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Spatial reference system
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A spatial reference system (SRS) or coordinate reference system (CRS) is a framework used to precisely measure locations on the surface of Earth as coordinates. It is thus the application of the abstract mathematics of coordinate systems and analytic geometry to geographic space. A particular SRS specification (for example, "Universal Transverse Mercator WGS 84 Zone 16N") comprises a choice of Earth ellipsoid, horizontal datum, map projection (except in the geographic coordinate system), origin point, and unit of measure. Thousands of coordinate systems have been specified for use around the world or in specific regions and for various purposes, necessitating transformations between different SRS.
Although they date to the Hellenistic period, spatial reference systems are now a crucial basis for the sciences and technologies of Geoinformatics, including cartography, geographic information systems, surveying, remote sensing, and civil engineering. This has led to their standardization in international specifications such as the EPSG codes[1] and ISO 19111:2019 Geographic information—Spatial referencing by coordinates, prepared by ISO/TC 211, also published by the Open Geospatial Consortium as Abstract Specification, Topic 2: Spatial referencing by coordinate.[2]
Types of systems
[edit]
The thousands of spatial reference systems used today are based on a few general strategies, which have been defined in the EPSG, ISO, and OGC standards:[1][2]
- Geographic coordinate system (or geodetic)
- A spherical coordinate system measuring locations directly on the Earth (modeled as a sphere or ellipsoid) using latitude (degrees north or south of the equator) and longitude (degrees west or east of a prime meridian).
- Geocentric coordinate system (or Earth-centered Earth-fixed)
- A three-dimensional cartesian coordinate system that models the Earth as a three-dimensional object, measuring locations from a center point, usually the center of mass of the Earth, along x, y, and z axes aligned with the equator and the prime meridian. This system is commonly used to track the orbits of satellites, because they are based on the center of mass. Thus, this is the internal coordinate system used by Satellite navigation systems such as GPS to compute locations using multilateration.
- Projected coordinate system (or planar, grid)
Layout of a UTM coordinate system - A standardized cartesian coordinate system that models the surface of Earth (or more commonly, a large region thereof) as a plane, measuring locations from an arbitrary origin point along x and y axes more or less aligned with the cardinal directions. Each of these systems is based on a particular Map projection to create a planar surface from the curved Earth surface. These are generally defined and used strategically to minimize the distortions inherent to projections. Common examples include the Universal transverse mercator (UTM) and national systems such as the British National Grid, and State Plane Coordinate System (SPCS).
- Engineering coordinate system (or local, custom)
- A cartesian coordinate system (2-D or 3-D) that is created bespoke for a small area, often a single engineering project, over which the curvature of the Earth can be safely approximated as flat without significant distortion. Locations are typically measured directly from an arbitrary origin point using surveying techniques. These may or may not be aligned with a standard projected coordinate system. Local tangent plane coordinates are a type of local coordinate system used in aviation and marine vehicles.
- Vertical reference frame
- a standard reference system for measuring elevation using vertical datums, based on levelling, a geoid model, or a chart datum (considering tides).
These standards acknowledge that standard reference systems also exist for time (e.g. ISO 8601). These may be combined with a spatial reference system to form a compound coordinate system for representing three-dimensional and/or spatio-temporal locations. There are also internal systems for measuring location within the context of an object, such as the rows and columns of pixels in a raster image, Linear referencing measurements along linear features (e.g., highway mileposts), and systems for specifying location within moving objects such as ships. The latter two are often classified as subcategories of engineering coordinate systems.
Components
[edit]The goal of any spatial reference system is to create a common reference frame in which locations can be measured precisely and consistently as coordinates, which can then be shared unambiguously, so that any recipient can identify the same location that was originally intended by the originator.[3] To accomplish this, any coordinate reference system definition needs to be composed of several specifications:
- A coordinate system, an abstract framework for measuring locations. Like any mathematical coordinate system, its definition consists of a measurable space (whether a plane, a three-dimension void, or the surface of an object such as the Earth), an origin point, a set of axis vectors emanating from the origin, and a unit of measure.
- A geodetic datum (horizontal, vertical, or three-dimensional) which binds the abstract coordinate system to the real space of the Earth. A horizontal datum can be defined as a precise reference framework for measuring geographic coordinates (latitude and longitude). Examples include the World Geodetic System and the 1927 and 1983 North American Datum. A datum generally consists of an estimate of the shape of the Earth (usually an ellipsoid), and one or more anchor points or control points, established locations (often marked by physical monuments) for which the measurement is documented.
- A definition for a projected CRS must also include a choice of map projection to convert the spherical coordinates specified by the datum into cartesian coordinates on a planar surface.
