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Utilizing geospatial analysis of U.S. Census data for studying the dynamics of urbanization and

land consumption

Toni Menninger, February 20, 2012

Abstract

1. Introduction

2. United States Census geography

2.1 The U.S. Census geographical hierarchy

2.2. Evolution of U.S. Census geographies

2.3. Census geographical area measurement

2.4. Summary

3. The geography of urbanization

3.1. Delimiting the city

3.2. Population density and land use efficiency

3.3 Studying the spatial distribution of population

4. Areal interpolation and dasymetric mapping

4.1. Overview

4.2. Applications of dasymetric mapping

5. Conclusion

Appendix: Population density algebra

References

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Abstract

Geographically referenced US census data provide a large amount of information about the

extent of urbanization and land consumption. Population count, the number of housing units

and their vacancy rates, and demographic and economic parameters such as racial composition

and household income, and their change over time, can be examined at different levels of

geographic resolution to observe patterns of urban flight, suburbanization, and reurbanization.

This paper will review the literature on prior application of census data in a geospatial setting. It

will identify strengths and weaknesses and address methodological challenges of census-based

approaches to the study of urbanization. Of special interest will be literature comparing and/or

integrating census data with alternative methodologies, e.g. based on Remote Sensing. The

general purpose of this paper is to lay the groundwork for the optimal use of high resolution

census data in studying urbanization in the United States.

1. Introduction

Urbanization, the expansion of human settlement, has long been studied by geographers,

economists, and social scientists. In recent decades, in parallel with rapid growth of the global

urban population, research interest in its causes and effects has “exploded” (Wang et al. 2012).

Urban growth is increasingly recognized as one of the most significant processes of human‐

induced global change. “Although only a small percentage of global land cover, urban areas

significantly alter climate, biogeochemistry, and hydrology at local, regional, and global scales.”

(Schneider et al. 2009). “The density, spatial distribution, and physical characteristics of human

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settlement are important drivers of social and environmental change at multiple scales” (Potere

and Schneider 2007). A growing research community has focused on measuring the physical

extent and change over time of urban settlements (Angel et al. 2005; Burchfield et al. 2006;

Kasanko et al. 2005; Schneider and Woodcock 2008; Potere et al. 2009; Schneider et al. 2009;

McDonald et al. 2010).

Much effort has also been made to study patterns, in addition to the extent, of urban

settlement (Camagni et al. 2002; Angel et al. 2005; Kasanko et al. 2005; Schneider and

Woodcock 2008; Clark et al. 2009; Schwarz 2010). Researchers hypothesize that form and

structure of the built environment are related to social, economic and environmental outcomes

and have an impact on humans’ quality of life. Identifying causes and effects of differences in

urban form might enable policy makers, planners and architects to better urban conditions and

reduce urbanization’s environmental footprint. A particularly vigorous research field is devoted

to the study of the dispersed, low-density settlement pattern commonly known as sprawl

(Downs 1999; Fulton et al. 2001; Galster et al. 2001; Ewing et al. 2003; Lopez and Hynes 2003;

Tsai 2005; Wolman et al. 2005; Burchfield et al. 2006; Carruthers and Ulfarsson 2008). Yet

perhaps the most striking aspect of the pertinent literature is the lack of consensus. For

example, Churchman (1999) identified more than 50 hypothesized advantages and

disadvantages of high urban density and concludes that researchers do not agree on any of

them.

Many researchers have stated the need for accurate and consistent metrics of urbanization. "A

key difficulty in studying cities is finding a practical way to define them" (Rozenfeld et al. 2011).

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Parr (2007) points out that cross-sectional comparisons of cities often fail to apply consistent

standards: "It hardly needs emphasising that city size must be measured meaningfully and

consistently over the entire range of cities under consideration." Angel et al. (2005) identify a

series of fundamental questions: "Where does the city end and the rural area begin? What is

the population of the city? What is the built-up area of the city? What is the average density in

the city? What is the degree of openness or sprawl in the city? How compact or dispersed is the

city? (…) These questions cannot be easily answered (…)." Wolman et al. (2005) contend that

conventionally used metrics tend to either overbound or underbound urban extent. The

research agenda they propose consists of three steps: defining appropriate and replicable

metrics of urbanization, measuring them across a wide sample of cities, and use the results in

multivariate models to test hypotheses concerning causes and effects of urban form. Similar

research strategies have been pursued by Ewing et al. (2003).

Two main sources of data can be identified in the urbanization literature: Remote sensing (RS)

derived land use data, and census population data. RS data are available for about the last

hundred years in the form of aerial photography, and for the last forty years in the form of

satellite imagery. Population data have been collected by national census authorities for

centuries. The remainder of this paper will review the use and usefulness of census data in the

study of urbanization in the United States, in particular in a geospatial setting. To this end, it is

necessary to first provide an overview of the geographic structure of U.S. Census data and its

evolution.

