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Quantifying and Visualizing Terrain Fabric from Digital Elevation Models
GUTH, Peter L. (email@example.com), U.S. Naval Academy, Department of Oceanography, 572 Holloway Road, Annapolis, MD 21402-5026
Key Words: digital elevation models (DEMs), fabric, eigenvector analysis, terrain analysis
Digital elevation models (DEMs) yield a terrain classification based on three variables: elevation, ruggedness, and topographic fabric or grain (tendency to form linear ridges). To quantify fabric, the analysis extracts eigenvectors and eigenvalues from a 3 by 3 matrix of the sums of the cross products of the directional cosines of the surface normals at each point in the DEM. For topography eigenvalue S1 is much greater than S2 and S3, and S2 and S3 are approximately equal. The ratios ln(S1/S2) and ln(S1/S3) correlate highly with relief (difference between highest and lowest elevations), standard deviation of elevation, average slope, and standard deviation of slope; any of these could categorize ruggedness. Uncorrelated with ruggedness, ratios (ln(S1/ S2)/ln(S2/ S3)) and ln(S2/ S3) measure the fabric or grain. Orientations of S2 and S3 define the dominant grain of the topography, and the ratio of S2 to S3 determines the strength of the grain. Average elevation correlates poorly with all other measures, defining the third element of the classification.
This fabric measures a point property of the DEM and the underlying topographic surface, but the property depends on the size of the region considered. This property varies in a systematic way, both spatially over a region and at a single point as the region size varies. With 30-m DEMs, regions as small as 100 elevations (300-m squares) produce meaningful results. The analysis appears relatively insensitive to DEM quality (U.S. Geological Survey Level 1 and Level 2 DEMs produce very similar results) or DEM spacing (10-m and 30-m DEMs also produce similar results).
Visualizing this organization of topography requires a variety of graphical techniques, including contoured stereographic projections of surface normals, graphs showing the variation in ruggedness and fabric strength as a function of analysis region size, colored maps showing the strength and orientation of the fabric, and contour or reflectance maps with the direction and strength of the fabric overlaid by vectors. Animations showing how these parameters vary with region size greatly assist in the analysis process.