Geomorphometry Terms

• Concentration (fraction of uniform): elevation distribution relative to a uniform concentration of elevations (a value of 1 equals the total number of data points divided by the relief present in the DEM) because this allows easy comparison of DEMs.  The scaling chosen for the x axis does not affect the shape of the distribution; equivalent results would appear if the x axis plotted the number or percentage of elevations in each interval.  The use of a uniform concentration for scaling does not imply that the distribution of elevations should be uniform throughout the elevation range. The actual distribution will depend on the terrain, with high concentrations in flat valleys or plateaus and low concentrations in steep mountains, but should vary in a reasonably continuous fashion.
• Roughness factor:     RoughnessFactor := 1 - sqrt(sqr(x1sq) + sqr(y1sq) + sqr(z1sq)) / NumPts   (Mark, 1975; Etzelmuller, 2000) where x1sq, y1sq, and z1sq are the sums of the squares of the directional cosines of the terrain normals.

Geomorphometric Parameters

 Parameter Formula Interpretation of Values Reference Flatness Ln(S1/S2) Large values indicate flat terrain, low values rugged terrain.  Correlates strongly and negatively with slope or relief. Guth papers listed in Terrain organization Organization Ln(S2/S3) Large values indicate a dominant linear fabric to the terrain, low values isotropic topography Guth papers listed in Terrain organization Orientation Trend of S3 Dominant trend to the terrain fabric, direction between 0 and 180°. Used in eigenvector analysis of SSO diagrams. Guth papers listed in Terrain organization Strength, c Ln(S1/S3) Large values indicate flat terrain, low values rugged terrain.  Very similar to the flatness parameter.  Correlates strongly and negatively with slope or relief. Used in eigenvector analysis of SSO diagrams. Fisher, Lewis, and Embleton, p.159 Shape, k Ln(S1/S2)/Ln(S2/S3) Large values indicate a dominant linear fabric to the terrain, low values isotropic topography.  Correlates moderately with organization. Fisher, Lewis, and Embleton, p.159 Ghost ratio (Percentage points on contour lines) / (Percentage elevations that are contour lines) Indicates the overrepresentation of contour line elevations in the DEM, an artifact of the digitizing process if the ghost ratio exceeds 1.  The ghost ratio is never significantly less than 1. Guth, 1999

S1, S2, and S3 are the eigenvalues from the 3x3 matrix of the sums of the cross products of the direction cosines for all points in the analysis region.

S1> S2> S3.

Last modified 5/24/2006