Statistical Characterization of Altitude Matrices by Computer. Report 6. An Integrated System of Terrain Analysis and Slope Mapping.
Abstract
A system is described which: (a) replaces existing sets of diverse terrain indices with a group of statistics for point-characteristics; (b) calculates all of these statistics in a single computer run from a single data set; and (c) utilizes available altitude matrix data. The procedures are applicable to Altitude matrix data at any grid mesh. From altitudes in each 3 x 3 submatrix, a quadratic surface is fitted and solved for its first and second horizontal and vertical derivatives at the central point. This yields the slope gradient, slope aspect, profile convexity, and plan convexity at every point in the original matrix, except for the peripheral rows and columns. These 'point' descriptors are presented as: (1) line-printer shaded maps; (2) histograms; (3) scatter plots of each pair; (4) matrix of pair-wise correlations, plus circular regressions on aspect, and several multiple regressions, and (5) summary (moment-based) statistics. In general, the five basic descriptors have little relation to each other, except that gradient is usually a quadratic function of altitude. A comparison is made with other approaches, such as spectral analysis and fractal modelling. The long-distance persistence properties of terrain mean that considerable extra variance at long wavelengths is usually incorporated when the study area is extended. Hence the auto correlation function varies with the length of series or size of area. Variance of derivatives are also affected, but means, skews, and kurtoses are not.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1979
- Accession Number
- ADA076558
Entities
People
- Ian S. Evans
Organizations
- Durham University