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2. United States Census geography

2.1 The U.S. Census geographical hierarchy

The primary source of data about settlement structure in the United States is the U.S. Census

Bureau. This section reviews the geographic structure of U.S. Census data and its evolution. It is

based on the Census Bureau’s Geographic Areas Reference Manual (U.S. Census Bureau 1994)

and the technical documentation for the decennial censuses 2000 and 2010 and due to space

restrictions must leave out many exceptions and special cases.

U.S. Census geography is currently based on a hierarchy of enumeration districts:

Nation → State → County → County subdivision → Census tract → Block group → Census block

Some geographic entities transcend the basic census hierarchy. Among them are Places and

Urban Areas, which are situated within states and are composed of census blocks, and

Metropolitan Areas (MAs), which are composed of counties but can transcend state lines.

The census block is the smallest Census Bureau geographic entity; it generally is an area

bounded by streets, streams, and the boundaries of legal and statistical entities. There were

more than 11 million blocks in 2010. Census tracts are relatively permanent geographic entities

within counties that have generally between 2500 and 8000 residents. They are delineated by a

committee of local data users to be as homogeneous as possible, approximating city

neighborhood communities, and bounded by visible features. Further, the census recognizes

and tabulates places (i.e. cities and towns). Incorporated places are delimited by their

administrative boundaries. Recognizable settlements that are not legally incorporated can be

defined as census-designated places (CDP). Urban areas are continuously built-up areas that

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meet minimum population and density criteria (at least 50,000 residents for Urbanized Areas

(UA) and 2,500 for Urban Clusters (UC) and 1,000 persons per square mile). Urban areas can

include territory that is not or only sparsely populated but serves urban functions, such as

commercial and industrial development, parks, and golf courses. Even clearly nonurban

enclaves of up to five square miles can be part of a UA if it gives it "a more regular appearance

and simplifies data presentations”. Census classifies all units as either rural or urban depending

on whether they are situated in an Urban Area.

Metropolitan Areas (also known as Core Based Statistical Areas, CBSA) group together counties

that have a high degree of economic and social integration (judged by commuting patterns)

with one or several urban centers. Census designates one or more Central Counties containing

the metropolitan core, the rest are known as Outlying Counties. Census also designates one or

more Principal Cities (Central Cities before 2010). Also, up to 2000, Census used to designate

one or more Central Places for each UA.

It must be pointed out that not all data collected by Census are available at all geographic

levels. The decennial census enumerates all residents and dwelling units and collects basic

demographic information (known as the short form) about each person. These results are

tabulated and released to block level. Census also collects more detailed socio-economic data

in regular surveys (the long form in earlier decennial censuses and now the American

Community Survey). These surveys are based on samples and are released at county, place, or

tract level. They cannot be disaggregated to block level because the sampling error would be

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unacceptable and also the privacy of respondents could not be maintained given that many

blocks have fewer than ten residents.

2.2. Evolution of U.S. Census geographies

Many geographers, historians and social scientists are interested in the development of cities

and draw on historical census data. This section will briefly explore the evolution of US

decennial census data since 1790 (U.S. Census Bureau 1994).

From the first census in 1790, data were reported by state, county and county subdivision.

State administrative boundaries were finalized by 1900 and counties were mostly finalized by

1920 and have been fairly stable since. However, county subdivision geography in many states

has been unstable and subject to frequent change. Populations of some incorporated places

were reported in the earliest censuses but they were systematically tabulated for the first time

in 1880. Unincorporated places were systematically covered since 1950 (and labeled Census

Designated Places (CDP) in 1980). Administrative boundaries of cities are unstable. They change

frequently due to annexation, consolidation, incorporation and disincorporation, especially in

the Midwest and South. They also often underbound or overbound the actual functional city.

From 1910 through 1940, Census categorized incorporated places of 2,500 or more residents as

urban and everything else as rural. The inherent capriciousness of place boundaries motivated

the Census Bureau to come up, in 1950, with its own delineation of Urbanized Areas (UAs) of at

least 50,000 people. Places outside of UAs with at least 2,500 population were still classified as

urban even when their density was low. That changed in 2000, when Urban Clusters (UCs) of at

least 2,500 residents were delineated regardless of place boundaries. The criteria for

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delineating urban areas are quite complex and have evolved over time although the main

population and density criteria have remained stable. Caution is therefore recommended when

analyzing census urban areas longitudinally. Interestingly, Census makes use of remote-sensing

derived land use data to help delineate Census 2010 urban areas.

