On the Use and Limitations of Trend Surface Models

Abstract

Although the technique of trend surface mapping has been developed in the main by geologists and geophysicists, its use has now diffused into a number of other fields including regional science, botany, meteorology, and geography. It would be wrong to be unduly critical of the pioneer applications of any technique, even where errors have been made, for there are few guidelines to help such explorers. On the other hand it is felt that trend surface methods are sufficiently well estab‐lishd in geography for there to be a need for a more critical appraisal of the method, especially in view of some careless or even erroneous applications that have been made recently by geographers. This paper will highlight what are considered to be some of the more important limitations of trend surface models, and will point to one or two specifically geographical problems.

UV, latitude, and spatial trends in prostate cancer mortality: All sunlight is not the same (United States)

“…Several imitations of trend surface analysis have been described [22]. Chief among these is that when these techniques are used for hypothesis generation, it may be difficult to develop hypotheses to explain the complex surfaces that result from higher order trends.…”

Spatial Autocorrelation Analysis of Trend Residuals in Biological Data

“…In population biology TSA has been used more for detecting clines or characterizing biological rules such as those of Bergmann and Allen, than for decomposing the variation itself (see Marcus and Vandermeer, 1966 for an early application in systematics; Gittins, 1968, in population ecology;Jorde, 1980 for a review). The main criticism against TSA was raised some years ago by Norcliffe (1969): "Many applications of TSA methods have simply been curve fitting exploration, followed by a posteriori justification as to why good fits have been obtained." Other problems with trend surface analysis, conceptual as well as practical, are described by Burrough (1986Burrough ( , 1987.…”

Trend surface analysis of major late Wisconsinan till sheets, Brantford–Woodstock area, southern Ontario

“…Statistical significance may be attained with rela-,tively poor fits and Howarth (1967) showed, using random numbers, that significant F ratios may be obtained with very low explanation percentages for non-random trends. Norcliffe (1969 , Table 11) computed minimum explanation levels of nonrandom trends for the 95 and 99% significance levels; these appear to give little information beyond acceptance or rejection of the F ratios.…”