Topography

# Topography

Overview
Topography is the study of Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

's surface
Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball...

shape and features or those of
Discussion

Recent Discussions
Encyclopedia
Topography is the study of Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

's surface
Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball...

shape and features or those of
planet
Planet
A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...

s, moons
Natural satellite
A natural satellite or moon is a celestial body that orbits a planet or smaller body, which is called its primary. The two terms are used synonymously for non-artificial satellites of planets, of dwarf planets, and of minor planets....

, and asteroids. It is also the description of such surface shapes and features (especially their depiction in maps).

The topography of an area can also mean the surface shape and features themselves.

In a broader sense, topography is concerned with local detail in general, including not only relief
Terrain
Terrain, or land relief, is the vertical and horizontal dimension of land surface. When relief is described underwater, the term bathymetry is used...

but also vegetative
Vegetation
Vegetation is a general term for the plant life of a region; it refers to the ground cover provided by plants. It is a general term, without specific reference to particular taxa, life forms, structure, spatial extent, or any other specific botanical or geographic characteristics. It is broader...

and human-made features, and even local history
Local history
Local history is the study of history in a geographically local context and it often concentrates on the local community. It incorporates cultural and social aspects of history...

and culture
Culture
Culture is a term that has many different inter-related meanings. For example, in 1952, Alfred Kroeber and Clyde Kluckhohn compiled a list of 164 definitions of "culture" in Culture: A Critical Review of Concepts and Definitions...

. This meaning is less common in America, where topographic maps with elevation
Elevation
The elevation of a geographic location is its height above a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface ....

contours have made "topography" synonymous with relief. The older sense of topography as the study of place still has currency in Europe.

For the purposes of this article, topography specifically involves the recording of relief or terrain
Terrain
Terrain, or land relief, is the vertical and horizontal dimension of land surface. When relief is described underwater, the term bathymetry is used...

, the three-dimensional quality of the surface, and the identification of specific landform
Landform
A landform or physical feature in the earth sciences and geology sub-fields, comprises a geomorphological unit, and is largely defined by its surface form and location in the landscape, as part of the terrain, and as such, is typically an element of topography...

s. This is also known as geomorphometry
Geomorphometry
Geomorphometry is the science of quantitative land surface analysis. It gathers various mathematical, statistical and image processing techniques that can be used to quantify morphological, hydrological, ecological and other aspects of a land surface. Common synonyms for geomorphometry are...

. In modern usage, this involves generation of elevation data in electronic form. It is often considered to include the graphic representation of the landform on a map
Map
A map is a visual representation of an area—a symbolic depiction highlighting relationships between elements of that space such as objects, regions, and themes....

by a variety of techniques
Cartographic relief depiction
Terrain or relief is an essential aspect of physical geography, and as such its portrayal presents a central problem in cartography, and more recently GIS and 3D Visualization....

, including contour line
Contour line
A contour line of a function of two variables is a curve along which the function has a constant value. In cartography, a contour line joins points of equal elevation above a given level, such as mean sea level...

s, Hypsometric tints
Hypsometric tints
Hypsometric tints are related to contour lines. They can be used to depict ranges of elevation as bands of color, usually in a graduated scheme, or as a color ramp applied to contour lines themselves. A typical scheme progresses from dark greens for lower elevations up through yellows/browns, and...

## Etymology

The term topography originated in ancient Greece
Ancient Greece
Ancient Greece is a civilization belonging to a period of Greek history that lasted from the Archaic period of the 8th to 6th centuries BC to the end of antiquity. Immediately following this period was the beginning of the Early Middle Ages and the Byzantine era. Included in Ancient Greece is the...

and continued in ancient Rome
Ancient Rome
Ancient Rome was a thriving civilization that grew on the Italian Peninsula as early as the 8th century BC. Located along the Mediterranean Sea and centered on the city of Rome, it expanded to one of the largest empires in the ancient world....

, as the detailed description of a place. The word comes from the Greek words  (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
Local history is the study of history in a geographically local context and it often concentrates on the local community. It incorporates cultural and social aspects of history...

'. In Britain and in Europe in general, the word topography is still sometimes used in its original sense.

Detailed military surveys in Britain
Great Britain
Great Britain or Britain is an island situated to the northwest of Continental Europe. It is the ninth largest island in the world, and the largest European island, as well as the largest of the British Isles...

(beginning in the late eighteenth century) were called Ordnance Survey
Ordnance Survey
Ordnance Survey , an executive agency and non-ministerial government department of the Government of the United Kingdom, is the national mapping agency for Great Britain, producing maps of Great Britain , and one of the world's largest producers of maps.The name reflects its creation together with...

s, 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
César-François Cassini de Thury
César-François Cassini de Thury , also called Cassini III or Cassini de Thury, was a French astronomer and cartographer.- Biography :...