The concept of Metropolitan Areas also goes back to 1950. Metropolitan Statistical Areas (MSA)

were delineated around a core Urbanized Area. Micropolitan Statistical Areas (μSA) with an

urban core of at least 10,000 but less than 50,000 residents were designated in 2003. The

criteria for metropolitan areas are revised every 10 years. Since metropolitan areas are

composed of counties, they are easier to track back in time than is the case for urban areas.

Census tracts, block groups and blocks were delineated successively since 1940 although

precursor small area districts have existed in a few cities since 1910. In 1940, all cities exceeding

50,000 residents were covered by census tracts and blocks. Coverage was expanded every

decade until complete coverage was reached in 1990. Census blocks are impermanent. Tracts

are more permanent and have a permanent numbering system to allow intercensal

comparison. Tracts can however be merged and split due to population change.

Tracts should be as homogeneous as possible at the outset but may become less homogeneous

due to demographic change. In practice, only dense urban tracts represent more or less

homogeneous communities. Rural tracts can encompass large areas. Tracts at the urban fringe

are often mixtures of urban and rural areas and may contain large amounts of open space. They

cannot be used to identify unpopulated areas as virtually all tracts have a minimum population.

For these reasons, tracts are of limited suitability to delineate urban extent. Even blocks can be

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quite large (frequently up to about 100 square kilometers) and inhomogeneous. They are also

often irregularly shaped. About one third of all blocks are unpopulated.

2.3. Census geographical area measurement

Historical census data are of limited value unless they can be located in geographic space.

Calculating population density requires at least knowledge of each enumeration district’s area.

The first comprehensive land and water area figures for counties were published as part of the

1880 census. Area figures for more populous places were provided between 1890 and 1930. In

1940, areal data were provided for all places of 1,000 residents or more and all county

subdivisions. However, areal data for tracts and other small-area geographic entities were not

provided before 1990. Since 1990, thanks to the Topologically Integrated Geographic Encoding

and Referencing (TIGER) System, all areas have been measured and all geographic entities

tabulated by the census have been available as geo-referenced vector files (Peters and

MacDonald 2004; Almquist 2010). In fact, digital geographic files were already prepared for

census 1970 and 1980 but their usefulness for GIS purposes is unclear.

2.4. Summary

The only census geography that appears largely consistent over more than a few decades is the

county. Counties have rarely changed in the last about 100 years and some county census

counts can be traced back 200 years or more. These county-based time series indicate where

population growth and decline has occurred but are not fine-grained enough to study

urbanization processes in detail.

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Population data on some individual cities and towns has been collected in the earliest censuses.

In a systematic fashion, incorporated places (and less systematically, unincorporated places)

have been covered since 1880 and areal measurements for most places were available from

1940. The limitation of these data series is that they are based on administrative boundaries

that are subject to frequent change and often do not coincide with the actual settlement area.

The Metropolitan Area and Urban Area geographies were introduced in 1950 to provide

functional geographic units that are not based on arbitrary administrative boundaries. These

statistical units are suitable for cross-sectional analysis. The Metropolitan Area is a collection of

counties and almost always contains some rural area. The Urban Area is a collection of census

blocks considered urban but can contain considerable amounts of nonurban land.

Census tracts are designed to be permanent units as far as possible but demographic change

makes splits and merges unavoidable. Census blocks are the smallest, very fine-grained building

blocks of census geography and cannot be expected to be permanent. The census tract is less

fine-grained but it is, to some extent, possible to follow individual census tracts longitudinally.

Census block or tract data can be used to construct nationwide population density maps of

relatively high resolution for the last three censuses, and, for some urban areas, maps of this

quality can potentially be traced back to cover the whole post-war period. Tract- or block-level

areal measurements, however, are only available for census 1990 and later.

Block-level data is eminently suitable for longitudinal analysis of urbanization processes of the

last twenty years. The major limitation of this approach is that these geographic units are

impermanent. Further, even though census blocks are the most homogeneous census units,

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their use can still give rise to ecological fallacies and the Modifiable Areal Unit Problem (MAUP)

(Openshaw 1984; Jelinsky and Wu 1996).

3. The geography of urbanization

“Cities’ shape can be defined by three variables: the surface of the built-up area, the

shape of the built-up area and the way the population density is distributed within this

same built-up area.” Bertaud and Malpezzi (2003:19)

The two concepts most widely used in the literature to characterize settlement patterns are

urban extent and population density. Measuring urban extent means delimiting an urban

boundary; measuring density requires measuring both the areal urban extent and the

population that it houses. A variety of additional concepts characterizing different aspects of

form and function of settlements have been developed, many of which are derived from

density measures and describe how urban intensity is distributed across geographic space.

