Title: Zastosowanie wskaźników koncentracji przestrzennej w badaniu procesów urban sprawl* = Application of spatial concentration indicators in the studies of urban sprawl processes


Sudra, Paweł

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Article : original article


Przegląd Geograficzny T. 88 z. 2 (2016)



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24 cm


This article reviews selected indicative methods allowing for analysis of the concentration and dispersion of settlement. A further aim is to evaluate the utility of these measures in studying the spontaneous process of suburbanisation known as “urban sprawl”. Following the model of the “dispersed city”, as opposed to the “compact city”, it is assumed that urban sprawl is associated with scattering of development. It is therefore reasonable to assume that spatial concentration indicators will allow for the at least partial description of its physiognomy. Urban sprawl is described as a multi-dimensional spatial phenomenon related to metropolitan deconcentration. Three fundamental spatial forms are observed: lowdensity sprawl, ribbon sprawl and leapfrog sprawl. Thereafter, issues are described in relation to the nature of the spatial dispersion and diffusion, the influence of centripetal and centrifugal forces, and the occurrence of the modified areal unit problem (MAUP), in the analysis of urbanisation. The four different measures chosen for actual review were the Gini coefficient, the C index of B. Kostrubiec, the average nearest neighbour method (Clark-Evans index) and Shannon entropy. Each of the indicators is analysed, with account taken of its theoretical and mathematical underpinnings, the adopted understanding of the spatial concentration concept, the impact of the delimitation of basic units on the results of spatial analyses, and available methods by which results may be presented. The Gini coefficient, based on the Lorenz curve, and initially used in econometrics, determines the cumulated concentration of features within a smaller or larger number of spatial units. It measures the unevenness of spatial distribution, but does not consider the mutual location of the basic units. A further limitation of this indicator in studying urban sprawl is that it takes no account of the precise locations of the objects. The spatial concentration index C, as proposed by B. Kostrubiec, is a measure of the concentration or dispersion of a set of elements – on a scale between concentration at one point and a spread across the maximum distance (range) it is possible to achieve within the boundaries of a certain area. The indicator is rarely used, but is of clear applicability, given the way it allows additional statistical parameters based on marginal distributions to be calculated. The average nearest neighbour method (Clark-Evans index), as derived from ecology, is widely known and applied in urbanisation studies. It allows for observation of the attractive forces associated with the locating of buildings and other new developments. This indicator resembles the previous one in combining recognition of the level of dispersion and the randomness of a set of features. Shannon entropy is a probabilistic measure of “disorder” and – in geography – a measure of segregation, the spatial organisation of an area, or, most simply, the proportion of the share of a phenomenon in territorial units. Entropy defines fragmentation or the filling of terrain with settlement. It is often used in researching land use and land cover change. This article concludes with a table describing the main features of the four indicators. Methods of multidimensional analysis of urban sprawl are also highlighted. These are important because the morphology of sprawl cannot be defined solely by reference to the degree of spatial concentration, which is understood and defined in various ways. Other important spatial dimensions include density, continuity, clustering, centralisation or the mixed use of land. In the author’s view, the most comprehensive assessment of the phenomenon of sprawl will be made possible if several methods are selected, and parallel analyses carried out using them. In these circumstances, complementary information will be obtained as regards the concentration and dispersion of development in an area.


