Urban sprawl in Canada and America: just how...

20 March 2003

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 7311Fax 416 287 7283

E-mail [email protected]://pc218.cus.utoronto.ca

Abstract

In the 1950s and 1960s, gross urban population density across Canada and America fell quickly and a newphrase, "urban sprawl", was coined to describe the phenomenon. This phrase meant different things toplanners, 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 withthe approval and encouragement of local governments, cooperation was promoted by land-use plannerswho saw such development as the cure for sprawl. In Canada, where land-use regulation is thought to havebeen more extensive, it might be argued that population density should therefore now be correspondinglyhigher. At the same time, residents typically think of urban sprawl as loss of open space, increasinghomogeneity, and built-form clutter. Many political battles have been fought by residents working toprevent planners from enacting exactly the kind of higher densities that planners thought would curbsprawl. Making novel use of data for block groups for the entire United States and correspondingdissemination areas in Canada, this paper explores the variation in, within, and among American andCanadian urban regions for evidence of changes in urban sprawl. For each urban region, the paperpresents a pair of new measures, average local density (LDr) and its standard deviation (Sr), that help tocharacterize urban form and that allow us to categorize urban regions by their reactions to differentnotions of sprawl.

* The financial support of the Social Sciences and Humanities Research Council of Canada (grant 410-00-0769) isgratefully acknowledged.

Urban sprawl in Canada and America: just how dissimilar? Page 1

20 March 2003

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 areintroduced 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 tobe heavily flavored by preconceptions and unstated values. There can be little hope of progress towardresolving the impasse reached in this debate until these preconceptions have been brought to thesurface.

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 theouter edge of the present Philadelphia, some of the loveliest countryside in the world is beingirretrievably 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 thisday a surprising amount of empty land. But it is scattered; a vacant lot here, a dump there—no oneparcel 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, andfor just plain scenery and breathing space… There are many local efforts by private and public groups tocontrol sprawl and save open space. But, each group is going at the problem from its special point of


20 March 2003

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 ajoint interest in open space but act more as antagonists than as allies—and all go down to piecemealdefeat.

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 ofnew urban development flows beyond our view, all around our chosen island. The wave mounts andmounts.

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 overwhelmingproblems of servicing such areas will be multiplied tenfold, and the countryside, that vague ideal forwhich we have sacrificed all else, will have moved out into another state. Against this, we would havenone of the traditional urban virtues to console us. For rurbanization is the kiss of death for city andcountry alike, as anyone who has been in California recently can attest. Although the goal is personaland 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 ofpublic works and community services, is fully accepted almost everywhere. It would simply have to beapplied at a much broader regional level and be geared to bold and positive criteria for futuremetropolitan 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. Dowe 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 0.3people per acre, and suburban residential development, with a density greater than 3.5 people peracre.

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 goodschool district, with bearable taxes and with a good chance of appreciating in value. That list of essential attributesdoes not reflect a deep sense of our dependence on the larger living world of plants and animals and microbes, of soiland water and air."5 In the empirical literature on sprawl, there is a debate about whether to measure sprawl using the density ofpopulation or the density of dwellings. Advocates of the dwellings approach argue that, with the decline in averagehousehold 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, thispaper uses population density measures throughout in keeping with the majority of the literature. However, thereader should be mindful of the "drift" in average population density that is possible over time because of a shrinkinghousehold 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 dis-

appearance 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


20 March 2003

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 havedistricts of dense population in the interior, with density falling off progressively as we proceed tothe 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 considerabledegree of overcrowding in the inner suburbs, or it must spread itself out … Spreading out is only possiblewhere 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 Alonso-

Muth-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 commutingcosts on housing consumption and well-being. A different argument is that higher income also changes consumption ofgoods in favour of those that are income elastic. To the extent that higher income therefore favours independentliving 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, metropolitan-

wide 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 landarea and population of the central city, and the second point being the land area and population of the entiremetropolitan 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 ofongoing urban sprawl. Edmonston and Guterbock (1984) use the same method to look at American cities from 1950 to1975 and conclude that there was no slackening in the rate of suburbanization (deconcentration) during 1970-75compared 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-urbanizedland areas. It is possible to separate urbanized and non-urbanized areas in the 1990 U.S. census, but data for 2000were not available at time of writing. Using persons per square kilometer of urbanized areas would give modestlyhigher densities. Gordon and Richardson (1997) report markedly higher urbanized population densities for 1990, but Ihave 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. Forexample, 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 )/ (Â

i 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

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 modelestimates for Canadian and U.S. cities.


