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

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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 ...

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.

Review paper by Toni Menninger, 2012

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    Utilizing geospatial analysis of U.S. Census data for studying the dynamics of urbanization and land consumption Utilizing geospatial analysis of U.S. Census data for studying the dynamics of urbanization and land consumption Document Transcript

    • Utilizing geospatial analysis of U.S. Census data for studying the dynamics of urbanization and land consumption Toni Menninger, February 20, 2012Abstract1. Introduction2. United States Census geography2.1 The U.S. Census geographical hierarchy2.2. Evolution of U.S. Census geographies2.3. Census geographical area measurement2.4. Summary3. The geography of urbanization3.1. Delimiting the city3.2. Population density and land use efficiency3.3 Studying the spatial distribution of population4. Areal interpolation and dasymetric mapping4.1. Overview4.2. Applications of dasymetric mapping5. ConclusionAppendix: Population density algebraReferences 1 Menninger 2012
    • AbstractGeographically referenced US census data provide a large amount of information about theextent of urbanization and land consumption. Population count, the number of housing unitsand their vacancy rates, and demographic and economic parameters such as racial compositionand household income, and their change over time, can be examined at different levels ofgeographic 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. Itwill identify strengths and weaknesses and address methodological challenges of census-basedapproaches to the study of urbanization. Of special interest will be literature comparing and/orintegrating census data with alternative methodologies, e.g. based on Remote Sensing. Thegeneral purpose of this paper is to lay the groundwork for the optimal use of high resolutioncensus data in studying urbanization in the United States.1. IntroductionUrbanization, 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 globalurban 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 areassignificantly alter climate, biogeochemistry, and hydrology at local, regional, and global scales.”(Schneider et al. 2009). “The density, spatial distribution, and physical characteristics of human 2 Menninger 2012
    • settlement are important drivers of social and environmental change at multiple scales” (Potereand Schneider 2007). A growing research community has focused on measuring the physicalextent 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 urbansettlement (Camagni et al. 2002; Angel et al. 2005; Kasanko et al. 2005; Schneider andWoodcock 2008; Clark et al. 2009; Schwarz 2010). Researchers hypothesize that form andstructure of the built environment are related to social, economic and environmental outcomesand have an impact on humans’ quality of life. Identifying causes and effects of differences inurban form might enable policy makers, planners and architects to better urban conditions andreduce urbanization’s environmental footprint. A particularly vigorous research field is devotedto 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). Yetperhaps the most striking aspect of the pertinent literature is the lack of consensus. Forexample, Churchman (1999) identified more than 50 hypothesized advantages anddisadvantages of high urban density and concludes that researchers do not agree on any ofthem.Many researchers have stated the need for accurate and consistent metrics of urbanization. "Akey difficulty in studying cities is finding a practical way to define them" (Rozenfeld et al. 2011). 3 Menninger 2012
    • Parr (2007) points out that cross-sectional comparisons of cities often fail to apply consistentstandards: "It hardly needs emphasising that city size must be measured meaningfully andconsistently over the entire range of cities under consideration." Angel et al. (2005) identify aseries of fundamental questions: "Where does the city end and the rural area begin? What isthe population of the city? What is the built-up area of the city? What is the average density inthe city? What is the degree of openness or sprawl in the city? How compact or dispersed is thecity? (…) These questions cannot be easily answered (…)." Wolman et al. (2005) contend thatconventionally used metrics tend to either overbound or underbound urban extent. Theresearch agenda they propose consists of three steps: defining appropriate and replicablemetrics of urbanization, measuring them across a wide sample of cities, and use the results inmultivariate models to test hypotheses concerning causes and effects of urban form. Similarresearch 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 lasthundred years in the form of aerial photography, and for the last forty years in the form ofsatellite imagery. Population data have been collected by national census authorities forcenturies. The remainder of this paper will review the use and usefulness of census data in thestudy of urbanization in the United States, in particular in a geospatial setting. To this end, it isnecessary to first provide an overview of the geographic structure of U.S. Census data and itsevolution. 4 Menninger 2012
