Abstract
Methodological establishment, based on the mathematical conception, of the quantification of spatial landform variation in mountainous regions is an important problem in constructing the prospective logging plan and forest road network plans.
The quantitative description of landform by means of theoretical models and/or parameters is taken as a starting point for this procedure.
As examples of DTM data, by 3600 grid-cells for three kinds of topographical map of different scale (1:5,000, 1:25,000, 1:50,000), processing by computers, the cases of two-dimensional autocorrelation analysis and spectral analysis are present.
Purpose of this article is to discuss the efficiency and the limitation of the quantitative technique as a new method for estimating landform variation in mountainous regions.
Main points of arguments addressed in this are as follows;
1) Pattern identification of anisotropic landform by autocorrelation function (correlogram) and implication of estimated spectral bias within a distribution as spatial surface variation.
2) Quantitative terrain models produced by double Fourier inverstransformation.
3) Statistical significance of standard deviation of extracted residual from harmonic trend-surface (quantitative terrain model) as the parameter of terrain roughness and convergence of double Fourier approximation.
4) Application of the parameter to the cutting volume calculation of earth work in the forest road construction.
It was suggested that for assessing the intricate landform variation and for recognizing the extracted spatial structure of relief concerning periodic or random range, a dominant wavelength or spectral distribution seemed to be valid and useful.
Standard deviation of surface variation is closely related to the mean altitude of area and it could be approximated by the equation Y= -2.38+0.31X (r²=0.98), where X is the mean altitude and Y is the standard deviation. Also the coefficient of variation ranged from about 25 to 30 percent.
A fundamental landform of the model area could be almost reappeared by the Fourier synthesis of the 10th equivalent harmonic order.
The development of these quantitative models provided a parameter in order to estimate terrain roughness. That is, the standard deviation of residual obtained from trend-surface might be indicated the convergence of double Fourier approximation (goodness-of-fit) to fit the real surface of DTM.
Relative value of standard deviation decreased steadily as the harmonic degree increased until the terminal convergent contribution ratio became about 90 to 98 percent.
This result shows that the raw spectrum is only an estimate of the contribution to the variance by the harmonics, and like all the sample estimates these may deviate markedly from the true population spectrum. The raw spectrum becomes more stable and a better estimate of the population spectrum as the sample size tends toward infinity, but we cannot continue sampling indefinitely and must end the analysis at some point. Our estimate of the sample spectrum can be improved by smoothing, because adjacent harmonic tend to be similar and an averaging process forces them to converge on a common.
