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Modeling 3D Land Surface

Topography refers to the "lay of the land" in terms of elevation, slope, and orientation.

Terrain "is a similar concept, used more to describe the land itself than the study of it." Relief " is often used to refer to the third dimension of a map whether in actuality (as in a "raised relief" map, or drawn, as with contours, hachures or shading) or the territory it describes.

Topography is similar to topology, popularly thought of as the mathematical study of surfaces. This may help explain its adoption in the world of geographers. Its actual original meaning, from Greek "topos" (place) and "graphein" (to draw), relates to the description of places rather than broad regions, in topographic surveys.

Most 18th and early 19th century national surveys did not record relief across the entire area of coverage, calculating only spot elevations at survey points. The United States Geological Survey (USGS) topographical survey maps included contour representation of relief, and so maps that show relief, especially with exact representation of elevation, came to be called topographic maps (or "topo" maps) in the United States , and the usage has spread internationally.

The understanding of topography is critical for a number of reasons. In terms of environmental quality, agriculture, and hydrology, understanding the topography of an area enables the understanding of watershed boundaries, drainage characteristics, water movement, and impacts on water quality.