The uses and limitations of fractal geometry in digital terrain modelling.
Item
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Title
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The uses and limitations of fractal geometry in digital terrain modelling.
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Identifier
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AAI9315515
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identifier
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9315515
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Creator
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Xia, Zong-Guo.
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Contributor
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Adviser: Keith C. Clarke
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Date
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1993
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Language
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English
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Publisher
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City University of New York.
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Subject
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Physical Geography | Geology
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Abstract
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In this study, fractal concepts and techniques are tested using nearly 200 DEMs produced by the USGS. The specific objectives include (1) an examination of statistical self-similarity of topographic data; (2) an evaluation of three most commonly used methods for estimating the fractal dimension of topographic surfaces; (3) a preliminary test of using fractal parameters to characterize various landforms and to delineate landform regions; and (4) an examination of the relationships between fractal parameters and geomorphic variables affecting landform characteristics.;The analysis of the computational results has led to the following conclusions: (1) the fractal model fits certain types of terrain surface better than others, and topography is only self-similar within quite limited scale ranges and in certain direction(s); (2) the fractal dimension of landforms varies within a wide range, the fractal dimension used to produce realistic-looking synthetic terrain (D = 2.2) only represents some special type of terrain surface, and a D value of 2.5 obtained by some early researchers is merely a result of artificial agglomeration of diversified terrain surfaces; (3) most DEMs from the mountain regions can be easily separated from those of plains or plateaus, and the fractal parameters of adjacent physiographic provinces are significantly different so that fractal segmentation of landform regions appears possible; (4) fractal parameters reflect well the effects of lithology, geological structure, and the stage of landform evolution on landform characteristics, but no clear relationship between fractal parameters and climate was identified possibly due to the relatively coarse resolution of the data; and (5) the variogram method is the most suitable method for estimating the fractal dimension of topographic profiles or surfaces, the box-counting method also produces reasonable results when careful consideration is given to the selection of the maximum cell size, the contour interval and the minimum r-squared value, and the walking dividers method can not be easily applied to self-affine fractals such as topographic profiles.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
