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Probability Surface Mapping: A New Approach to Trend Surface Mapping

1977; Wiley; Volume: 2; Issue: 2 Linguagem: Inglês

10.2307/621853

1475-5661

Neil Wrigley,

Land Use and Ecosystem Services

Many of the variables measured or utilized in the course of geographical research have so far been viewed as unmappable by the trend surface mapping method. The paper presents a method which allows the surface mapping of categorizations or orderings. The resulting maps are called probability surface maps. Probability surface models are first outlined and then illustrated using the example of the perception of aircraft noise disturbance around Manchester (Ringway) Airport. Other topics discussed are the testing of probability surfaces of progressively higher order and the construction and testing of residual maps. TEN years have now elapsed since Chorley and Haggett (1965) published their influential paper on trend surface mapping in this journal. During this period, as geographers have become increasingly aware of the assumptions, limitations and potentialities of regression models, a deeper understanding of trend surface models has developed. However, despite this deeper understanding, it is possible to identify only one basic extension to the range of applicability of trend surface mapping. The original geological applications of trend surface mapping involved variables which could in principle be observed at all points over an entire area. Most of the trend surface mapping examples which Chorley and Haggett discussed reflected this original area of application and were basically isarithmic maps describing continuous surfaces. Nevertheless, Chorley and Haggett stressed that they regarded trend surface mapping as having a potentially wider range of applicability not 'restricted to such conventional isarithmic surfaces as terrain elevation or isobaric pressure'. Following this statement, geographers have extended trend surface mapping to less conventional surfaces, such as surfaces of social phenomena, or cirque elevation, based upon fundamentally discontinuous point-valued information. The distinction between continuously and discontinuously distributed spatial data has been acknowledged in such extensions (Unwin and Hepple, 1974; Norcliffe, 1969), and in applications involving spatially discontinuous data it has been usual to provide some form of conceptual link between the point pattern observations and the continuous response surface being constructed. Unwin (i973), for example, has argued that 'any surfaces fitted to such (spatially discontinuous) data will contour variability in a potential for development', and thus trend surface maps produced from such data are best regarded as potential surfaces. Although trend surface mapping has thus been extended to spatially discontinuous variables, a common characteristic of all variables previously mapped by the trend surface method is their high order level of measurement. All have been quantitative, variables measured at the ratio or