A COMPARISON OF POLYNOMIAL AND FOURIER MODELS IN MAP ANALYSIS.
Abstract
The problem of selecting an optimum model for trend analysis of mapped data involves the question of the structure of a single observation under various models. The commonly used polynomial functions structure the data in such a way that a succession of fitted surfaces, linear, quadratic, cubic, etc., can be constructed. The less commonly used but increasingly popular Fourier series model structures the data to produce a series of harmonic surfaces having wave forms of diminishing wave length as the order of the surface rises. Present implications appear to be that when the map shows cyclical forms, the Fourier model is to be preferred. The general problem, however, also includes the question of extrapolating the map beyond the limits of control, and in this respect the polynomial and Fourier models differ very markedly. The present report is an expository study, in which a given set of gridden map data is analyzed with both models, and some of the resulting maps are compared. These maps are then extrapolated beyond the grid, and they demonstrate for the example chosen that extrapolation for short distances from low-order polynomial surfaces is more satisfactory than extrapolation from Fourier maps. However, as the order of the polynomial surface rises, the extrapolated values rapidly increase or decrease beyond bound, whereas Fourier maps of all orders display periodic repetition of the pattern in the control grid. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1966
- Accession Number
- AD0635476
Entities
People
- W. C. Krumbein
Organizations
- Northwestern University