20 March 2003

(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 automobile-

oriented 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 blockgroups 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.


20 March 2003

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

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.

S2* = 200+exp(LD20.2454

)

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

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, lessthan a bold new horizon. Housing Policy Debate, 11(4), 821-879.


20 March 2003

Bussière, R., and Snickars, F. 1970. Derivation of the negative exponential model by an entropymaximising 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, 490-496.

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 PolicyDebate, 10(3), 513-40.

Edmonston, B., and Guterbock, T.M. 1984. Is suburbanization slowing down? Recent trends in populationdeconcentration 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: anexamination of urban density gradients. Urban Studies, 22, 209-217.

Ewing, R. 1997. Is Los Angeles-style sprawl desirable? American Planning Association Journal, 63(1), 107-126.

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 PlanningAssociation 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 UrbanEconomics, 1, 61-98.

Lower Mainland Regional Planning Board of B.C. 1956. Economic Aspects of Urban Sprawl: A TechnicalReport. New Westminster, B.C: The Board. 45 p.

Mills, E.S. 1972. Studies in the Structure of the Urban Economy. Baltimore: Johns Hopkins UniversityPress.

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

Figure 1 Mean versus variation in local population density.

Local Mean Population Density

Loca

l Var

iati

on in

Den

sity

Source See text.


20 March 2003

Figure 2 Uniformly populated dots with regular 2 km spacing, showing count of neighborswithin 2 km.

50

50 50 50 50

50 50 50 50

50 50 50

50 50

50505050

5050

200

150 200 200 150

200 250 250 200

250 250 200

250 200

150200200150

250200

Source See text.


20 March 2003

Figure 3 Uniformly populated dots with irregular 2 km spacing, showing count of neighborswithin 2 km.

50

50 50 50 50 50

50 50 50 50

50 50

50 50

50

50

50505050

200

100 200 200 200 150

150 250 250 200

150 250

150 200

150

150

150150150100

Source See text.


20 March 2003

Figure 4 Cumulative proportion of dots (Block Groups, Dissemination Areas, or EnumerationAreas) by population resident in dot.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 500 1000 1500 2000 2500 3000 3500

Population in Block Group, Dissemination Area, or Enumeration Area

Cum

ulat

ive

prop

orti

on o

f BG

s, D

As,

or E

As

US BG (091) 2000Canada DA 2001US BG (090) 1990Canada EA 1996

Source U.S. data calculated from 2000 Census of Population and Housing Summary File 1using summary level 091 block groups and 1990 Census STF3a using summary level090 block groups. Canadian data calculated from the 2001 Census Geosuite databaseand the 1996 Census GEOREF database. Calculations by the author.


20 March 2003

Figure 5 Cumulative proportion of population by local density (LD2).

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

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)

Cum

ulat

ive

prop

orti

on o

f po

pula

tion

US BG (091) 2000Canada DA 2001US BG (090) 1990Canada EA 1996

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 1using summary level 091 block groups and 1990 Census STF3a using summary level090 block groups. Canadian data calculated from the 2001 Census Geosuite databaseand the 1996 Census GEOREF database. Calculations by the author.


20 March 2003

Figure 6 Average local density (LD2) by size of metropolitan area for comparable smallerAmerican urban regions in 2000 and smaller Canadian urban regions, 2001.

0

500

1,000

1,500

2,000

2,500

0 200,000 400,000 600,000 800,000 1,000,000

Population

Loca

l D

ensi

ty (

LD2)

America 2000Canada 2001


Source U.S. data calculated from 2000 Census of Population and Housing Summary File 1using summary level 091 block groups. Canadian data calculated from the 2001Census Geosuite database. Calculations by the author.


20 March 2003

Figure 7 Average local density (LD2) by size of metropolitan area for comparable large urbanregions: America 1990 and Canada 1996.

