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Topography is the study of the forms and features of
land surface Terrain or relief (also topographical relief) involves the vertical and horizontal dimensions of land surface. The term bathymetry is used to describe underwater relief, while hypsometry studies terrain relative to sea level. The Latin word ...
s. The topography of an area may refer to the land forms and features themselves, or a description or depiction in maps. Topography is a field of
geoscience Earth science or geoscience includes all fields of natural science related to the planet Earth. This is a branch of science dealing with the physical, chemical, and biological complex constitutions and synergistic linkages of Earth's four sphe ...
and planetary science and is concerned with local detail in general, including not only relief, but also natural, artificial, and cultural features such as roads, land boundaries, and buildings. In the United States, topography often means specifically ''relief'', even though the USGS topographic maps record not just elevation contours, but also roads, populated places, structures, land boundaries, and so on. Topography in a narrow sense involves the recording of relief or
terrain Terrain or relief (also topography, topographical relief) involves the vertical and horizontal dimensions of land surface. The term bathymetry is used to describe underwater relief, while hypsometry studies terrain relative to sea level. The ...
, the three-dimensional quality of the surface, and the identification of specific
landform A landform is a natural or anthropogenic land feature on the solid surface of the Earth or other planetary body. Landforms together make up a given terrain, and their arrangement in the landscape is known as topography. Landforms include hills, m ...
s; this is also known as geomorphometry. In modern usage, this involves generation of elevation data in digital form (
DEM DEM was the ISO 4217 currency code for the Deutsche Mark, former currency of Germany Computing * Digital elevation model, a digital representation of ground-surface topography or terrain ** .dem, a common extension for USGS DEM files * Discre ...
). It is often considered to include the graphic representation of the landform on a map by a variety of
cartographic relief depiction Terrain cartography or relief mapping is the depiction of the shape of the surface of the Earth on a map, using one or more of several techniques that have been developed. Terrain or relief is an essential aspect of physical geography, and as su ...
techniques, including
contour line A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a plane section of the three-dimensional gra ...
s, hypsometric tints, and relief shading.


Etymology

The term ''topography'' originated in
ancient Greece Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity ( AD 600), that comprised a loose collection of cult ...
and continued in ancient Rome, as the detailed description of a place. The word comes from the Greek (''topos'', "place") and (''-graphia'', "writing"). In classical literature this refers to writing about a place or places, what is now largely called '
local history Local history is the study of history in a geographically local context, often concentrating on a relatively small local community. It incorporates cultural and social aspects of history. Local history is not merely national history writ small b ...
'. In Britain and in Europe in general, the word topography is still sometimes used in its original sense. Detailed military surveys in
Britain Britain most often refers to: * The United Kingdom, a sovereign state in Europe comprising the island of Great Britain, the north-eastern part of the island of Ireland and many smaller islands * Great Britain, the largest island in the United King ...
(beginning in the late eighteenth century) were called Ordnance Surveys, and this term was used into the 20th century as generic for topographic surveys and maps. The earliest scientific surveys in France were called the Cassini maps after the family who produced them over four generations. The term "topographic surveys" appears to be American in origin. The earliest detailed surveys in the United States were made by the "Topographical Bureau of the Army," formed during the War of 1812, which became the
Corps of Topographical Engineers The U.S. Army Corps of Topographical Engineers was a branch of the United States Army authorized on 4 July 1838. It consisted only of officers who were handpicked from West Point and was used for mapping and the design and construction of federal ...
in 1838. After the work of national mapping was assumed by the
U.S. Geological Survey The United States Geological Survey (USGS), formerly simply known as the Geological Survey, is a scientific agency of the United States government. The scientists of the USGS study the landscape of the United States, its natural resources, a ...
in 1878, the term topographical remained as a general term for detailed surveys and mapping programs, and has been adopted by most other nations as standard. In the 20th century, the term topography started to be used to describe surface description in other fields where mapping in a broader sense is used, particularly in medical fields such as neurology.


Objectives

An objective of topography is to determine the position of any feature or more generally any point in terms of both a horizontal
coordinate system In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sign ...
such as latitude, longitude, and
altitude Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...
. Identifying (naming) features, and recognizing typical landform patterns are also part of the field. A topographic study may be made for a variety of reasons: military planning and geological exploration have been primary motivators to start survey programs, but detailed information about
terrain Terrain or relief (also topography, topographical relief) involves the vertical and horizontal dimensions of land surface. The term bathymetry is used to describe underwater relief, while hypsometry studies terrain relative to sea level. The ...
and surface features is essential for the planning and construction of any major civil engineering, public works, or reclamation projects.