Thus, a CRS definition will typically consist of a "stack" of dependent specifications, as exemplified in the following table:
| EPSG code | Name | Ellipsoid | Horizontal datum | CS type | Projection | Origin | Axes | Unit of measure |
|---|---|---|---|---|---|---|---|---|
| 4326 | GCS WGS 84 | GRS 80 | WGS 84 | ellipsoidal (lat, lon) | — | equator/prime meridian | equator, prime meridian | degree of arc |
| 26717 | UTM Zone 17N NAD 27 | Clarke 1866 | NAD 27 | cartesian (x,y) | Transverse Mercator: central meridian 81°W, scaled 0.9996 | 500 km west of (81°W, 0°N) | equator, 81°W meridian | metre |
| 6576 | SPCS Tennessee Zone NAD 83 (2011) ftUS | GRS 80 | NAD 83 (2011 epoch) | cartesian (x,y) | Lambert Conformal Conic: center 86°W, 34°20'N, standard parallels 35°15'N, 36°25'N | 600 km grid west of center point | grid east at center point, 86°W meridian | US survey foot |
Examples by continent
[edit]Examples of systems around the world are:
Asia
[edit]- Chinese Global Navigation Grid Code, China
- Israeli Cassini Soldner, Israel
- Israeli Transverse Mercator, Israel
- Jordan Transverse Mercator, Jordan
Europe
[edit]- British national grid reference system, Britain
- Lambert-93 (fr), the official projection in Metropolitan France
- Hellenic Geodetic Reference System 1987, Greece
- Irish grid reference system, Ireland
- Irish Transverse Mercator, Ireland
- SWEREF 99 (sv), Sweden
North America
[edit]- United States National Grid and State Plane Coordinate System (SPCS), US
- Modified transverse Mercator coordinate system, Canada
Worldwide
[edit]Identifiers
[edit]A Spatial Reference System Identifier (SRID) is a unique value used to unambiguously identify projected, unprojected, and local spatial coordinate system definitions. These coordinate systems form the heart of all GIS applications.
Virtually all major spatial vendors have created their own SRID implementation or refer to those of an authority, such as the EPSG Geodetic Parameter Dataset.
SRIDs are the primary key for the Open Geospatial Consortium (OGC) spatial_ref_sys metadata table for the Simple Features for SQL Specification, Versions 1.1 and 1.2, which is defined as follows:
CREATE TABLE SPATIAL_REF_SYS
(
SRID INTEGER NOT NULL PRIMARY KEY,
AUTH_NAME CHARACTER VARYING(256),
AUTH_SRID INTEGER,
SRTEXT CHARACTER VARYING(2048)
)
In spatially enabled databases (such as IBM Db2, IBM Informix, Ingres, Microsoft SQL Server, MonetDB, MySQL, Oracle RDBMS, Teradata, PostGIS, SQL Anywhere and Vertica), SRIDs are used to uniquely identify the coordinate systems used to define columns of spatial data or individual spatial objects in a spatial column (depending on the spatial implementation). SRIDs are typically associated with a well-known text (WKT) string definition of the coordinate system (SRTEXT, above). Here are two common coordinate systems with their EPSG SRID value followed by their WKT:
UTM, Zone 17N, NAD27 — SRID 2029:
PROJCS["NAD27(76) / UTM zone 17N",
GEOGCS["NAD27(76)",
DATUM["North_American_Datum_1927_1976",
SPHEROID["Clarke 1866",6378206.4,294.9786982138982,
AUTHORITY["EPSG","7008"]],
AUTHORITY["EPSG","6608"]],
PRIMEM["Greenwich",0,
AUTHORITY["EPSG","8901"]],
UNIT["degree",0.01745329251994328,
AUTHORITY["EPSG","9122"]],
AUTHORITY["EPSG","4608"]],
UNIT["metre",1,
AUTHORITY["EPSG","9001"]],
PROJECTION["Transverse_Mercator"],
PARAMETER["latitude_of_origin",0],
PARAMETER["central_meridian",-81],
PARAMETER["scale_factor",0.9996],
PARAMETER["false_easting",500000],
PARAMETER["false_northing",0],
AUTHORITY["EPSG","2029"],
AXIS["Easting",EAST],
AXIS["Northing",NORTH]]
WGS84 — SRID 4326
GEOGCS["WGS 84",
DATUM["WGS_1984",
SPHEROID["WGS 84",6378137,298.257223563,
AUTHORITY["EPSG","7030"]],
AUTHORITY["EPSG","6326"]],
PRIMEM["Greenwich",0,
AUTHORITY["EPSG","8901"]],
UNIT["degree",0.01745329251994328,
AUTHORITY["EPSG","9122"]],
AUTHORITY["EPSG","4326"]]
SRID values associated with spatial data can be used to constrain spatial operations — for instance, spatial operations cannot be performed between spatial objects with differing SRIDs in some systems, or trigger coordinate system transformations between spatial objects in others.
See also
[edit]References
[edit]- ^ a b "Using the EPSG geodetic parameter dataset, Guidance Note 7-1". EPSG Geodetic Parameter Dataset. Geomatic Solutions. Archived from the original on 15 December 2021. Retrieved 15 December 2021.
- ^ a b "OGC Abstract Specification Topic 2: Referencing by coordinates Corrigendum". Open Geospatial Consortium. Archived from the original on 2021-07-30. Retrieved 2018-12-25.
