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Petrisor AI. Geostatistical metods for the analysis of territorial systems. 2011.

Abstract: This paper originates in the hypothesis according to which the methodological transfer of instruments used to analyze ecological systems to the analysis of territorial systems is possible and beneficial. In order to test the hypothesis, the research process was organized according to the following objectives: (1) in order to provide a theoretical foundation of the transfer, the concept of "territorial system" is analyzed in detail and compared with similar concepts from ecology (discipline used as the origin of statistical methods) and spatial planning; (2) the instruments used in the analysis of territorial systems are critically reviewed, underlining their lacks and limitations; (3) statistical methods potentially usable to analyze the territorial systems are presented, focusing on those already used in ecology; (4) the transfer consists of several diverse case studies, carried out as much as possible at different spatial scales, and (5) the results of all previous stages are analyze to derive general conclusions, as well as a hierarchy of the methods and an algorithm for using the instruments.

Analyses of the "territorial system" concept show that it is merely an objective reality, rather than a theoretical construct. According to the general definition of systems, it is a functioning structure. The structure consists of elements interrelated such that common goals can be achieved. The elements are natural and anthropic; their share allows for a structural differentiation of predominantly natural territorial systems from those strongly anthropized. The properties characteristic to the territorial systems include the openness, universality, integrality expressed by coherence and synergy, self-regulation and self-control, complexity including variable geometry subjected to the fractal character and oneness, dynamic equilibrium governed by causality and characterized by resistance to change, functionality and organization. For the urban systems, there are several additional characteristics: hierarchy, centrality, specialization, and primacy. The dynamics of territorial systems is governed by natural laws aiming towards the natural equilibrium in natural subsystems and by the human species in the anthropic ones, through structuring interventions based on the mental projection of the socioeconomic objectives of communities and resulting from ordering the objects from the space managed by these communities. The dynamics are explained by theories of localization (Thünen's rings, Alfred Weber's theory of rational localization), models of development (Jean Fourastié's model, Walter Christaller's theory of central places), theories of growth (the neoclassic theory of regional growth, the post-keynesian theory, the theory of the base of exports explaining regional growth, theories of economic stages, theories of growth poles and centers, the theory of the process of diffusion of innovation, the theory of life cycle, the theory of long waves and chronological cycles of life), modern morphological theories (the theory of catastrophes, the theory of urban shape, the theory of fractals, the theory of dissipative structures, the theory of chaos). Economic influences are explained by the theory of urban attraction, the theory of urban economic base, the theory of spatial diffusion, the theory of dominance). Urban dynamics relies on models such as the catastrophic models, Lotka-Volterra model, Forrester's model, master equation model, Leeds or Brussels models.

The critical analysis of applying the systemic reasoning to identify the base units in geography, ecology, and spatial planning indicates that based on the spatial scale, components, and key properties, the hierarchies of ecological, geographical, and spatial systems can easily be paralleled. On the one hand, the analysis confirms once again that territorial systems represent an objective reality, with clear delimitations of the whole and its components and well defined properties, and on the other hand it reveals differences between the analyzed disciplines, with two consequences. First, the same territorial reality is perceived differently, and second, common terms could coin different territorial objects. Despite of the differences, correspondences can be made, especially based on the spatial scale of each hierarchical level. In this context, it has to be stressed out that each discipline does not distinguish a single system, but an entire hierarchy where the complexity of each level increases with its spatial scale, even though some key properties are preserved. Among the properties characteristic to the systems defined by the three disciplines analyzed, a very important role is played by the diversity (variety, heterogeneity). If acknowledging that the ecodiversity includes biodiversity and overlaps with geodiversity, it can be argued that during the dynamics of anthropization biodiversity decreases while geodiversity increases with the degree of anthropization. The explanation resides in the consumption of natural resources, appreciated using the concept of primary eco-energy. Furthermore, the systemic analysis reveals differences between the natural dynamics, subject to natural laws, such as the older theory of successional cycles or the newer one based on adaptive cycles in ecology, and the one determined by the influence of anthropic factors. The harmonization between natural and man-driven dynamics is conceptually achieved by the notion of "sustainable development", which has also an important spatial dimension. The dynamics of anthropized and anthropic systems is mainly determined by socioeconomic and political factors.