Techniques

There are a variety of approaches to studying topography. Which method(s) to use depends on the scale and size of the area under study, its accessibility, and the quality of existing surveys.


Field survey

Surveying helps determine accurately the terrestrial or three-dimensional space position of points and the distances and
angle In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the ''vertex'' of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles a ...
s between them using leveling instruments such as
theodolite A theodolite () is a precision optical instrument for measuring angles between designated visible points in the horizontal and vertical planes. The traditional use has been for land surveying, but it is also used extensively for building and ...
s, dumpy levels and
clinometer An inclinometer or clinometer is an instrument used for measuring angles of slope, elevation, or depression of an object with respect to gravity's direction. It is also known as a ''tilt indicator'', ''tilt sensor'', ''tilt meter'', ''slop ...
s. Work on one of the first topographic maps was begun in France by Giovanni Domenico Cassini, the great Italian astronomer. Even though remote sensing has greatly sped up the process of gathering information, and has allowed greater accuracy control over long distances, the direct survey still provides the basic control points and framework for all topographic work, whether manual or GIS-based. In areas where there has been an extensive direct survey and mapping program (most of Europe and the Continental U.S., for example), the compiled data forms the basis of basic digital elevation datasets such as
USGS DEM The USGS DEM standard is a geospatial file format developed by the United States Geological Survey for storing a raster-based digital elevation model. It is an open standard, and is used throughout the world. It has been superseded by the USGS's ow ...
data. This data must often be "cleaned" to eliminate discrepancies between surveys, but it still forms a valuable set of information for large-scale analysis. The original American topographic surveys (or the British "Ordnance" surveys) involved not only recording of relief, but identification of landmark features and vegetative land cover.


Remote sensing

Remote sensing Remote sensing is the acquisition of information about an object or phenomenon without making physical contact with the object, in contrast to in situ or on-site observation. The term is applied especially to acquiring information about Earth ...
is a general term for geodata collection at a distance from the subject area.


Passive sensor methodologies

Besides their role in photogrammetry, aerial and satellite imagery can be used to identify and delineate terrain features and more general land-cover features. Certainly they have become more and more a part of
geovisualization Geovisualization or geovisualisation (short for geographic visualization), also known as cartographic visualization, refers to a set of tools and techniques supporting the analysis of geospatial data through the use of interactive visualization. ...
, whether maps or GIS systems. False-color and non-visible spectra imaging can also help determine the lie of the land by delineating vegetation and other land-use information more clearly. Images can be in visible colours and in other spectrum.


Photogrammetry

Photogrammetry is a measurement technique for which the
co-ordinates In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sign ...
of the points in 3D of an object are determined by the measurements made in two photographic
image An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensiona ...
s (or more) taken starting from different positions, usually from different passes of an aerial photography flight. In this technique, the common points are identified on each image. A line of sight (or
ray Ray may refer to: Fish * Ray (fish), any cartilaginous fish of the superorder Batoidea * Ray (fish fin anatomy), a bony or horny spine on a fin Science and mathematics * Ray (geometry), half of a line proceeding from an initial point * Ray (gr ...
) can be built from the camera location to the point on the object. It is the intersection of its rays (
triangulation In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle me ...
) which determines the relative three-dimensional position of the point. Known control points can be used to give these relative positions absolute values. More sophisticated
algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...
s can exploit other information on the scene known a priori (for example, symmetries in certain cases allowing the rebuilding of three-dimensional co-ordinates starting from one only position of the camera).


Active sensor methodologies

Satellite RADAR mapping is one of the major techniques of generating Digital Elevation Models (see below). Similar techniques are applied in
bathymetric Bathymetry (; ) is the study of underwater depth of ocean floors (''seabed topography''), lake floors, or river floors. In other words, bathymetry is the underwater equivalent to hypsometry or topography. The first recorded evidence of water de ...
surveys using sonar to determine the terrain of the ocean floor. In recent years,
LIDAR Lidar (, also LIDAR, or LiDAR; sometimes LADAR) is a method for determining ranges (variable distance) by targeting an object or a surface with a laser and measuring the time for the reflected light to return to the receiver. It can also be ...
(LIght Detection And Ranging), a remote sensing technique that uses a laser instead of radio waves, has increasingly been employed for complex mapping needs such as charting canopies and monitoring glaciers.