1. Aguilera F., Valenzuela L.M., Botequilha-Leitao A., 2011, Landscape metrics in the analysis of urban land use patterns: A case study in a Spanish metropolitan area, Landscape and Urban Planning, 99, 3, s. 226-238. ; - ; 2. Alonso-Villar O., 2011, Measuring concentration: Lorenz curves and their decompositions, The Annals of Regional Science, 47, 2, s. 451-475. ; - ; 3. Arbia G., Espa G., Giuliani D., 2015, Analysis of spatial concentration and dispersion [w:] C. Karlsson, M. Andersson, T. Norman (red.), Handbook of Research Methods and Applications in Economic Geography, Edward Elgar Publishing, Cheltenham, s. 135-157. ; 4. Batty M., 1974, Spatial entropy, Geographical Analysis, 6, 1, s. 1-31. ; - ; 5. Batty M., Chin N., Besussi E., 2002, State of the Art Review of Urban Sprawl Impacts and Measurement Techniques. Deliverable Report D1, SCATTER, European Commission, www.casa.ucl.ac.uk/scatter/download/Scatter_D1.pdf (5.03.2016) ; 6. Boots B., Getis A., 1988, Point Pattern Analysis, Sage University Paper Series on Quantitative Applications in the Social Sciences, series 07–001, Sage Publications. ; 7. Broitman D., Czamanski D., 2012, Cities in competition, characteristic time, and leapfrogging developers, Environment and Planning B: Planning and Design, 39, 6, s. 1105-1118. ; - ; 8. Cabral P., Augusto G., Tewolde M., Araya Y., 2013, Entropy in urban systems, Entropy, 15, 12, s. 5223-5236. ; - ; 9. Carruthers J. I., Ulfarsson G. F., 2003, Urban sprawl and the cost of public services, Environment and Planning B, 30, 4, s. 503-522. ; - ; 10. Chilczuk M., 1975, Osadnictwo wiejskie: metody badań koncentracji zabudowy i kształtów wsi, PWN, Warszawa. ; 11. Chin N., 2002, Unearthing the roots of urban sprawl: a critical analysis of form, function and methodology, CASA Working Papers 47, Centre for Advanced Spatial Analysis (UCL), London. ; 12. Chojnicki Z. Czyż T., 1989, Charakterystyka małych miast regionu poznańskiego a koncepcja kontinuum miejsko-wiejskiego [w:] P. Korcelli, A. Gawryszewski (red.), Współczesne przemiany regionalne systemów osadniczych w Polsce, Prace Geograficzne, IGiPZ PAN, 152, Warszawa, s. 139-157. ; 13. Clark P.J., Evans F.C., 1954, Distance to nearest neighbor as a measure of spatial relationships in population, Ecology, 35, 4, s. 445-453. ; - ; 14. Colby C., 1933, Centrifugal and centripetal forces in urban geography, Annals of the Association of American Geographers, 23, s. 1-20. ; - ; 15. Curry L., 1964, The random economy: An exploration in settlement theory, Annals of the Association of American Geographers, 54, s. 138-146. ; - ; 16. Dacey M.F., 1962, Analysis of central place and point patterns by nearest neighbour method, Land Studies in Geography, Ser. B, 24, s. 55-75. ; 17. Dieleman F., Wegener M., 2004, Compact city and urban sprawl, Built Environment, 30, 4, s. 308-323. ; - ; 18. Donnelly K.P., 1978, Simulations to determine the variance and edge effect of total nearest neighbour distance, [w:] I. Hodder (red.), Simulation Methods in Archaeology, Cambridge University Press, s. 91-95. ; 19. Duncan O.D., Cuzzort R.P., Duncan B., 1961, Statistical Geography: Problems in Analyzing Areal Data, Free Press (Macmillan), New York. ; 20. Dziewoński K., 1987, Strefa podmiejska – próba ujęcia teoretycznego, Przegląd Geograficzny, 59, 1-2, s. 55-63. ; 21. Ebdon D., 1985, Statistics in Geography, Blackwell, Oxford, 2 wyd. ; 22. Ewing R., 1997, Is Los Angeles-style sprawl desirable?, Journal of the American Planning Association, 63, 1, s. 107-126. ; - ; 23. Ewing R., Hamidi S., 2014, Measuring Sprawl 2014, Smarth Growth America. ; 24. Franz G., Maier G., Schröck P., 2006, Urban Sprawl – How Useful is this