Measuring Sprawl and Its Impacts

Abstract

Across the nation, the debate over metropolitan sprawl and its impacts continues decade after decade. To elevate the debate, a decade ago, researchers developed compactness/sprawl indices for metropolitan areas and counties that have been widely used in health and other research. In this study, we develop refined compactness/sprawl indices based on definitions and procedures in earlier studies by Ewing and colleagues and validate them against transportation outcomes. The indices are being made available to researchers who wish to study the causes, costs and benefits, and solutions to sprawl and to practitioners who wish to check their community’s success in containing sprawl.

Keywords

growth management transportation urban form urban sprawl

Introduction

In 1958, William Whyte in his book The Exploding Metropolis referred to a new notion in planning, “Suburban Sprawl,” and alerted Americans that their cities were becoming more sprawling. So began the debate over sprawl and its impacts. There is still little agreement on the definition of sprawl or its alternatives: compact development, pedestrian-friendly design, transit-oriented development, and the catch-all term “smart growth.” There is also little consensus about how sprawl impacts everything from housing affordability and traffic congestion to open space preservation and air quality (Burchell 1998, 2002; Bruegmann 2006; Duany, Plater-Zyberk, and Speck 2001; Ewing 1997; Ewing, Pendall, and Chen 2002; Gordon and Richardson 1997; Hayden 2004; Hirschhorn 2005). Duany, Plater-Zyberk, and Speck (2001) use cultural, aesthetic, and ecological reasons to reject suburban sprawl as human habitat. At the other end of the spectrum, Bruegmann (2006) describes suburban sprawl as a natural manifestation of the American Dream of a big house in the suburbs.

A decade ago, Smart Growth America (SGA) and the U.S. Environmental Protection Agency (EPA) sought to raise the level of the debate over metropolitan sprawl, from purely subjective and qualitative to largely objective and quantitative. They sponsored research to operationally define sprawl and study its relationship to quality-of-life outcomes. The resulting indices place sprawl at one end of a continuous scale and compactness at the other. These compactness/sprawl indices have been widely used in health and other research. Sprawl has been studied in relation to traffic fatalities (Ewing, Schieber, and Zegeer 2003), physical inactivity, obesity, heart disease, cancer prevalence (Cho et al. 2006; Doyle et al. 2006; Ewing et al. 2003; Fan and Song 2009; Griffin et al. 2012; Joshu et al. 2008; Kelly-Schwartz et al. 2004; Kim et al. 2006; Kostova 2011; Lee, Ewing, and Sesso 2009; Plantinga and Bernell 2007), air pollution (Schweitzer and Zhou 2010; Stone 2008), extreme heat events (Stone, Hess, and Frumkin 2010), residential energy use (Ewing and Rong 2008), social capital (Nguyen 2010), emergency response times (Trowbridge, Gurka, and O’connor 2009), teenage driving (McDonald and Trowbridge 2009; Trowbridge and McDonald 2008), and private-vehicle commute distances and times (Ewing, Pendall, and Chen 2003; Holcombe and Williams 2012; Zolnik 2011). While most studies have linked sprawl to negative outcomes, there have been exceptions (see, in particular, Kahn 2006; Holcombe and Williams 2012).

In this study, we develop refined compactness/sprawl indices based on definitions and procedures in Ewing, Pendall, and Chen (2002). It has been more than a decade since the original indices were developed, and much has changed since then. Also, new data sources have become available since the early 2000s, and these allow us to improve the construct validity of the original indices. In this study, we update the indices to 2010, refine and enhance the four original compactness factors (density, mix use, degree of centering and street connectivity) using the most recent databases and adding new metrics, and finally validate the sprawl indices against commuting data from the American Community Survey. Compactness indices have also been developed for urbanized areas, counties, and census tracts, and all are posted on a National Institutes of Health website in the hope that other researchers will use the indices to study the costs and benefits of sprawl.¹

Literature Review

As the costs of sprawl have become more apparent, the term urban sprawl has gone from urban planning construct to public policy concern. But what exactly is urban sprawl? In the early 1990s, sprawl was defined qualitatively for purposes of growth management in Florida (Ewing 1997). The definition ultimately adopted by the State encompassed the following urban forms: (1) leapfrog or scattered development, (2) commercial strip development, (3) expanses of low-density development, and (4) expanses of single-use development (as in bedroom communities, regional malls, and business parks).

All four prototypical patterns (leapfrog etc.) are characterized by poor accessibility. In scattered or leapfrog development, residents and service providers must pass vacant land on their way from one developed use to another. In classic strip development, the consumer must pass other uses on the way from one store to the next; it is the antithesis of multipurpose travel to an activity center. Of course, in low-density, single-use development, everything is far apart because of large private land holdings and segregation of land uses. The potential link to public policy is clear. In sprawl, poor accessibility of land uses to one another may leave residents with no alternative to miles and miles of automobile travel.

Measuring Sprawl

Starting around 2000, researchers sought to develop objective measures of sprawl that could be related to measurable outcomes. The purpose was to raise the level of the debate over sprawl from subjective and qualitative to objective and quantitative.

Early attempts to measure the extent of urban sprawl were mostly crude. Several researchers created measures of urban sprawl that focused on density (Pendall 1999; Fulton et al. 2001; Lopez and Hynes 2003; Anthony 2004; Lang 2003; Pendall and Carruthers 2003). Density may have been the primary indicator of sprawl in the early studies because it is easy to measure and captures one important dimension of sprawl. However, this flies in the face of both the technical literature and popular conceptions of sprawl. The most notable feature of early studies was the failure to define sprawl in all its complexity.

The same mistakes made in early quantitative studies of sprawl, neglect of land use interactions and empirical outcomes, have been made in recent studies using satellite imagery (Besussi and Chin 2003; Burchfield et al. 2006; Malpezzi and Guo 2001; Torrens and Alberti 2000). These studies use land cover maps derived from satellite imagery to compute form parameters such as fragmentation, edge density, and fractal dimension (Huang, Lu, and Sellers 2007; Martellozzo and Clarke 2011; Poelmans and Van Rompaey 2009). Increasing availability and quality of satellite imagery have made it easier in recent years to study this dimension of urban sprawl (Batisani and Yarnal 2009; Thapa and Murayama 2010; Bhatta, Saraswati, and Bandyopadhyay 2010). However, these methods are limited in their ability to distinguish patterns of high accessibility from patterns of low accessibility because they ignore land use and street patterns.

