Measuring Sprawl Alternative Measures of Urban Form in U.S. Metropolitan Areas

Measuring "Sprawl:" Alternative Measures of Urban Form in U.S Metropolitan Areas By Stephen Malpezzi and Wen-Kai Guo Revised, January 15, 2001 The Center for Urban Land Economics Research The University of Wisconsin 975 University Avenue Madison, WI 53706-1323 smalpezzi@bus.wisc.edu wgou@bus.wisc.edu http://wiscinfo.doit.wisc.edu/realestate ii iii Stephen Malpezzi is Associate Professor and Wangard Faculty Scholar in the Department of Real Estate and Urban Land Economics, and an associate member of the Department of Urban and Regional Planning, of the University of Wisconsin-Madison Wen-Kai (Kevin) Guo is a Ph.D candidate in Food Science at the University of Wisconsin-Madison Comments on this and closely related work have been provided by Alain Bertaud, Michael Carliner, Mark Eppli, Richard Green, James Shilling, Kerry Vandell, Anthony Yezer and participants at the Homer Hoyt Institute/Weimer School's January 1999 and January 2000 sessions as well as the June 1999 Midyear meeting of the American Real Estate and Urban Economics Association Comments and criticisms of this paper are welcome The research we describe was supported by the University of Wisconsin's Graduate School, the Wangard Faculty Scholarship, and the UW Center for Urban Land Economics Research Opinions in this paper are those of the authors, and not reflect the views of any of the above individuals, or of any institution iv v Introduction Economists and other social scientists have tried to study urban form more or less rigorously for the better part of two centuries The earliest commonly cited work is that by German scholars such as von Thunen (1826) and somewhat later work by Lösch (1944) In this century pioneering English-speaking scholars include Clark (1951), Hoyt (1939, 1966), and Burgess (1925) The 60s and 70s saw a further flowering with work such as Alonso (1964), Mills (1972), Muth (1969), and Wheaton (1977) among many others Song (1996) provides a particularly nice discussion of some alternative measures Excellent reviews and extensions of this large literature can be found in Anas, Arnott and Small (1998), Fujita (1989), and Turnbull (1995) The economics of location has been a fertile academic field for some forty years, and is enjoying resurgence due partly to the high profile of recent work on the economics of location by generalist economists such as Krugman (1991) But this academic resurgence is nothing compared to the eruption of interest in urban form by a wider range of political and social commenters One watershed was certainly journalist Joel Garreau’s excellent popularization Edge City (1991), which broadened the audience for discussion of urban form But the real explosion of interest in urban form has been due to the growing concern and exploding reference to urban sprawl What environmental activists and now many others call sprawl is certainly not new to urban economists The phenomenon of rapid growth on the periphery of the city is something that has been a core feature of most of the literature mentioned above, and the much larger literature that lies behind it To give just one example, Edwin Mills’ classic 1972 book studies the decentralization of urban population in a large sample of U.S cities going back to the latter part of the 19th century Sam Bass Warner’s Streetcar Suburbs, coming out of a different scholarly tradition, is another well-known early examination of decentralization Perhaps the first dividing line between urban economists and many other urban observers is the use of the word sprawl, with its pejorative connotations While a number of authors have used the term sprawl in the academic literature (see references below), most urban economists have preferred less value-laden terms, such as urban decentralization (Mills 1999) or accessibility (Song 1996) But economists have lost the lexicographic battle To give just one example, we did a simple Internet search on the term "urban decentralization" using Infoseek.com The search engine returned 27 hits We repeated an identical search using the term "urban sprawl." The engine returned 5,946 hits With all the extraordinary