On the frequency distribution of land slope

Slope frequency distributions are computed from Digital Elevation Models (DEMs) of 18 areas from five different geographic and physiographic regions. Over 160,000 slope estimates are used in the definition of the slope frequency distribution for each area. Analysis of several transformations of the slope data indicates that no single transformation is capable of normalizing all slope distributions. This is, in part, due to the arbitrary placement of the boundaries of the map sheets used in the data collection. The square root of sine, however, provides better results than sine, log-tangent, or several other transformations. The degree of (positive) skewness of gradients in degrees correlates with the proportion of slopes below 2° or 5° (r_s = + 0·93), as does the kurtosis (r_s = + 0·91).