A notable feature of urban form measures in these studies is the different sprawl ratings given to different metros by different analysts. With the exception of Atlanta, which always ranks as one of the worst, the different variables used to operationalize sprawl lead to very different results. In one study, Portland was ranked among the least sprawling and Los Angeles was ranked among the most sprawling (Glaeser, Kahn, and Chu 2001). In another study, the two cities’ rankings were reversed (Nasser and Overberg 2001). Another notable shortcoming was the failure to validate sprawl metrics against logical outcomes such as travel characteristics of the population. If sprawl has any consistently recognized outcome, it is automobile dependence. We would expect to find that after controlling for other relevant influences, sprawling urban areas have relatively high auto ownership, low transit and walking commute mode shares, and long drive times to work.

Most scholars now agree that sprawl is a multidimensional phenomenon that is best quantified by a combination of measures (Galster et al. 2001; Ewing, Pendall, and Chen 2002; Cutsinger et al. 2005; Frenkel and Ashkenazi 2008; Torrens 2008; Jaeger et al. 2010; Mubareka et al. 2011). But this can lead to more questions than answers. What are the dimensions of sprawl? How are they best measured? Should these dimensions be combined into an overall sprawl index and, if so, how? Is sprawl in all dimensions necessary to call an urban area “sprawling”? Are tradeoffs allowed?

The first multidimensional measures of sprawl were developed by Galster et al. (2001). They disaggregated land use patterns into eight dimensions: density, continuity, concentration, clustering, centrality, nuclearity, heterogeneity (mixing), and proximity. Sprawl was defined as any pattern of land use that has low levels in one or more of these dimensions. The researchers operationally defined each dimension and successfully quantified six of the eight measures for 13 urbanized areas. Cutsinger et al. (2005) updated the index by using twelve conceptually distinct dimensions of land use patterns that were operationalized for fifty large U.S. metropolitan areas.

Another early effort was that of Ewing, Pendall, and Chen (2002). They quantified sprawl in two steps: first, using principal component analysis, they developed indices for four components of urban form—development density, land use mix, activity centering, and street accessibility. They then combined the four factors into an overall compactness/sprawl index. Both the individual factors and overall index were then validated against transportation outcome measures.

Methods

Our definition of sprawl is borrowed directly from the literature review. Sprawl is any development pattern characterized by poor accessibility and automobile dependence. As in Ewing, Pendall, and Chen (2002), low-density, single-use, uncentered, or poorly connected development is, ipso facto, sprawling, while any development pattern with moderate to high densities, mixed uses, strong centers, and well-connected streets is compact.

Sample

The unit of analysis in this study is the metropolitan area. A metropolitan area is a region that consists of a densely populated urban core and its less-populated surrounding territories that are economically and socially linked to it. The criteria for defining metropolitan areas changed in 2003. Smaller MSAs remained the same, but larger metropolitan areas, previously referred to as consolidated metropolitan statistical areas (CMSAs) are now defined as MSAs. Different portions of CMSAs, previously referred to as primary metropolitan statistical areas (PMSAs), have been redefined and reconfigured as metropolitan divisions. For example, the old New York CMSA consisted of eleven counties in two states and four PMSAs: New York PMSA, Nassau-Suffolk PMSA, Dutchess County PMSA, and Newburgh, NY-PA PMSA. The current New York MSA consists of twenty-three counties in three states and four metropolitan divisions. The New York MSA now is strikingly heterogeneous, whereas the old New York PMSA contained only the five boroughs that make up New York City. Metropolitan divisions do not perfectly substitute for PMSAs, as they have different size thresholds (2.5 million vs. 1 million population), but they come as close to representing homogenous units as we can come with current census geography. Metropolitan divisions are designated for each of the eleven largest MSAs.²

The sample in this study is limited to medium and large metropolitan areas, and metropolitan divisions where they are defined. It initially included a total of 228 areas with more than two hundred thousand population in 2010.³ The rationale for thus limiting our sample is simple: the concept of sprawl has particular relevance to large areas where the economic, social, and environmental consequences of sprawl can be significant. The concept of sprawl does not have much relevance to small MSAs such as Lewiston, Idaho, and Casper, Wyoming.

A total of seven metropolitan areas and divisions were ultimately dropped from our sample because of the lack of local employment dynamics (LED) data, a key data source for measuring sprawl. These metropolitan areas, or a portion of them, are located in Massachusetts, which does not participate in the LED program. This reduces the final sample size to 221 MSAs and metropolitan divisions.

Consistent with Ewing, Pendall, and Chen (2002) methodology, we excluded rural areas from our analysis. We operationalized and measured compactness only for “urban portions” of metropolitan areas. The urban portion is defined as a sum of urban census tracts in a metropolitan area. Urban census tracts are defined as census tracts with population densities of one hundred people per square miles or more.

Principal Components

We used principal component analysis to derive four separate compactness factors, one for development density, another for land use mix, a third for activity centering, and a fourth for street connectivity.

Development Density

Low residential density is on everyone’s list of sprawl indicators. A principal component representing density was extracted from our data set as a weighted sum of eight separate density variables (see Table 1). Our first five density variables are the same as in the original compactness index (Ewing, Pendall, and Chen 2002): gross density of urban and suburban census tracts (popden), percentage of the population living at low suburban densities (lt1500), percentage of the population living at medium to high urban densities (gt12500), urban density based on the National Land Cover Database⁴ (urbden), and estimated density at the center of the metropolitan area derived from a negative exponential density function (dgcent).

Table 1.

Variable Loadings of Four Factors for 2010.

