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Methodology for Analyzing Urban Spatial Structure
distance of the population relative to the size of the city (Galster et al. 2001). Urban fragmentation, or compactness, is a more complex phenomenon. We use two measures to capture different aspects of it: a proximity index (PI) that measures a city’s circularity without considering the intensity of land use in different parts of the city, and a clustering index (CLI) that measures the concentration of activity and people in certain areas. Details of these five measures are presented below along with their relationship to the idea of sprawl. 1. Density. The most basic measure of urban spatial structure is density. The gross density is the number of people per hectare of urbanized land or the number of jobs per hectare of urbanized land. Of course, this overall measure ignores the great variation in density within cities, but is nonetheless useful to get a sense of the intensity of land use. Population and employment density in Mexican cities are calculated using the total urban land area measure from the Cartografia Urbana for each time period as the denominator. Population and job numbers come from the corresponding Census of Population and Housing and Economic Census, and have been matched to the census tract codes in the Cartografia Urbana. Figure B.1 shows the variation in population densities for a sample of cities, contrasting the more sprawling Tlaxcala-Apizaco with more compact Orizaba. Less sprawling cities have higher densities. 2. Density gradient. Population and employment densities decline as one moves farther from the center of the city. The density gradient reflects the city’s centrality by measuring the rate at which density declines at greater distances from the city center. It stems from the standard model of urban land markets and urban structure, the monocentric city model (Alonso 1964; Mills 1967; Muth 1969). This model is based on an assumption that all employment occurs in the city center, which generates a concentration of land value and population density in the center. This obviously unrealistic assumption enables the model to reflect the fundamental importance of the access of the city center as the point most proximate to everywhere else in the city. Moreover, the model yields results that are strongly upheld in reality; almost every city in the world exhibits a strong tendency toward greater density in city centers (Bertaud and Malpezzi 2003). Because density does not decrease in a linear fashion at greater distances from the city center, the gradient is best described by a negative exponential function. This takes the form: Ds = D0*e-gs, where Ds is the density at distance s from the city center, D0 is the density at the city center, and g is the gradient. Density gradients are generally negative, thus we take their inverse. Higher values therefore indicate a steeper slope and greater monocentricity. This is illustrated in figure B.2, focusing on the cities of Cuernavaca and Zitácuaro. In Mexico, jobs are much more centralized than residential space. To get a visual sense of the shape of density gradients for jobs and people, figure B.3 presents gross population density at different distances from the city center for Aguascalientes, León, and Guanajuato, in 1990, 2000, and 2010; and figure B.4 shows the number of jobs in the same format. Jobs consistently have a much steeper density gradient than population does Mexico Urbanization Review • http://dx.doi.org/10.1596/978-1-4648-0916-3