- ^ A guide to coordinate systems in Great Britain (PDF), D00659 v2.3, Ordnance Survey, 2020, p. 11, archived from the original (PDF) on 24 September 2015, retrieved 2021-12-16
External links
[edit]
Wikidata has the property:
- spatialreference.org – A website with more than 13000 spatial reference systems, in a variety of formats.
- OpenGIS Specifications (Standards) Archived 2004-12-13 at the Wayback Machine
- OpenGIS Simple Features Specification for CORBA (99-054)
- OpenGIS Simple Features Specification for OLE/COM (99-050)
- OpenGIS Simple Features Specification for SQL (99-054, 05-134, 06-104r3)
- OGR Archived 2006-04-22 at the Wayback Machine — library implementing relevant OGC standards
- EPSG.org - Official EPSG Geodetic Parameter Dataset webpage. Search engine for EPSG defined reference systems.
- EPSG.io/ - Full text search indexing over 6000 coordinate systems
- Galdos Systems INdicio CRS Registry
Spatial reference system
View on Grokipediafrom Grokipedia
A spatial reference system (SRS), also known as a coordinate reference system (CRS), is a standardized framework that defines the coordinate system used to locate geographic features and represent spatial data on the Earth's surface, typically incorporating a datum, ellipsoid, and optional projection to ensure accurate positioning and measurement.[1][2][3]
SRSs are essential in geographic information systems (GIS) and geospatial applications for integrating data from diverse sources, enabling precise mapping, analysis, and visualization by aligning features to a common reference.[4][1] Without a consistent SRS, spatial data can appear misaligned or distorted, leading to errors in distance calculations, area measurements, and spatial queries.[5][2]
Key components of an SRS include the datum, which models the Earth's shape and orientation using an ellipsoid to approximate its irregular surface; the ellipsoid, a mathematical representation of the Earth's curvature (e.g., GRS80 in NAD83); and, for projected systems, a map projection that transforms three-dimensional spherical coordinates into two-dimensional planar ones using linear units like meters.[1] There are two primary types: geographic coordinate systems, which use angular units such as latitude and longitude in degrees without projection (e.g., for global datasets); and projected coordinate systems, which apply projections like Universal Transverse Mercator (UTM) to minimize distortion in specific regions.[5][1]
SRSs are often identified by unique codes from the EPSG Geodetic Parameter Dataset, such as EPSG:4326 for the widely used World Geodetic System 1984 (WGS84), which serves as the global standard for GPS and international mapping due to its compatibility with satellite-based positioning.[2][6] Other notable examples include NAD83 (EPSG:4269) for North America and equal-area projections like Eckert IV (EPSG:54012) for accurate areal computations in statistical analysis.[2][6] These systems facilitate transformations between different SRSs, ensuring interoperability in fields like environmental monitoring, urban planning, and resource management.[3]
Fundamentals
Definition and purpose
A spatial reference system (SRS), also referred to as a coordinate reference system (CRS), is a conceptual schema for the description of referencing by coordinates, defining the minimum data required to specify coordinate reference systems and coordinate operations.[7] It consists of a coordinate system associated with a datum that establishes a reference frame for positions on or near the Earth's surface, enabling the mathematical transformation of coordinates between different systems to link real-world locations with digital representations.[8] According to ISO 19111 modeling, an SRS is composed of key elements such as a geodetic datum and a coordinate system, providing a structured framework for geospatial positioning.[9] The fundamental purpose of an SRS is to facilitate accurate georeferencing in disciplines including geographic information systems (GIS), cartography, surveying, and navigation, where precise location representation is critical for data integration and analysis.[10] By defining how coordinates correspond to physical locations, SRS ensure the interoperability of spatial data across diverse software platforms, datasets, and geographic regions, allowing features from varied sources—such as roads, parcels, or elevation models—to align consistently for mapping, querying, and decision-making.[8] SRS are necessary to address the Earth's irregular oblate spheroid shape, which cannot be accurately represented on flat maps or in simple 3D models without distortion; the datum component approximates this geometry using parameters like semi-major axis and flattening to enable reliable real-world tying of coordinates.[8] Without such systems, geospatial data would lack a standardized basis for measurement, leading to errors in positioning and analysis across global or regional scales.[10] This bridging role underpins the hierarchical structure of SRS parameters, ensuring seamless coordination in complex geospatial workflows.[9]Historical development
The foundations of spatial reference systems trace back to ancient civilizations, where early attempts to systematize geographic positions laid the groundwork for modern coordinate frameworks. In the 2nd century BC, the Greek astronomer Hipparchus introduced the concept of latitude and longitude as a grid system for locating positions on Earth, building on earlier Babylonian and Egyptian astronomical observations. This system was refined and popularized by Claudius Ptolemy in his seminal work Geographia around 150 AD, which compiled coordinates for over 8,000 locations based on a spherical Earth model, enabling the first comprehensive world maps despite inaccuracies in scale and projection.