Advances in Spatial Analysis

The origins of modern spatial analysis lie in the development of quantitative geography and regional science in the late 1950s. The use of quantitative procedures and techniques to analyse patterns of points, lines, areas and surfaces depicted on analogue maps or defined by co-ordinates in two-or three-dimensional space characterise the initial stage. Later on, more emphasis was placed on the indigenous features of geographical space, on spatial choices and processes, and their implications for the spatio-temporal evolution of complex spatial systems. Spatial analysis, as it has become over the past four decades, is more than spatial statistics and data analysis, and goes far beyond data sampling, data manipulation, exploratory and confirmatory spatial data analysis, into areas of spatial modelling encompassing a large and diverse set of models in both the environmental and the social sciences. In the environmental sciences, they range from physical dispersion models (e.g. for suspended particulates), chemical reaction models (e.g. photochemical smog), and biological systems models (e.g. for ecosystems in water), through deterministic process and stochastic process models of regional environmental quality management, and integrated models for environment-energy-economic assessment. For many models, especially the physical dispersion models, chemical reaction models, and biological systems models, the geographical location of the site is not considered to be of overriding importance. The variation in model results over space can be achieved by obtaining different inputs to the area in question. Process models include deterministic versions which attempt to describe a particular sequence in terms of known physical laws, and stochastic model versions which aim to describe a particular process such as erosion, groundwater movement and absorption of pollutants in terms of probability theory. For such processes, there is an interaction between the spatial process and a substrate. This substrate provides a one-, two-or three-dimensional framework within which the process model can operate. The space in which the process is modelled is disaggregated into a set of finite elements which are usually assumed to be internally homogeneous. Two-dimensional models generally use as their data small pixels (see Fischer et al., 1996).