    • 2. United States Census geography2.1 The U.S. Census geographical hierarchyThe primary source of data about settlement structure in the United States is the U.S. CensusBureau. This section reviews the geographic structure of U.S. Census data and its evolution. It isbased 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 spacerestrictions 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 blockSome geographic entities transcend the basic census hierarchy. Among them are Places andUrban Areas, which are situated within states and are composed of census blocks, andMetropolitan 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 areabounded by streets, streams, and the boundaries of legal and statistical entities. There weremore than 11 million blocks in 2010. Census tracts are relatively permanent geographic entitieswithin counties that have generally between 2500 and 8000 residents. They are delineated by acommittee of local data users to be as homogeneous as possible, approximating cityneighborhood communities, and bounded by visible features. Further, the census recognizesand tabulates places (i.e. cities and towns). Incorporated places are delimited by theiradministrative boundaries. Recognizable settlements that are not legally incorporated can bedefined as census-designated places (CDP). Urban areas are continuously built-up areas that 5 Menninger 2012
    • 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 caninclude territory that is not or only sparsely populated but serves urban functions, such ascommercial and industrial development, parks, and golf courses. Even clearly nonurbanenclaves of up to five square miles can be part of a UA if it gives it "a more regular appearanceand simplifies data presentations”. Census classifies all units as either rural or urban dependingon whether they are situated in an Urban Area.Metropolitan Areas (also known as Core Based Statistical Areas, CBSA) group together countiesthat 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 containingthe metropolitan core, the rest are known as Outlying Counties. Census also designates one ormore Principal Cities (Central Cities before 2010). Also, up to 2000, Census used to designateone or more Central Places for each UA.It must be pointed out that not all data collected by Census are available at all geographiclevels. The decennial census enumerates all residents and dwelling units and collects basicdemographic information (known as the short form) about each person. These results aretabulated and released to block level. Census also collects more detailed socio-economic datain regular surveys (the long form in earlier decennial censuses and now the AmericanCommunity Survey). These surveys are based on samples and are released at county, place, ortract level. They cannot be disaggregated to block level because the sampling error would be 6 Menninger 2012
    • unacceptable and also the privacy of respondents could not be maintained given that manyblocks have fewer than ten residents.2.2. Evolution of U.S. Census geographiesMany geographers, historians and social scientists are interested in the development of citiesand draw on historical census data. This section will briefly explore the evolution of USdecennial 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 by1920 and have been fairly stable since. However, county subdivision geography in many stateshas been unstable and subject to frequent change. Populations of some incorporated placeswere reported in the earliest censuses but they were systematically tabulated for the first timein 1880. Unincorporated places were systematically covered since 1950 (and labeled CensusDesignated Places (CDP) in 1980). Administrative boundaries of cities are unstable. They changefrequently due to annexation, consolidation, incorporation and disincorporation, especially inthe 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 asurban and everything else as rural. The inherent capriciousness of place boundaries motivatedthe Census Bureau to come up, in 1950, with its own delineation of Urbanized Areas (UAs) of atleast 50,000 people. Places outside of UAs with at least 2,500 population were still classified asurban even when their density was low. That changed in 2000, when Urban Clusters (UCs) of atleast 2,500 residents were delineated regardless of place boundaries. The criteria for 7 Menninger 2012
    • delineating urban areas are quite complex and have evolved over time although the mainpopulation and density criteria have remained stable. Caution is therefore recommended whenanalyzing census urban areas longitudinally. Interestingly, Census makes use of remote-sensingderived 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 anurban core of at least 10,000 but less than 50,000 residents were designated in 2003. Thecriteria for metropolitan areas are revised every 10 years. Since metropolitan areas arecomposed 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 althoughprecursor small area districts have existed in a few cities since 1910. In 1940, all cities exceeding50,000 residents were covered by census tracts and blocks. Coverage was expanded everydecade until complete coverage was reached in 1990. Census blocks are impermanent. Tractsare more permanent and have a permanent numbering system to allow intercensalcomparison. 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 homogeneousdue to demographic change. In practice, only dense urban tracts represent more or lesshomogeneous communities. Rural tracts can encompass large areas. Tracts at the urban fringeare often mixtures of urban and rural areas and may contain large amounts of open space. Theycannot 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 8 Menninger 2012