[11] Advancements accelerated in the 17th and 18th centuries with improved understandings of Earth's shape. Isaac Newton proposed in his 1687 Principia Mathematica that Earth is an oblate spheroid due to rotational forces, challenging the prevailing spherical assumption and influencing subsequent geodetic measurements. In France, the Cassini family, led by Giovanni Domenico Cassini and his descendants, conducted extensive triangulation surveys starting in the late 17th century, culminating in the Cassini grid—a national coordinate system based on conic projections that mapped France with unprecedented accuracy by the mid-18th century. These efforts marked a shift toward empirical, regionally precise reference frameworks.[12][13][12] The 19th and early 20th centuries saw the proliferation of national datums to support large-scale surveying and mapping. In the United States, the North American Datum of 1927 (NAD27) was established through a comprehensive readjustment of over 26,000 survey stations using the Clarke 1866 ellipsoid, providing a consistent horizontal reference for North America that addressed inconsistencies in earlier local systems. Post-World War II, the advent of satellite geodesy, including launches like Sputnik in 1957, spurred international efforts for global reference systems by enabling precise measurements of Earth's gravitational field and orbit dynamics. The International Association of Geodesy (IAG), tracing its roots to the 1862 Mitteleuropäische Gradmessung and formally organized under the International Union of Geodesy and Geophysics in 1919, played a pivotal role in coordinating these advancements.[14][15][16][17] In the modern era, spatial reference systems evolved to accommodate global navigation and digital technologies. The World Geodetic System 1984 (WGS84), developed by the U.S. Department of Defense and released in 1984, became the standard for the Global Positioning System (GPS), integrating satellite data with a geocentric ellipsoid for worldwide accuracy within meters. The 1990s brought formalized international standards through ISO/Technical Committee 211 (ISO/TC 211), established in 1994 to develop interoperable norms for geographic information, including reference system identifiers and transformations. More recently, the Geocentric Datum of Australia 2020 (GDA2020), adopted in 2017, incorporates plate tectonics by aligning with the International Terrestrial Reference Frame, accounting for Australia's annual 7 cm drift. The launch of the EPSG (European Petroleum Survey Group) registry in the early 1990s further standardized codes for thousands of coordinate systems, facilitating data exchange in geospatial applications.[18][19]Key Components
Reference datum
A reference datum is a set of parameters that defines the origin, orientation, and scale of a coordinate system relative to the Earth's surface, typically modeled using an ellipsoid or the geoid.[20] It serves as the foundational reference for geospatial measurements, ensuring positions are tied to a consistent model of the Earth.[21] Reference datums are classified into horizontal and vertical types. Horizontal datums specify positions on the Earth's surface, such as latitude and longitude, with examples including the North American Datum of 1983 (NAD83) for North America.[22] Vertical datums define elevations relative to a reference surface like mean sea level, as in the North American Vertical Datum of 1988 (NAVD88).[23] Realizations of these datums can be satellite-based, such as the International Terrestrial Reference System (ITRS), or terrestrial, relying on ground surveys.[24] Key parameters of a reference datum include those defining the reference ellipsoid, such as the semi-major axis and flattening . For the World Geodetic System 1984 (WGS84) ellipsoid, meters and .[25] The flattening is calculated as , where is the semi-minor axis.[23] Geoid undulation models, which quantify the separation between the ellipsoid and the geoid, are also essential; the Earth Gravitational Model 2008 (EGM2008) provides global undulations to degree and order 2159 for height conversions.[25] Datums are realized through transformations, often using the 7-parameter Helmert method, which includes three translations, three rotations, and one scale factor to align coordinate frames.[26] Epoch-specific realizations like the International Terrestrial Reference Frame 2020 (ITRF2020) account for changes over time, with updates such as ITRF2020-u2023 incorporating three additional years of data to maintain accuracy.[27] Challenges in reference datums arise from datum shifts due to plate tectonics, with velocities typically ranging from 1-2 cm/year in many regions, necessitating periodic updates to the reference frame.[28]Coordinate system
A coordinate system in the context of a spatial reference system (SRS) defines the mathematical framework for expressing the positions of points through a set of axes, an origin, and associated units of measure. It specifies the geometry used to locate points in space, such as planar (2D) or geocentric (3D) configurations, enabling the assignment of numerical coordinates to geometric features. According to the Open Geospatial Consortium (OGC) Abstract Specification, a coordinate system consists of one or more coordinate axes, each with a direction and scale, forming the basis for coordinate tuples that represent locations relative to a reference frame.[9] The International Organization for Standardization (ISO) 19111 standard further describes it as the set of rules governing the arrangement of coordinate axes and the units in which coordinates are expressed, distinguishing it from the underlying reference model provided by the datum.[7] Common types of coordinate systems in SRS include Cartesian, which uses orthogonal axes (x, y, z) with linear measurements in units like meters, suitable for 3D Euclidean space such as Earth-centered, Earth-fixed (ECEF) representations. Geographic coordinate systems, in contrast, employ angular coordinates: latitude (φ) for north-south position, longitude (λ) for east-west position, and height (h) for vertical position, often combining angular units for the former two with linear units for the latter. Polar and cylindrical variants extend these by using radial distance (r) and angular measures (θ, z), though they are less prevalent in standard geospatial applications compared to Cartesian and geographic types. The OGC specification outlines these as coordinate system types, with Cartesian emphasizing rectangular grids and geographic aligning with spherical or ellipsoidal geometries.