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Trend-Surface Mapping in Geographical Research

R. J. Chorley and P. Haggett
Transactions of the Institute of British Geographers
No. 37 (Dec., 1965), pp. 47-67
DOI: 10.2307/621689
Stable URL: http://www.jstor.org/stable/621689
Page Count: 21
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Trend-Surface Mapping in Geographical Research
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Abstract

The nature of trend-surface models is examined in terms of the dissection of areal distributions into regional trend components, local residuals and random or unexplained noise. The construction of trend surfaces falls broadly under two heads: the more selective graphical and grid methods and those which are more basically computational and more objective. The most important of the latter is the method of fitted orthogonal polynomical regressions by which surfaces of different order are fitted to the data by the method of least squares. Such fitting is especially facilitated by high-speed electronic computers. The information output from trend-surface analysis is both descriptive and interpretative. The description of regional trends is given by equations, matrices of computed values and computer-printed maps. The reduction in the sum of squares and confidence limits give the relation of these surfaces to the original data. Regional trend-surface interpretation involves the identification of major, discrete and interlocking trends, but the identification of residuals from these surfaces has, through its application to oil exploration, proved an especial focus of interest. It is suggested that the geographical exploitation of trend-surface analysis might take the forms of improved isarithmic mapping, simplified description of complex areal patterns, comparative areal analysis, and the construction of process-response models. The latter are conceptual frameworks with reference to which areal information is 'structured' in attempts to explain areal distributions in terms of sets of process factors.

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