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
War of 1812
The War of 1812 was a military conflict fought between the forces of the United States of America and those of the British Empire. The Americans declared war in 1812 for several reasons, including trade restrictions because of Britain's ongoing war with France, impressment of American merchant...

,. which became the Corps of Topographical Engineers
Corps of Topographical Engineers
The U.S. Army Corps of Topographical Engineers, was separately authorized on 4 July 1838, consisted only of officers, and was used for mapping and the design and construction of federal civil works such as lighthouses and other coastal fortifications and navigational routes. It included such...

in 1838]]. After the work of national mapping was assumed by the U.S. Geological Survey 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 map
Map
A map is a visual representation of an area—a symbolic depiction highlighting relationships between elements of that space such as objects, regions, and themes....

ping in a broader sense is used, particularly in medical fields such as neurology
Neurology
Neurology is a medical specialty dealing with disorders of the nervous system. Specifically, it deals with the diagnosis and treatment of all categories of disease involving the central, peripheral, and autonomic nervous systems, including their coverings, blood vessels, and all effector tissue,...

.

## 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
Coordinate system
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element. The order of the coordinates is significant and they are sometimes identified by their position in an ordered tuple and sometimes by...

such as latitude, longitude, and altitude
Altitude
Altitude or height is defined based on the context in which it is used . As a general definition, altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The reference datum also often varies according to the context...

. Identifying (naming) features and recognizing typical landform patterns are also part of the field.

A topographic study
Surveying
See Also: Public Land Survey SystemSurveying or land surveying is the technique, profession, and science of accurately determining the terrestrial or three-dimensional position of points and the distances and angles between them...

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
Terrain, or land relief, is the vertical and horizontal dimension of land surface. When relief is described underwater, the term bathymetry is used...

and surface features is essential for the planning
Planning
Planning in organizations and public policy is both the organizational process of creating and maintaining a plan; and the psychological process of thinking about the activities required to create a desired goal on some scale. As such, it is a fundamental property of intelligent behavior...

and construction
Construction
In the fields of architecture and civil engineering, construction is a process that consists of the building or assembling of infrastructure. Far from being a single activity, large scale construction is a feat of human multitasking...

of any major civil engineering
Civil engineering
Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including works like roads, bridges, canals, dams, and buildings...

, public works
Public works
Public works are a broad category of projects, financed and constructed by the government, for recreational, employment, and health and safety uses in the greater community...

, or reclamation projects.

## Techniques of topography

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

### Direct survey

Surveying helps determine accurately the terrestrial or three-dimensional space
Three-dimensional space
Three-dimensional space is a geometric 3-parameters model of the physical universe in which we live. These three dimensions are commonly called length, width, and depth , although any three directions can be chosen, provided that they do not lie in the same plane.In physics and mathematics, a...

position of points and the distances and angles between them using leveling instruments such as theodolite
Theodolite
A theodolite is a precision instrument for measuring angles in the horizontal and vertical planes. Theodolites are mainly used for surveying applications, and have been adapted for specialized purposes in fields like metrology and rocket launch technology...

s, dumpy level
Dumpy level
A dumpy level, builder's auto level, leveling instrument, or automatic level is an optical instrument used to establish or check points in the same horizontal plane...

s and clinometers.

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 US, for example), the compiled data forms the basis of basic digital elevation datasets such as USGS DEM
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...

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
Remote sensing is the acquisition of information about an object or phenomenon, without making physical contact with the object. In modern usage, the term generally refers to the use of aerial sensor technologies to detect and classify objects on Earth by means of propagated signals Remote sensing...

is a general term for geodata collection at a distance from the subject area.

#### Aerial and satellite imagery

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
Geovisualization, short for Geographic Visualization, refers to a set of tools and techniques supporting geospatial data analysis through the use of interactive visualization....

, whether maps
MAPS
Maps is the plural of map, a visual representation of an area.As an acronym, MAPS may refer to:* Mail Abuse Prevention System, an organisation that provides anti-spam support...

or GIS systems. False-color and non-visible spectra
Spectrum
A spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by...

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 of the points in 3D
Three-dimensional space
Three-dimensional space is a geometric 3-parameters model of the physical universe in which we live. These three dimensions are commonly called length, width, and depth , although any three directions can be chosen, provided that they do not lie in the same plane.In physics and mathematics, a...

of an object are determined by the measurements made in two photographic image
Image
An image is an artifact, for example a two-dimensional picture, that has a similar appearance to some subject—usually a physical object or a person.-Characteristics:...

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 (optics)
In optics, a ray is an idealized narrow beam of light. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very...

) can be built from the camera location to the point on the object. It is the intersection of its rays (triangulation
Triangulation
In trigonometry and geometry, triangulation is the process of determining the location of a point by measuring angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly...