    • quite large (frequently up to about 100 square kilometers) and inhomogeneous. They are alsooften irregularly shaped. About one third of all blocks are unpopulated.2.3. Census geographical area measurementHistorical 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 the1880 census. Area figures for more populous places were provided between 1890 and 1930. In1940, areal data were provided for all places of 1,000 residents or more and all countysubdivisions. However, areal data for tracts and other small-area geographic entities were notprovided before 1990. Since 1990, thanks to the Topologically Integrated Geographic Encodingand Referencing (TIGER) System, all areas have been measured and all geographic entitiestabulated by the census have been available as geo-referenced vector files (Peters andMacDonald 2004; Almquist 2010). In fact, digital geographic files were already prepared forcensus 1970 and 1980 but their usefulness for GIS purposes is unclear.2.4. SummaryThe only census geography that appears largely consistent over more than a few decades is thecounty. Counties have rarely changed in the last about 100 years and some county censuscounts can be traced back 200 years or more. These county-based time series indicate wherepopulation growth and decline has occurred but are not fine-grained enough to studyurbanization processes in detail. 9 Menninger 2012
    • 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 from1940. The limitation of these data series is that they are based on administrative boundariesthat 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 providefunctional geographic units that are not based on arbitrary administrative boundaries. Thesestatistical units are suitable for cross-sectional analysis. The Metropolitan Area is a collection ofcounties and almost always contains some rural area. The Urban Area is a collection of censusblocks considered urban but can contain considerable amounts of nonurban land.Census tracts are designed to be permanent units as far as possible but demographic changemakes splits and merges unavoidable. Census blocks are the smallest, very fine-grained buildingblocks of census geography and cannot be expected to be permanent. The census tract is lessfine-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 ofrelatively high resolution for the last three censuses, and, for some urban areas, maps of thisquality can potentially be traced back to cover the whole post-war period. Tract- or block-levelareal measurements, however, are only available for census 1990 and later.Block-level data is eminently suitable for longitudinal analysis of urbanization processes of thelast twenty years. The major limitation of this approach is that these geographic units areimpermanent. Further, even though census blocks are the most homogeneous census units, 10 Menninger 2012
    • 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 areurban extent and population density. Measuring urban extent means delimiting an urbanboundary; measuring density requires measuring both the areal urban extent and thepopulation that it houses. A variety of additional concepts characterizing different aspects ofform and function of settlements have been developed, many of which are derived fromdensity measures and describe how urban intensity is distributed across geographic space.When these metrics are analyzed longitudinally, they give insight into the dynamics ofurbanization processes over time. Often examined in the literature are measures of theexpansion of urban extent, which gives rise to land consumption measures, and changes indensity.The purpose of this section is to give an overview over different approaches to measuringurbanization, in particular with respect to the use of U.S. census data. 11 Menninger 2012
    • 3.1. Delimiting the cityLocating the city geographically requires to define what is meant by an urban area and todelineate its boundary. “The extent of the city is important in a number of respects, not least inrelation to the question of city size, an issue of considerable significance in urban and regionalanalysis.” (Parr 2007) Various researchers have studied urban land consumption as the increasein 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 andWoodcock (2008) observe: “Two difficulties arise when comparing any set of metropolitanareas: defining what types of land are in fact ‘urban’; and, determining what geographical areashould be considered.” And Potere et al. (2009) add: “There is currently no generally accepteddefinition of ‘urban land’”. The contemporary city is not easy to physically pinpoint because ithas become “increasingly porous” (Parr 2007). Cromartie and Swanson (1996) observe that“large cities have expanded beyond traditional borders to form sprawling urban regions”, givingrise to “increasingly complex U.S. settlement patterns” and the “growing complexity of therural-urban frontier”. Rozenfeld et al. (2011) state that “a key difficulty in studying cities isfinding a practical way to define them” and discuss three main approaches: relying on thecensus Metropolitan Area definitions; relying on legal boundaries of cities; and constructing thecity from micro (i.e. small area census) data. Other approaches rely on the Census urban areadesignation, on remote sensing data, and on survey data such as the National ResourcesInventory (NRI) (Fulton et al. 2001; Lang 2003; Carruthers 2008) or cadastral data. 12 Menninger 2012
