The size distribution, scaling properties and spatial organization of urban clusters: A global and regional percolation perspective

ISPRS International Journal of Geo-Information

Volumn 5, Issue 7, 2016, Pages

  Fluschnik, Till ^a   Kriewald, Steffen ^a   Ros, Anselmo García Cantú ^a   Zhou, Bin ^a   Reusser, Dominik E ^a   Kropp, Jürgen P ^a,b   Rybski, Diego ^a  

^a POTSDAM INSTITUTE FOR CLIMATE IMPACT RESEARCH   (Germany)

^b UNIVERSITY OF POTSDAM   (Germany)

Author keywords

City clusters; Percolation; Taylor's law; Zipf's law

Indexed keywords

EID: 85009726380     PISSN: None     EISSN: 22209964     Source Type: Journal    
DOI: 10.3390/ijgi5070110     Document Type: Article

References (47)

1. Auerbach, F. Das gesetz der bevölkerungskonzentration. Petermanns Geogr. Mitt. 1913, 59, 73-76.
2. Rybski, D. Auerbach's legacy. Environ. Plan. A 2013, 45, 1266-1268.
3. Zipf, G.K. Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology (Reprint of 1949 Edition); Martino Publishing: Mansfield, CT, USA, 2012.
4. Gibrat, R. Les Inégalités Économiques; Libraire du Recueil Sierey: Paris, France, 1931.
5. Simon, H.A. On a class of skew distribution functions. Biometrika 1955, 42, 425-440.
6. Makse, H.A.; Andrade, J.S.; Batty, M.; Havlin, S.; Stanley, H.E. Modeling urban growth patterns with correlated percolation. Phys. Rev. E 1998, 58, 7054-7062.
7. Gabaix, X. Zipf's law for cities: An explanation. Q. J. Econ. 1999, 114, 739-767.
8. Rybski, D.; Ros, A.G.C.; Kropp, J.P. Distance weighted city growth. Phys. Rev. E 2013, 87, 042114.
9. Eeckhout, J. Gibrat's law for (All) cities. Am. Econ. Rev. 2004, 94, 1429-1451.
10. Kriewald, S.; Fluschnik, T.; Reusser, D.; Rybski, D. OSC: Orthodromic Spatial Clustering, R package version 1.0.0. Available online: https://CRAN.R-project.org/package=osc (accessed on 7 April 2011).
11. Rozenfeld, H.D.; Rybski, D.; Andrade, J.S., Jr.; Batty, M.; Stanley, H.E.; Makse, H.A. Laws of population growth. Proc. Natl. Acad. Sci. USA 2008, 105, 18702-18707.
12. Stauffer, D.; Aharony, A. Introduction To Percolation Theory; Taylor & Francis: London, UK, 1994.
13. ESA (European Space Agency). The Ionia GlobCover Project. GlobCover Land Cover 2009 v2.3. Available online: http://ionia1.esrin.esa.int (accessed on 21 August 2011).
14. Center for International Earth Science Information Network (CIESIN), Columbia University; International Food Policy Research Institute (IFPRI), The World Bank; Centro Internacional de Agricultura Tropical (CIAT). Global Rural-Urban Mapping Project, Version 1 (GRUMPv1): Settlement Points. Website, 2011. Available online: http://sedac.ciesin.columbia.edu/data/dataset/grump-v1-settlement-points (accessed on 26 November 2011).
15. Rozenfeld, H.D.; Rybski, D.; Gabaix, X.; Makse, H.A. The area and population of cities: New insights from a different perspective on cities. Am. Econ. Rev. 2011, 101, 2205-2225.
16. Zanette, D.H.; Manrubia, S.C. Role of intermittency in urban development: A model of large-scale city formation. Phys. Rev. Lett. 1997, 79, 523-526.
17. Batty, M. The size, scale, and shape of cities. Science 2008, 319, 769-771.
18. Schweitzer, F.; Steinbrink, J. Estimation of megacity growth-Simple rules versus complex phenomena. Appl. Geogr. 1998, 18, 69-81.
19. Kinoshita, T.; Kato, E.; Iwao, K.; Yamagata, Y. Investigating the rank-size relationship of urban areas using land cover maps. Geophys. Res. Lett. 2008, 35, L17405.
20. Arcaute, E.; Hatna, E.; Ferguson, P.; Youn, H.; Johansson, A.; Batty, M. Constructing cities, deconstructing scaling laws. J. R. Soc. Interface 2014, 12, 20140745.
