Probability Surface Mapping

A New Approach to Trend Surface Mapping

Bibliographic Data

ID8962818
AuthorsNeil Wrigley (0000-0002-3967-5668, corresponding author)
Year1977
Volume2
Issue2
Pages129-129
Publication date1977-01-01
Peer ReviewedYes
Open AccessNo
TypeARTICLE
VenueTransactions of the Institute of British Geographers (JOURNAL)
Journal identifiersISSN: 0020-2754 • E-ISSN: 1475-5661
PublisherWiley (PUBLISHER • GB)
DOI10.2307/621853
OpenAlexW2317656951
LanguageEN
Citations received4
References cited7

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

Geometry · Surface (topology · Land Use and Ecosystem Services · Mathematics · Soil Geostatistics and Mapping · Spatial and Panel Data Analysis

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