Cross-Scale Analysis of Surface-Adjusted Measurements in Digital Elevation Models

Abstract

Terrain is commonly modeled in GIScience on a grid of pixels, assuming that elevation values are constant within any single pixel of a Digital Elevation Model (DEM) (a ‘rigid pixel’ paradigm). This paradigm can generate imprecise measurements because it does not account for the slope and curvature of the terrain within each pixel. The objective of this research is to relax the rigid pixel assumption, allowing detection of possible sub-pixel variations (a ‘surface-adjusted’ paradigm). The surface-adjusted approach incorporates the slope and curvature of the terrain into computations, and fills a critical gap in the literature regarding the impacts of rigid-pixel paradigm in terrain modeling uncertainty.

Demonstration of the surface-adjusted paradigm is proposed along two lines. First, this research employs realistic digital terrain using different interpolation methods and the information from adjacent pixels, searching for a more accurate interpolation of elevation values. Sub-pixel variations in DEMs across different resolutions is investigated to develop a foundation of surface-adjusted computations. Second, surface-adjusted area measurements are investigated. Area is commonly measured in Euclidean space and so the slope and curvature of the terrain is ignored, resulting in under-estimation, especially in higher slope or rough terrain.

This research examines the sensitivity of surface adjustment to different interpolation methods, different contiguity configurations, different terrain type and a progression of spatial resolutions. There is a general increase in the residuals at coarser resolutions. RMSE values decrease to varying degrees moving from rough and non-uniform terrain to smooth and uniform terrain. It found that bicubic interpolation can increase the accuracy of estimating elevation and area from regular gridded DEMs at coarse resolutions and in rough and/or non-uniform terrain. In fine DEM resolutions, and/or smooth and uniform terrains, linear or bilinear methods provide the highest accuracy. The bicubic method also incur the highest processing time. Therefore, to maintain a balance between the increased computations needed to measure surface-adjusted elevation and area against the improvement in precision or for large volume data sets, linear and bilinear methods seem to be better choices.