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

0 5,000,000 10,000,000 15,000,000 20,000,000 25,000,000

Population

Loca

l D

ensi

ty (

LD2)

America 2000Canada 2001




20 March 2003

Figure 8 Efficiency frontier (S2 versus LD2) for comparable smaller urban regions: America2000 and Canada 2001.

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0 500 1,000 1,500 2,000 2,500

Local Density (LD2)

Stan

dard

Dev

iati

on o

f LD

2 (S

2)

America 2000Canada 2001Planning efficiency frontier

Note LD2 is weighted average local density measured at 2 km. radius. S2 is the weightedstandard deviation of local density within 2 km. radius. PEF is S2 predicted byplanning efficiency frontier at observed LD2.



20 March 2003

Figure 9 Efficiency frontier (S2 versus LD2) for comparable larger urban regions: America 2000and Canada 2001.

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000

Local Density (LD2)

Stan

dard

Dev

iati

on o

f LD

2 (S

2)

America 2000Canada 2001Planning efficiency frontier

Note LD2 is weighted average local density measured at 2 km. radius. S2 is the weightedstandard deviation of local density within 2 km. radius. PEF is S2 predicted byplanning efficiency frontier at observed LD2.



20 March 2003

Figure 10 Change in LD2 and S2: America urban regions from 1990 to 2000, and Canadian urbanregions from 1996 to 2001.

-300

-200

-100

0

100

200

300

400

500

-300 -200 -100 0 100 200 300 400 500 600

Change in LD2 from preceding cenus

Chan

ge in

S2

from

pre

cedi

ng c

ensu

s

AmericaCanada

Note LD2 is weighted average local density measured at 2 km. radius. S2 is the weightedstandard deviation of local density within 2 km. radius.

Source U.S. data calculated from 2000 Census of Population and Housing Summary File 1 usingsummary level 091 block groups. Canadian data calculated from the 2001 Census Geosuitedatabase. Calculations by the author.


20 March 2003

Table 1 Predicted gross population density in suburb: Clark's density gradient model estimates.

City, Year 5 km from 10 km fromcity center city center

(persons/km2) (persons/km2)

New York, 1940 25,090 13,430London, 1939 16,727 8,953Boston, 1940 7,649 2,995Manchester, 1931 7,154 3,275Sydney, 1947 5,365 2,456Los Angeles, 1940 5,365 2,456

Source: Clark (1951: 492-493). Calculations by author.


20 March 2003

Table 2 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 9,161,927 314,000,000 persons or more 92,846 283,181 328

New York--Northern New Jersey--Long Island, NY--NJ--CT, CMSA 21,200 27,065 783Los Angeles--Riverside--Orange County, CA, CMSA 16,374 87,944 186Chicago--Gary--Kenosha, IL--IN--WI, CMSA 9,158 17,941 510Washington--Baltimore, DC--MD--VA--WV, CMSA 7,608 24,803 307San Francisco--Oakland--San Jose, CA, CMSA 7,039 19,083 369Philadelphia--Wilmington--Atlantic City, PA--NJ--DE--MD, CMSA 6,188 15,372 403Boston--Worcester--Lawrence, MA--NH--ME--CT, CMSA 5,819 14,574 399Detroit--Ann Arbor--Flint, MI, CMSA 5,456 17,004 321Dallas--Fort Worth, TX, CMSA 5,222 23,579 221Houston--Galveston--Brazoria, TX, CMSA 4,670 19,956 234Atlanta, GA, MSA 4,112 15,861 259

1,000,000 to 3,999,999 persons 68,672 486,166 141100,000 to 999,999 persons 62,758 977,622 64Rural or small urban (under 100,000 persons) 57,145 7,414,958 8

Canada, 2001 30,007 9,012,112 34,000,000 persons or more 4,683 5,903 793

Toronto 4,683 5,903 7931,000,000-3,999,999 6,477 12,244 529100,000-999,999 8,988 73,485 122Rural or small urban (under 100,000 persons) 9,859 8,920,481 1

Source 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

Table 3 Cumulative proportion of population by LD2 in Canada, 1996 and 2001, and America, 1990and 2000.