attention paid to sprawl, it is quite interesting that only recently have some of those involved in the policy discussion attempted to define it Consider the following quotation: sprawl in all its forms is seldom satisfactorily defined Urban sprawl is often discussed without an associated definition at all Some writers make no attempt at all at definition, while others engage in little more than emotional rhetoric, as in "the great urban explosion (which) has scattered pieces of debris over the countryside for miles around the crumbling centre a destruction of the qualities of the city" Despite its contemporary relevance, the quotation is from a paper by Robert Harvey and W.A.V Clark, written 35 years ago.1 Our view is that discussions about sprawl, whether academic or policy oriented, are greatly hampered by loose definition and inadequate measurement Our intention in this paper is to contribute toward improving the measurement of sprawl Using a consistent data source, we compute some familiar measures such as average population density of the metropolitan area, and the familiar negative exponential density gradient We also compute some less often used measures, such as those based on gravity models, and some which are fairly new, including measures based on order statistics, measures of fit of various models, and measures that incorporate the notion of autocorrelation We also investigate the use of data reduction techniques to collapse some of these disparate measures into a univariate index We also evaluate how well each one of our measures incorporates the information contained in the others, i.e., to get some sense of "which measure is best." We also estimate simple models of the determinants of each of the measure, using right-hand side variables suggested by the urban economics literature as well as some of the sociological explanations for decentralization.2 While we investigate a large number of measures, we certainly not exhaust all possible measures For example, our data tell us little directly about how much space within a tract is devoted to one land use or another, Harvey and Clark (1965) Harvey and Clark took the internal quotation from Pearson (1957) The simple models are estimated with an eye towards facilitating comparisons and validating measures of urban form They are best viewed as exploratory See our companion paper, Malpezzi (2000) for a more detailed model, albeit with the estimation focused on a single measure or how much space is privately owned vs publicly owned These are important components of some people’s views of sprawl Our explanatory models are exploratory and simple We mention here and discuss again below the fact that more complete models would deal with the potential endogeneity of some of our right hand side variables, as well as utilize a more complete vector of determinants For example, for tractability this paper abstracts from the effect of housing prices as an equilibrating mechanism, in contradistinction to Malpezzi and Kung (1998), which argues that housing price gradients and location may be jointly determined We also limit ourselves to data from the 1990 Census, that is, our measures are developed from a single cross section Measures that focus on tract level changes are only one class of many possible extensions to our measurement effort here Previous Research The literature on urban form is huge Our intention in this paper is to focus on measurement, so our review here is extremely selective Readers interested in a broader review of the literature on sprawl are referred to Malpezzi (2000), Ewing (1997), and Gordon and Richardson (1997) among others Those who wish a more detailed review of the academic approach to urban form should consult Anas, Arnott and Small (1998), as well as McDonald (1989), Wheaton (1979), and Ingram (1979) Surely the simplest measure of sprawl, and one used any number of times by urban economists and others, is the average density of the metropolitan area Brueckner and Fansler (1983) and Peiser (1989) are among well-known papers by urban economists that use this measure Far too many papers to cite focus on the negative exponential density gradient and its many derivatives and