Coordinate reference systems (coordinate systems with a datum). The following is adapted from OpenGIS® Spatial Referencing by Coordinates (Topic 2) specification.

A coordinate reference system consists of one coordinate system that is related to the earth through one datum. The coordinate system is composed of a set of coordinate axes with specified units of measure. This concept implies the mathematical rules that define how coordinate values are calculated from distances, angles and other geometric elements and vice versa.

A datum specifies the relationship of a coordinate system to the earth, thus ensuring that the abstract mathematical concept "coordinate system" can be applied to the practical problem of describing positions of features on or near the earth's surface by means of coordinates. The resulting combination of coordinate system and datum is a coordinate reference system. Each datum subtype can be associated with only specific types of coordinate systems. The datum implicitly (occasionally explicitly) contains the values chosen for the set parameters that represent the degrees of freedom of the coordinate system. A datum therefore implies a choice regarding the approximate origin and orientation of the coordinate system.

For the purposes of this specification, a coordinate reference system shall not change with time, with the exception of engineering coordinate reference systems defined on moving platforms such as cars, ships, aircraft and spacecraft. The intention is to exclude the option to describe the time variability of geodetic coordinate reference systems as a result of e.g. tectonic motion. This variability is part of the subject matter of geophysical and geodetic science. The model for spatial referencing by coordinates described in this specification is in principle not suitable for such zero-order geodetic problems. Such time-variability of coordinate reference systems shall be covered in the spatial referencing model described in this specification by creating different coordinate reference systems, each with a different datum, for (consecutive) epochs. The date of realisation of the datum shall then be included in its definition. It is further recommended to include the date of realisation in the names of those datums and coordinate reference systems.


Principal sub-types of coordinate reference system

Geodetic survey practice usually divides coordinate reference systems into a number of sub-types. The common classification criterion for sub-typing of coordinate reference systems can be described as the way in which they deal with earth curvature. This has a direct effect on the portion of the earth's surface that can be covered by that type of CRS with an acceptable degree of error. Thus the following principal sub-types of coordinate reference system are distinguished:

Geocentric: Type of coordinate reference system that deals with the earth's curvature by taking the 3D spatial view, which obviates the need to model the earth's curvature. The origin of a geocentric CRS is at the approximate centre of mass of the earth.

Geographic: Type of coordinate reference system based on an ellipsoidal approximation of the geoid. This provides an accurate representation of the geometry of geographic features for a large portion of the earth's surface. Geographic coordinate reference systems can be 2D or 3D. A 2D Geographic CRS is used when positions of features are described on the surface of the reference ellipsoid; a 3D Geographic CRS is used when positions are described on, above or below the reference ellipsoid.

Projected: Type of coordinate reference system that is based on an approximation of the shape of the earth's surface by a plane. The distortion that is inherent to the approximation is carefully controlled and known. Distortion correction is commonly applied to calculated bearings and distances to produce values that are a close match to actual field values.

Engineering: Type of coordinate reference system that is that is used only in a contextually local sense. This sub-type is used to model two broad categories of local coordinate reference systems:

  • earth-fixed systems, applied to engineering activities on or near the surface of the earth;
  • coordinates on moving platforms such as road vehicles, vessels, aircraft or spacecraft.

Image: An Image CRS is an Engineering CRS applied to images. Image CRSs are treated as a separate sub-type because a separate user community exists for images with its own vocabulary. The definition of the associated Image Datum contains two data attributes not relevant for other datums and coordinate reference systems.

Vertical: Type of coordinate reference system used for the recording of heights or depths. Vertical CRSs make use of the direction of gravity to define the concept of height or depth, but its relationship with gravity may not be straightforward. By implication ellipsoidal heights (h) cannot be captured in a vertical coordinate reference system. Ellipsoidal heights cannot exist independently, but only as inseparable part of a 3D coordinate tuple defined in a geographic 3D coordinate reference system.

Temporal: Used for the recording of time in association with any of the listed spatial coordinate reference systems only.


Additional sub-types of coordinate reference system

In addition to the principal sub-types, so called because they represent concepts generally known in geodetic practice, two more sub-types have been defined to permit modelling of certain relationships and constraints that exist between the principal sub-types. These additional sub-types are Compound coordinate reference system and Derived coordinate reference system.

Compound coordinate reference system
The traditional separation of horizontal and vertical position has resulted in coordinate reference systems that are horizontal (2D) in nature and vertical (1D). It is established practice to combine the horizontal coordinates of a point with a height or depth from a different coordinate reference system. The coordinate reference system to which these 3D coordinates are referenced combines the separate horizontal and vertical coordinate reference systems of the horizontal and vertical coordinates. Such a coordinate system is called a compound coordinate reference system (Compound CRS). It consists of an ordered sequence of the two or more single coordinate reference systems.

Derived coordinate reference system
Some coordinate reference systems are defined by applying a coordinate conversion to another coordinate reference system. Such a coordinate reference system is called a Derived CRS and the coordinate reference system it was derived from by applying the conversion is called the Source or Base CRS. A coordinate conversion is an arithmetic operation with zero or more parameters that have defined values. The Source CRS and Derived CRS have the same Datum. The best-known example of a Derived CRS is a Projected CRS, which is always derived from a source Geographic CRS by applying the coordinate conversion known as a map projection.

In principle, all sub-types of coordinate reference system may take on the role of either Source or Derived CRS with the exception of a Geocentric CRS and a Projected CRS. The latter is modelled as an object class under its own name, rather than as a general Derived CRS of type "projected". This has been done to honour common practice, which acknowledges Projected CRSs as one of the best known types of coordinate reference systems.

An example of a Derived CRS: one of which the unit of measure has been modified with respect to an earlier defined Geographic CRS, which then takes the role of Source CRS.

GeoAPI 1.0