Component Matrix		Data Sources	Factor Loadings
Density factor
popden	Gross population density	Census 2010	0.900
empden	Gross employment density	LED 2010	0.898
lt1500	Percentage of the population living at low suburban densities	Census 2010	−0.597
gt12500	Percentage of the population living at medium to high urban densities	Census 2010	0.879
urbden	Net population density of urban lands	NLCD	0.925
dgcent	Estimated density at the center of the metro area derived from a negative exponential density function	Census 2010, Tiger 2010	0.948
popdcen	Weighted average population density of centers	Census 2010	0.810
empdcen	Weighted average employment density of centers	LED 2010	0.817
Eigenvalue			5.82
Explained variance			72.80%
Mix use factor
jobpop	Job–population balance	LED 2010	0.834
jobmix	Degree of job mixing (entropy)	LED 2010	0.921
walkscor	Weighted average Walk Score	Walk Score Inc.	0.870
Eigenvalue			2.30
Explained variance			76.72%
Centering factor
varpop	Coefficient of variation in census block group population densities	Census 2010	0.495
varemp	Coefficient of variation in census block group employment densities	LED 2010	0.313
dgrad	Density gradient moving outward from the CBD	Census 2010, Tiger 2010	−0.375
popcen	Percentage of MSA population in CBD or subcenters	Census 2010	0.833
empcen	Percentage of MSA employment in CBD or subcenters	LED 2010	0.847
Eigenvalue			1.90
Explained variance			37.89%
Street factor
smlblk	Percentage of small urban blocks	Census 2010	0.871
avgblksze	Average block size	Census 2010	−0.804
avgblklng	Average block length	NAVTEQ 2012	−0.649
intden	Intersection density	TomTom 2007	0.729
4way	Percentage of 4-or-more-way intersections	TomTom 2007	0.380
Eigenvalue			2.51
Explained variance			50.03%

Note: LED = Local Employment Dynamics (LED) database; NLCD = National Land Cover Database.

The sixth density variable, which is new, is analogous to the first, except it is derived with employment data from the Local Employment Dynamics (LED) database⁵ (empden). The LED data were aggregated from census block geography to generate total jobs by 2-digit NAICS code for every block group in the nation. This was then divided by land area to produce a density measure.

The last two variables are related to employment centers identified by the authors as a part of this study.⁶ The two variables are weighted average population density (popdcen) and weighted average employment density (empdcen) of all centers within a metro area. The average densities were weighted by the sum of block group jobs and residents as a percentage of the MSA total.

Land Use Mix

Segregated land uses are also on most lists of sprawl development patterns. Conversely, mixed and integrated land uses sit atop lists of pedestrian-friendly, transit-oriented, and smart growth patterns. A principal component representing land use mix was extracted from our data set as a weighted sum of three separate mix variables (see Table 1).

The first two variables of the mix use factor represent the balance between jobs and population (jobpop); and the diversity of land uses (entropy). Although using the same variables as Ewing, Pendall, and Chen (2002) to operationalize mixed use, we computed them differently using one-mile buffers around the centers of block groups rather than computing them within the boundaries of block groups. The reason is that the latter are sensitive to the size of a block group. The larger the area, the higher the value of mixed use variables because the block group will contain more activity in total. By using a uniform one-mile buffer, we make the unit of analysis comparable for all block groups.

The two mixed-use variables were calculated for each block group’s buffer using block-level population data from the 2010 Census, and block-level employment data from the 2010 LED database. The first variable is a job-population balance measure (jobpop). This variable equals one for block groups with one job for every five people; zero for block groups with only jobs or residents within the one-mile ring of their center, and intermediate values for intermediate cases. All values were weighted by the sum of block group jobs and residents as a percentage of the MSA total.

We also derived a job mix variable (jobmix). The variable, an entropy measure, equals one for block groups with equal numbers of jobs in each sector; zero for block groups with all jobs in a single sector within the ring; and intermediate values for intermediate cases. The sectors considered in this case were retail, entertainment, health, education, and personal services. Values were weighted by the sum of block group population and employment as a percentage of the MSA total.

A third mixed-use variable is metropolitan weighted average Walk Score (walkscore). It was computed using data from Walk Score, Inc. to measure proximity to amenities, with different amenities weighted differently and amenities discounted as the distance to them increases up to one mile and a half, where they are assumed to be no longer accessible on foot.⁷ Classic Walk Score data were purchased for the population centers of the MSA census tracts. We obtained the latitude and longitude coordinates of census tracts’ population centers from a Census website.⁸ Values were weighted by the sum of census tract population and employment as a percentage of the MSA total.

Activity Centering

Commercial strip development is on most lists of sprawl development patterns. The antithesis of strips are urban centers. Urban centers are concentrations of activity that provide economies of scale, facilitate modal choices and multipurpose trip making, foster an identity in the urban landscape, and are vastly different than commercial strips. This concentration, or centeredness, can relate to population or employment, and may take the form of a single dominant center or multiple subcenters. Compactness is associated with centers of all types, and sprawl with the lack of centers of any type.

Centering is the compactness dimension with the most significant improvement compared to Ewing et al.’s indices. Ewing, Pendall, and Chen (2002) measured metropolitan centering in terms of concentrations of employment in or around (within three miles) historic central business districts (CBDs) of metropolitan areas, and at a considerable distance (more than 10 miles) from historic CBDs. This way of measuring centering does not make much sense when applied to medium-size MSAs because most of the jobs and population fall within three miles of CBDs. It also doesn’t make sense in large polycentric metropolitan areas, where historic CBDs have sometimes been eclipsed by edge cities. A principal component representing activity centering was extracted from our data set as a weighted sum of five separate centering variables (see Table 1).

The first centering variable came straight out of Ewing, Pendall, and Chen (2002) and the 2010 census. It is the coefficient of variation in census block group population densities, defined as the standard deviation of block group densities divided by the average density of block groups (varpop). The more variation in population densities around the mean, the more centering and/or subcentering exists within the MSA.

The second centering variable is analogous to the first, except it is derived with employment data from the LED database. It is the coefficient of variation in census block group employment densities, defined as the standard deviation of block group densities divided by the average density of block groups (varemp). The more variation in employment densities around the mean, the more centering and/or subcentering exists within the MSAs.

The third variable contributing to the centering factor is the density gradient moving outward from the CBD, estimated with a negative exponential density function. The faster density declines with distance from the center, the more centered (in a monocentric sense) the metropolitan area will be (dgrad).