    • County level analyses of urban change are common in the suburbanization literature. A typicalapproach is to divide Census metropolitan areas into core, inner ring suburban and outer ringsuburban counties, or into core city and suburbs (e. g. Morrill 1992; Katz and Lang 2003; Cox2011). Morrill (1992) cautions that counties are “imperfect units” but uses them “becauseconsistent data are available”. This level of analysis gives insight into broad national trends inurbanization and demographic change but can be misleading because metropolitan areas cancontain large amounts of rural territory and open space (Cromartie and Swanson 1996; Lang2003), and it cannot reveal population change within a county.Administrative city boundaries are used as units of analysis because that is often the onlyavailable long term data set. González-Val and Lanaspa (2011) studied the population growth ofthe 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 betweenCensus urban area size and population. Downs (1999) also used Census urban areas as baseunits 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 ofcentral cities”. Schneider and Woodcock (2008) agree: “Political boundaries, while often usedto delineate urban space, are not a reliable means of doing so since they change frequentlyover time, overestimate or underestimate urban land use and are not comparable across or 13 Menninger 2012
    • within nations”. It is noteworthy that Census abandoned the designation of urban area centralcities in 2010. Fulton et al. (2001) and Lang (2003) rejected the urbanized area designationbecause it excludes low-density suburban development that “should be included as built-upparts of metropolitan areas” (Lang 2001: 760). Wolman et al. (2005) similarly contend that theUA 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 accuratemethod of delimiting the physical city has frequently forced urban specialists, includinggeographers, to use either legal cities or urbanized areas as the area component in studyingurban problems on a comparative basis. The failure of these two city bases to reflect the actualspatial extent of urban development has led to conspicuous discrepancies in the results ofcomparative 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-tunecensus geographic units, Buckwalter and Rugg called for defining the urban footprint solely onthe basis of remote sensing imagery. The literature on urban remote sensing is extensive anddiscussing advantages and shortcomings of this method is beyond the scope of this review. Itshould be noted however that due to “the intrinsically mixed landscape that makes up mostcities and towns” (Potere et al. 2009), definitional ambiguities apply to any urban landclassification 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 averageof 4,000 people); are consistently defined across the Nation; are usually subdivided as 14 Menninger 2012
    • population grows to maintain geographic comparability over time; and can be aggregated toform county-level statistical areas when needed.” Their approach is to classify census tracts intofive categories according to the rural-urban settlement continuum defined by the USDAEconomic 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 censustracts according to the City Clustering Algorithm (CCA). The algorithm defines a “city” as acluster of contiguous units (i.e. census tracts) that have a minimum population density and arewithin a prescribed distance from the closest neighbor in the cluster. This approach allows forexperimentation with different threshold values for density and distance and could be appliedto subtract geographies as well. Approaches based on subtract geographies are however rareaccording to the literature reviewed for this paper.3.2. Population density and land use efficiencyDensity is calculated as a number of units in a given land area and can refer to residential oremployment population, dwelling units, residential or commercial space or indeed any measureof urban activity or intensity that can be determined on the basis of areal units. The inverse ofdensity – 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 isresidential density. While the concept of density is intuitively appealing and is often taken forgranted, 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 15 Menninger 2012
    • counts when considering density, and about how to measure it”. When reporting density, theanalyst should always explain the definitions used and make sure that any comparison betweencities 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 basearea 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 correctlydetermining population density is one of the fundamental unsolved problems in urbangeography. The terms gross and net density have been used, where net residential density ismeant to exclude nonresidential land from the base area (Alexander 1993; Churchman 1999;Forsyth 2003). Researchers of land consumption disagree however which areas should beexcluded from the urban land category. As discussed, the Census Bureau includes urbangreenspace as well as unpopulated enclaves up to five square miles in size in its urban areadesignation. Wolman et al. (2005) in contrast have called for excluding undevelopable landfrom the urban footprint but forest and agricultural land at the urban fringe would beconsidered as "potentially available for development" and included in the urban area. While theaforementioned authors clearly distinguish between urban land in terms of land use and thebuilt environment in terms of land cover (i.e. built-up or developed land, land covered ordominated by man-made structures, impervious land cover), many researchers in the urbanremote sensing community use these terms interchangeably: “When vegetation (e.g. a golfcourse or park) dominates a pixel, these areas are not considered urban, even though – interms of land use – they may function as urban space.” (Potere et al. 2009). It is important thateach analyst make their terminology explicit. 16 Menninger 2012