When these metrics are analyzed longitudinally, they give insight into the dynamics of

urbanization processes over time. Often examined in the literature are measures of the

expansion of urban extent, which gives rise to land consumption measures, and changes in

density.

The purpose of this section is to give an overview over different approaches to measuring

urbanization, in particular with respect to the use of U.S. census data.

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3.1. Delimiting the city

Locating the city geographically requires to define what is meant by an urban area and to

delineate its boundary. “The extent of the city is important in a number of respects, not least in

relation to the question of city size, an issue of considerable significance in urban and regional

analysis.” (Parr 2007) Various researchers have studied urban land consumption as the increase

in urban extent over time within a metropolitan area (Fulton et al. 2001; Angel et al. 2005;

Burchfield et al. 2006; Schneider and Woodcock 2008; McDonald et al. 2010). Schneider and

Woodcock (2008) observe: “Two difficulties arise when comparing any set of metropolitan

areas: defining what types of land are in fact ‘urban’; and, determining what geographical area

should be considered.” And Potere et al. (2009) add: “There is currently no generally accepted

definition of ‘urban land’”. The contemporary city is not easy to physically pinpoint because it

has become “increasingly porous” (Parr 2007). Cromartie and Swanson (1996) observe that

“large cities have expanded beyond traditional borders to form sprawling urban regions”, giving

rise to “increasingly complex U.S. settlement patterns” and the “growing complexity of the

rural-urban frontier”. Rozenfeld et al. (2011) state that “a key difficulty in studying cities is

finding a practical way to define them” and discuss three main approaches: relying on the

census Metropolitan Area definitions; relying on legal boundaries of cities; and constructing the

city from micro (i.e. small area census) data. Other approaches rely on the Census urban area

designation, on remote sensing data, and on survey data such as the National Resources

Inventory (NRI) (Fulton et al. 2001; Lang 2003; Carruthers 2008) or cadastral data.

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County level analyses of urban change are common in the suburbanization literature. A typical

approach is to divide Census metropolitan areas into core, inner ring suburban and outer ring

suburban counties, or into core city and suburbs (e. g. Morrill 1992; Katz and Lang 2003; Cox

2011). Morrill (1992) cautions that counties are “imperfect units” but uses them “because

consistent data are available”. This level of analysis gives insight into broad national trends in

urbanization and demographic change but can be misleading because metropolitan areas can

contain large amounts of rural territory and open space (Cromartie and Swanson 1996; Lang

2003), and it cannot reveal population change within a county.

Administrative city boundaries are used as units of analysis because that is often the only

available long term data set. González-Val and Lanaspa (2011) studied the population growth of

the largest American cities since 1790 based on place level Census data. Rozenfeld et al. (2011)

observe that “it is problematic to define cities through their fairly arbitrary legal boundaries”

(Rozenfeld et al. 2011).

The Census urban area designation has been chosen as unit of analysis by Galster et al. (2001)

as basis for a number of sprawl measures. Marshall (2007) found a scaling relationship between

Census urban area size and population. Downs (1999) also used Census urban areas as base

units and divided them into central city (as designated by Census) and fringe area. Ewing et al.

(2002) criticized the “reliance on political, and hence economically arbitrary, boundaries of

central cities”. Schneider and Woodcock (2008) agree: “Political boundaries, while often used

to delineate urban space, are not a reliable means of doing so since they change frequently

over time, overestimate or underestimate urban land use and are not comparable across or

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within nations”. It is noteworthy that Census abandoned the designation of urban area central

cities in 2010. Fulton et al. (2001) and Lang (2003) rejected the urbanized area designation

because it excludes low-density suburban development that “should be included as built-up

parts of metropolitan areas” (Lang 2001: 760). Wolman et al. (2005) similarly contend that the

UA tends to underbound urban extent whereas the metropolitan area overbounds it.

Buckwalter and Rugg (1986) made the same point 20 years earlier: “The lack of an accurate

method of delimiting the physical city has frequently forced urban specialists, including

geographers, to use either legal cities or urbanized areas as the area component in studying

urban problems on a comparative basis. The failure of these two city bases to reflect the actual

spatial extent of urban development has led to conspicuous discrepancies in the results of

comparative urban studies that require precise land use delimitation”. While Wolman et al.

advocate using remote sensing derived land use information as ancillary data to fine-tune

census geographic units, Buckwalter and Rugg called for defining the urban footprint solely on

the basis of remote sensing imagery. The literature on urban remote sensing is extensive and

discussing advantages and shortcomings of this method is beyond the scope of this review. It

should be noted however that due to “the intrinsically mixed landscape that makes up most

cities and towns” (Potere et al. 2009), definitional ambiguities apply to any urban land

classification scheme including those based on remote sensing.