The analysis of instruments used to analyze the territorial systems indicates that the common features of all these methods are their subjectivity and the fact that they are purely qualitative or semi-quantitative, meaning that they record general trends of phenomena, without allowing for testing causal hypotheses. Subjectivity is manifested directly (e.g., non-quantitative description is purely subjective, but even the quantitative one is influenced by the availability of data, by the manner of interpreting them without an "universal" statistical method), as well as indirectly (SWOT or LFA analyses, even though they have a sequential algorithm, depend on the characteristics of the research team, available information, and contextual priorities). Moreover, the analysis reveals the existence of a methodological transfer among disciplines; a good example is offered by the application of statistical methods to biology, resulting into a new discipline - biostatistics. The transfer of methods from and to geography resulted into new sciences - space science, GIScience; their applications expand beyond the limits of geography into other disciplines. Furthermore, concepts of physics, biology, and ecology had been transferred to geography; some of them substantiate the theories explaining the organization and dynamics of territorial systems.

The inventory of statistical methods allows for establishing a hierarchy starting from the descriptive ones, aiming to present without explaining the essence of population data, to the entire arsenal of inductive statistics, extrapolating information obtained from the analysis of sample data to the entire population through the statistical inference. Accounting that the progress of science is made verifying hypotheses and theories through the study of samples, yielding uncertain results, their generalization would be impossible without the use of statistical methods, since it would lack the quantitative appreciation (measurement) of the degree of uncertainty. Moreover, the usage of statistical methods offers a possibility to validate experiments, provided that data are analyzed using the same statistical methodology and the conditions of experimental design are comparable. A final argument in sustaining the need of applying statistical methods in the analysis of territorial systems is that quantitative analysis is a part of the algorithm of systemic analysis.

Among the statistical methods, a special category is represented by the geostatistical ones. Their origin is placed in a wide range of considerations at the border between geography and statistics; some are closer to geography - those based on using the Geographical Information Systems (GIS), other closer to statistics - two-dimensional exploratory analysis used to extrapolate, detect clusters, or spatial predictions. Furthermore, there are combinations of geographical and statistical methods, consisting of the geographical representation of the results of statistical analyses or statistical analysis of geographical data. Therefore, a possible hierarchy of these methods distinguishes five areas: (1) "pure" statistical and mathematical methods, theoretical constructs; (2) very abstract geostatistical methods; (3) pure interference methods; (4) geostatistical methods with little abstract character, and strongly connected to the territorial reality, and (5) purely geographic, descriptive methods.

The paper relies on six case studies, each attempting to exemplify the application of one or more geostatistical methods for different issues in geography, depicting particular aspects of the structure and dynamics of territorial systems. In some cases, both micro- and macro-scale analyses were used.

1. The geostatistical analysis of land use is used as an instrument for studying the dynamics of diversity correlated with urban dynamics. Starting from the structure of territorial systems and one of their essential features, diversity, as well as from the fact that the anthropization of territorial systems is tightly related to their diversity, synergy, and spatial coherence, three types of processes affecting land cover and use are identified: the expansion of cities and re-urbanization transform areas belonging initially to other land cover classes to become urban or built-up - phenomenon called urbanization; in opposition, de-urbanization transforms areas classified initially as urban or built-up to other land cover classes. Urban restructuring does not affect land cover, but land use and characterizes areas classified initially and finally as urban or built-up. The methodology consisted of spatial prediction via ordinary kriging, producing a generalization over the national territory allowing for pinpointing regions characterized by a high intensity of the aforementioned processes. Based on the geographical principle of connecting them with the territorial reality, the detection of such areas is explained by socioeconomic features of the areas, proving that the economic activities are the main causes of the processes specific to the anthropized regions, which, at their turn, induce land cover and use changes. Moreover, the analyses revealed the dependency of these changes on the spatial distribution of primary eco-energies and of the degree of urbanization for both micro-scale (Saratel river basin) and macro-scale (national territory).

