This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Preprints) and either DOI or URL of the article must be cited.
Area is an integral part of any spatial database and has a significant role in many geographic analyses and applications. Planar algorithms that are widely used to calculate area ignore the slope and curvature of the terrain and result in under-estimation, particularly as pixel size increases or in uneven terrain. Calculating surface area using a regular DEM can overcome this issue by considering localized variations on the terrain surface. This paper investigates the scale- and algorithm-dependence of surface area calculations. The expectation is that for any individual pixel, the improvement in measurements can be relatively small, however, the additive effects across the study area can become significant. The method of dividing each DEM pixel into eight 3D triangles is commonly used to calculate surface area. In this research, the elevation of triangle vertices are estimated using different interpolation methods to establish rates of under-estimation for progressively larger pixels. These methods are validated against vertex elevations on a 3 meter lidar data benchmark. Bi-Cubic interpolation outperforms other interpolation methods for calculating DEM surface areas, with Linear, Bi-Linear and Jenness methods performing nearly as well, especially at coarser resolution. Relative accuracies are shown to degrade somewhat in rougher terrain.
This paper was presented at the Geomorphometry 2018 conference in Boulder, CO in August 2018.