The next two centering variables measure the proportion of employment and population within CBDs and employment subcenters. For computing them, we first identified the location of CBDs and employment subcenters for all metropolitan areas using R statistical software. R is a free, open source software with excellent graphic capabilities. It has become one of the fastest-growing statistical computing tools, particularly for analysis of spatial data. To identify CBDs, we ran a local spatial autocorrelation procedure using the local Moran’s I statistic (Anselin 1995). With this procedure, it is possible to quantify the degree of clustering of neighboring zones with high levels of density. This method has been used by Baumont and Le Gallo (2003) and Riguelle, Thomas, and Verhetsel (2007). Local Moran’s I is defined as

I_{i} = \frac{(x_{i} - \bar{x})}{\sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{2} / n} \sum_{j = 1}^{n} w_{i j} (x_{j} - \bar{x})

where I_i is the local Moran’s I coefficient, x is the value of employment density, w_ij is the matrix of spatial weights, and n is the number of observations.

By calculating z values of the local Moran statistic (see Anselin 1995; Getis and Ord 1996), it is then possible to identify four types of spatial clusters:

High–High: High values around neighbors with high values (cluster)

Low–Low: Low values around neighbors with low values (cluster)

High–Low: High values around neighbors with low values (outlier)

Low–High: Low values around neighbors with high values (outlier)

Using LED data of block groups, the Moran’s I analysis was done for all metropolitan areas. The High–High clusters with the highest employment density in each MSA were considered as CBD candidates. However, not all of them are CBDs. We excluded the hot spots containing large employers such as hospitals, malls, and university campuses by requiring that the employment share in each sector be no more than 75 percent of total employment. We identified CBDs for a total of 356 metropolitan areas. These generally coincided with CBDs in the 1980 U.S. census, the last time they were designated.

Having CBDs for 356 metropolitan areas, we then identified employment subcenters as the positive residuals estimated from an exponential employment density function using Geographically Weighted Regression method (GWR). GWR estimates an employment density surface utilizing only nearby observations for any data point (block group), with more weight given to the closest observations. The dependent variable of the GWR estimations is the employment density of a block group and the independent variable is the distance of the block group centroid from the CBD. We used the Adaptive kernel type with 30 numbers of neighbors. The block groups with highest positive residuals (residuals 4 times greater than predicted values) were candidates for employment subcenters. As with CBD identification, we excluded block groups containing large employers such as hospitals, regional malls, and university campuses by requiring that the employment share in each sector be no more than 75 percent of total employment. Finally we excluded cases when their ratio of employment to population was less than 2.5 (following Gordon, Richardson, and Wong 1986). We identified a total of 451 subcenters in 132 metropolitan areas.

Out of 374 metropolitan areas in the United States, we found 224 MSAs to be monocentric (have only one center), 132 to be polycentric (have more than one center), and 18 metropolitan areas to have no CBD or subcenter. This procedure resulted in two new centering variables as the percentage of MSA population (popcen) and employment (empcen) in CBDs and subcenters.

Street Connectivity

Accessibility is not only a function of land use patterns but of street network design, a fourth dimension of compactness/sprawl. After all, it is the streets that connect the land uses. Accessibility is usually measured in terms of number of activities that can be reached within a given travel time. Clearly, this depends on street connectivity. A principal component representing street connectivity was extracted from our data set as a weighted sum of five separate street variables (see Table 1).

Street connectivity is related to block size since smaller blocks translate into shorter and more direct routes. Large block sizes indicate a lack of street connections and alternate routes. So, three street connectivity variables were computed for each MSA based on blocks size: average block length (avgblklngh), average block size (avgblksze) and the percentage of blocks that are less than 1/100 square mile, which is the typical size of an urban block (smlblk).

These three variables were part of Ewing et al.’s original compactness metrics. To them, we have added two new variables. They are intersection density and percentage of 4-or-more-way intersections. Intersections are where street connections are made and cars must stop to allow pedestrians to cross. The higher the intersection density, the more walkable the city (Jacobs 1993). Intersection density has become the most common metric in studies of built environmental impacts on individual travel behavior (Ewing and Cervero 2010).

Another common metric in such studies is the percentage of 4-or-more-way intersections (Ewing and Cervero 2010). This metric provides the purest measure of street connectivity, as 4-way intersections provide more routing options than 3-way intersections. A high percentage of 4-way intersections does not guarantee walkability, as streets may connect at 4-way intersections in a super grid of arterials. But it does guarantee routing options.

We produced a national database of street intersection locations, including for each intersection feature a count of streets that meet there using the TomTom road database.⁹ The resulting national intersection database contains 13.1 million features; 77 percent of these are three-way intersections, and the remaining 23 percent are four- or more-way intersections. For each MSA, the total number of intersections in the urbanized portion of MSA was divided by the land area to obtain intersection density (intden), while the number of 4-or-more-way intersections was multiplied by 100 and divided by the total number of intersections to obtain the percentage of 4-or-more way intersections (4way).

Individual Compactness/Sprawl Factors

Principal component analysis is a statistical technique used to extract one or a few uncorrelated factors from a larger number of correlated variables. It is a special type of factor analysis, where new variables are derived that represent the variance common to the original variables. The extracted factors, or principal components, are weighted combinations of the original variables. The higher the correlation between a variable and a principal component, the greater the loading and the more weight the original variable is given in the overall principal component score. The greater the correlation among the original variables, the more variance is captured by a single principal component.

For each dimension of compactness, we ran principal component analysis on the measured variables, and the principal component that captured the largest share of common variance among the measured variables was selected to represent that dimension. Factor loadings (the correlation between a variable and a principal component), eigenvalues (the explanatory power of a single principal component), and percentages of explained variance are shown in Table 1.

The eigenvalue of the density factor is 5.82, which indicates that this one factor accounts for about three quarters of the total variance in the data set. As anticipated, the percentage of the population living at less than 1,500 persons per square mile loads negatively on the density factor. The rest load positively.

The eigenvalue for the mix factor is 2.30, which indicates that this one factor accounts for more than three quarters of the total variance in the data set. All component variables load positively on the mix factor.