Concept?, ERSA Conference Papers, 105, European Regional Science Association. ; 25. Frenkel A., Orenstein D., 2011, A pluralistic approach to defining and measuring urban sprawl, [w:] X. Yang (red.), Urban Remote Sensing: Monitoring, Synthesis and Modeling in the Urban Environment, Wiley-Blackwell, Chichester. ; 26. Galster G., Hanson R., Ratcliffe M., Wolman H., Coleman S., Freihage J., 2001, Wrestling Sprawl to the Ground: Defining and measuring an elusive concept, Housing Policy Debate, 12, 4, s. 681-717. ; - ; 27. Gehlke C. E., Biehl K., 1934, Certain effects of grouping upon the size of the correlation coefficient in census tract material, Journal of the American Statistical Association, 29, 185A, s. 169-170. ; - ; - ; 28. Getis A., 1964, Temporal analysis of land use patterns with the use of nearest neighbor and quadrat methods, Annals of the Association of American Geographers, 54, s. 391-3998. ; - ; 29. Ghani N.L.A., Abidin S.Z., Khalid N.E.A., 2014, Urban sprawl shape description, Malayasian Journal of Computing, 2, 1, s. 27-36. ; 30. Gini C., 1912, Variabilità e mutabilità, Studi economico-giuridici pubblicati per cura della Facoltà di Giurisprudenza della Regia Università di Cagliari, Anno III, parte 2. ; 31. Golachowski S., Kostrubiec B., Zagożdżon A., 1974, Metody badań geograficzno-osadniczych, PWN, Warszawa. ; 32. Haedo C., Mouchart M., 2011, A Stochastic Independence Approach for Different Measures of Global Specialization, Institut de Statistique, Biostatistique et Sciences Actuarielles (ISBA), Discussion Paper 2011/06, Université catholique de Louvain. ; 33. Jażdżewska I., 1999, Przemiany funkcjonalne i morfologiczne przestrzeni geograficznej wsi Rzgów w świetle metod numerycznych, Szlakami Nauki, 28, Łódzkie Towarzystwo Naukowe, Łódź.3 ; 34. Jażdżewska I., 2008, Przemiany miejskiej sieci osadniczej w Polsce w świetle metod matematycznych, Wydawnictwo Uniwersytetu Łódzkiego, Łódź. ; 35. Kostrubiec B., 1971, Analiza matematyczna zbioru osiedli województwa opolskiego, [w:] S. Golachowski (red.), Struktury i procesy osadnicze, Instytut Śląski, Opole-Wrocław. ; 36. Kostrubiec B., 1972, Analiza zjawisk koncentracji w sieci osadniczej – problemy metodyczne, Prace Geograficzne, IG PAN, 93, Warszawa. ; 37. Kostrubiec B., 1977, Metody badania koncentracji przestrzennej, [w:] Z. Chojnicki (red.), Metody ilościowe i modele w geografii, PWN, Warszawa, s. 63-76. ; 38. Kwan M-P., Weber J., 2008, Scale and accessibility: Implications for the analysis of land use–travel interaction, Applied Geography, 28, s. 110-123. ; - ; 39. Lang R., Sanchez T., LeFurgy J., 2006, Beyond Edgeless Cities: Office Geography in the New Metropolis, Virginia Tech, National Center for Real Estate Research, Blacksburg. ; 40. Li C., Li J., Wu J., 2013, Quantifying the speed, growth modes, and landscape pattern changes of urbanization: a hierarchical patch dynamics approach, Landscape Ecology, 28, s. 1875-1888. ; - ; 41. Lisowski A., Grochowski M., 2009, Procesy suburbanizacji. Uwarunkowania, formy, konsekwencje, [w:] Ekspertyzy do Koncepcji Przestrzennego Zagospodarowania Kraju 2008-2033, 1, Ministerstwo Rozwoju Regionalnego, Warszawa, s. 221-280. ; 42. Lorenz M.O., 1905, Methods of measuring the concentration of wealth, Publications of the American Statistical Association, 9, 70, s. 209-219. ; - ; 43. Majid M.R., Yahya H., 2010, Sprawling of a Malaysian city: What type and what solutions?, [w:] J.G. Teng (red.), Proceedings of the First International Conference on Sustainable Urbanization (ICSU 2010), 15-17 XII 2010 Hong Kong, Hong Kong Polytechnic University. ; 44. McGarigal K., Marks B.J., 1995, FRAGSTATS. Spatial pattern analysis program