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Principal component analysis is often used with remote sensing to decrease the dimensionality of multi-band imagery and to realign data with new axes to maximize variance in the imagery (Campbell and Wynne, 2011). Relief shaded maps using illumination from numerous aspect directions and inclinations from the horizon can also be input to principal component analysis (PCA), resulting in principal component maps that optimize variance and mimic relief shading. Using 15° increments of azimuth and inclination to vary illumination direction yields 121 relief shadings of the Churfirsten, Switzerland at 30 m. resolution, one of the sample elevation models available from http://shadedrelief.com/SampleElevationModels/ (Kennelly et al., 2021). PCA results in the three principal component images shown in Figure 1, accounting for more than 99% of the variance found in the 121 input relief shadings. While the first two principal component maps are similar to relief shading illuminated from near the horizon and separated by 90 degrees of azimuth, the third principal component map is similar to slope shading [ABSTRACT FROM AUTHOR]

Cartographers tout the merits of relief shading in giving terrain a three-dimensional appearance, while tending to ignore or discourage the use of shadowing for the shadow's tendency to obscure the underlying topographic details. It is possible, however, to discard relief shading and use only shadows from multiple light sources to create shadowing effects that have similar landform details and with the potential for a more dramatic three-dimensional effect when compared to relief shading. We present comparisons of a standard elevation model illuminated by a clear sky with a) relief shading, b) shadows, and c) relief shading plus shadows in Figure 1. We observe that adding relief shading to a shadowed rendering (Figure 1c) does not add much topographic detail to the shadow-based terrain representation (Figure1b). This may seem non-intuitive, as terrain is being represented not by the orientation of the land's surface with respect to a light source which is the basis of relief shading, but rather by the shadows cast by landforms that are aligned with the illumination direction. This result underscores the importance of illumination models that represent numerous point sources throughout the sky to simulate natural lighting conditions and result in soft shadows. Another important comparison between relief shading and representing terrain with shadows is that vertical exaggeration of the elevation model can produce more dramatic effects with the latter, as seen in the top row of Figure 2. This enhanced effect can be attributed to longer shadows with vertically exaggerated terrain. By contrast, vertical exaggeration of terrain for relief shading as seen in the bottom row of Figure 2 may make illuminated areas lighter and non-illuminated areas darker in grayness, but general patterns of lighter and darker areas remain the same while undergoing tonal modulations. These patterns are locked into place by the static nature of landform locations as opposed to the dynamic nature of their shadows' extents. [ABSTRACT FROM AUTHOR]