21. Small, C.; Elvidge, C.D.; Balk, D.; Montgomery, M. Spatial scaling of stable night lights. Remote Sens. Environ. 2011, 115, 269-280.
22. Bunde, A.; Havlin, S., Eds. Fractals and Disordered Systems; Springer-Verlag: New York, NY, USA, 1991.
23. Berry, B.J.L.; Okulicz-Kozaryn, A. The city size distribution debate: Resolution for US urban regions and megalopolitan areas. Cities 2012, 29, S17-S23.
24. Makse, H.A.; Havlin, S.; Stanley, H.E. Modeling urban-growth patterns. Nature 1995, 377, 608-612.
25. Bitner, A.; Holyst, R.; Fialkowski, M. From complex structures to complex processes: Percolation theory applied to the formation of a city. Phys. Rev. E 2009, 80, 037102.
26. Murcio, R.; Sosa-Herrera, A.; Rodriguez-Romo, S. Second-order metropolitan urban phase transitions. Chaos Soliton Fract. 2013, 48, 22-31.
27. Arcaute, E.; Molinero, C.; Hatna, E.; Murcio, R.; Vargas-Ruiz, C.; Masucci, P.; Batty, M. Regions and Cities in Britain through Hierarchical Percolation. Available online: http://arxiv.org/abs/1504.08318v2 (accessed on 10 July 2016).
28. Clauset, A.; Shalizi, C.R.; Newman, M.E.J. Power-Law distributions in empirical data. SIAM Rev. 2009, 51, 661-703.
29. Vuong, Q.H. Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 1989, 57, 307-333.
30. Stanley, H.E. Scaling, universality, and renormalization: Three pillars of modern critical phenomena. Rev. Mod. Phys. 1999, 71, S358-S366.
31. Taylor, L.R. Aggregation, variance and mean. Nature 1961, 189, 732-735.
32. Smith, H.F. An empirical law describing heterogeneity in the yields of agricultural crops, Part: 1. J. Agric. Sci. 1938, 28, 1-23.
33. de Menezes, M.A.; Barabasi, A.L. Fluctuations in network dynamics. Phys. Rev. Lett. 2004, 92, 028701.
34. Eisler, Z.; Bartos, I.; Kertész, J. Fluctuation scaling in complex systems: Taylor's law and beyond. Adv. Phys. 2008, 57, 89-142.
35. Bates, D.M.; DebRoy, S. R-Documentation: Nonlinear Least Squares. Available online: http://stat.ethz.ch/R-manual/R-patched/library/stats/html/nls.html (accessed on 7 April 2011).
36. Weinrib, A. Long-range correlated percolation. Phys. Rev. B 1984, 29, 387-395.
37. Prakash, S.; Havlin, S.; Schwartz, M.; Stanley, H.E. Structural and dynamic properties of long-range correlated percolation. Phys. Rev. A 1992, 46, R1724-R1727.
38. Bettencourt, L.;West, G. A unified theory of urban living. Nature 2010, 467, 912-913.
39. Batty, M. Defining city size. Environ. Plan. B-Plan. Des. 2011, 38, 753-756.
40. Rybski, D.; Reusser, D.E.;Winz, A.L.; Fichtner, C.; Sterzel, T.; Kropp, J.P. Cities as nuclei of sustainability? Environ. Plan. B 2016, doi:10.1177/0265813516638340.
41. Sutton, P.; Roberts, D.; Elvidge, C.; Baugh, K. Census from Heaven: An estimate of the global human population using night-Time satellite imagery. Int. J. Remote Sens. 2001, 22, 3061-3076.
42. Potere, D.; Schneider, A.; Angel, S.; Civco, D.L. Mapping urban areas on a global scale: which of the eight maps now available is more accurate? Int. J. Remote Sens. 2009, 30, 6531-6558.
43. Zhou, B.; Rybski, D.; Kropp, J.P. On the statistics of urban heat island intensity. Geophys. Res. Lett. 2013, 40, 5486-5491.
44. Jefferson, M. The law of the primate city. Geogr. Rev. 1939, 29, 226-232.
45. Arcaute, E.; Hatna, E.; Ferguson, P.; Youn, H.; Johansson, A.; Batty, M. Constructing cities, deconstructing scaling laws. J. R. Soc. Interface 2014, 12, 20140745.
46. Pisarenko, V.F.; Sornette, D. Robust statistical tests of Dragon-Kings beyond power law distributions. Eur. Phys. J. Spec. Top. 2012, 205, 95-115.
47. Pumain, D.; Moriconi-Ebrard, F. City size distributions and metropolisation. GeoJournal 1997, 43, 307-314.