Abstract
Since the mid-twentieth century, most cities worldwide have undergone a rapid expansion in urban land use. Along with the expansion, several problems, such as excessive loss of prime agricultural land and increasing traffic congestion have arisen. Thus, understanding and measurements of the expansion scale and its speed are crucial to planners and officials during urban planning and management processes. To measure such geographic phenomena, Shannon first devised entropy theory, and then Batty developed it into spatial entropy. The recently developed spatial entropy model, which was used to measure urban sprawl, introduced area to represent spatial asymmetry. However, most models did not consider spatial discretization, particularly the impact of distance. This study attempted to construct an integrated gravity-spatial entropy model to delineate distance and spatial diffusion impacts on population distribution. Then, we tested the model using Shanghai’s temporal land use and community statistical data. Application results for the new gravity-spatial model show that it is a useful tool for identifying spatial and temporal variations of urban sprawl.
Similar content being viewed by others
References
Aguilera A, Ugalde E. 2014. Graph entropy as tool for understanding complex urban networks. The case of Ensenada city, Mexico. Int J Soc Syst Sci, 6: 87–99
Bao T F, Peng Y, Cong P J, Wang J L. 2010. Analysis of crack propagation in concrete structures with structural information entropy. Sci China Tech Sci, 53: 1943–1948
Batty M. 1974. Spatial entropy. Geogr Anal, 6: 1–31
Batty M. 2010. Space, scale, and scaling in entropy maximizing. Geogr Anal, 42: 395–421
Besussi E, Chin N. 2003. Identifying and measuring urban sprawl. In: Longley P A, Batty M, eds. Advanced Spatial Analysis: The CASA Book of GIS. Redlands, CA: ESRI Press. 109–128
Brueckner J K. 2000. Urban sprawl: Diagnosis and remedies. Int Region Sci Rev, 23: 160–171
Brueckner J K, Mills E, Kremer M. 2001. Urban sprawl: Lessons from urban economics. In: Burtless G, Pack J R, eds. Brookings-Wharton Papers on Urban Affairs. Washington DC: Brookings Institution Press. 65–97
Brunner A. 2013. The effects of urban sprawl on daily life: Smart growth implementation of Atlantic station. In: Transportation Research Board 92nd Annual Meeting
Carlesi S, Bocci G, Moonen A C, Frumento P, Bàrberi P. 2013. Urban sprawl and land abandonment affect the functional response traits of maize weed communities in a heterogeneous landscape. Agric, Ecosyst Environ, 166: 76–85
Carruthers J I, Ulfarsson G F. 2002. Fragmentation and sprawl: Evidence from interregional analysis. Growth Change, 33: 312–340
Ewing R. 1997. Is Los Angeles-style sprawl desirable? J Am Plan Assoc, 63: 107–126
Ewing R, Pendall R, Chen D. 2002. Measuring sprawl and its impact: The character and consequences of metropolitan expansion. Washington DC: Smart Growth America
Frenkel A, Ashkenazi M. 2008. Measuring urban sprawl: How can we deal with it? Environ Plan B Plan Design, 35: 56
Hasse J E, Lathrop R G. 2003. Land resource impact indicators of urban sprawl. Appl Geogr, 23: 159–175
James P, Troped P J, Hart J E, Joshu C E, Colditz G A, Brownson R C, Ewing R, Laden F. 2013. Urban sprawl, physical activity, and body mass index: Nurses’ health study and nurses’ health study II. Am J Pub Health, 103: 369–375
Jiang F, Liu S H, Yuan H, Zhang Q. 2007. Measuring urban sprawl in Beijing with geo-spatial indices. J Geogr Sci, 17: 469–478
Miao S, Dou J, Chen F, Li J, Li A. 2012. Analysis of observations on the urban surface energy balance in Beijing. Sci China Earth Sci, 55: 1881–1890
Mills E S. 1970. Urban density functions. Urban Stud, 7: 5–20
Mogridge M J. 1972. The use and misuse of entropy in urban and regional modelling of economic and spatial systems. TRID
Ottensmann J R. 1977. Urban sprawl, land values and the density of development. Land Econ, 53: 389–400
Pooler J. 1983. Information theoretic methods of spatial model building: A guide to the unbiased estimation of the form of probability distributions. Socio-Econ Plan Sci, 17: 153–164
Rooij M. 2008. The analysis of change, Newton’s law of gravity and association models. J Roy Stat Soc A Sta, 171: 137–157
Ruan B F, Wu H R. 2015. Urban sustainable development capacity evaluation model research and application based on entropy and distance functions. In: 2015 International Symposium on Computers & Informatics
Shannon C E, Weaver W, Blahut R E, Hajek B. 1949. The Mathematical Theory of Communication. Urbana: University of Illinois Press. 117
Singh B. 2014. Urban growth using Shannon’s Entropy: A case study of Rohtak city. Int J Adv Remote Sens GIS, 3: 544–552
Solecki W, Seto K C, Marcotullio P J. 2013. It’s time for an urbanization science. Environ Sci Policy Sust Dev, 55:12–17
Sun X L, Jia L M, Dong H H, Qin Y, Guo M. 2010. Urban expressway traffic state forecasting based on multimode maximum entropy model. Sci China Tech Sci, 53: 2808–2816
Sutton P C. 2003. A scale-adjusted measure of “urban sprawl” using nighttime satellite imagery. Remote Sens Environ, 86: 353–369
Tan M H, Li X B, Lu C H. 2005. Urban land expansion and arable land loss of the major cities in China in the 1990s. Sci China Ser D-Earth Sci, 48: 1492–1500
Theil H, Finizza A J. 1971. A note on the measurement of racial integration of schools by means of informational concepts. J Math Sociol, 1: 187–193
Thomas R W. 1981. Information statistics in geography. Norwich: Geo Abstracts
Tolman R C, Fine P C. 1948. On the irreversible production of entropy. Rev Modern Phys, 20: 51
Wang F H, Guldmann J M. 1996. Simulating urban population density with a gravity-based model. Socio-Econ Plan Sci, 30: 245–256
Wilson A. 2010. Entropy in urban and regional modelling: Retrospect and prospect. Geogr Anal, 42: 364–394
Wu J, Guo Z Y. 2010. An exploration for the macroscopic physical meaning of entropy. Sci China Techn Sci, 53: 1809–1816
Wu Z J, Hu M, Yue D L, Wehner B, Wiedensohler A. 2011. Evolution of particle number size distribution in an urban atmosphere during episodes of heavy pollution and new particle formation. Sci China Earth Sci, 54: 1772–1778
Xia G, Zhai Y, Cui Z. 2013. Characteristics of entropy generation and heat transfer in a microchannel with fan-shaped reentrant cavities and internal ribs. Sci China Tech Sci, 56: 1629–1635
Yeh A G O, Li X. 2001. Measurement and monitoring of urban sprawl in a rapidly growing region using entropy. Photogramm Eng Remote Sens, 67: 83–90
Yue W Z, Liu Y, Fan P L. 2013. Measuring urban sprawl and its drivers in large Chinese cities: The case of Hangzhou. Land Use Policy, 31: 358–370
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, J., Qiu, R., Xiong, L. et al. A gravity-spatial entropy model for the measurement of urban sprawl. Sci. China Earth Sci. 59, 207–213 (2016). https://doi.org/10.1007/s11430-015-5192-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11430-015-5192-5