extensions According to Greene and Barnbrock (1978), the first to use the negative exponential function was the German scholar Bleicher (1892).3 In many respects, the function was popularized by the work of Colin Clark in geography, and later by Edwin Mills, Richard Muth, and others in economics Many authors have noted that the monocentric negative exponential is not always a terribly good fit for many metropolitan communities; see Richardson (1988), Kau and Lee (1976), and Kain and Apgar (1979) for examples Here we note the following key points (1) Without doubt the univariate negative exponential fits some cities reasonably well, and others quite badly (2) Despite this, it is still often used partly because of the advantages of having a univariate index of Although McDonald, in his excellent (1989) review, suggests that Stewart (1947) apparently first fit the negative exponential form described here Most observers would agree that it was Clark (1951) who popularized the form among modern urban scholars decentralization or sprawl (see, for example, Jordan, Ross and Usowski 1998) (3) It is apparently neglected in the literature that the measure of fit of such a simple univariate model is in its own way a measure of sprawl, as we will discuss below Most individual papers that measure decentralization, or 'sprawl,' focus on one measure or at most a few measures There are exceptions, of course Several papers have examined differences among functions theoretically and using simulation methods Ingram (1971) examined average distances, negative exponential functions, a linear reciprocal function, among others, and Guy (1983) examined a number of accessibility measures in a broadly similar fashion Broadly speaking, these papers clarify differences among candidate functions, and tell us which might best capture stylized facts of observed patterns, but not offer empirical tests per se Some papers have tested a limited number of specific hypotheses, e.g whether a single parameter exponential function performs as well as some flexible form (e.g Kau and Lee) In many respects Song (1996) is a paper that parallels this one, in that it uses actual data to test a wide range of alternative forms Song estimates a variety of gravity, distance and exponential models using tract level data from Reno, Nevada Best-fit criteria suggest that gravity measures and, especially, a negative exponential measure, perform much better than linear distance measures As Song is careful to note, results from a single metro area are suggestive, but it remains to examine other forms, and especially to test forms across other metropolitan areas Most analysts would admit the possibility of differing performance for a given estimator in, say, Los Angeles compared to Boston or Portland, for example In our paper, we follow Song in examining a range of possible measures of urban form, but rather than focus on a single location, we examine a wide range of U.S metropolitan areas More recently, Galster et al (2000) have independently undertaken an exercise in some respects similar to ours Galster and colleagues estimate a series of measures of urban form for a dozen large MSAs (in contrast to our measures, for some 300) Later, we will briefly compare our results to Galster et al.'s, and to Song's The Measurement of Urban Form In this section we discuss some measures of sprawl and related measures of urban form First we introduce some notation We use a capital P to indicate the population of a metropolitan area, and small p to indicate the population of a tract Capital A denotes the area of the metropolitan area, and small a denotes the area of the tract Capital D refers to the density of the metropolitan area, i.e D=P/A, and small d, d=p/a, is the density of a tract Distance from the city center is denoted by the letter u Letters i and j index tracts within a metropolitan area, and k indexes metropolitan areas themselves Generally we construct a measure for each metropolitan area, and for notational simplicity we usually drop the subscript k Average Density The most common measure is average density in the metropolitan area.: (1) Average MSA density; for each MSA, D=P/A In our database of MSA