Several approaches have been proposed to use small area census units to delimit cities.

Cromartie and Swanson (1996) reject the county level approach and prefer the tract level:

“Census tracts are large enough to have acceptable sampling error rates (containing an average

of 4,000 people); are consistently defined across the Nation; are usually subdivided as

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population grows to maintain geographic comparability over time; and can be aggregated to

form county-level statistical areas when needed.” Their approach is to classify census tracts into

five categories according to the rural-urban settlement continuum defined by the USDA

Economic Research Service (ERS). To be part of the most urban among these classes, denoted

“Metro core”, at least 50% of the tract population must be within the urbanized area.

Rozenfeld et al. (2011) proposed to build cities “from the bottom up” by aggregating census

tracts according to the City Clustering Algorithm (CCA). The algorithm defines a “city” as a

cluster of contiguous units (i.e. census tracts) that have a minimum population density and are

within a prescribed distance from the closest neighbor in the cluster. This approach allows for

experimentation with different threshold values for density and distance and could be applied

to subtract geographies as well. Approaches based on subtract geographies are however rare

according to the literature reviewed for this paper.

3.2. Population density and land use efficiency

Density is calculated as a number of units in a given land area and can refer to residential or

employment population, dwelling units, residential or commercial space or indeed any measure

of urban activity or intensity that can be determined on the basis of areal units. The inverse of

density – the land area per capita – can be conceptualized as a measure of land use efficiency.

By far the most widely used measure of urban density in the urbanization literature is

residential density. While the concept of density is intuitively appealing and is often taken for

granted, several authors have cautioned that it is actually “a very complex concept”

(Churchman 1999). According to Forsyth (2003), there is "a surprising lack of clarity about what

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counts when considering density, and about how to measure it”. When reporting density, the

analyst should always explain the definitions used and make sure that any comparison between

cities or across time is based on consistent metrics (Churchman 1999).

Crude density, the average population per areal unit, is sensitive to the delineation of the base

area and "varies greatly depending on the base land area used in the density calculation.”

(Forsyth 2003) As discussed in the preceding section, how to delimit the base area for correctly

determining population density is one of the fundamental unsolved problems in urban

geography. The terms gross and net density have been used, where net residential density is

meant to exclude nonresidential land from the base area (Alexander 1993; Churchman 1999;

Forsyth 2003). Researchers of land consumption disagree however which areas should be

excluded from the urban land category. As discussed, the Census Bureau includes urban

greenspace as well as unpopulated enclaves up to five square miles in size in its urban area

designation. Wolman et al. (2005) in contrast have called for excluding undevelopable land

from the urban footprint but forest and agricultural land at the urban fringe would be

considered as "potentially available for development" and included in the urban area. While the

aforementioned authors clearly distinguish between urban land in terms of land use and the

built environment in terms of land cover (i.e. built-up or developed land, land covered or

dominated by man-made structures, impervious land cover), many researchers in the urban

remote sensing community use these terms interchangeably: “When vegetation (e.g. a golf

course or park) dominates a pixel, these areas are not considered urban, even though – in

terms of land use – they may function as urban space.” (Potere et al. 2009). It is important that

each analyst make their terminology explicit.

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3.3 Studying the spatial distribution of population

The crude population density calculated from a certain base area is an average that gives rise to

ecological fallacies because population distributions are rarely homogeneous. "The

conventional crude population density is not a good measure of the density at which the

population lives." (Craig 1984). Stairs (1977) proposed the population weighted density (or

person-average density) (PWD) as an alternative to conventional crude density. PWD can be

calculated whenever the base area can be disaggregated into a set of subunits and population

and area of each are known, and is defined as the average subunit density weighted by subunit

population (see appendix). To illustrate the concept, he considered a hypothetical country

consisting of a densely populated city, sparsely populated farmland, and an unpopulated desert

area. Although most of the population is concentrated in the city, the crude density for the

whole country is very low due to the large amount of unpopulated land. The population

weighted density is a much higher number. While the crude density reflects correctly that most

land is not or sparsely populated, the population weighted density more accurately reflects the

conditions under which most residents live. Craig (1984) expanded on Stairs’ concept and

suggested to use the geometric instead of arithmetic population weighted mean density.

