The Use of Spherical Statistics to Analyze Digital Elevation Models: An Example From LIDAR and ASTER GDEM

The use of spherical statistics for comparing and analyzing different digital elevation models (DEMs) is proposed in this letter by the new software package VecStatGraphs3D. Spherical data deal with angular data such as unit vector in 3-D space and are used in disciplines such as meteorology, geomatics, biology, and geology. Usually, the most common descriptor to analyze DEMs is the root-mean-square error (linear statistic), but this statistic itself cannot describe the error positional distributions. Comparing homologous points in two different DEMs generates 3-D vectors, which can be analyzed by means of spherical statistics. A 3-D vector is defined by its module (linear statistics) and colatitude and longitude (spherical statistics). While several graphical and statistical tools are available for the analysis of directional data in 3-D, these tools consider only the angular magnitude and work with unit vectors. In this letter, the open-source software package VecStatGraphs3D is described. It works in the R environment and provides statistics for modules (linear), colatitude and longitude (spherical), and graphics for the joint analysis of 3-D vectors. The spatial locations of singular points between two DEMs of different spatial resolution: LIDAR (5 m) and ASTER Global Digital Elevation Map (30 m) are compared as examples using VecStatGraphs3D. The interactive 3-D graphics reveal spatial patterns and assist in understanding the effect of the DEM resolution on the uncertainty of the spatial locations of relief.