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Present day Earth altimetry (and bathymetry). Data from the National Geophysical Data Center's TerrainBase Digital Terrain Model.

Terrain, or relief, is the third or vertical dimension of land surface. When relief is described underwater, the term bathymetry is used. Topography has recently become an additional synonym, though in many parts of the world it retains its original more general meaning of description of place.

Terrain is used as a general term in physical geography, referring to the lie of the land. This is usually expressed in terms of the elevation, slope, and orientation of terrain features. Terrain affects surface water flow and distribution. Over a large area, it can affect weather and climate patterns.

The understanding of terrain is critical for a number of reasons.

• The terrain of a region largely determines its suitability for human settlement: flatter, alluvial plains tend to be better farming soils than steeper, rockier uplands.

• In terms of environmental quality, agriculture, and hydrology, understanding the terrain of an area enables the understanding of watershed boundaries, drainage characteristics, water movement, and impacts on water quality. Complex arrays of relief data are used as input parameters for hydrology transport models (such as the SWMM or DSSAM Models) to allow prediction of river water quality.

• Understanding terrain also supports on soil conservation, especially in agriculture. Contour plowing is an established practice enabling sustainable agriculture on sloping land; it is the practice of plowing along lines of equal elevation instead of up and down a slope.

• Terrain is militarily critical because it determines the ability of armed forces to take and hold areas, and to move troops and material into and through areas. An understanding of terrain is basic to both defensive and offensive strategy.

• Terrain is important in determining weather patterns. Two areas close to each other geographically may differ radically in precipitation levels or timing because of elevation differences or a "rain shadow" effect.

Land surface may appear fractal, anisotropic and non-periodic. However, the land surface is controlled by the underlying geologic structures and the climate affecting the surface. Land surface can be rather smooth but also very rough and dissected and complex. Areas of land surface that have relatively homogeneous morphometric properties are called landforms.

Geomorphology is in large part the study of the formation of terrain or topography. Terrain is formed by intersecting processes:

• Geological processes: migration of tectonic plates, faulting and folding, volcanic eruptions
• Erosional processes: water and wind erosion, landslides
• Extra-terrestrial: meteorite impacts

Tectonic processes such as orogenies cause land to be elevated, and erosional (and weathering) processes cause land to be worn away to lower elevations.

Land surface parameters are quantitative measures of various morphometric properties of a surface. The most common examples are used to derive slope or aspect of a terrain or curvatures at each location. These measures can also be used to derive hydrological parameters that reflect flow/erosion processes. Climatic parameters are based on the modelling of solar radiation or air flow.

Land surface objects or landforms are definite physical objects (lines, points, areas) that differ from the surrounding objects. The most typical examples are lines of watersheds, stream patterns, ridges, break-lines, pools, borders of specific landforms etc.

Look up terrain in Wiktionary, the free dictionary.

• Geomorphometry
• Cartographic relief depiction (2-D relief map)
• Raised-relief map (3-D relief map)
• Relief ratio
• Subterranea