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

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.