[9] ISO 19111 classifies them similarly, noting that geographic systems are inherently tied to ellipsoidal or spherical coordinate representations for global positioning.[7] Axes orientation in coordinate systems follows conventions like right-handed or left-handed triads, where a right-handed system adheres to the right-hand rule: if the index finger points along the positive x-axis and the middle finger along the positive y-axis, the thumb indicates the positive z-axis. Geocentric systems position the origin at Earth's center with axes aligned to the equator and prime meridian, while topocentric systems use a local origin on the surface with axes oriented east-north-up (ENU) relative to the tangent plane. Vertical components distinguish ellipsoidal height, measured along the normal to the reference ellipsoid, from orthometric height, which references the geoid approximating mean sea level. The National Geodetic Survey (NGS) documentation emphasizes right-handed orientations in geocentric Cartesian systems for consistency in ellipsoidal modeling.[29] OGC standards specify geocentric versus topocentric distinctions to ensure interoperability in spatial data exchange.[9] Units in coordinate systems are either angular, for directions like latitude and longitude, or linear, for distances like height or planar offsets. Angular units include degrees (360° per circle), radians (2π per circle), and gons (400 gon per circle, also known as gradians). Linear units commonly comprise meters (SI standard) and feet (international or U.S. survey). ISO 19111 mandates explicit unit definitions within coordinate system metadata to support precise computations.[7] For angular conversions, the standard formula transforms degrees to radians as , a fundamental relation used in geospatial calculations to align with trigonometric functions in Cartesian projections.[7] Coordinate systems integrate with the reference datum by anchoring their origin and orientation to the datum's defined surface and frame; for instance, in geographic systems, longitude zero is conventionally set at the Greenwich meridian, establishing the east-west reference relative to the datum's prime meridian. This linkage ensures that coordinates are meaningful only within the datum's context, as the datum provides the physical realization of the abstract axes. The NGS highlights this integration in geodetic datums like WGS 84, where the Greenwich meridian serves as the longitude origin for global consistency.[23] OGC guidelines reinforce that coordinate systems must reference datum parameters to form a complete SRS.[9]Map projection
A map projection is a systematic mathematical transformation that represents the three-dimensional surface of the Earth, modeled as an ellipsoid, onto a two-dimensional plane, converting curvilinear coordinates such as latitude and longitude into Cartesian coordinates suitable for mapping.[11] This process is essential to projected spatial reference systems, as it enables the creation of flat maps while inevitably introducing distortions due to the impossibility of perfectly preserving all geometric properties from a sphere or ellipsoid to a plane.[11] The choice of projection depends on the intended use, balancing trade-offs among shape, area, distance, and direction. Map projections are characterized by specific properties that determine what aspects of the Earth's surface they preserve. Conformal projections maintain angles and local shapes, ensuring that meridians and parallels intersect at right angles and that the scale is equal in all directions at any point, though they distort areas and distances away from the standard line or point.[11] The Mercator projection exemplifies conformality, making it suitable for navigation where angle preservation is critical.[11] Equal-area projections preserve the size of regions relative to the globe, avoiding area distortion but typically compromising on shapes and angles; the Mollweide projection is a pseudocylindrical example that achieves this globally.[11] Equidistant projections maintain true distances from a central point or along specified lines, such as meridians, but distort other distances and areas; the azimuthal equidistant projection demonstrates this property from its center.[11] Projections are classified based on the developable surface onto which the globe is conceptually projected, primarily cylindrical, conic, or azimuthal. Cylindrical projections treat the globe as wrapped by a cylinder tangent along a meridian or equator, resulting in straight, parallel meridians and parallels; the Universal Transverse Mercator (UTM) is a widely used transverse cylindrical variant for regional mapping.[11] Conic projections imagine the globe projected onto a cone tangent or secant at standard parallels, with meridians as straight lines converging at the apex and parallels as arcs; the Lambert conformal conic projection is common for mid-latitude regions like North America.[11] Azimuthal projections use a plane tangent to the globe at a pole or other point, preserving directions from the center; the polar stereographic projection serves polar mapping effectively.[11] Distortions in map projections arise from the differential stretching or compression of the Earth's surface and can be quantified using Tissot's indicatrix, a tool that depicts local scale distortion as an ellipse at each point on the map, derived from the projection of an infinitesimal circle on the globe.[11] The indicatrix's major and minor axes represent maximum and minimum scale variations, with its ellipticity indicating angular distortion and area change showing areal distortion.[11] A key metric is the linear scale factor , defined as the ratio of the infinitesimal distance on the map to the corresponding distance on the Earth , given by which equals 1 along standard lines but varies elsewhere, highlighting where the projection is true to scale.[11] Common parameters define the orientation and scale of a projection to minimize distortion in a target area. The central meridian is the reference longitude along which the projection is often true to scale, such as 96° W for continental U.S. mappings.[11] Standard parallels are latitudes of tangency or secancy where the scale is exact, typically two for conic projections like 33° N and 45° N in the Lambert conformal conic.[11] False easting and northing are arbitrary offsets added to coordinates to prevent negative values and set a convenient origin, such as 500,000 meters easting in the UTM system.[11]| Classification | Developable Surface | Key Characteristics | Example |