    • 3.3 Studying the spatial distribution of populationThe crude population density calculated from a certain base area is an average that gives rise toecological fallacies because population distributions are rarely homogeneous. "Theconventional crude population density is not a good measure of the density at which thepopulation lives." (Craig 1984). Stairs (1977) proposed the population weighted density (orperson-average density) (PWD) as an alternative to conventional crude density. PWD can becalculated whenever the base area can be disaggregated into a set of subunits and populationand area of each are known, and is defined as the average subunit density weighted by subunitpopulation (see appendix). To illustrate the concept, he considered a hypothetical countryconsisting of a densely populated city, sparsely populated farmland, and an unpopulated desertarea. Although most of the population is concentrated in the city, the crude density for thewhole country is very low due to the large amount of unpopulated land. The populationweighted density is a much higher number. While the crude density reflects correctly that mostland is not or sparsely populated, the population weighted density more accurately reflects theconditions under which most residents live. Craig (1984) expanded on Stairs’ concept andsuggested 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 weighteddensity (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 israised “what the fundamental unit of density actually is” (Craig 1984). Ideally, the fundamentalunit would be perfectly homogeneous. “Any (and every) subdivision of an areal unit increases 17 Menninger 2012
    • the average population weighted density” (Craig 1984), unless the unit is perfectlyhomogeneous. This property gives rise to the modifiable areal unit problem, in particular thescale problem (calculating PWD at different scales will systematically affect the outcome) butalso the aggregation problem (choice of an alternative set of areal units might change theoutcome) (Openshaw 1984: 8). That may explain why the concepts proposed by Stairs and Craigare 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. TheIndex of Dissimilarity, Gini index and Shannon Entropy measure the degree to which apopulation distribution deviates from evenness (Massey and Denton 1988; Tsai 2005; Burt et al.2009; Schwarz 2010; see Appendix). The population density gradient (Bertaud and Malpezzi2003; Ewing et al. 2003) measures the decline of population density with increasing distancefrom 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 metropolitanarea’s low-density (200 to 3,500 persons per square mile) and high-density census tracts. It isnoteworthy that these density-related metrics only require population and areal data in tabularform. The exact geographic layout does not affect the calculation. They are easy to calculateand can consistently be applied longitudinally as long as small area census data of comparableresolution are available (i.e. at least since 1990 for the U.S.). A comprehensive analysis ofpopulation distribution across the United States at census block level seems never to have beenundertaken. 18 Menninger 2012
    • Other metrics are derived from landscape ecology and measure characteristics of urban formsuch 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 theliterature reviewed here, these metrics were calculated on grid-based representations of landuse 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 populationdensity maps to a grid-based density surface, as described below, may offer a viable approach.4. Areal interpolation and dasymetric mapping4.1. OverviewWe have seen in preceding sections that the spatial analysis of urban population density basedon census geographic units poses a number of challenges.1. Census geographic units give rise to ecological fallacies because they are likely to beheterogeneous. 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 ofadministrative entities and enumeration districts are largely arbitrary. If a different scale ordifferent aggregation units were chosen, the results could be dramatically different. MAUP isalso reflected in the fact that the actual object of study, the city, cannot be easily identified interms of the available zonal system (the census geography). In order to solve the MAUP, 19 Menninger 2012
    • 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 studiedlongitudinally because geographic units change over time. The problem is least severe withcounties, moderately severe with tracts, and very severe with block groups and blocks. Thelongitudinal study of places, urban areas, and metropolitan areas is also highly problematic dueto 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 accuratelyestimating, the exact population of any areal unit at any scale, it would be easy to avoidecological fallacies, to move between different zone systems, and to conduct analyses at anyscale and level of aggregation or disaggregation. It would also be possible to unambiguouslydelimit 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 smoothpycnophylactic interpolation. The overlay operation is a simple solution to the zone problemand depends on the assumption of zonal homogeneity. The target zone is superimposed on thesource zone and values of source zones are transferred to the target zone according to theproportion 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 20 Menninger 2012
