Urban Allometric Growth

Nordbeck, Stig

doi:10.1080/04353684.1971.11879355

Cited by 84 publications

(56 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Equation (2), the coefficient a 2 is called the proportionality coefficient, a measure of space standard (Nordbeck 1971), because by rearranging, Equation (2) becomes a 2 ϭ A/P b 2 , which is a ratio between land area and population size and is related to the mean population density of an urban area. In other words, the space standard is the mean reciprocal population density.…”

Section: Development Of Urban-indicators Estimation Modelsmentioning

confidence: 99%

“…In other words, the space standard is the mean reciprocal population density. The exponent b 2 , which is called the scaling factor in biol-ogy, is the most important, because it describes how the land area A in Equation (2) is scaled to the population size P. According to Nordbeck (1971), the relationship in Equation 2 displays the surface-volume constraints, based on the consideration that area has two dimensions while population has three (or a volume). As a result, the value of the exponent b should be 2/3, or 0.67.…”

Section: Development Of Urban-indicators Estimation Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Urban Indicators of China from Radiance-Calibrated Digital DMSP-OLS Nighttime Images

2002

Annals of the Association of American Geographers

142

View full text Add to dashboard Cite

in 30-arc-second grids in byte format is evaluated for its usefulness in extracting urban indicators data of China. With the aid of image-processing and Environmental Systems Research Institute's ArcView GIS software with 3-D Analysis extension, zonal variations of radiance were extracted and three-dimensional models created using Triangulated Irregular Network (TIN) functionality for thirty-five cities. Two variables were extracted from the TIN model: surface area and volume. These were used separately as independent variables in the form of an allometric growth model to estimate the following urban indicators for individual Chinese cities: nonagricultural population, gross domestic product (GDP), built-up area, and electricity consumption. The estimates obtained were checked against data supplied by the Statistical Bureau of China for 1997, the same period during which the DMSP-OLS images were acquired. It was found that urban indicators of acceptable accuracy could be obtained, provided that cities designated as Special Economic Zones (SEZs) were excluded. Volume appeared to be slightly better than surface area in estimating these urban indicators. In all cases, total nonagricultural population for all the cities combined could be very accurately estimated, indicating the usefulness of the radiance-calibrated DMSP-OLS nighttime images to determine the level of urbanization in China. The three-dimensional TIN model portrays an illuminated urban area (IUA) dome, the shape of which is affected by the internal structure of the city. The core of the city invariably exhibits the highest level of light intensity in the DMSP-OLS nighttime image. However, only a very limited amount of land-use information could be extracted. The image was also found to be useful in detecting the special urban phenomenon in China known as the extended metropolitan region, in which rural and urban uses intermixed and small towns developed. In conclusion, despite the low spatial resolution, the radiance-calibrated DMSP-OLS nighttime images are capable of providing useful demographic and socioeconomic data for cities.

show abstract

Section: Development Of Urban-indicators Estimation Modelsmentioning

confidence: 99%

Section: Development Of Urban-indicators Estimation Modelsmentioning

confidence: 99%

Urban Indicators of China from Radiance-Calibrated Digital DMSP-OLS Nighttime Images

2002

Annals of the Association of American Geographers

142

View full text Add to dashboard Cite

show abstract

“…Then, it was employed to describe the relationship between a system of cities and the largest city within the urban system (Beckmann, 1958;Carroll, 1982). From then on, a large number of works were devoted to exploring the scaling relationships between urban area and population, indicating size and shape in the growth of human communities (Batty and Longley, 1994;Chen, 2010;Lee, 1972;Lo and Welch, 1977;Longley, 1991;Nordbeck, 1971;Tobler, 1969). The empirical studies put the allometric analyses of cities in a dilemma of dimension .…”

