Comparing the accuracy of estimated terrain elevations across spatial resolution

Terrain is modelled in Geographic Information Science on a grid, assuming that elevation values are constant within any single pixel of a Digital Elevation Model (DEM). Pixels are considered flat and rigid, for computational simplicity (a ‘rigid pixel’ paradigm). This paradigm does not account for the slope and curvature of terrain within each pixel, generating imprecise measurements, particularly as pixel size increases or in uneven terrain. This paper relaxes the rigid pixel assumption, allowing for possible sub-pixel variations in slope and curvature (a ‘surface-adjusted’ paradigm). This paper compares different interpolation methods to investigate sub-pixel variations for estimating elevation of arbitrary points given a regular grid. Tests interpolating elevation values for 20,000 georeferenced off-centroid random points from a regular grid DEM are presented, using a variety of exact and inexact local deterministic interpolation methods within contiguity configurations incorporating first and second order neighbours. The paper examines the accuracy of surface-adjusted estimations across a progression of spatial resolutions (10 m, 30 m, 100 m, and 1,000 m DEMs) and a suite of terrain types varying in latitude, altitude, slope, and roughness, validating off-centre estimates against direct elevation measurements on 3 m resolution lidar DEM. Results illustrate that the Bi-quadratic and Bi-cubic interpolation methods outperform Weighted Average, Linear, and Bi-linear methods at coarse resolutions and in rough or non-uniform terrain. In smooth or flat terrain and at finest resolutions, the interpolation method impacts estimation accuracy less or not at all. The type of contiguity configuration appears to play a role in estimation errors as well, with tighter neighbourhoods exhibiting higher accuracy. The analysis also examined regularized mathematical surfaces, adding autocorrelated randomly distributed noise to simulate terrain. The results of experiments based on regularized smooth mathematical surfaces do not translate directly to terrain modelling. The analysis also considers the balance between the increased computation times needed to measure surface-adjusted elevation against improvements in accuracy.