The eigenvalue of the centering factor is 1.90, which indicates that this factor accounts for about 38 percent of the total variance in the data sets. The density gradient loads negatively on the centering factor as expected. The rest load positively.

The eigenvalue of the street factor is 2.51, which indicates that this factor accounts for more than a half of the total variance in the data set. As expected, the average block size and average block length load negatively on the street factor. The rest load positively.

Overall Compactness/Sprawl Index for 2010

Although density has received more attention as a dimension of sprawl than have other factors, similar to Ewing, Pendall, and Chen (2002), we could think of no rationale for giving different weights to the four factors. All four factors affect the accessibility or inaccessibility of development patterns. Each factor can move an MSA along the continuum from sprawl to compact development. Thus, the four were simply summed, in effect giving each dimension of sprawl equal weight in the overall index.

The second and more difficult issue was whether to, and how to, adjust the resulting compactness index for MSA size. As areas grow, so do their labor and real estate markets, and their land prices. Their density gradients accordingly shift upward, and other measures of compactness (intersection density, for example) follow suit. The simple correlation between the sum of the four compactness factors and the population of the MSA is 0.575, significant at .001 probability level. Thus, the largest urbanized areas, perceived as the most sprawling by the public, actually appear less sprawling than smaller urbanized areas when sprawl is measured strictly in terms of the four factors, with no consideration given to area size.

We used the same methodology as Ewing, Pendall, and Chen (2002) to account for metropolitan area size. We regressed the sum of the four compactness factors on the natural logarithm of the population of the MSAs. The standardized residuals became the overall measure of compactness. As such, this index is uncorrelated with population. In effect, the degree of sprawl in each metropolitan area is defined relative to other metropolitan areas of comparable size. However, the overall index still has a high correlation (r = 0.866) with the sum of four factors before adjustment.

We transformed the overall compactness index into a metric with a mean of 100 and a standard deviation of 25 for ease of use and understanding. More compact metropolitans have index values above 100, while the more sprawling have values below 100.

Figure 1 shows the compactness scores for 221 metropolitan areas and divisions. By these metrics, New York and San Francisco are the most compact large metropolitan divisions while Hickory, North Carolina, and Atlanta, Georgia, are the most sprawling metropolitan areas. Again all metropolitan areas and divisions in Massachusetts, including the Boston metropolitan division, are not in the list because of the lack of availability of employment data (LED) for this state. Table 2 presents overall compactness scores and individual component scores for the 10 most compact and the 10 most sprawling large metropolitan areas.

Figure 1.

Compactness score for 221 metropolitan areas and divisions in the United States (the darker the color, the more compact).

Table 2.

Compactness/Sprawl Scores for 10 Most Compact and 10 Most Sprawling Metropolitan Areas and Divisions in 2010.

Rank	Metropolitan Area	index	denfac	mixfac	cenfac	strfac
Ten most compact metropolitan areas
1	New York–White Plains–Wayne, NY-NJ, metro division	203.4	384.3	159.3	213.5	193.8
2	San Francisco–San Mateo–Redwood City, CA, metro division	194.3	185.9	167.2	230.9	162.8
3	Atlantic City–Hammonton, NJ, metro area	150.4	96.3	100.1	154.5	130.7
4	Santa Barbara–Santa Maria–Goleta, CA, metro area	146.6	112.3	148.9	109.5	122.1
5	Champaign–Urbana, IL, metro area	145.2	100.0	123.3	153.6	82.8
6	Santa Cruz–Watsonville, CA, metro area	145.0	98.9	146.2	107.9	112.2
7	Trenton–Ewing, NJ, metro area	144.7	115.9	128.0	97.4	139.1
8	Miami–Miami Beach–Kendall, FL, metro division	144.1	160.2	136.4	117.9	166.9
9	Springfield, IL, metro area	142.2	90.4	100.5	160.0	96.7
10	Santa Ana–Anaheim–Irvine, CA, metro division	139.9	161.9	155.0	79.6	181.8
Ten most sprawling metropolitan areas
212	Kingsport–Bristol–Bristol, TN-VA, metro area	60.0	78.7	40.5	89.7	82.9
213	Augusta–Richmond County, GA-SC, metro area	59.2	85.2	60.7	88.5	73.9
214	Greenville–Mauldin–Easley, SC, metro area	59.0	86.7	72.9	81.1	71.4
215	Riverside–San Bernardino–Ontario, CA, metro area	56.2	103.7	111.2	77.0	80.3
216	Baton Rouge, LA, metro area	55.6	91.3	72.0	69.7	80.4
217	Nashville-Davidson–Murfreesboro–Franklin, TN, metro area	51.7	91.5	63.9	96.2	77.0
218	Prescott, AZ, metro area	49.0	82.3	53.2	58.2	70.0
219	Clarksville, TN-KY, metro area	41.5	84.5	39.7	74.5	60.8
220	Atlanta–Sandy Springs–Marietta, GA, metro area	41.0	97.8	85.5	89.9	75.9
221	Hickory–Lenoir–Morganton, NC, metro area	24.9	78.6	40.5	67.0	56.9

Relationship to Transportation Outcomes

The association between the built environment and travel behavior is confirmed by more than 200 empirical studies. This literature is summarized in recent reviews by Cao, Mokhtarian, and Handy (2009), Heath et al. (2006), Pont et al. (2009), Graham-Rowe et al. (2011), and Salon et al. (2012), and also in meta-analyses by Leck (2006) and Ewing and Cervero (2010). From the meta-analysis of Ewing and Cervero (2010), we would expect to find positive associations of development density, land use mix, and street connectivity with both walking and transit use, and a negative association between these same variables and driving distances (and presumably drive times too).

We have explicitly defined sprawl in terms of poor accessibility and automobile dependence. So it follows that sprawl indices can be validated against measures of automobile dependence. We used data from the 2011 American Community Survey (ACS), that is, 5-year estimates to validate our compactness metrics. First, we computed average vehicle ownership per household, walk and transit mode shares, and average drive times for census metropolitan areas and divisions. We used data on gender, age, race, household size from the 2010 Census, and computed percentages and mean values to describe socio-economic status. These are control variables. We acquired gasoline price data at the MSA level from the Oil Price Information Service (OPIS). Retail prices are average prices from samples of stations in each MSA and are reported with all relevant taxes included. These prices are the true posted ‘sign’ prices (as they would appear outside a gas station). Table 3 shows a list of all dependent and independent variables used in the validation.