Section: Introductionmentioning

confidence: 99%

An allometric scaling relation based on logistic growth of cities

Chen

2014

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

The relationships between urban area and population size have been empirically demonstrated to follow the scaling law of allometric growth. This allometric scaling is based on exponential growth of city size and can be termed "exponential allometry", which is associated with the concepts of fractals. However, both city population and urban area comply with the course of logistic growth rather than exponential growth. In this paper, I will present a new allometric scaling based on logistic growth to solve the abovementioned problem. The logistic growth is a process of replacement dynamics. Defining a pair of replacement quotients as new measurements, which are functions of urban area and population, we can derive an allometric scaling relation from the logistic processes of urban growth, which can be termed "logistic allometry". The exponential allometric relation between urban area and population is the approximate expression of the logistic allometric equation when the city size is not large enough. The proper range of the allometric scaling exponent value is reconsidered through the logistic process. Then, a medium-sized city of Henan Province, China, is employed as an example to validate the new allometric relation. The logistic allometry is helpful for further understanding the fractal property and self-organized process of urban evolution in the right perspective.Comment: 24 pages, 10 figures, 4 table

show abstract

“…The radial dimension based on concentric circles is to a growing monofractal what capacity dimension is to growing multifractals, while the fractal dimension based on variable urban boundaris is to a growing monofractal what correlation dimension is to growing multifractals. In fact, two kinds of allometric scaling relations between city size and shape have been researched for a long time (Batty and Longley, 1994;Bettencourt, 2013;Lee, 1989;Lo, 2002;Lo and Welch, 1977;Nordbeck, 1971). One is the longitudinal allometry of urban growth, which can be studied using time series data, and the other is the transversal allometry, or cross-sectional allometry, of urban systems, which can be studied using the rank-size series data (Chen, 2014a;Pumain and Moriconi-Ebrard, 1997).…”

Section: Discussionmentioning

confidence: 99%

“…The process of self-organizing evolution of cities follows the law of allometric scaling, which has been researched by many scientists (Arcaute et al, 2005;Batty, 2008;Batty, 2013;Batty and Longley, 1994;Bettencourt, 2013;Bettencourt et al, 2007;Chen, 2014a;Chen and Zhou, 2008;Louf and Barthelemy, 2014a;Louf and Barthelemy, 2014b;West, 2017;Luo and Chen, 2014). Allometric modeling can be utilized to describe the scaling relations between urban and rural population (Chen, 2014b;Naroll and Bertalanffy, 1956), relations between an urban system and its central city (Beckmann, 1958;Zhou, 1995), relations between urban area and population size (Batty and Longley, 1994;Lee, 1989;Lo and Welch, 1977;Nordbeck, 1971), relations between urban area and boundary (Batty and Longley, 1994;Chen, 2013), relations between different cities of an urban system (Chen and Jiang, 2009), scaling of building geometries Gould, 1971), and so on. Among all these models, the most frequent one is the urban area-population allometry, which indicates the scaling relation between size and shape in the growth of human communities.…”

Section: Introductionmentioning

confidence: 99%

Fractal dimensions derived from spatial allometric scaling of urban form

Chen

Wang

2019

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

The improved city clustering algorithm can be used to identify urban boundaries on a digital map, and the results are a set of isolines. The relationships between the urban measurements within the variable boundaries follow allometric scaling law, which indicates spatial allometry of cities. This paper is devoted to exploring the fractal dimension proceeding from urban spatial allometry. By theoretical reasoning and empirical analysis of urban traffic network, we can derive a set of fractal dimension from the spatial allometry and reveal the basic property of the new fractal parameters. The findings are as follows. First, the fractal dimension values of traffic lines are higher than those of traffic nodes. Second, the fractal dimension values based on variable boundaries are lower than those based on the concentric circles. Conclusions can be reached that the fractal dimensions coming from spatial allometry are a type of correlation dimension rather than capacity dimension, and the relative growth rate of traffic points is greater than that of traffic nodes. This study provides new way of understanding allometry, fractals, and scaling in urban systems.

show abstract

Urban Allometric Growth

Cited by 84 publications

References 3 publications

Urban Indicators of China from Radiance-Calibrated Digital DMSP-OLS Nighttime Images

Urban Indicators of China from Radiance-Calibrated Digital DMSP-OLS Nighttime Images

An allometric scaling relation based on logistic growth of cities

Fractal dimensions derived from spatial allometric scaling of urban form

Contact Info

Product

Resources

About