results, described below, this variable is denoted MSADENS While widely used, the limitations of the measure are obvious Consider two different single-county MSAs of equal area and equal population Suppose the first contains all of its population in a city covering, say, a fourth of the area of the county, the rest of which is rural and lightly settled Suppose the other MSA has a uniform population distribution Our measure, average density, is the same But most observers would consider the second MSA as exhibiting more "sprawl" than the first Of course there is no reason to limit ourselves to average densities Other moments, and nonparametric measures can also be considered, as below Alternative Density Moments In this paper we construct several new indicators of population density gradients, based on the densities of the Census tracts in each MSA The starting point for each MSA is to compute these tract densities, and then to sort tracts by descending density We then construct several indicators of "sprawl", one for each MSA: (2) Maximum tract density, DENMAX = max(di) (3) Minimum tract density, DENMIN = min(di) (4) DENMED: the density of the "median tract weighted by population," that is, median(di) when tracts are sorted by density, the tract containing the median person in the MSA For example, suppose the population of the MSA is 100 people, in tracts: consider the simplest measures, like average density and our order-statistics measures, because within a single MSA there is nothing to "fit" with such a measure As we mentioned above, Song found that in Reno gravity measures and, especially, a negative exponential measure, perform much better than linear distance measures Song is careful to note that such results may or may not generalize to other metropolitan areas Our Table 5, above, suggests that the fit of similar models will in fact be quite different in one metro area or another R-squared of a univariate exponential density model varied from near nil to about 90 percent; and we argued above that this fit was in and of itself valuable information about urban form While there is a noticeable tendency for larger MSAs to have lower r-squared, there are small metro areas with low r-squared, and among large MSAs the fit ranges from circa 0.2 for New York and Los Angeles to circa 0.6 for Atlanta and Boston, with Chicago in between Another way to examine how the "best model" varies by MSA is to consider what, if anything, is gained from the simplest negative exponential model, to one where a flexible fourth power polynomial is fit to the log of density (the basis for DRSQ1_4 described above) Figure plots the unadjusted R-squared for the fourth power model against that for the simplest model, for all MSAs in our study Metro areas along the 45° line, such as Jersey City and West Palm Beach at the bottom, and Laredo near the top, see little improvement from fitting a more flexible form On the other hand, Jamestown-Dunkirk NY, Grand Rapids MI, and Florence SC, among others, see substantial improvement from adding power terms These results confirm that Song's conjecture that "best fit" within MSAs varies by MSA is quite correct Galster et al.'s more recent study has proceeded independently from this one but along somewhat similar lines, that is estimating a series of measures, in their initial study for a set of 13 large metropolitan areas In their careful effort Galster et al divide each metro area up into half-mile grids, rather than relying on Census tracts They define a number of elements of "sprawl" or decentralization: density, continuity (how much "leapfrog" development), concentration (whether land use is used uniformly across the MSA or in a few locations), compactness (the size of the built-up area's footprint), centrality (whether most development is close to the CBD or far away), nuclearity (whether an MSA tends toward monocentricity or polycentricity), diversity (whether land uses are mixed within subareas of the MSA) and proximity (whether different land uses are close to each other within an MSA) Galster et al calculate specific measures of each of these concepts using their grid system; computational details are provided in their paper They then