Terrain maps displaying hill-shading with curvature

Abstract

Many types of maps can be created by neighborhood operations on a continuous surface such as provided by a digital elevation model. These most commonly include first derivatives slope or aspect, and second derivatives planimetric or profile curvature. Such variables are often used in geomorphic analyses of terrain. First derivatives also provide subtle enhancements to hill-shaded maps. For example, some maps combine oblique and vertical illumination, with the latter reflecting variations in slope. This study illustrates how second derivative maps, in conjunction with hill-shading, can cartographically enhance topographic detail. A simple conic model indicates that image-tone edges where slope or aspect varies by less than 0.5° are visible on curvature maps. Hill-shaded images combined with curvature enhance the continuity of naturally occurring tonal edges, especially in strongly illuminated areas. Variations in planimetric and profile curvature seem to be especially effective at highlighting convergent and divergent drainages and variations in erosion rate between or within sedimentary units, respectively. Shading curvature with consideration given to illumination models can add detail to hill-shaded terrain maps in a manner similar to cognitive models employed by map viewers.