The Use of Trend-Surface Parameters in Inter-Urban Comparisons

Abstract

The general problem of comparing isarithmic maps of different urban areas is examined. Proposed solutions by Merriam and Sneath (1966) and Haggett (1967) are revised in the light of the indicated instability of coefficients under shifts in the grid systems for such maps. A number of stable classifications of city structures can be built up which are invariant under orthogonal grid rotations but most of these break down under non-orthogonal rotations. Variances accounted for by successive terms (linear, quadratic, cubic) appeared stable and are recommended for preliminary analysis. The fundamental problems of pattern analysis remain unresolved by trend-surface coefficients. The argument in the paper is largely empirical and is illustrated from simulated urban patterns and by fifteen sample metropolitan areas from the United States.