rank each MSA by each element, and compute an overall index of sprawl by adding the six component indexes 19 For most of these concepts, we have one or more measures that are related, although given the differences in our data structure the details of construction are different In brief, Galster et al.'s density is conceptually similar to our MSADENS;, their continuity is similar to our RSQ_1;, concentration is related to our DENMED, compactness is proxied by our DCENTAVG; and centrality is measured by our KMB1_1 We have no direct measure of nuclearity, but RSQ1_4 will presumably be high if nuclearity is low We have no direct analogue of diversity or proximity because we have no information on other land uses Figure shows that our measures are related The vertical axis is our preferred single measure, the density of the tract containing the median person, when tracts are sorted by density The horizontal axis is Galster et al.'s sprawl index, based on the sum of the ranks of each of their six components New York is the "least sprawled" MSA according to both measures; Atlanta the "most sprawled;" in general the two measures show substantial correlation Second Stage Results: Determinants of Urban Form This section describes a set of ordinary least squares regressions of each potential sprawl measure against a consistent set of right-hand side variables This time we include the factor scores as left hand side variables These results are contained in Table (We did not include the factor scores in Table because they are linear combinations of the other dependent variables by construction) The first three rows of Table represent independent variables that reflect the physical constraints that a metropolitan area faces The first is a dummy variable for being adjacent to a metropolitan area The next two are dummy variables for whether the suburbs or the central city are adjacent to a large body of water, such as an ocean or one of the Great Lakes These geographic variables were constructed by reviewing maps of each metropolitan area Many of our measures stem from the monocentric model of the city, which is oft criticized In fact, many metropolitan areas have more than one central city This has led some authors such as Jordan, Ross and Usowski (1998) to limit their analysis to metropolitan areas that have a single central city But for our purposes, this is undesirable because having multiple central cities may well be a key aspect of sprawl, so we wouldn't want to restrict the sample this way As an ad hoc adjustment, we have included the 20 number of central cities in each metropolitan area as an independent variable Follain and Malpezzi (1981) and Mills and Price (1985) among others, argue that central city externalities such as high poverty, crime, and bad schools will tend to engender blight flight We picked a single representative blight flight measure, namely the central city murder rate, to represent these negative externalities In a number of preliminary regressions, Jersey City, New Jersey, and the New York metropolitan area consistently came up as outliers in many respects We've already seen that these are extremely dense places, especially Jersey City We therefore included dummy variables in these regressions, although an alternate set without them yielded qualitative similar results The first thing to notice from Table is that there is a wide range in overall predictive performance Adjusted r-squares range from less than 10 percent for the indicator representing "Improvement In Unadjusted R-Squares Between Linear And Four-Power Standard Urban Models," to almost 0.9 in some of the density moments and gravity measures The most consistent performer of all the independent variables is clearly the size of the metropolitan area This is really not terribly surprising Generally, the larger the metropolitan area, the denser, and the flatter the gradient (although, as noted above, the relationship is not necessarily a simple one; there are a number of smaller metropolitan areas with very flat gradients) Generally, fast growing metropolitan areas tend to be less dense and more dispersed, as metropolitan areas with multiple central cities Perhaps the most surprising