Cumulative proportion of populationLocal density (LD2) America Canada

BG BG EA DA1990 2000 1996 2001

Under 10 persons/km2 0.01 0.01 0.01 0.01Under 20 persons/km2 0.02 0.01 0.03 0.02Under 40 persons/km2 0.04 0.03 0.07 0.07Under 80 persons/km2 0.12 0.09 0.17 0.17Under 160 persons/km2 0.22 0.19 0.22 0.23Under 320 persons/km2 0.32 0.29 0.28 0.29Under 640 persons/km2 0.45 0.43 0.37 0.37Under 1,280 persons/km2 0.65 0.64 0.51 0.50Under 2,560 persons/km2 0.85 0.85 0.76 0.75Under 5,120 persons/km2 0.94 0.94 0.93 0.92Under 10,240 persons/km2 0.98 0.98 1.00 1.00


Source U.S. data calculated from 2000 Census of Population and Housing Summary File 1 usingsummary 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 CensusGEOREF database. Calculations by the author.


20 March 2003

Table 4 Local density and variation in Canada, 1996 and 2001, and in America, 1990 and 2000, by sizeof urban agglomeration.

Population LD2 S2

(000s)

America, 2000 281,422 1,644 2,9204,000,000 persons or more 92,846 3,304 4,5001,000,000 to 3,999,999 persons 68,672 1,300 988100,000 to 999,999 persons 62,759 801 723Rural or small urban (under 100,000 persons) 57,145 285 328

America, 1990 248,710 1,584 2,8104,000,000 persons or more 61,674 3,846 4,7421,000,000 to 3,999,999 persons 63,102 1,377 1,109100,000 to 999,999 persons 65,837 825 743Rural or small urban (under 100,000 persons) 58,097 270 329

Canada, 2001 30,007 1,820 2,0164,000,000 persons or more 4,683 3,681 2,2741,000,000-3,999,999 6,477 3,102 2,370100,000-999,999 8,988 1,560 1,065Rural or small urban (under 100,000 persons) 9,859 331 432

Canada, 1996 28,847 1,780 1,9604,000,000 persons or more 4,264 3,635 2,2431,000,000-3,999,999 6,169 3,046 2,322100,000-999,999 8,505 1,579 1,048Rural or small urban (under 100,000 persons) 9,910 367 456

Note LD2 is weighted average local density measured at 2 km. radius. S2 is the weighted standarddeviation of local density within 2 km. radius.



20 March 2003

Table 5 Population density in the ten largest urban regions in Canada, 2001, and America, 2000,showing comparable density in previous census.

Previous Census Latest CensusUrban Region Population Land AD LD2 S2 Population Land AD LD2 S2

area area(000s) (sq km) (000s) (sq km)

New York CMSA 18,087 20,192 896 6,787 7,192 21,200 27,065 783 6,855 7,552Toronto CMA 4,264 11,707 364 3,635 2,243 4,683 5,903 793 3,681 2,274Montreal CMA 3,327 7,990 416 3,634 2,715 3,426 4,047 847 3,632 2,776Los Angeles CMSA 14,532 87,972 165 3,012 2,252 16,374 87,944 186 3,200 2,323Chicago CMSA 8,066 14,553 554 2,904 2,506 9,158 17,941 510 2,892 2,583San Francisco CMSA 6,253 19,084 328 2,602 2,246 7,039 19,083 369 2,872 2,365Vancouver CMA 1,832 5,630 325 2,638 1,536 1,987 2,879 690 2,826 1,684Hamilton CMA 624 2,718 230 2,266 1,372 662 1,372 483 2,246 1,382Philadelphia CMSA 5,899 13,845 426 2,498 2,609 6,188 15,372 403 2,231 2,394Winnipeg CMA 667 8,165 82 2,157 1,198 671 4,151 162 2,123 1,176Calgary CMA 822 10,203 81 2,030 948 951 5,083 187 2,032 951Ottawa - Hull CMA 1,010 11,347 89 1,845 1,223 1,064 5,318 200 1,908 1,271Boston CMSA 4,172 8,043 519 2,087 2,146 5,819 14,574 399 1,840 2,038Quebec CMA 672 6,292 107 1,775 1,299 683 3,154 216 1,747 1,339Washington MSA 3,924 10,274 382 1,880 1,604 7,608 24,803 307 1,733 1,517Edmonton CMA 863 19,047 45 1,605 857 938 9,419 100 1,672 918London CMA 399 4,191 95 1,686 817 432 2,333 185 1,635 850Detroit CMSA 4,665 13,405 348 1,614 1,098 5,456 17,004 321 1,404 994Houston CMSA 3,711 18,408 202 1,216 782 4,670 19,956 234 1,397 940Dallas CMSA 3,885 18,046 215 1,186 700 5,222 23,579 221 1,333 831