|---|---|---|---|
| Cylindrical | Cylinder tangent or secant to globe | Straight parallel meridians and parallels; distortion increases toward poles | Transverse Mercator (UTM)[11] |
| Conic | Cone tangent or secant along parallels | Radiating meridians, arc parallels; suited for mid-latitudes | Lambert Conformal Conic[11] |
| Azimuthal | Plane tangent at a point | True directions from center; circular or radial patterns | Polar Stereographic[11] |
Transformation parameters
Transformation parameters define the mathematical adjustments—such as translations, rotations, and scaling—required to convert coordinates between different spatial reference systems (SRS), particularly to align disparate datums like local surveys to global frames such as WGS 84.[30] These parameters ensure spatial data compatibility by modeling the relative positions, orientations, and sizes of coordinate frames, often derived from geodetic observations or empirical grids.[31] Affine transformations provide a general framework for 2D and 3D conversions, preserving parallelism and ratios of distances. In 2D, they involve six parameters: two translations, one rotation angle, one scale factor, and two shear factors, expressed as a 3x3 matrix applied to homogeneous coordinates. For 3D, twelve parameters extend this to include additional rotations and anisotropic scales, forming a 4x4 matrix for full spatial mapping. A specialized case for 3D datum shifts is the Bursa-Wolf model, which uses seven similarity parameters: translations (in meters), rotations (in arcseconds), and scale (in parts per million). The transformation relates geocentric position vectors (source) and (target) via where is the rotation matrix constructed from the angles, approximating rigid body motions for small distortions.[32] Concatenated transformations handle multi-step pipelines, such as combining a datum shift with a map projection, to achieve conversions between complex SRS. The PROJ library supports these as sequential operations, enabling efficient chaining of affine, Helmert (Bursa-Wolf), and projection steps for arbitrary CRS pairs.[33] Accuracy varies by method and region; parameter errors or unmodeled effects like epoch-specific crustal motion (due to tectonic plate shifts over time) can introduce positional discrepancies of meters or more if fixed parameters are used across epochs. Grid-based approaches like NTv2 enhance precision to centimeter levels by interpolating from high-resolution shift grids tailored to local distortions, outperforming parametric models in heterogeneous areas.[31][34] In GIS software, transformation parameters facilitate seamless data integration through on-the-fly reprojection, where tools like QGIS automatically apply conversions to display layers from diverse SRS in a unified project frame, minimizing manual intervention while preserving original data integrity.[35]Classification
Geographic reference systems
Geographic reference systems, also known as geographic coordinate systems, define positions on the Earth's surface using angular coordinates of latitude and longitude, typically measured relative to a reference datum's ellipsoid, with height optionally included for three-dimensional positioning.[36] These systems represent locations directly on the curved surface of the Earth without any map projection, providing a framework for global spatial referencing.[37] A prominent example is the World Geodetic System 1984 (WGS84) geographic system, identified by the EPSG code 4326, which employs latitude and longitude in degrees on the WGS84 ellipsoid.[38] One key advantage of geographic reference systems is their seamless global coverage, as they inherently account for the Earth's curvature without introducing projection-related distortions in angular measurements or spherical distances. This makes them ideal for applications requiring worldwide consistency, such as navigation and the integration of diverse global datasets.[37] However, these systems operate in a non-Euclidean space, where distances and areas must be computed using spherical trigonometry rather than simple Cartesian metrics, complicating certain analyses like straight-line measurements. For instance, the great-circle distance between two points is often calculated using the haversine formula: where is the Earth's radius, and are the latitudes, and and are the differences in latitude and longitude, respectively (with angles in radians).[39] Geographic reference systems are widely used in GPS positioning, where devices output coordinates in latitude, longitude, and height relative to the WGS84 datum for real-time navigation.[38] In web mapping, EPSG:4326 serves as the de facto standard for representing locations in digital maps and geospatial web services, enabling interoperability across platforms.[40] Variants of these systems include spherical approximations, which treat the Earth as a perfect sphere for simplified computations, and ellipsoidal models, which use a more precise oblate spheroid to better match the planet's actual shape and yield accurate distance calculations over long ranges.[41] Ellipsoidal systems integrate with reference datums to minimize errors in geodetic positioning.[37]Projected reference systems