result is that for the log of median MSA income The tendency is for higher income metropolitan areas to be denser and to have steeper gradients Now when we examine unadjusted two-way plots of gradients and income, such a result would not be surprising, since larger metropolitan areas tend to have higher incomes, and we've already noted that higher densities at least would be expected for metropolitan areas of greater size But we would expect the result to be opposite in sign once we've controlled for population in the regression, based on the precepts of the standard urban model In particular, we would expect flatter gradients for higher income metropolitan areas It remains to be seen whether this contrary result holds up in more carefully specified models in future work Metropolitan areas with higher central city murder rates tend to be less dense, everything else equal, with flatter gradients as the blight flight view of the world suggests The performance of the geographic variables is 21 somewhat mixed, but in general, greater geographic constraints are related to higher density moments and somewhat greater dispersion Again returning to comparisons across dependent variables, examining Table we find that in many respects the order statistics measures performed very well The measures of spatial autocorrelation including rsquared and the gravity coefficients performed less well Average population density, the simplest measure and one used by papers such as Brueckner and Fansler and Peiser, among others, performs surprisingly well Based on Table 4's results we would say that the simple average density measure so commonly used performs fairly well, although we would prefer our order statistics measures given a choice Conclusions In this paper we have attempted to move the discussion of "sprawl" ahead by considering a range of measures that can be constructed from a single year’s Census tract-level data We have not exhausted the possible set of measures that could be constructed; in particular, we have not constructed any dynamic measures based on changes But we have constructed and compared a fuller set than has been analyzed before in a cross-metropolitan context We generally find, perhaps not surprisingly, that many alternative measures exist and that widely speaking, most tell the same story The indicators most commonly used by urban economists, average population density and the density gradient, perform reasonably well We propose an alternate measure based on order statistics that we think has some advantages We also discussed some extensions to our current work, including the use of spatial autocorrelation based measures and measures based on changes Armed with these and other indexes, academic research into "urban sprawl" can place today’s policy debates on a firmer footing Armed with the indicators we've constructed and detailed in this paper, cross-MSA empirical research can proceed on a range of issues These include a more detailed treatment of the costs and benefits of "sprawl," including a particular focus on the interplay between transportation and urban form However, there are still significant gains to be had by further research on these measurement issues In addition to applying more of the recent technology from urban geography, such as alternative models of spatial autocorrelation, urban decentralization is a dynamic phenomenon As 2000 Census data becomes available there could be large gains to carrying 22 out similar exercises for more recent data (and for other Census years), permitting the modeling of decentralization in changes 23 References Allen, W Bruce, Dong Liu and Scott Singer Accessibility Measures of U.S Metropolitan Areas Transportation Research B, 27B(6), 1993, pp 439-49 Alonso, William Location and Land Use Harvard University Press, 1964 Anas, Alex, Richard Arnott and Kenneth Small Urban Spatial Structure Journal of Economic Literature, 36(3), September 1998, pp 1426-64 Anselin, Luc and Raymond J.G.M Florax (eds.) 