While crude density is very sensitive to the choice of the base area, population weighted

density (PWD) is not. The latter, however, is sensitive to the subdivision chosen, in other words,

to the spatial resolution of the population data, whereas the first is not. Thus the question is

raised “what the fundamental unit of density actually is” (Craig 1984). Ideally, the fundamental

unit would be perfectly homogeneous. “Any (and every) subdivision of an areal unit increases

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the average population weighted density” (Craig 1984), unless the unit is perfectly

homogeneous. This property gives rise to the modifiable areal unit problem, in particular the

scale problem (calculating PWD at different scales will systematically affect the outcome) but

also the aggregation problem (choice of an alternative set of areal units might change the

outcome) (Openshaw 1984: 8). That may explain why the concepts proposed by Stairs and Craig

are rarely considered in contemporary urbanization literature (an exception is Rozenfeld et al.

2011). Yet they can provide a corrective to the shortcomings of the widely used crude density.

A number of other approaches exist for quantitatively assessing population distribution. The

Index of Dissimilarity, Gini index and Shannon Entropy measure the degree to which a

population distribution deviates from evenness (Massey and Denton 1988; Tsai 2005; Burt et al.

2009; Schwarz 2010; see Appendix). The population density gradient (Bertaud and Malpezzi

2003; Ewing et al. 2003) measures the decline of population density with increasing distance

from the Central Business District (CBD) and is an indicator of compactness. Lopez and Hynes

(2003) measured dispersion as the difference between the population shares of a metropolitan

area’s low-density (200 to 3,500 persons per square mile) and high-density census tracts. It is

noteworthy that these density-related metrics only require population and areal data in tabular

form. The exact geographic layout does not affect the calculation. They are easy to calculate

and can consistently be applied longitudinally as long as small area census data of comparable

resolution are available (i.e. at least since 1990 for the U.S.). A comprehensive analysis of

population distribution across the United States at census block level seems never to have been

undertaken.

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Other metrics are derived from landscape ecology and measure characteristics of urban form

such as fragmentation, contiguity, and compactness (Galster et al. 2001; Angel et al. 2005;

Kasanko et al. 2005; Wolman et al. 2005; Schneider and Woodcock 2008; Schwarz 2010). In the

literature reviewed here, these metrics were calculated on grid-based representations of land

use maps. Because census geographic units vary in size, increasing from center to periphery,

they may not be suitable for studying urban form. Converting census-derived population

density maps to a grid-based density surface, as described below, may offer a viable approach.

4. Areal interpolation and dasymetric mapping

4.1. Overview

We have seen in preceding sections that the spatial analysis of urban population density based

on census geographic units poses a number of challenges.

1. Census geographic units give rise to ecological fallacies because they are likely to be

heterogeneous. This is especially the case for large area units (metropolitan area, county, place)

but tracts and even blocks must also be expected to be heterogeneous.

2. They also give rise to the modifiable areal unit problem (MAUP) because the boundaries of

administrative entities and enumeration districts are largely arbitrary. If a different scale or

different aggregation units were chosen, the results could be dramatically different. MAUP is

also reflected in the fact that the actual object of study, the city, cannot be easily identified in

terms of the available zonal system (the census geography). In order to solve the MAUP,

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geographers need to “agree upon what constitutes the objects of geographical enquiry”

(Openshaw 1984: 33).

3. Census geographic units give rise to the incompatible zone problem when studied

longitudinally because geographic units change over time. The problem is least severe with

counties, moderately severe with tracts, and very severe with block groups and blocks. The

longitudinal study of places, urban areas, and metropolitan areas is also highly problematic due

to changing boundaries.

The most widely known approach to these problems is areal interpolation (Wu et al. 2005;

Reibel 2007; Tapp 2010; Holt and Lu 2011). If we had a way of knowing, or accurately

estimating, the exact population of any areal unit at any scale, it would be easy to avoid

ecological fallacies, to move between different zone systems, and to conduct analyses at any

scale and level of aggregation or disaggregation. It would also be possible to unambiguously

delimit settlement area and analyze its form and structure at any level of detail. Conceptually,

areal interpolation is a switch from visualizing population density as a choropleth (thematic)

map to visualizing it as a continuous density surface (Moon 2003).

The main types of areal interpolation are overlay, dasymetric mapping, and smooth

pycnophylactic interpolation. The overlay operation is a simple solution to the zone problem

and depends on the assumption of zonal homogeneity. The target zone is superimposed on the

source zone and values of source zones are transferred to the target zone according to the

proportion of each source zone in each target zone (area weighting) (Wu and Wang 2005: 61).

The overlay operation can be modified to take account of ancillary data about the actual

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population distribution if such is known (Reibel 2007: 611f). The simplest case would be a third

zonal control data layer, for example representing areas known to be unpopulated or

representing streets and roads which can be used to infer population distribution (Reibel and

Bufalino 2005).