for quantifying landscape structure, General Technical Report PNW-GTR-351, US Department of Agriculture, Forest Service, Pacific Northwest Research Station. ; 45. McKenzie R.D., 1926, The Scope of Human Ecology, 20th Annual Meeting, 1925, Paper and Proceedings, 20, American Sociological Society, Washington D.C., s. 141-154. ; 46. Miedviedkov J.V., 1966, Regularnaja komponenta v sietach rassielenija izobrazennych na kartie, Izviestia AN SSSR, Seria Gieografičeskaja, 4, s. 110-122. ; 47. Mitchell A., 2005, The ESRI Guide to GIS Analysis, 2, ESRI Press, Redlands, CA. ; 48. Openshaw S., 1983, The Modifiable Areal Unit Problem, Geo Books, Norwich, UK. ; 49. Shannon C.E., 1948, A mathematical theory of communication, Bell System Technical Journal, 27, s. 379-423, 623-656. ; - ; - ; 50. Song Y., Qiu Q., Guo Q., Lin J., Li F., Yu Y., Li X., Tang L., 2010, The application of spatial Lorenz curve (SLC) and Gini coefficient in measuring land use structure change, [w:] The 18th International Conference on Geoinformatics: GIScience in Change, 18-20 VI 2010, Beijing University, Beijing, s. 1-5. ; 51. Soule D.C. (red.), 2006, Urban Sprawl – a Comprehensive Reference Guide, Greenwood Press, London. ; 52. Squires G.D. (red.), 2002, Urban Sprawl: Causes, Consequences and Policy Responses, Urban Institute Press, Washington D.C. ; 53. Steinhaus H., 1947, O wskaźniku zagęszczenia i rozproszenia, Przegląd Geograficzny, 21, 1-2, s. 1-3. ; 54. Stępniak M., 2014, Przekształcenia przestrzennego rozmieszczenia zasobów mieszkaniowych w Warszawie w latach 1945-2008, Prace Geograficzne, IGiPZ PAN, 245, Warszawa. ; 55. Straszewicz L., 1985, Strefa podmiejska. Pojęcia i definicje, Folia Geographica, 5, Acta Universitatis Lodziensis, s. 7-16. ; 56. Szmytkie R., 2014, Metody analizy morfologii i fizjonomii jednostek osadniczych, Rozprawy Naukowe Instytutu Geografii i Rozwoju Regionalnego, 35, Uniwersytet Wrocławski, Wrocław. ; 57. Śleszyński P. (red.), 2013, Wskaźniki zagospodarowania i ładu przestrzennego w gminach, Biuletyn KPZK PAN, 252, Warszawa. ; 58. Theil H., 1967, Economics and Information Theory, North-Holland, Amsterdam. ; 59. Thomas R.W., 1981, Information Statistics in Geography, Geo Abstracts, University of East Anglia, Norwich, UK. ; 60. Torrens P.M., Alberti M., 2000, Measuring Sprawl, CASA Working Paper 27, Centre for Advanced Spatial Analysis (UCL), London. ; 61. Uhorczak F., 1932, Z metodyki badań nad osadnictwem, Czasopismo Geograficzne, 10, 1-3, s. 11-28. ; 62. Verzosa L.C.O., Gonzalez R.M., 2010, Remote sensing, geographic information systems and Shannon's entropy: measuring urban sprawl in a mountainous environment, [w:] W. Wagner, B. Székely (red.), ISPRS TC VII Symposium – 100 Years ISPRS, Vienna, Austria, 5-7 VII 2010, IAPRS, 38, Part 7A. ; 63. Wędrowska E., 2010, Wykorzystanie entropii Shannona i jej uogólnień do badania rozkładu prawdopodobieństwa zmiennej losowej dyskretnej, Przegląd Statystyczny, 57, 4, s. 39-53. ; 64. Wong D.W.S., Lasus H., Falk R.F., 2009, Exploring the variability of segregation index D with scale and zonal systems an analysis of thirty US cities, Environment and Planning A, 31, s. 507-522. ; - ; 65. Yeh A.G.O., Li X., 2001, Measurement and monitoring of urban sprawl in a rapidly growing region using entropy, Photogrammetry and Remote Sensing, 67, 1, s. 83-90. ; 66. Zierhoffer A., 1934, Pewien wzór na określenie stopnia rozproszenia i skupienia osiedli wiejskich, [w:] H. Arctowski (red.), Zbiór prac poświęconych przez Towarzystwo Geograficzne we Lwowie Eugeniuszowi Romerowi w 40-lecie jego twórczości naukowej, Towarzystwo Geograficzne, Lwów, s. 488-494.


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