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and Density in Cities with Congestion Journal of Urban Economics, 43(2), March 1998, pp 258-72 White, Michelle J Commuting Journeys are Not Wasteful Journal of Political Economy, 1988 Yinger, John City and Suburb: Urban Models with More Than One Employment Center Journal of Urban Economics, 31, March 1992, pp 181205 29 Population Density Distance from Center Population Density Figure 1-A Figure 1-B Distance from Center 30 Persons per Square Kilometer Metropolitan Area Average Density 10,000 JC NY PAT 1,000 100 10 ANH NAU CHI LA SF NWK T RN OAK BOS PHL HON CLE PRV SJS LWL FTMIL L MIABAL DC DET MSX WAT BUF MON NHA NFK T PA NBM HT LBRO LHM HRT AKR BDC SLK CIN PGH GRY HMO FLT ELP SDI DAL DT N NO ATHOU L GAL SBN FWO RAC NSH WIL SCZ SAT DNB FIM MIN SRA LAN GRR YNG KEN ALN SEA SMA ST L DEN MEM ORL FYN LVL FTC M N ABQT DO WPB IND CT NLN KAL ANN RDG MEL AT COL GBY RLG OXN RKF PDR PT M TAC PME ERI ST C JKL ROC CT EKCM ELK DAB BAT POO SWB OMH WOR CSC MAD GSC MUN BDR HAL HBG RCH T PK YRK LEWBIN BRN VAL VMB BNT AUS SYR GNC SAC FWA ALB HAG AT H INC ROA SA V LEX LAN AL T LBK MOD SRS SWO MEM NSH MAC CDR GNV ELM MNL BGR PHX CPX DES APL OKC SAG FPC CGA KNX BIR LAC BNH LKL BUR JMI BRY CNO PEN DAV SPK SBY DCI SWV MCH TAL JNC BOI CSC JWI SMO SHR BUR LIM ANA PEO GAD COS WAC EVN LOWN WK SHN LRA KOK CHM BEU MOB WWV JMS PCF ALG RCM CMO T YL WCH SIL SLM ASN IOW LCL SIX FWB JKB PRK WLO MT GAUG HAW FSC DBQ KNK T UL MNO JT N BRZ JHN HIK CUM ANC ODS PRO ABL T JDN HACHT OCL KILUTSBR R DOT WNC T US SCP CVL FRO CCO BXI BIL ST C DAN SNS JOP LAW FAL DCA AMR SDT SYCC XC AXL ST J WMP FSA PBA RVR LSV MRC LMT VT X EAU LFL T EX WFT LYN FCL WAS T UC GLNNPL BAK SNG VIS FAZ EUG BEL SFE FAR END MDO PUE RLD Y AX BLG RNO LAR RDC LCN GRY DUL RCY GFM CHY BSM GFK YAZ CAS 10,000 100,000 1,000,000 10,000,000 MSA Population, 1990 Figure Density of Weighted Median Tract Density of Census Tract Containing Median Person 100,000 NY JC 10,000 SF 1,000 100 10 10,000 CHI ANH HON NOSJS MIA OAK NWK SDI PHL LAR NAU ELP C PHX DET DEN CLE SAC NBM M ST SLK INC ABQ LSVBUF PUEFLR MIL BAL LBK ST BOSDC POO MOD SEA SBR PRV SAT CPX BDC MSX NFK DAL V AL OMH AMR PRO T PA T RN FRO RNO SPK BAK MCH UCWPB COL PGH KEN NBC ANC FAR SGM ODS TT DO MIN HOU FWO ERI MEM VT X MDT BRD LFI LEX OXN BRY ANN CIN RKF LVL SCZ COSSMA NHA LAW KCM ST L APL ORL GBY BOI OKC SXC MON AL T FCL WIL SIX SNS SAV MAD IOW TAC LEO DES CAS LWK ALN WAT RVR SRA SBN JKL ABL MUN FWB NIA CGA DA V WCH AUS DT NIND SIL ST J BLG FIM HMO TRAC PK OWN AKR RCH ROA BDR GRY KAL GRR LAC BRN LAK AUR SHR HRT DBQ MT G BRO WOR GFK FYN L WL YNG AT L MEL EUG ROC FLT SYR FWA CDR FT MLAN T UL YAX BXI GAL PCF BEU END GFM CT N ALG WAC SLM JWI JMS ALB BIL RLG RLD P AW DAB BSM ELM SNG CHM DCI TAL PEN CSC HAL PEO CSC BAT SWB YAZ GNV AT C EVN BIR WNC CHY MRC KOK WLO NSH BNH AUG SAG LEW BRM MOB ANI LRA PT M SMO HBG NSH CCO FPC LHM PAS VIS MEM WFT BIN LCL ORG BNT MAC JOL MUS YCC RDG UT R NPL DNB MNL BEV BGRT SWO T US RCY CHT LFL ELK JNC CT E EX NLN SRS LKL T HA CNO LYN BCR EAU PRK LIM MDO OLY PME VMB PKE AXL LAN GSC GNC SWV BUR FAZ RCM CMO JDN MNO JMI HAG BUR ASN DUL JT N KIL KNK ANA YRK KNX PBA RDC LMT SDT GAD PDR WWV SCP JOP CVL FSA JKB WMP HT L HAW GRY HIK DOT SFE DAN SBY FSC CUM AT H BRZ ANS OCL BEL T YL FAL JHN SHN DCA ST C WAS LCN GLN 100,000 1,000,000 MSA Population Figure 31 LA 10,000,000 Coefficient of Log Density Population Density Gradient One Parameter Model 0.2 ANC 0.1 ORG 0.0 -0.1 -0.2 -0.3 NAU BRZ JC SBR WPB RVR HMO SLK SAC JDN AUR MELLAK MON ANH OXN DUL SWB GSC BNT GAL GNC BAK FPCATBEU T PA C JKB NHA E SF OAK RLG T UC BRN CHY DET CHI SDI CHTPDR HIK JKLCT GRR PGH KILST V AL ALNALB PHX DAB BCR HBG JOL ATHOU L DCPHL M OKC MSX DAL DT N FWO NSH NFK SJS DA V ROC YAX SRA RNO VIS CLE SCZ SYR COL SAG LKL JHN APL YRK HON ST L CAS PAS NWK SHNLMT BXI CPX MIA ORL SEA KCM FRO CCO HT L NLN BIR MAC NIA CSC ST C HAW KNXAUS LRA SNS CSC FSC VMB MRC PAW RCHPRV DOT SAT SFE MINBOS NPL NO DAN FWB CIN SGM BEL EUG SMA ST C T DO IND AUG UT R T UL FTMEM M MOB BDR CUM RAC WIL LIM JWI YNG ELP POO DEN BAL SRS MIL BRM LFL FSA WCH HRT PKE GRY BNH LSVMEM AKR GNV BA T ANS CT N RDC YANA AZ WFT JOP LHM PEN CNO JMS LAN TDCA EX ELK OCL SWV BEV MOD GLN WLO LCL TAL ERI DES WAS TAC BUF PRK SLM WOR EAU DNB SWO SHR ANI WWV LVL FWA BDC MT G RCY SDTHAG FCL LEO AT H TPEO RN LAN CHM GRY EVN MDO RLD SCP AL TOLY CGA LYN BSM BLG WNC SPK YCC KEN SAV PME ANN SXC LEX AMR