Table 3.

Variables Used to Explain Transportation Outcomes.

Variables		Data Sources
Dependent variables
walkshr	Percentage of commuters walking to work	ACS 2007-2011
transitshr	Percentage of commuters using public transportation	ACS 2007-2011
hhveh	Average vehicle ownership per household	ACS 2007-2011
drivetime	Average journey-to-work drive time in minutes	ACS 2007-2011
Independent variables
pop	Metropolitan population	Census 2010
hhsize	Average household size	Census 2010
age1524	Percentage of population 15–24 years old	Census 2010
male	Percentage of male population	Census 2010
white	Percentage of white population	Census 2010
income	Income per capita	ACS 2007-2011
fuel	Average fuel price for the metropolitan area	OPIC database 2010
index	MSA compactness index for 2010
denfac	Density factor (a weighted combination of 8 density variables)
mixfac	Mix factor (a weighted combination of 3 mixed-use variables)
cenfac	Centering factor (a weighted combination of 5 centering variables)
strfac	Street factor (a weighted combination of 5 street-related variables)

Note: All variables are log transformed.

We estimated two sets of regression models. Our first set of regressions used the overall compactness index for 2010 (index) as an independent variable. The second set of regressions used the four compactness/sprawl factors individually (denfac, mixfac, cenfac, and strfac) as independent variables. In both set of regressions, the dependent variables were logged so as to be normally distributed and all independent variables were also transformed into log form to achieve a better fit with the data, reduce the influence of outliers, and adjust for nonlinearity of the data. The transformations had the added advantage of allowing us to interpret regression coefficients as elasticities.

Results for models with the overall compactness index are presented in Table 4. Control variables mostly have the expected signs and often are significant. The compactness index (index) has the expected strong positive relationships to walk and transit mode shares, and the expected strong negative relationship to average vehicle ownership per household. A household of comparable socioeconomic status can meet travel demands with fewer cars in a compact metropolitan area because vehicle trips are less numerous, shorter, and more efficiently linked into trip chains. This phenomenon is known as car shedding.

Table 4.

Relationships of the Overall Indices to Transportation Outcomes.

	walkshr	transitshr	hhveh	drivetime
Constant	−11.86	−0.62	−6.01	4.69
Pop	0.01 (0.44)	0.42 (8.35)***	−0.01 (−1.28)	0.04 (3.79)***
Hhsize	−0.65 (−1.92)*	0.69 (1.24)	0.80 (9.07)***	0.40 (3.81)***
age1524	1.47 (9.19)***	1.74 (6.61)***	0.13 (3.02)**	−0.15 (−3.40)***
Male	−0.79 (−0.45)	−10.63 (−3.66)***	0.82 (1.79)	−0.99 (−1.90)
White	0.55 (3.65)***	0.21 (0.83)	0.12 (3.03)**	−0.15 (−3.27)***
Income	0.55 (3.33)***	2.14 (7.80)***	0.25 (5.80)***	0.25 (4.51)***
Fuel	2.45 (5.18)***	3.35 (4.28)***	−0.88 (−7.17)***	0.21 (1.49)
Index	0.39 (4.22)***	1.15 (7.57)***	−0.06 (−2.45)**	−0.05 (−1.85)
Adjusted R²	0.542	0.728	0.416	0.479

Note: All values are log-log transformed; t statistics are in parentheses.

p < .05; **p < .01; ***p < .001.

The relationship between the index and average drive time is not significant (though it has the expected negative sign). Our result for average drive time parallels Ewing, Pendall, and Chen (2002). While commute distances may be shorter in compact areas, driving speeds may be higher, causing insignificant differences in commute times. The American Community Survey only provides commute times, not distances; hence, we cannot confirm this theory.

As noted, the coefficients of these log-log models are elasticities. For every percentage increase in the compactness index, the walk mode share increases by 0.39 percent, the transit mode share increases by 1.15 percent, the vehicle ownership rate declines by 0.06 percent, and the average drive time declines by 0.05 percent. Based on these results, we consider the overall compactness index to be validated.

The new multidimensional compactness factors are mostly significant with the expected signs (see Table 5). The density factor, denfac, and centering factor, cenfac, are the most important correlates of walking, followed by the mix factor, mixfac. The big surprise is that the street factor is not significant and has an unexpected sign. It is widely assumed that small blocks, frequent intersections, and high street connectivity translate into greater walkability. At least in this aggregate analysis, this does not appear to be the case.

Table 5.

Relationships of Individual Compactness Factors to Transportation Outcomes.

	walkshr	transitshr	hhveh	drivetime
Constant	−11.84	−1.73	−4.04	2.62
Pop	−0.09 (−2.51)**	0.18 (3.09)***	0.03 (3.08)**	0.06 (5.69)***
Hhsize	−0.54 (−1.63)	0.86 (1.50)	0.77 (9.57)***	0.54 (5.41)***
age1524	1.25 (7.99)***	1.60 (5.91)***	0.11 (2.89)**	−0.07 (−1.56)
Male	−0.96 (−0.58)	−10.85 (−3.82)***	0.63 (1.59)	0.62 (−1.30)
White	0.63 (4.28)***	0.30 (1.20)	0.04 (1.10)	−0.13 (−3.05)**
Income	0.44 (2.77)**	2.05 (7.49)***	0.24 (6.23)***	0.32 (6.22)***
Fuel	1.92 (4.15)***	3.05 (3.80)***	−0.91 (−8.11)***	0.44 (3.31)**
Denfac	0.82 (3.69)***	0.83 (2.14)*	−0.37 (−6.94)***	−0.32 (−2.79)**
Mixfac	0.25 (2.13)**	0.60 (2.89)**	−0.14 (−4.79)***	−0.14 (−3.84)***
Cenfac	0.36 (3.81)***	0.73 (4.41)***	−0.01 (−0.52)	−0.01 (−0.25)
Strfac	−0.23 (−1.93)	0.37 (1.81)	−0.06 (−2.24)*	0.16 (4.58)***
Adjusted R²	0.605	0.743	0.564	0.578

Note: All values are log-log transformed; t statistics are in parentheses.

p < .05; **p < .01; ***p < .001.