2. The search of an indicator relevant for measuring territorial disparities in Romania (macro-scale analysis) and the mountain and sub-Carpathian area of Ialomita river basin (micro-scale analysis) starts from the analysis of theories attempting to explain the mechanisms of territorial development as a process, beginning with the role of territorial disparities and the methods used to measure them. The study relies on the hypothesis (partially verified by the results) that other than the gross domestic product (GDP) for such an approach there must be one or more indices, even artificial, accounting for the economy, demography, infrastructure, and life quality. The research used a complex set of instruments such as correlation analysis, multiple regression analysis, factor analysis, ordinary kriging prediction, the Drane - Aldrich - Creanga test, GIS modeling, and their combinations, and produced apparently different, but convergent results. Nationwide, the results indicate that such an index is a mathematical combination of the GDP, number of inhabitants per room, and rate of scholar abandon, while for the micro-scale analysis the index combines the number of high school graduates and number of people employed in the agriculture. Even though different, the two indices share a common feature - they combine indices reflecting different economic, social or cultural aspects. Other conclusions refer to the methodology: once the methods become more abstract and mathematical, they tend to reflect almost exclusively some aspects, and only the sum of partial results is able to provide a realistic image, corresponding to what is known about the analyzed system.

3. The application of methods used to study biological diversity to territorial systems proved, through the computation and mapping of the spatial distribution of the values of the diversity indices, the validity of such a methodological transfer for one of the key properties of the systems. Furthermore, the results indicated that, if analyzed from the standpoint of the successional cycles, anthropized and anthropic systems can be assimilated to young ecological systems due to their low diversity. Moreover, similar to the geostatistical analysis of land cover, the results showed that their dynamics is influenced by socioeconomic and/or political factors. The correspondence between the results and reality justifies the transfer of statistical methods from ecology to geography.

4. The study of the orientation of county, national, express, and auto-route motorways and railroads used a complex set of instruments consisting of the analysis of variance, regression, and other statistical tests, followed by mapping the results. From a theoretical standpoint, such analyses can be assigned to one or both of the following two directions of research: geopolitical and strategic analysis of motorway and railroad connections between Romania and other European countries, and multi-level polycentric development, where accessibility plays a key role; the latter can be broadened and tied to the mechanism of spatial development, and the role of territorial gaps in this process. Regardless of the perspective, the results indicate a disconnection among the Romanian regions and the other European countries, due mainly to the configuration of the relief. The limits of this case study are first due to the fact that the analyses addressed exclusively the orientation. The research can continue accounting for other parameters, such as the traffic flows or condition of routes, which could constitute important barriers for the multimodal transport.

5. The geostatistical analysis of the distribution of areas affected by clime change in Romania according to 2100 predictions constitutes a return to the applications situated at the border between ecology and the geography of territorial systems. The study was based on ordinary kriging predictions and GIS modeling. Its results indicate that the predicted changes will mostly affect the mountain areas, even though there are subtle differences based on the specified method. It is noteworthy mentioning, from a methodological viewpoint, that both abstract analyses (such as the prediction via ordinary kriging of the areas mostly affected by clime changes) and concrete analyses (such as the hierarchy of counties based on the possible impact of clime change against them) were carried out. Nevertheless, such analyses are only a first step, consisting of the determination of exposure. The risk due to clime change can be assessed only based on an analysis of the vulnerability through the distribution of their physical, geographical, ecological, and socioeconomic characteristics.

6. The study of potential accessibility and optimization of the national security corridor by analogy with the least square method is a geo-strategic analysis similar to the study of the orientation of county, national, express, and auto-route motorways and railroads in Romania, but based on a statistical and mathematical model, consisting of the construction of two indices. The first, called potential accessibility, starts from the universal definition of accessibility based on the isochrones and consists of summing up the population of potentially accessible settlements. The second is built by analogy with the least square methods and quantifies whether the route is minimal, if the sum of squared distances between the station-settlements and those potentially accessible is minimized, ignoring the configuration due to the relief. Such indices prove their utility in arguing the choice of a route or portion as the optimal one from a strategic perspective. Both macro-scale (European) and micro-scale (national) analyses were carried out.

Overall, the case studies confirmed the underlying hypothesis, allowing in addition for to establish a hierarchy of the geostatistical methods, phrase recommendations and restrictions pertaining to their use, and elaborate an algorithm of application, consisting of the following steps: (1) decide whether a study or research is carried out; (2) formulate the hypotheses and objectives; (3) review the literature to identify conceptual and methodological gaps; (4) choose along with the statistician the appropriate methodology, (5) obtain the data, and (6) analyze the data and interpret the results comparing them with other similar studies and against the underlying research hypotheses.

Keywords: human geography, systems, statistics, dynamics, ecology


Posted by Alexandru-Ionut Petrisor


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