LCN FAL FLT OMH GFK AXL RDG T HA NSH DBQ ROA SBY ASN PCF PRO WMP FAR FAZNBC FYN MUSBRD HAL RKF COS JNC BGR CVL T YL SIL MADABQ GFM MNOCDR KAL PBA WAT CMO SMO KOK BUR WAC BUR PT M LBK BRO LAR BIL SBN ABL KNK ALG MNL BOI LAC GADSIXFLR GBY BRY T US MDT RCM PUE LAWFIM JMI LWL JTX N ODS VT IOW OWN ELM MUNTMCH PK NBM INC STSNG J BIN DCI LWK END LEW LFI LA NY -0.4 10,000 100,000 1,000,000 10,000,000 MSA Population R-Squared of Simple Model Figure Fit of Population Density Gradient One Parameter Model 1.0 0.8 0.6 0.4 0.2 0.0 10,000 VTOWN X LAR DCI JMI BUR END GFM MUN SNG SMO LWK SIX JT NGAD PUE TUS YLSIL T ROA CASRCYMDT PCF BUR LAW TASN PK LCN GFK Y PEN COS MNL BIL AZA ALG FAL KNK XL ELM LWL IOW DCA BIN GLNFAR MAD MT G T UL KOK T EXMUS CNO SBY LVL OLY BLG GRY BSM CMO AUG LAN MCH INC RDC LAC RCM JNC WAC KAL ATFSA H WMP AT L TAL FWA TAC GBY SBN SHR TLFI HA HAL ABL OCL BOI ODS MNO CDR NWKMIN MOB PBA WAS BEL BIR BRD LFL EAU PME T OMH FAZ YCC SLM RKF JMS BA SAV MEM CVLNSH BAL FCLBRO EUG KNX POO RDG WWV PRO DBQ AKR BUF ST JDAN ANA LEX MIL FYN BOS FWB HAG CSC LYN WAT T DO PRV KEN LBK PKEPEOFLT MDO IND NBM NPL JOP ST L SCP WCH FRO CGA CIN SEA ANS C LEWSXC NBCST BRY WNC GNV EVNSPKABQ DET RAC YNG LSV ROC BXIRNO DES RLD WIL GRY HRT PT MFSC DNBSWV CHY HAW DC ERI LKLLRA BNH LCL LHM AUS FLR CUM WLO MEM HOU JHN CT N BDC SRA SNS NSH SFE LMT T UCRCH COL CLE LAN ANN SRS PRK SDT DOT MAC CHM WORSYR PHL ALT T RN YRK LIM MOD MRC SAT PGH ANI DA NFK DEN UT RVCSC DAL BRM NO CCO DAB NIA ELP KCM FIM CT ESAC MIA RVR ELK JKL CHI SWO ORL OKC BGR NLN AMRDUL ALN VIS DT N HIK WFT HT HBG FT SAG M YAX ALB L LEO BAK NAU SHN ANC CPX JOL GNC JKB SDI GRR BCR SGM HON PHX APL ST C CHTPDR FWO OAK VAL KIL MON SMA BRNPAW GSC RLG MSX SJS VMB SF T PA JWI BDR AT C SWB BEV PAS BNT SCZ FPC BEU NHA LAK GAL SLK MEL OXN ANH JDN AUR ORG STSBR M HMO WPB BRZ JC 100,000 1,000,000 MSA Population Figure 32 NY LA 10,000,000 Undadjusted R2, 4th Power Model Fit of Linear, Fourth Power SUE Models 1.00 0.80 0.60 0.40 0.20 OWN VT X YAZ LAR GFM BSM CMO SILSMO END FSC AT H GLNBIL DCI BUR JMI LCN MDT T YL BEL RCY ST CDAN MUN TAL T EXLWL DBQWAS KNK LWK ROA BUR KOK GAD SIX LAW SBY BINGFK PCF SNG FSA RDC TPUE US FARAXL GNV EUG JT N ALGCAS LFL IOW RAC PEN YCC HAG GRYDCA WNCKEN SHR FWA TASN PK MNL PBA T HABLG FAL RDG COS RCM BRO MUS MNO NBC T ULG MCH ELM LIM MT SCP NSH EAUWAC MAD LAN CNO OLY BRY DOT SLM ANS ANA RNO INC LVL ABL SAV LEW AUG T UC WMP SBN PME SFE CVL WCH ODS BIR LFI CDR JNC OCL BAT GBY LAC CHY HAL MOB KAL FYN RKF CUM PRO GRR BAL OMH JMS ABQ WAT NWK MEM AT L TAC JOP CGA KNX ROC BUF BOI BDC FCL BRD MIN BOS PKE SXC FAZ BNH L YN ANI WLO ST J T DO PT M FWB DUL DAV LBK DNB FLT FRO MIL PRV YRK DES POO AKR FLR WOR NPLWWV T RN YAX CIN LEX JDN WFT SYRLAN MDO LHM CSC MRC PEO SRA NBM MEMHRT SEA IND JHN DET AL TCOL ERI MAC EVN BXI SAT ST L SPK RLD HAW AUS GRY YNG WIL SRS LMT BDR BRN LCL LSV SAC CHM DC SWV SHN CTLRA N BAK CCO CHT NSH PRK NHA SNS LKL SWO BCR HIK RCH DEN CLE ELK HOU JWI AT C NO SGM JKL NLN UT RSDT ELP ANCVIS ANN MOD PGH SBR DAB GSC RVR CSC SAG AMR PAW NIA BRM DT CT E PHL MN GNCFT BNT HBG DAL NFK ALN FIM MIA KCM ORL KIL OKC APL PAS CHI JOL BGR VAL JKB LEO BEU BRZ RLGPDR ALB HT L FPC NAU HMO SDI CPX SCZ PHX AUR SF FWO NY ST C HON MSX OAK GAL BEV SMA MON TVMB PA SJS SWB SLK LA OXN ORG LAK ST MANH MEL WPB JC 0.00 0.00 0.20 0.40 0.60 0.80 Undadjusted R2, Linear Model Figure Density of Weighted Median Tract Compare Galster et al Results to Dens Of Tract Containing Median Person 100,000 NY 10,000 SF LA CHI MIA PHL DC DAL HOU BOS 1,000 DET DEN AT L 100 10 20 30 40 50 60 Galster et al Total Sprawl Index Figure 33 70 1.00 ... Measurement of Urban Form In this section we discuss some measures of sprawl and related measures of urban form First we introduce some notation We use a capital P to indicate the population of a metropolitan. .. example In our paper, we follow Song in examining a range of possible measures of urban form, but rather than focus on a single location, we examine a wide range of U.S metropolitan areas More... Metropolitan Areas Journal of Housing Research, 1996 Malpezzi, Stephen The Determinants of Urban Sprawl in U.S Metropolitan Areas University of Wisconsin, Center for Urban Land Economics Research Working