Note AD is area-wide density (persons per square kilometer). LD2 is weighted average local densitymeasured at 2 km. radius. S2 is the weighted standard deviation of local density within 2 km.radius.



20 March 2003

Table 6 Leaders in Local Density for their size: Canada, 2001, and America, 2000.

Urban Region Population LD2

New York CMSA 21,199,865 6,855Toronto CMA 4,682,897 3,681Montréal CMA 3,426,350 3,632Vancouver CMA 1,986,965 2,826Honolulu MSA 876,156 2,324HamiltonCMA 662,401 2,246Laredo MSA 193,117 1,739Regina CMA 192,800 1,586Guelph CMA 117,344 1,486Peterborough CMA 102,423 1,001Kokomo MSA 101,541 621

Note LD2 is weighted average local density measured at 2 km. radius. Selection of "leaders" is fromamong 290 urban regions in Canada and America that have populations of 100,000 persons ormore. Method is described in text. In this method, the smallest urban region (Kokomo) in thecombined sample is always labeled a leader by this method.

Source U.S. data calculated from 2000 Census of Population and Housing Summary File 1 usingsummary 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 CensusGEOREF database.


20 March 2003

Table 7 Good performers and poor performers in Canada, 2001, and America, 2000.LD2 S2

Population Actual Potential Actual PEF

(a) Good performersNew York 21,199,865 6,855 6675 7,552 6428Toronto 4,682,897 3,681 4033 2,274 2009Calgary 951,395 2,032 2370 951 854Saskatoon 225,927 1,536 1467 736 625Regina 192,800 1,586 1392 625 646

(b) Poor performersRochester 1,098,201 1,006 2486 1,043 434Hartford 1,183,110 971 2549 1,010 423Reading 373,638 1,109 1735 1,322 467Boston 5,819,100 1,840 4336 2,038 760Lancaster 470,658 837 1874 1,090 384

Note LD2 is weighted average local density measured at 2 km. radius. S2 is the weighted standarddeviation of local density within 2 km. radius. PEF is S2 predicted by planning efficiencyfrontier at observed LD2.

Source U.S. data calculated from 2000 Census of Population and Housing Summary File 1 usingsummary 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 CensusGEOREF database. Combined set of Canadian and American urban regions includes only thoseover 100,000 population. Calculations by the author.


20 March 2003

Table 8 "Constant boundary" urban regions whose LD2 rose from previous to latest census and whose S2fell, categorized by leader-laggard status in previous census.

(a) Leader in 1990Honolulu

(b) Near leader in 1990Billings Bloomington College Station FargoGreen Bay Lubbock Merced ModestoSioux Falls St. Joseph Stockton

(c) Near laggard in 1990Appleton WI Asheville Bellingham Clarksville TNDavenport Des Moines Dothan AL Fort MyersFresno Lexington Madison OmahaFort Walton Beach Greenville Jackson Killeen TXPensacola Portland ME Redding CA Santa FeSt. Cloud Wausau

(d) Laggard in 1990Baton Rouge Charleston Daytona Beach Grand RapidsHarrisburg Jacksonville Johnson City KnoxvilleLakeland Little Rock Nashville Portland OR

Note LD2 is weighted average local density measured at 2 km. radius. S2 is the weighted standarddeviation of local density within 2 km. radius. Leader: LD2 at or above LD2

8. Near leader: LD2not more than 500 persons/km2 below LD2

*. Near laggard: LD2 500-1,000 persons/km2 belowLD2

*. Laggard: LD2 more than 1,000 persons/km2 below LD2*


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