, 2000.
LD2
S2
Population
Actual Potential
Actual
PEF
(a) Good performers
New York
Toronto
Calgary
Saskatoon
Regina
21,199,865
4,682,897
951,395
225,927
192,800
6,855
3,681
2,032
1,536
1,586
6675
4033
2370
1467
1392
7,552
2,274
951
736
625
6428
2009
854
625
646
(b) Poor performers
Rochester
Hartford
Reading
Boston
Lancaster
1,098,201
1,183,110
373,638
5,819,100
470,658
1,006
971
1,109
1,840
837
2486
2549
1735
4336
1874
1,043
1,010
1,322
2,038
1,090
434
423
467
760
384
Note
LD2 is weighted average local density measured at 2 km. radius. S2 is the weighted standard
deviation of local density within 2 km. radius. PEF is S2 predicted by planning efficiency
frontier at observed LD2.
Source
U.S. data calculated from 2000 Census of Population and Housing Summary File 1 using
summary level 091 block groups and 1990 Census STF3a using summary level 090 block groups.
Canadian data calculated from the 2001 Census Geosuite database and the 1996 Census
GEOREF database. Combined set of Canadian and American urban regions includes only those
over 100,000 population. Calculations by the author.
20 March 2003
Urban sprawl in Canada and America: just how dissimilar?
Table 8
Page 34
"Constant boundary" urban regions whose LD2 rose from previous to latest census and whose S2
fell, categorized by leader-laggard status in previous census.
(a) Leader in 1990
Honolulu
(b) Near leader in 1990
Billings
Green Bay
Sioux Falls
Bloomington
Lubbock
St. Joseph
College Station
Merced
Stockton
Fargo
Modesto
(c) Near laggard in 1990
Appleton WI
Davenport
Fresno
Fort Walton Beach
Pensacola
St. Cloud
Asheville
Des Moines
Lexington
Greenville
Portland ME
Wausau
Bellingham
Dothan AL
Madison
Jackson
Redding CA
Clarksville TN
Fort Myers
Omaha
Killeen TX
Santa Fe
(d) Laggard in 1990
Baton Rouge
Harrisburg
Lakeland
Charleston
Jacksonville
Little Rock
Daytona Beach
Johnson City
Nashville
Grand Rapids
Knoxville
Portland OR
Note
LD2 is weighted average local density measured at 2 km. radius. S2 is the weighted standard
deviation of local density within 2 km. radius. Leader: LD2 at or above LD28. Near leader: LD2
not more than 500 persons/km2 below LD2*. Near laggard: LD2 500-1,000 persons/km2 below
LD2*. Laggard: LD2 more than 1,000 persons/km2 below LD2*
Source
U.S. data calculated from 2000 Census of Population and Housing Summary File 1 using
summary level 091 block groups and 1990 Census STF3a using summary level 090 block groups.
Canadian data calculated from the 2001 Census Geosuite database and the 1996 Census
GEOREF database. Calculations by the author.
20 March 2003