Instead of performing these steps within a zonal (i.e. vector) environment, the analyst could

transfer the source zones to a finer scale raster system and from there reaggregate the pixel

values to the target zones. In this setting, an ancillary raster data layer, often based on remote

sensing derived land cover data (Mennis 2003; Reibel and Agrawal 2007), can be used to

increase the accuracy of the population estimation. The process of improving zonal population

density maps by using an independent set of ancillary data is known as dasymetric mapping and

was originally developed by John K. Wright in 1936, who used USGS quadrangle maps to

eliminate uninhabited areas (Tapp 2010).

Smooth pycnophylactic interpolation takes zone-based population data as input and transforms

them into a smooth raster surface. The term pycnophylactic refers to the property of volume

preservation. Geometrically, one can imagine a surface that initially maps each source zone as a

plateau the height of which corresponds to its population density. The interpolation algorithm

then smoothes the landscape over while leaving the volume (i.e. population) over each zone

constant so that no population be created or destroyed. The resulting population density

surface can be used to aggregate population data to any spatial scale and unit, to perform

analytical operations, and to create maps with more detail and higher accuracy than a

conventional choropleth map could provide. Reibel (2007: 608) remarks that smoothing

22 Menninger 2012

techniques “take advantage of the ubiquitous spatial autocorrelation of data to make relatively

accurate estimates by assuming an uninterrupted surface”. Their major drawback is that

population, unlike topography, is not really a continuous phenomenon: there are in fact abrupt

transitions between settled and unsettled areas, as both Wright (Tapp 2010: 216) and

Openshaw (Moon and Farmer 2001: 46) have pointed out. The continuous surface may also

create “spurious impressions of precision” (Yuan et al. 1997).

New and increasingly sophisticated techniques have recently been referred to as “Intelligent

Dasymetric Mapping” (Mennis and Hultgren 2006). LandScan USA, a nationwide high-resolution

population density model that includes both a nighttime residential and a daytime ambient

population distribution estimate, resulted from a “multi-dimensional dasymetric modeling

approach”. “It involves a significant level of analyst intervention to validate input data and

modeling parameters, as well as to improve precision of the model output based on local

knowledge.” (Bhaduri et al. 2007)

4.2. Applications of dasymetric mapping

The quality of a dasymetric map depends greatly on the quality of the ancillary data used in its

creation. Ancillary data sources that have been used include raster based land use and

topographic data, and vector data such as streets and roads (Reibel and Bufalino 2005), address

point data sets (Moon 2003; Zandbergen 2011), and parcel or cadastral data (Maantay 2007;

Tapp 2010). These latter data types are especially helpful in spatially locating rural and urban

fringe population. As discussed, census tracts and blocks tend to be small where population is

dense but increase in areal extent in suburban and rural areas. This is precisely what makes

23 Menninger 2012

delineating the urban boundary so challenging. “Enumeration districts (EDs) in rural areas pose

aggregation difficulties due to their large geographic size.” (Tapp 2010) Information about the

location of buildings, parcels and roads can be used to predict population distribution within a

census areal unit and in particular to identify open space. According to Tapp (2010), address

and parcel data are superior to street data because potential settlement structures are

pinpointed more precisely. Certainly, an accurate data set with all building coordinates in the

United States would enable much more detailed population mapping. Such a data set may be

feasible in the near future but currently, such data sets are only available sporadically from

local government sources (Sanford 2011: 20), which severely limits the scope of application.

Remote sensing derived raster land use land cover (LULC) maps have been used as ancillary

data by Yuan et al. (1997), Mennis (2003), Reibel and Agrawal (2007), Sanford (2011), amongst

others. The simplest approach is the binary mask method “in which all the areas known to be

uninhabited are removed from the population density surface” (Tapp 2010). That includes open

water, perennial ice and snow, and wetlands (Wolman et al. 2005). A more sophisticated

method consists in assigning density weights to different land use classes. Urban LULC classes

are expected to receive higher weights than non-urban or vegetated classes. When a mixture of

land uses is present in a given census district, the population of that district is redistributed on a

per pixel basis according to the relative weight of each pixel’s class and each LULC class’s

proportion of the district’s area. A shortcoming of this method is that LULC classifications may

not adequately distinguish between residential and (unpopulated) commercial urban land, as

well as between different types of residential land (Mennis 2003). More generally, LULC land

use classes are not homogenous with respect to population density nor can different classes’

24 Menninger 2012

density be expected to maintain a constant ratio. There is, to be sure, a strong correlation

between small area census population or dwelling unit density and remotely sensed land use

data but the relationship is highly variable (Yuan et al. 1997; Chen 2002; Pozzi and Small 2005;

Morton and Yuan 2009).

It is instructive to compare different applications of the method outlined above. Yuan et al.