Projected reference systems combine a geographic coordinate reference system with a map projection to produce planar coordinates, typically in meters, suitable for regional-scale mapping where distances and areas need to be measured accurately on a flat surface. These systems transform angular geographic coordinates (latitude and longitude) into Cartesian coordinates (e.g., easting and northing) by applying a mathematical projection that minimizes distortion within a defined area, such as a country or zone. Unlike global geographic systems, projected systems prioritize local accuracy for applications requiring metric outputs, often using conformal projections to preserve shapes and angles.[42][11] Selection of a projected reference system depends on the region's shape and the desired balance of distortions in scale, shape, and area. For elongated north-south regions, transverse cylindrical projections like the Transverse Mercator are chosen to minimize east-west distortion, with zones typically 6 degrees wide to keep scale errors below 1:1,000 (e.g., for maps at 1:50,000 scale). Conic projections, such as Lambert Conformal Conic, suit east-west extents by setting two standard parallels where scale is true, reducing distortion across mid-latitudes. Polar regions favor azimuthal projections to center distortion at the periphery while preserving directions from the pole. The scale factor along the central line or parallels is often set slightly below 1 (e.g., 0.9996) to ensure the projection converges properly and avoids negative coordinates.[11] Common classes include Transverse Mercator-based systems like the Universal Transverse Mercator (UTM), which divides the world into 60 zones numbered 1 to 60 from 180°W eastward, each with a central meridian scale factor of 0.9996; UTM is widely used for its global coverage and meter-based grids.[43][11] State Plane Coordinate Systems in the U.S. employ Transverse Mercator for north-south states and Lambert Conformal Conic for east-west ones, tailored to minimize distortion within each state or zone.[44] In Europe, the ETRS89-LAEA (EPSG:3035) uses a Lambert Azimuthal Equal-Area projection centered at 52°N, 10°E to provide equal-area representation for continental statistical analysis, preserving areas without shape distortion at the periphery.[45] Azimuthal projections, such as the Lambert Azimuthal Equal-Area or Stereographic, are applied to polar regions for their directional fidelity from the pole.[11] Grid systems in projected reference systems use a false origin offset from the natural projection origin to ensure all coordinates are positive within the region of use. For example, in UTM, the false easting is 500,000 meters at the central meridian, and false northing is 0 meters in the northern hemisphere or 10,000,000 meters in the southern to avoid negative values. The easting coordinate in the Transverse Mercator projection is calculated as: where is the central meridian scale factor, is the radius of curvature in the prime vertical, , , , and are longitude and latitude, is the central meridian, and is the ellipsoid eccentricity. This series expansion approximates the ellipsoidal surface for computational efficiency while maintaining sub-meter accuracy within zones.[11] These systems support large-scale mapping, such as topographic sheets at 1:24,000 or 1:50,000, where planar coordinates facilitate engineering calculations like distance measurements and area computations. They are essential for cadastral surveys, infrastructure planning, and GIS analyses requiring precise local metrics, such as in the U.S. State Plane system for construction projects or UTM for military and exploration fieldwork.[11][44]Specialized reference systems
Specialized reference systems extend beyond standard horizontal geographic or projected systems to address specific dimensional or contextual needs, such as vertical elevations, local engineering applications, temporal dynamics, celestial positioning, and image-specific coordinates. These systems are tailored for domains where global Earth-tied references are insufficient or impractical, ensuring precise measurements in specialized environments.[23] Vertical spatial reference systems (SRS) focus on defining heights or depths relative to a reference surface, typically the geoid or ellipsoid, to account for gravity variations and Earth's irregular shape. The geoid represents an equipotential surface approximating mean sea level, while ellipsoidal heights are measured perpendicular to a mathematical ellipsoid. For instance, the Earth Gravitational Model 2008 (EGM2008) provides a global geoid model with 2.5 arc-minute resolution, combining satellite gravimetry, altimetry, and terrestrial data to compute geoid undulations up to ±100 meters. In regional contexts, gravity-related datums like the North American Vertical Datum of 1988 (NAVD88) establish orthometric heights referenced to a continental geopotential surface, held fixed at the single tide gauge at Pointe-au-Père, Rimouski, Quebec, which defines mean sea level there, and used extensively for surveying and mapping in North America, although it is scheduled to be replaced in 2026 by the North American-Pacific Geopotential Datum of 2022 (NAPGD2022) as part of the modernized National Spatial Reference System (NSRS).[46][47][48] These systems enable accurate elevation data for applications requiring height above sea level, distinct from purely horizontal positioning.[46] Engineering SRS often employ local Cartesian coordinate systems decoupled from global Earth models, using an arbitrary origin and axes aligned to project-specific needs for simplicity and reduced computational overhead. In construction and mining, these systems define positions relative to a site-chosen benchmark, such as a survey pillar, with coordinates expressed in easting, northing, and elevation units like meters, avoiding distortions from large-scale projections. For example, mine grids typically rotate axes to align with tunnel orientations or site layouts, facilitating precise relative positioning without tying to national datums, which minimizes errors in confined spaces where absolute global coordinates are irrelevant. This approach prioritizes operational efficiency, with transformations to global systems applied only if integration with external data is required.