The centering factor is also the most important correlate of transit use, followed by the density factor, street factor, and mix factor. Activities are concentrated in centers, and hence easily served by transit. All of the compactness factors are inversely related to vehicle ownership per household, although only three, the density factor, mix factor, and street factor, are statistically significant. The density factor has the strongest relationship to vehicle ownership. A dense urban environment usually offers alternatives to the automobile; the automobile has less utility in such an environment because of traffic congestion and parking problems. All of compactness factors but street connectivity have negative signs in the drive time equation. Mix and street factors are the most significant, followed by the density factor. The street factor is positively related to average drive time. This may be due to the increased wait time at intersections in a dense street network.

The four factors representing individual dimensions of sprawl have, in most cases, the expected relationships to transportation outcomes. So they have not only face and construct validity but also a measure of internal validity.

Discussion

Comparison with the Original Study

This study used the same basic methodology as Ewing, Pendall, and Chen (2002) to measure the compactness of medium and large metropolitan areas and divisions for 2010, but refined it using the most recent databases and adding new metrics. The variables used in the refined indices are either substitutes for the original variables (refinements, we would argue) or additions to fill in for omitted variables with intuitive relations to sprawl. For example, the weighted average population density of centers is a substitute, while the weighted average employment density of centers is an addition to capture the fact that some centers are “employment centers” while others are “population centers.” The same considerations apply to the other dimensions of sprawl. To population density, for example, a new variable was added, employment density. It captures a distinct dimension of the construct “density.” That is, employment is distinct from population, and both appear in the literature as measures of density. Walk Score was added to the mix factor. It captures something missing from the original mix factor, proximity to amenities. The coefficient of variation in employment densities was added to the centering factor, analogous to same variable for population density, again to fill a void. Finally, intersection density and percentage four-way intersections were added to the street factor to capture aspects of street network design missing from the Ewing index. These are the two most widely used street variables in built environment-travel literature, and were notably absent from the Ewing index.

The addition of these variables does not result in additional factors or dimensions of sprawl. We still have four: density, mix, centering, and streets. Nor does it change the essential nature of the overall compactness index, a single index for each MSA. Thus, we don’t believe the addition of a few variables adds substantially to the “complexity” of the revised indices.

For the seventy-six areas that are included in both studies, the compactness rankings are generally consistent across years. The Spearman correlation between the compactness rankings in 2000 and 2010 is 0.635, significant at the .001 probability level, which indicates, in general, that the compact areas in 2000 are found to be still compact in 2010 and the sprawling areas in 2000 are still sprawling. New York is the most compact region followed by San Francisco for both years. Atlanta is the fourth most sprawling area in 2000 and the most sprawling area of the 76 in 2010. Riverside–San Bernardino–Ontario, California, is the most sprawling in 2000 and the third most sprawling area of the 76 in 2010.

There are, however, metropolitan areas with significantly different ranking in 2010 than in 2000. One of the surprising cases is the Las Vegas–Paradise, Nevada, metropolitan area. Its ranking rises from the 30th most compact area in 2000 to the 16th in 2010 due to its high score in all four dimensions. This is consistent with Fulton et al. (2001) study that found Las Vegas is getting more compact. “Las Vegas led the nation with an increase in its metropolitan density of 50 percent, thus rising in the overall density rankings from 114th in 1982 to 14th in 1997”. (Fulton et al. 2001, 7)

Refinements in operationalizing sprawl, is another reason for differences in rankings between years. Land use mix and activity centering are the two dimensions with the most significant changes. As contributors to centering, we now consider not only central business districts (CBDs) but employment subcenters. The existence of subcenters is what distinguishes polycentric regions from monocentric regions. The Washington, D.C., metropolitan division is an example of polycentric region. As shown in Figure 2, we identified eleven subcenters (dark color) in the division. Out of seventy-six metropolitan areas, the Washington, D.C., division, indeed, has the 27th highest score for activity centering in 2010 while it had the 41st highest score in 2000. Its overall compactness ranking rises from the 52nd most compact in 2000 to the 27th most compact in 2010 because of its change on the centering score.

Figure 2.

Central business district and employment subcenters in Washington, D.C., metropolitan division.

We also standardized the unit of analysis for mix use metrics by measuring them in one-mile buffers from the centroid of block groups. Out of seventy-six areas that are included in both years, Phoenix has the 19th highest mix factor score in 2000 while it has the 24th lowest mix score in 2010. As a result, the Phoenix metropolitan area’s overall ranking drops from the 18th most compact in 2000 to the 14th most sprawling in 2010.

Finally, the changes in compactness score in some areas are due to changes in metropolitan boundaries. Out of seventy-six metropolitan areas in both samples, Detroit moved up from the 14th most sprawling in 2000 to the 5th most compact in 2010. The 2010 Detroit, Michigan, metropolitan division covers only about a fifth of the area of the 2000 Detroit PMSA. The division is mostly limited to the Detroit’s downtown and surroundings. The lowest density portions of Detroit PMSA are not included in the 2010 metropolitan division (see Figure 3). In particular, Warren–Troy–Farmington Hills, Michigan, is now its own metropolitan division, and a very sprawling one, the 20th most sprawling out of 221 metropolitan areas in 2010, at that.

Figure 3.

Detroit 2010 metropolitan division (dark) versus Detroit 2000 PMSA boundary (light).

Case Examples

In 1997, the Journal of the American Planning Association published a pair of point–counterpoint articles now listed by the American Planning Association as “classics” in the urban planning literature. In the first article, “Are Compact Cities Desirable?” Peter Gordon and Harry Richardson argued in favor of urban sprawl as a benign response to consumer preferences. In the counterpoint article, “Is Los Angeles–Style Sprawl Desirable?” Reid Ewing argued for compact cities as an alternative to sprawl. They disagreed at the time about almost everything: the characteristics, causes, and costs of sprawl, and the cures for any costs associated with sprawl.