(1997), in a study of the Little Rock, Ark., metropolitan area, combined census tract level data

with a LULC map. Using linear regression to estimate population density coefficients for each

LULC class, they found that the coefficients for all non-urban classes could not be distinguished

from zero. The resulting population distribution model was essentially the census choropleth

overlaid with a binary mask, in which all nonurban classes were treated as unpopulated.

Mennis (2003), in a study of Census block group data for the Philadelphia region, estimated

LULC class coefficients not by regressing over all census districts but by “empirical sampling”.

He picked out those block groups that were entirely contained within a single LULC class and

calculated their average density. In this model, the density coefficients for nonurban land were

very small but not zero and the coefficients were found to vary considerably within the study

region.

Sanford (2011), finally, used techniques similar to Yuan and colleagues to perform an urban

area change analysis for the St. Louis metropolitan area. Remarkably, it is the only study I have

been able to identify that used dasymetric mapping in a longitudinal setting, and the only that

used high resolution census block geographies. The author combined population with

imperviousness data to delineate the urban area, reasoning that “remote sensing methods for

25 Menninger 2012

urban detection neglect well-vegetated areas with urban population density, while the use of

population data alone neglects many commercial and industrial areas, blighted or abandoned

urban areas, and other developed areas where no one resides.” He used a classification scheme

that consists of the four classes urban, vegetation, soil and water and located 27% of the

population in vegetated areas. The difference to the other cases is striking: Yuan and

colleagues found nobody and Mennis only a fraction (about 2%) of the population in nonurban

classes. Even though St. Louis might be particularly affected by urban blight and

suburbanization, this contrast calls for an explanation.

I conjecture that in these studies, the role of MAUP has not been adequately accounted for.

Openshaw, in his 1984 cry of alarm, cited example after example of spurious correlations

attributable to spatial autocorrelation, scale and aggregation effects. Clearly, the role of

aggregation effects in correlating population and land use calls for in investigation. None of the

studies reviewed here have made any attempt to account for MAUP. The method employed by

Mennis made sure that only small homogeneous census areas were used for coefficient

estimation, thus neglecting mixed land use. Yuan et al., on the other hand, used census tracts,

which are hardly ever homogeneous. In a setting in which population is highly correlated with

urban LULC classes and most spatial units contain a mixture of urban and nonurban land use, it

is not surprising that the regression would fail to find a significant coefficient for the nonurban

classes. Could it be that an attempt at solving the modifiable areal unit problem ended up

making it worse?

26 Menninger 2012

5. Conclusion

U.S. Census data have been collected since 1790 at a variety of spatial scales. This review has

identified significant potential as well as challenges inherent in the use of these data for

studying urbanization at various spatial and temporal scales. Researchers must carefully

consider the possibility of ecological fallacies, the modifiable areal unit problem (MAUP) and

zonal incompatibility. Areal interpolation is a well-established approach toward overcoming

incompatible zone problems and may help avoid MAUP. Dasymetric mapping techniques make

use of ancillary data to improve the accuracy of population density maps and might be useful to

better constrain the urban area concept. An important consideration is that employing

dasymetric techniques for longitudinal studies requires that both ancillary data and census data

be consistently available for two or more points in time.

Decennial censuses since 1990 have provided high resolution, fully georeferenced data in the

form of census block counts, opening the possibility for studying urbanization processes

nationwide longitudinally and at high spatial resolution. This research has yet to be undertaken.

27 Menninger 2012

Appendix: Population density algebra

We consider a territory A composed of subareas Ai (i=1…N) with population Pi and density

Di=Pi/Ai. Then the crude population density D is

∑ ∑

∑ ∑

This reveals D to be the area weighted mean of the subarea densities. Similarly, population

weighted density is defined as the mean density weighted by population:

∑ ∑

∑

The population weighted geometric mean density DGM can be determined by the identity

∑

Here all unpopulated subunits have to be excluded (Di>0). This metric is formally related to the

Shannon entropy as defined in information science.

It is always D <= DGM <= Dw. It also follows from the definitions that subdividing the areal

units will increase Dw and DGM until the units are homogeneous. Further, expanding the base

area by including surrounding unpopulated land would decrease D but leave Dw unchanged.

Stairs (1977) suggests the index I=1-D/Dw as an index of population concentration. The index

ranges from 0 in a uniformly populated area to 1 “in a country all of whose people stand on one

spot”. Similarly, the index of dissimilarity (Schwarz 2010; Burt et al. 2009:128), ID, ranges from

0 (evenness) to 1:

∑| |

ID is closely related to the Gini index: both are based on locational coefficients and the Lorenz

curve (Burt et al. 2009: 124-129). Burt et al. (2009) and Tsai (2005) erroneously suggest that

Gini and ID are the same. These density-related metrics only require population and areal data

in tabular form.

28 Menninger 2012

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