Forms of topographic data

Terrain is commonly modelled either using vector ( triangulated irregular network or TIN) or gridded (
Raster image upright=1, The Smiley, smiley face in the top left corner is a raster image. When enlarged, individual pixels appear as squares. Enlarging further, each pixel can be analyzed, with their colors constructed through combination of the values for ...
) mathematical models. In the most applications in
environmental science Environmental science is an interdisciplinary academic field that integrates physics, biology, and geography (including ecology, chemistry, plant science, zoology, mineralogy, oceanography, limnology, soil science, geology and physical geograp ...
s, land surface is represented and modelled using gridded models. In civil engineering and entertainment businesses, the most representations of land surface employ some variant of TIN models. In
geostatistics Geostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets. Developed originally to predict probability distributions of ore grades for mining operations, it is currently applied in diverse disciplines including pe ...
, land surface is commonly modelled as a combination of the two signals – the smooth (spatially correlated) and the rough (noise) signal. In practice, surveyors first sample heights in an area, then use these to produce a Digital Land Surface Model in the form of a TIN. The DLSM can then be used to visualize terrain, drape remote sensing images, quantify ecological properties of a surface or extract land surface objects. Note that the contour data or any other sampled elevation datasets are not a DLSM. A DLSM implies that elevation is available continuously at each location in the study area, i.e. that the map represents a complete surface. Digital Land Surface Models should not be confused with Digital Surface Models, which can be surfaces of the canopy, buildings and similar objects. For example, in the case of surface models produces using the lidar technology, one can have several surfaces – starting from the top of the canopy to the actual solid earth. The difference between the two surface models can then be used to derive volumetric measures (height of trees etc.).


Raw survey data

Topographic survey information is historically based upon the notes of surveyors. They may derive naming and cultural information from other local sources (for example,
boundary Boundary or Boundaries may refer to: * Border, in political geography Entertainment * ''Boundaries'' (2016 film), a 2016 Canadian film * ''Boundaries'' (2018 film), a 2018 American-Canadian road trip film * Boundary (cricket), the edge of the pl ...
delineation may be derived from local
cadastral A cadastre or cadaster is a comprehensive recording of the real estate or real property's metes-and-bounds of a country.Jo Henssen, ''Basic Principles of the Main Cadastral Systems in the World,'/ref> Often it is represented graphically in a cad ...
mapping). While of historical interest, these field notes inherently include errors and contradictions that later stages in map production resolve.


Remote sensing data

As with field notes, remote sensing data (aerial and satellite photography, for example), is raw and uninterpreted. It may contain holes (due to cloud cover for example) or inconsistencies (due to the timing of specific image captures). Most modern topographic mapping includes a large component of remotely sensed data in its compilation process.


Topographic mapping

In its contemporary definition, topographic mapping shows relief. In the United States, USGS topographic maps show relief using
contour lines A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a plane section of the three-dimensional grap ...
. The USGS calls maps based on topographic surveys, but without contours, "planimetric maps." These maps show not only the contours, but also any significant streams or other bodies of water,
forest cover Forest cover is the amount of forest that covers a particular area of land. It may be measured as relative (in percent) or absolute (in square kilometres/square miles). Around a third of the world's surface is covered with forest, with closed-canop ...
, built-up areas or individual buildings (depending on scale), and other features and points of interest. While not officially "topographic" maps, the national surveys of other nations share many of the same features, and so they are often called "topographic maps." Existing topographic survey maps, because of their comprehensive and encyclopedic coverage, form the basis for much derived topographic work. Digital Elevation Models, for example, have often been created not from new remote sensing data but from existing paper topographic maps. Many government and private publishers use the artwork (especially the contour lines) from existing topographic map sheets as the basis for their own specialized or updated topographic maps.See for example the publications o
National Geographic Trails Illustrated Maps
and DeLorme products.
Topographic mapping should not be confused with geologic mapping. The latter is concerned with underlying structures and processes to the surface, rather than with identifiable surface features.