[49][50] Temporal aspects in SRS introduce dynamic elements to account for Earth's changing geometry, particularly crustal deformations from plate tectonics, by incorporating time-dependent parameters into reference frames. The International Terrestrial Reference System (ITRS) exemplifies this, realized through the International Terrestrial Reference Frame (ITRF), which models station velocities due to plate motions at rates of 1-10 cm/year, allowing coordinates to evolve over epochs like ITRF2020. Plate motion models within ITRS, such as those derived from global navigation satellite systems (GNSS) observations, enable propagation of positions from a reference epoch (e.g., 2010.0) to current times, ensuring consistency in long-term geodetic monitoring amid tectonic shifts. This dynamism is crucial for maintaining accuracy in regions of high deformation, where static frames would accumulate errors exceeding 1 meter per decade.[51] Other specialized SRS include celestial systems for astronomical observations and image-based systems for remote sensing. Celestial SRS, such as the International Celestial Reference System (ICRS), define positions on the celestial sphere using right ascension and declination axes aligned with quasi-inertial directions from extragalactic radio sources, providing a stable frame independent of Earth's rotation for tracking stars and galaxies. In remote sensing, image-based SRS use pixel coordinates (row and column indices) georeferenced to a ground coordinate system via control points or affine transformations, linking each pixel's value to real-world locations in a specified SRS like UTM. This enables raster data integration into broader geospatial analyses by mapping intrinsic image geometry to external references.[52] Integration of specialized components often occurs through compound coordinate reference systems (CRS), which concatenate horizontal and vertical SRS to form a unified 3D framework. For example, combining the World Geodetic System 1984 (WGS 84, EPSG:4326) for latitude-longitude with the EGM96 geoid model (EPSG:5773) yields a compound CRS like EPSG:9707, where heights are orthometric relative to the geoid, supporting applications in navigation and altimetry that require both planar and elevational precision. These compounds maintain separability for transformations while providing comprehensive positioning.[53]Standards and Identification
International standards
The International Organization for Standardization's Technical Committee 211 (ISO/TC 211) plays a central role in developing standards for geographic information and geomatics, including those for spatial reference systems (SRS), with ISO 19111 serving as the foundational standard for spatial referencing by coordinates.[18] The Open Geospatial Consortium (OGC) complements this through its OpenGIS standards, which promote interoperability, notably via the Well-Known Text (WKT) format for encoding coordinate reference systems (CRS).[54] Additionally, the International Association of Geodesy (IAG) and the International Federation of Surveyors (FIG) contribute to geodesy standards, focusing on reference frames and their practical implementation in surveying and spatial data management.[55] ISO 19111:2019 defines the conceptual schema for describing referencing by coordinates, specifying the minimum data elements, relationships, and metadata needed for both static and dynamic SRS, including support for time-varying datums that account for changes in Earth's shape and orientation. This standard introduces subtypes for temporal and parametric coordinate reference systems, enabling the representation of positions that evolve over time, such as those influenced by geophysical processes.[56] The OGC's WKT 2 format, aligned with ISO 19111:2019, provides a compact, human- and machine-readable string representation of SRS; for example, a geographic coordinate system like WGS 84 can be encoded asGEOGCRS["WGS 84",DATUM["World Geodetic System 1984",ELLIPSOID["WGS 84",6378137,298.257223563,AUTHORITY["EPSG","7030"]],AUTHORITY["EPSG","6326"]],CS[ellipsoidal,2],AXIS["geodetic latitude (Lat)",north],AXIS["geodetic longitude (Lon)",east],UNIT["degree",0.0174532925199433,AUTHORITY["EPSG","9122"]]].[54]
For interoperability, ISO 19111 and OGC standards establish an abstract model distinguishing coordinate reference systems (CRS), which link coordinates to real-world locations via datums, from broader spatial reference systems (SRS) that encompass additional contextual elements like projections.[9] These frameworks mandate metadata requirements for spatial data infrastructures (SDI), such as detailed descriptions of coordinate operations and datum ensembles, to ensure seamless data exchange and integration across global systems, as outlined in ISO 19115 for geospatial metadata.[57]
The evolution of ISO 19111 reflects advancing needs in geospatial technology; the 2003 edition (second) focused on static referencing, while the 2019 revision (third) incorporated time-dependent elements, such as dynamic datums, to address real-world variability in reference frames.[58] As of 2025, the United Nations Committee of Experts on Global Geospatial Information Management (UN-GGIM) leverages ISO 19111 and related standards for the Global Geodetic Reference Frame to support sustainable development goals, including standardization for environmental monitoring and resource management.[59] Updates to vertical datums, accounting for climate-induced sea-level changes, are being advanced through IAG initiatives on dynamic reference frames and vertical datum unification.[60] Global mean sea-level rise rates have exceeded 3 mm/year in recent decades.[61]