In the original debate, Ewing challenged the notion that Los Angeles is compact, while Gordon and Richardson labeled planning initiatives in Portland a failure. The Los Angeles metropolitan division, with a new compactness index of 136.7, ranks as the 21st most compact metropolitan areas in the United States among 221 MSAs in our sample. In a parallel analysis focusing on urbanized areas, Los Angeles saw an impressive rise in its compactness ranking, from 18th in 2000 to 8th in 2010. The reason: infill development. “Contradicting metropolitan L.A.’s reputation as the capital of unbridled sprawl, roughly two-thirds of new housing built there between 2005 and 2009 was infill—constructed in previously developed areas rather than on raw land in the exurbs” (Boxall 2012). Los Angeles is certainly more compact today than suggested by Ewing in 1997.

The change in Portland’s compactness ranking is also interesting. Portland fell from the sixth most compact in 2000 to 80th in 2010 because of the boundary changes. The high ranking in 2000 applied to the Portland PMSA, basically the area subject to an urban growth boundary. The metropolitan area now includes Vancouver, Washington, and its surroundings in addition to the Portland PMSA (as shown in Figure 4). The new area is all outside the UGB.

Figure 4.

Portland metropolitan area boundary in 2010 versus Portland PMSA boundary in 2000.

Our findings show that some metropolitan areas have had more success in creating dense, mixed, and overall compact development required to support transportation choices and walkable neighborhoods as alternatives to the automobile in their communities. The following are examples of cities in metro areas that performed well on the four index factors, as well as the local public policies that contributed to their success.

Santa Barbara, California, is the fourth most compact, connected metro area nationally and has the best score among small metro areas for its land use mix factor. Several public policies have contributed to Santa Barbara’s high land use mix score. The City of Santa Barbara’s zoning codes allow residential uses in most commercial zones. Encouraging mixed use also has become a priority in the city’s 2011 General Plan Update. The update outlined three principles of development, one of which is to “encourage a mix of land uses to include strong retail and workplace centers, residential living in commercial centers with easy access to grocery stores and recreation, connectivity and civic engagement and public space for pedestrians.”

The City of Madison, Wisconsin, is the most compact, connected medium-sized metro area in the country and also has the highest score nationally for activity centering, meaning people and businesses are concentrated downtown and in subcenters. Several public policies have contributed to Madison’s high activity centering score. Madison has several homebuyer assistance programs that help residents purchase homes, many of which encourage residency downtown and reinvestment in existing housing stock. One example is the Mansion Hill—James Madison Park Neighborhood Small Cap TIF Loan Program. This program provides zero percent interest, forgivable second mortgage loans to finance a portion of the purchase price and the rehabilitation costs of a residential property located in the Mansion Hill–James Madison Park neighborhood of downtown Madison. In 2012, the City of Madison adopted a new Downtown Plan, which aims to strengthen Madison’s downtown neighborhood. The plan includes nine strategies to guide the future growth of this core neighborhood while “sustaining the traditions, history and vitality that make Madison a model city.”

Finally, in the case of Los Angeles, several public policies have contributed to Los Angeles’s high compactness score. The Los Angeles Transit Neighborhood Plans project “aims to support vibrant neighborhoods around transit stations, where people can live, work and shop or eat out, all within a safe and pleasant walk to transit stations.” Also Los Angeles’s Affordable Housing Incentives Ordinance gives developers the option to build up to 25 percent above the otherwise allowable residential density level if they include affordable housing in their project. It also reduces parking requirements and expedites the development approval process.

These public policies have helped Santa Barbara, Madison, and Los Angeles achieve high index scores. These are by no means the only policies, however, that can improve how a community is built and the quality of life for the people who live there.

We acknowledge that metropolitan areas based on county boundaries are not perfect units of analysis for defining sprawl and its impacts. However, it is clear that sprawl is ordinarily conceptualized at the metropolitan level, encompassing cities and their suburbs. When we say Atlanta sprawls badly, we are probably referring to metropolitan Atlanta, not the city of Atlanta or Fulton County. Certain phenomena are manifested at the regional or metropolitan level, such as ozone levels and racial segregation. And we have also developed and posted compactness indices for less commonly used urbanized area boundaries. Moreover, consistent with Ewing, Pendall, and Chen 2002 methodology, we excluded rural areas from our analysis. We operationalized and measured compactness only for the “urban portion” of metropolitan areas. So, it is not a sum of counties anymore. The urban portion is defined as a sum of urban census tracts in a metropolitan area. Urban census tracts are defined as census tracts with population density of hundred people per square miles or more. We also excluded rural blocks from our analysis of street connectivity.

Our indices are being made available to researchers who wish to study the causes of sprawl, costs and benefits of sprawl, and solutions to sprawl and to practitioners who wish to check their success in containing sprawl in each of its four dimensions. The literature suggests that there will be benefits as well as costs to sprawl, particularly in the areas of housing affordability and desegregation. Nothing as widely embraced by consumers as sprawl can be all bad. However, sprawl may be primarily associated with private benefits for sprawl dwellers and social costs for the rest of us. If so, it makes sense for government to intervene in the market to mitigate the latter (Ewing 1997).

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: National Institutes of Health and the Ford Foundation.

Notes

Author Biographies

Shima Hamidi is a doctoral candidate in City and Metropolitan Planning at the University of Utah. Her dissertation deals with the impact of sprawl on various aspects of quality of life.

Reid Ewing is a professor of City and Metropolitan Planning at the University of Utah. He is the director of the PhD program and Metropolitan Research Center at the university. His research focuses on the interaction of land use and transportation.

Ilana Preuss is vice president and chief of staff at Smart Growth America (SGA). She manages the communications strategy of the organization and works with staff across projects to promote SGA’s work to influence federal and state policies on smart growth issues.

Alex Dodds is Smart Growth America’s deputy director of communications. She joins the team after several years in campaign communications, most recently running online communications and media outreach for a campaign at Change to Win, a labor federation.

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