Digital elevation modeling

The digital elevation model (DEM) is a raster-based
digital Digital usually refers to something using discrete digits, often binary digits. Technology and computing Hardware *Digital electronics, electronic circuits which operate using digital signals **Digital camera, which captures and stores digital i ...
dataset of the topography ( hypsometry and/or
bathymetry Bathymetry (; ) is the study of underwater depth of ocean floors (''seabed topography''), lake floors, or river floors. In other words, bathymetry is the underwater equivalent to hypsometry or topography. The first recorded evidence of water de ...
) of all or part of the Earth (or a telluric planet). The pixels of the dataset are each assigned an elevation value, and a header portion of the dataset defines the area of coverage, the units each pixel covers, and the units of elevation (and the zero-point). DEMs may be derived from existing paper maps and survey data, or they may be generated from new satellite or other remotely sensed radar or sonar data.


Topological modeling

A
geographic information system A geographic information system (GIS) is a type of database containing geographic data (that is, descriptions of phenomena for which location is relevant), combined with software tools for managing, analyzing, and visualizing those data. In a ...
(GIS) can recognize and analyze the spatial relationships that exist within digitally stored spatial data. These topological relationships allow complex spatial modelling and analysis to be performed. Topological relationships between geometric entities traditionally include adjacency (what adjoins what), containment (what encloses what), and proximity (how close something is to something else). * reconstitute a sight in synthesized images of the ground, * determine a trajectory of overflight of the ground, * calculate surfaces or volumes, * trace topographic profiles,


Topography in other fields

Topography has been applied to different science fields. In neuroscience, the
neuroimaging Neuroimaging is the use of quantitative (computational) techniques to study the structure and function of the central nervous system, developed as an objective way of scientifically studying the healthy human brain in a non-invasive manner. Incre ...
discipline uses techniques such as EEG topography for
brain mapping Brain mapping is a set of neuroscience techniques predicated on the mapping of (biological) quantities or properties onto spatial representations of the (human or non-human) brain resulting in maps. According to the definition established in ...
. In ophthalmology,
corneal topography Corneal topography, also known as photokeratoscopy or videokeratography, is a non-invasive medical imaging technique for mapping the anterior curvature of the cornea, the outer structure of the eye. Since the cornea is normally responsible for som ...
is used as a technique for mapping the surface curvature of the
cornea The cornea is the transparent front part of the eye that covers the iris, pupil, and anterior chamber. Along with the anterior chamber and lens, the cornea refracts light, accounting for approximately two-thirds of the eye's total optical powe ...
. In tissue engineering,
atomic force microscopy Atomic force microscopy (AFM) or scanning force microscopy (SFM) is a very-high-resolution type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the opti ...
is used to map nanotopography. In
human anatomy The human body is the structure of a human being. It is composed of many different types of cells that together create tissues and subsequently organ systems. They ensure homeostasis and the viability of the human body. It comprises a head, ...
, topography is superficial human anatomy. In mathematics the concept of topography is used to indicate the patterns or general organization of features on a map or as a term referring to the pattern in which variables (or their values) are distributed in a space.


Topographers

Topographers are experts in topography.


See also

*
Cartography Cartography (; from grc, χάρτης , "papyrus, sheet of paper, map"; and , "write") is the study and practice of making and using maps. Combining science, aesthetics and technique, cartography builds on the premise that reality (or an im ...
*
Digital elevation model A digital elevation model (DEM) or digital surface model (DSM) is a 3D computer graphics representation of elevation data to represent terrain or overlaying objects, commonly of a planet, moon, or asteroid. A "global DEM" refers to a discrete gl ...
*
Fall line (topography) A fall line refers to the line down a mountain or hill which is most directly downhill; that is, the direction a ball or other body would accelerate if it were free to move on the slope under gravity. Mathematically the fall line, the line of gr ...
*
Geomorphology Geomorphology (from Ancient Greek: , ', "earth"; , ', "form"; and , ', "study") is the scientific study of the origin and evolution of topographic and bathymetric features created by physical, chemical or biological processes operating at or ...
* Global Relief Model *
Hypsography Hypsometry () is the measurement of the elevation and depth of features of the Earth's surface relative to mean sea level. On Earth, the elevations can take on either positive or negative (below sea level) values. The distribution is theorised ...
* Marine topography *
Topographic map In modern mapping, a topographic map or topographic sheet is a type of map characterized by large- scale detail and quantitative representation of relief features, usually using contour lines (connecting points of equal elevation), but histori ...


References

{{Authority control Cartography Geography