    • population distribution if such is known (Reibel 2007: 611f). The simplest case would be a thirdzonal control data layer, for example representing areas known to be unpopulated orrepresenting streets and roads which can be used to infer population distribution (Reibel andBufalino 2005).Instead of performing these steps within a zonal (i.e. vector) environment, the analyst couldtransfer the source zones to a finer scale raster system and from there reaggregate the pixelvalues to the target zones. In this setting, an ancillary raster data layer, often based on remotesensing derived land cover data (Mennis 2003; Reibel and Agrawal 2007), can be used toincrease the accuracy of the population estimation. The process of improving zonal populationdensity maps by using an independent set of ancillary data is known as dasymetric mapping andwas originally developed by John K. Wright in 1936, who used USGS quadrangle maps toeliminate uninhabited areas (Tapp 2010).Smooth pycnophylactic interpolation takes zone-based population data as input and transformsthem into a smooth raster surface. The term pycnophylactic refers to the property of volumepreservation. Geometrically, one can imagine a surface that initially maps each source zone as aplateau the height of which corresponds to its population density. The interpolation algorithmthen smoothes the landscape over while leaving the volume (i.e. population) over each zoneconstant so that no population be created or destroyed. The resulting population densitysurface can be used to aggregate population data to any spatial scale and unit, to performanalytical operations, and to create maps with more detail and higher accuracy than aconventional choropleth map could provide. Reibel (2007: 608) remarks that smoothing 21 Menninger 2012
    • techniques “take advantage of the ubiquitous spatial autocorrelation of data to make relativelyaccurate estimates by assuming an uninterrupted surface”. Their major drawback is thatpopulation, unlike topography, is not really a continuous phenomenon: there are in fact abrupttransitions between settled and unsettled areas, as both Wright (Tapp 2010: 216) andOpenshaw (Moon and Farmer 2001: 46) have pointed out. The continuous surface may alsocreate “spurious impressions of precision” (Yuan et al. 1997).New and increasingly sophisticated techniques have recently been referred to as “IntelligentDasymetric Mapping” (Mennis and Hultgren 2006). LandScan USA, a nationwide high-resolutionpopulation density model that includes both a nighttime residential and a daytime ambientpopulation distribution estimate, resulted from a “multi-dimensional dasymetric modelingapproach”. “It involves a significant level of analyst intervention to validate input data andmodeling parameters, as well as to improve precision of the model output based on localknowledge.” (Bhaduri et al. 2007)4.2. Applications of dasymetric mappingThe quality of a dasymetric map depends greatly on the quality of the ancillary data used in itscreation. Ancillary data sources that have been used include raster based land use andtopographic data, and vector data such as streets and roads (Reibel and Bufalino 2005), addresspoint 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 urbanfringe population. As discussed, census tracts and blocks tend to be small where population isdense but increase in areal extent in suburban and rural areas. This is precisely what makes 22 Menninger 2012
    • delineating the urban boundary so challenging. “Enumeration districts (EDs) in rural areas poseaggregation difficulties due to their large geographic size.” (Tapp 2010) Information about thelocation of buildings, parcels and roads can be used to predict population distribution within acensus areal unit and in particular to identify open space. According to Tapp (2010), addressand parcel data are superior to street data because potential settlement structures arepinpointed more precisely. Certainly, an accurate data set with all building coordinates in theUnited States would enable much more detailed population mapping. Such a data set may befeasible in the near future but currently, such data sets are only available sporadically fromlocal 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 ancillarydata by Yuan et al. (1997), Mennis (2003), Reibel and Agrawal (2007), Sanford (2011), amongstothers. The simplest approach is the binary mask method “in which all the areas known to beuninhabited are removed from the population density surface” (Tapp 2010). That includes openwater, perennial ice and snow, and wetlands (Wolman et al. 2005). A more sophisticatedmethod consists in assigning density weights to different land use classes. Urban LULC classesare expected to receive higher weights than non-urban or vegetated classes. When a mixture ofland uses is present in a given census district, the population of that district is redistributed on aper pixel basis according to the relative weight of each pixel’s class and each LULC class’sproportion of the district’s area. A shortcoming of this method is that LULC classifications maynot adequately distinguish between residential and (unpopulated) commercial urban land, aswell as between different types of residential land (Mennis 2003). More generally, LULC landuse classes are not homogenous with respect to population density nor can different classes’ 23 Menninger 2012
