The “M” in digital elevation models

Abstract

The “M” in digital elevation models (DEM) stands for model, which literally means “a schematic description of a system, theory, or phenomenon that accounts for its known or inferred properties and may be used for further study of its characteristics.” A DEM fulfills the requirement of “a schematic description” of terrain. However, how to make it account for the “known or inferred properties” warrants further scrutiny. This article outlines three properties of terrain and examines their four implications to DEM generation. The three properties are as follows: (1) each terrain point has a single, fixed elevation; (2) terrain points have an order and sequence that is determined by their elevations; and (3) terrain has skeletons. The four implications to DEM generation methods are as follows: (1) a method must be a bijection; (2) a method must be an isomorphism in order to preserve elevation sequence; (3) a method must guarantee that the vertical error at any point, not just checkpoints, is acceptable in order to assure the vertical accuracy of a DEM; and (4) a method must involve generalization if terrain skeletons are to be preserved. These implications are discussed in the context of light detection and ranging-derived DEMs. Generalization is highlighted as the top priority for future research.

Keywords:

• DEM
• terrain modeling
• generalization
• isomorphism