) 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
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

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).

Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...

mapping is one of the major techniques of generating Digital Elevation Models (see below). Similar techniques are applied in bathymetric
Bathymetry
Bathymetry is the study of underwater depth of lake or ocean floors. In other words, bathymetry is the underwater equivalent to hypsometry. The name comes from Greek βαθύς , "deep", and μέτρον , "measure"...

surveys using sonar
Sonar
Sonar is a technique that uses sound propagation to navigate, communicate with or detect other vessels...

to determine the terrain of the ocean floor. In recent years, LIDAR
LIDAR
LIDAR is an optical remote sensing technology that can measure the distance to, or other properties of a target by illuminating the target with light, often using pulses from a laser...

(Light Detection and Ranging), a remote sensing technique using 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
Triangulated irregular network
A triangulated irregular network is a digital data structure used in a geographic information system for the representation of a surface...

or TIN) or gridded (Raster image) mathematical models. In the most applications in environmental sciences, 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
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 petroleum geology, hydrogeology, hydrology, meteorology,...

, 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 (also known as a digital elevation model
Digital elevation model
A digital elevation model is a digital model or 3-D representation of a terrain's surface — commonly for a planet , moon, or asteroid — created from terrain elevation data....

). 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
LIDAR
LIDAR is an optical remote sensing technology that can measure the distance to, or other properties of a target by illuminating the target with light, often using pulses from a laser...

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 (topology)
In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S. More precisely, it is the set of points in the closure of S, not belonging to the interior of S. An element of the boundary...

delineation may be derived from local cadastral 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. 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
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

, forest
Forest
A forest, also referred to as a wood or the woods, is an area with a high density of trees. As with cities, depending where you are in the world, what is considered a forest may vary significantly in size and have various classification according to how and what of the forest is composed...

cover, 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 generally 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

Topographic mapping should not be confused with Geologic map
Geologic map
A geologic map or geological map is a special-purpose map made to show geological features. Rock units or geologic strata are shown by color or symbols to indicate where they are exposed at the surface...

ping. 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
Raster graphics
In computer graphics, a raster graphics image, or bitmap, is a data structure representing a generally rectangular grid of pixels, or points of color, viewable via a monitor, paper, or other display medium...

-based digital
Digital
A digital system is a data technology that uses discrete values. By contrast, non-digital systems use a continuous range of values to represent information...

dataset of the topography (hypsometry
Hypsometry
Hypsometry is the measurement of land elevation relative to sea level. Bathymetry is the underwater equivalent...

and/or bathymetry
Bathymetry
Bathymetry is the study of underwater depth of lake or ocean floors. In other words, bathymetry is the underwater equivalent to hypsometry. The name comes from Greek βαθύς , "deep", and μέτρον , "measure"...

) 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
Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...

or sonar
Sonar
Sonar is a technique that uses sound propagation to navigate, communicate with or detect other vessels...

data.

### Topological modeling

A geographic information system
Geographic Information System
A geographic information system, geographical information science, or geospatial information studies is a system designed to capture, store, manipulate, analyze, manage, and present all types of geographically referenced data...

(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
Neuroscience
Neuroscience is the scientific study of the nervous system. Traditionally, neuroscience has been seen as a branch of biology. However, it is currently an interdisciplinary science that collaborates with other fields such as chemistry, computer science, engineering, linguistics, mathematics,...

, the neuroimaging
Neuroimaging
Neuroimaging includes the use of various techniques to either directly or indirectly image the structure, function/pharmacology of the brain...

discipline uses techniques such as EEG topography for brain mapping
Brain mapping
Brain mapping is a set of neuroscience techniques predicated on the mapping of quantities or properties onto spatial representations of the brain resulting in maps.- Overview :...

. In ophthalmology
Ophthalmology
Ophthalmology is the branch of medicine that deals with the anatomy, physiology and diseases of the eye. An ophthalmologist is a specialist in medical and surgical eye problems...

, corneal topography
Corneal topography
Corneal topography, also known as photokeratoscopy or videokeratography, is a non-invasive medical imaging technique for mapping the surface curvature of the cornea, the outer structure of the eye...

is used as a technique for mapping the surface curvature of the cornea
Cornea
The cornea is the transparent front part of the eye that covers the iris, pupil, and anterior chamber. Together with the lens, the cornea refracts light, with the cornea accounting for approximately two-thirds of the eye's total optical power. In humans, the refractive power of the cornea is...

.

In human anatomy
Human anatomy
Human anatomy is primarily the scientific study of the morphology of the human body. Anatomy is subdivided into gross anatomy and microscopic anatomy. Gross anatomy is the study of anatomical structures that can be seen by the naked eye...

, 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.