    • density be expected to maintain a constant ratio. There is, to be sure, a strong correlationbetween small area census population or dwelling unit density and remotely sensed land usedata 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 datawith a LULC map. Using linear regression to estimate population density coefficients for eachLULC class, they found that the coefficients for all non-urban classes could not be distinguishedfrom zero. The resulting population distribution model was essentially the census choroplethoverlaid 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, estimatedLULC 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 andcalculated their average density. In this model, the density coefficients for nonurban land werevery small but not zero and the coefficients were found to vary considerably within the studyregion.Sanford (2011), finally, used techniques similar to Yuan and colleagues to perform an urbanarea change analysis for the St. Louis metropolitan area. Remarkably, it is the only study I havebeen able to identify that used dasymetric mapping in a longitudinal setting, and the only thatused high resolution census block geographies. The author combined population withimperviousness data to delineate the urban area, reasoning that “remote sensing methods for 24 Menninger 2012
    • urban detection neglect well-vegetated areas with urban population density, while the use ofpopulation data alone neglects many commercial and industrial areas, blighted or abandonedurban areas, and other developed areas where no one resides.” He used a classification schemethat consists of the four classes urban, vegetation, soil and water and located 27% of thepopulation in vegetated areas. The difference to the other cases is striking: Yuan andcolleagues found nobody and Mennis only a fraction (about 2%) of the population in nonurbanclasses. Even though St. Louis might be particularly affected by urban blight andsuburbanization, 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 correlationsattributable to spatial autocorrelation, scale and aggregation effects. Clearly, the role ofaggregation effects in correlating population and land use calls for in investigation. None of thestudies reviewed here have made any attempt to account for MAUP. The method employed byMennis made sure that only small homogeneous census areas were used for coefficientestimation, 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 withurban LULC classes and most spatial units contain a mixture of urban and nonurban land use, itis not surprising that the regression would fail to find a significant coefficient for the nonurbanclasses. Could it be that an attempt at solving the modifiable areal unit problem ended upmaking it worse? 25 Menninger 2012
    • 5. ConclusionU.S. Census data have been collected since 1790 at a variety of spatial scales. This review hasidentified significant potential as well as challenges inherent in the use of these data forstudying urbanization at various spatial and temporal scales. Researchers must carefullyconsider the possibility of ecological fallacies, the modifiable areal unit problem (MAUP) andzonal incompatibility. Areal interpolation is a well-established approach toward overcomingincompatible zone problems and may help avoid MAUP. Dasymetric mapping techniques makeuse of ancillary data to improve the accuracy of population density maps and might be useful tobetter constrain the urban area concept. An important consideration is that employingdasymetric techniques for longitudinal studies requires that both ancillary data and census databe consistently available for two or more points in time.Decennial censuses since 1990 have provided high resolution, fully georeferenced data in theform of census block counts, opening the possibility for studying urbanization processesnationwide longitudinally and at high spatial resolution. This research has yet to be undertaken. 26 Menninger 2012
    • Appendix: Population density algebraWe consider a territory A composed of subareas Ai (i=1…N) with population Pi and densityDi=Pi/Ai. Then the crude population density D is ∑ ∑ ∑ ∑This reveals D to be the area weighted mean of the subarea densities. Similarly, populationweighted 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 theShannon entropy as defined in information science.It is always D <= DGM <= Dw. It also follows from the definitions that subdividing the arealunits will increase Dw and DGM until the units are homogeneous. Further, expanding the basearea 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 indexranges from 0 in a uniformly populated area to 1 “in a country all of whose people stand on onespot”. Similarly, the index of dissimilarity (Schwarz 2010; Burt et al. 2009:128), ID, ranges from0 (evenness) to 1: ∑| |ID is closely related to the Gini index: both are based on locational coefficients and the Lorenzcurve (Burt et al. 2009: 124-129). Burt et al. (2009) and Tsai (2005) erroneously suggest thatGini and ID are the same. These density-related metrics only require population and areal datain tabular form. 27 Menninger 2012
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