How to represent a terrain surface and interpret it has always been a fundamental issue in many disciplines, including geography, surveying and environmental science. Representation techniques have evolved through time with the rise of new technologies. When considering cartography, the objective was to facilitate the user’s interpretation of the terrain portrayed on a map. As mentioned by Morato-Moreno
[1], the scientific representation of terrain elevation started around the end of the sixteenth century with the use of contour lines to represent points at the same depth in a riverbed. By the end of the 1950s, the increased power of computers enabled researchers to create and manipulate an electronic version of a map called a digital terrain model (DTM). Miller and Laflamme
[2] define the DTM as “a statistical representation of the continuous surface of the ground by a large number of selected points with known X, Y, Z coordinates in an arbitrary coordinate field”. Other terms are also used to describe terrain surface. The most common alternative term is the digital elevation model (DEM). Li et al.
[3] consider that the DTM represents the spatial distribution of various types of information on the terrain, not only the elevation, while the DEM only measures the elevation of the bare Earth surface. Other types of information are morphometric data (slope, curvature), terrain features (geomorphological features, rivers, lakes) and environmental data such as soil, geology or climate.
DEMs were constructed mainly for applications in civil engineering. Originally, the set of points were obtained from ground surveys or through photogrammetric processes. The surface was formed by triangulating these points into triangulated irregular networks (TINs). With the development of remote sensing, data became increasingly available, covering larger areas and being easier to process, so that digital models could be created at different scales with increasing precision. These data were often produced or stored as raster images, where each pixel contained an elevation, for ease of processing. Consequently, much research was carried out to create more advanced tools for terrain analysis on regular square grids. More specifically, geomorphometry developed as a discipline on its own
[4], providing new techniques for terrain partitioning and classification, including object-based image analysis—OBIA
[5]. DEMs were also produced from existing data, as found on topographic maps, such as contour lines and streams. The generated DEM could be either a TIN
[6] or a square grid
[7].
The creation and development of airborne lidar (Light Detection and Ranging) brought higher resolution, with a resolution around or below one metre and larger volumes of data
[8]. As pointed out by Clarke and Romero
[9], higher-resolution data brought new sources of error, and algorithms faced new issues. For example, drainage computation methods that were efficient on low-resolution images were no longer accurate with the presence of new features such as roads and culverts, requiring specific drainage enforcement methods
[10].
While TIN and square grids are the most common DEM structures, other types of meshes can be used, such as equilateral triangles and hexagonal grids
[11]. Data structures are mainly chosen according to the data source format, terrain representation and the type of usage.
In addition to computational analysis, data structures are also built from DEMs for reasoning and interpretation purposes. Interest in describing the terrain through such structures can be traced back to earlier works from Cayley
[12]. Cayley reasoned on contour lines to define feature points on the terrain that are summits (local maximums), immits (local minimums) and knots (saddles). He then characterised ridge and course (or thalweg) lines, pointing out that they start at a saddle and end at a maximum or a minimum. Shortly after, Maxwell
[13] presented mathematical formulae relating the different types of points. He also introduced hills and dales as districts where lines of slope run to the same maximum or minimum point and he showed that hills are bounded by thalwegs and that dales are bounded by ridges. Most importantly, he demonstrated that hills and dales each form a partition of the terrain.
These early works established the basic foundations for reasoning on terrain. and they led Pfaltz
[14] to formalize terrain data as a graph structure called the surface network. Other structures were also introduced, such as the contour tree and the Reeb graph
[15]. These data structures explicitly represent hierarchical and adjacency relationships between terrain elements. They can be used to identify terrain objects that are relevant to a particular analysis, such as the identification of landforms.
This entry gives an overview of the main data structures used for 2D terrain representation and analysis.
Section 2 presents some approaches that build a two-dimensional representation directly from data. These structures were mainly defined for computational analysis.
Section 3 introduces more advanced structures, especially surface networks, that can characterise terrain features and store hierarchical or topological relationships between the features.
Section 3 also presents recent developments for the use of extended surface networks applied to the cognitive representation of the terrain based on topographic saliences, skeletons and topo-contexts.
Section 4 concludes the entry and briefly mentions new research avenues opened by the recent developments of surface networks and related techniques for terrain modelling.
