What actually is a Coordinate Reference System?
Explanation of the Coordinate Reference System with the components Coordinate System,
Reference System, Reference Definition and Reference Frame.
Kempen (Germany), May 19, 2021
Dipl.-Ing. Fred Killet - Killet GeoSoftware Ing.-GbR - Escheln 28a - 47906 Kempen - Germany
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Published in VDVmagazin, Verband Deutscher Vermessungsingenieure, Booklet 4/2021

The geographic Coordinate Reference System uses an ellipsoidal model of the earth to describe the position of objects with two- or three-dimensional coordinates on its surface. The position of the synthetic ellipsoid with respect to the real earth is described with a geodetic Reference System or with a geodetic Datum (see below). In the general linguistic usage the abbreviation CRS for the Coordinate Reference System is common.

Components of the Coordinate Reference System

For the professional handling of coordinates additional information is needed beside the coordinate values, so that it cannot come to incorrect use and wrong representation of the objects described by the coordinates.
The ISO 19111 standardizes the spatial referencing by coordinates in the Geographic Information Technology. It specifies which descriptive information must be transferred when coordinates are exchanged and refers to this as Coordinate Reference System (CRS).
The Coordinate Reference System always consists exactly of a geodetic Reference System and a Coordinate System.

Coordinate Reference System = Geodetic Reference System + Coordinate System

The components of the Coordinate Reference System and the requirements for the data transfer of coordinates are illustrated schematically in the following diagram.
The Geodetic Reference System - in the parlance of the ISO 19111 called as Geodetic Datum - is the physical component of the Coordinate Reference System (e.g. ETRS89, DHDN, RD/83, 42/83).
The Coordinate System is the mathematical component of the Coordinate Reference System. It is defined by mathematical formulas which assign equivalent coordinates as numerical values to point positions (e.g. GK3, GK6, UTM, Lat/Lon, X/Y/Z). Coordinates are only unambiguous if the Coordinate Reference System is completely specified.

Effect of deviations in Coordinate Reference System

The use of different parameters of the Coordinate System, the geodetic Reference System, the Reference Definition or the Reference Frame will lead to more or less different results when transforming coordinates.
In the following map, as an example, the same coordinate is shown in each of the different Reference Systems ETRS89, DHDN and ED50. As can be seen, the points are a several hundred meters apart.

Special feature of the Reference System WGS84

A special feature is to be considered with the conversion of coordinates of a fixed Reference System into the Reference System WGS84, which refers to the gravity center of the earth, and with the appropriate back calculation. The WGS84 is a dynamic Reference System that is influenced by the continental drift of the different continental plates. This process describes the slow movement, splitting, and unification of continents on the earth's globe. The time course of this movement is constantly documented in the form of ITRS epochs. In addition to the parameters already described, the reference frame of the continent with the ITRS epoch at the time of the measurement or coordinate transformation is required for calculations from and into WGS84. WGS84 coordinates can be accurately transformed to a fixed Coordinate Reference System only if the ITRS epoch of the WGS84 coordinates is known.
As an example, the Reference System ETRS89 which is fixed for the Eurasian Plate is considered here in more detail. At the 1989.0 epoch, the ITRS and the ETRS were identical. At this time, ETRS89 has been defined for the Eurasian Continental Plate and has been identified with the suffix 89. ETRS89 is firmly tied to the Eurasian Plate via fundamental stations and moves with about 2.5 cm per year over the global system defined by WGS84. It follows that the coordinates from an accurate current GPS measurement in the WGS84 Reference System in Europe can deviate by up to 80 cm from the actual coordinates in ETRS89.

Designation of the Coordinate Reference Systems

Here are some examples of the correct designation of a Coordinate Reference System:
UTM coordinates on the ETRS89 datum
Gauss-Krueger coordinates with three degree meridian stripes on the DHDN90 datum
Gauss-Krueger coordinates with six degree meridian stripes on the S42 datum
Geographical coordinates in DMS notation on the WGS84 datum at epoch 2005.

Another possibility for the unique naming of Coordinate Reference Systems is the use of EPSG codes. EPSG is a system of globally unique key numbers for Coordinate Reference Systems and other geodetic datasets. The information on the EPSG codes is available in a publicly accessible online database. Here are some examples of EPSG codes of Coordinate Reference Systems:
3857 - WGS84 / Pseudo-Mercator - Google Maps, OpenStreetMap, Card provider on the web
4326 - WGS84 / Geographical Coordinates - worldwide system for GPS
25832 - ETRS89 / UTM zone 32N - from 6°E to 12°E in Germany, Austria, Switzerland
25833 - ETRS89 / UTM zone 33N - from 12°E to 18°E in Germany and Austria
31466 - DHDN / Gauß-Krueger zone 2 - west of 7,5°E in Germany
31467 - DHDN / Gauß-Krueger zone 3 - from 7,5°E to 10,5°E in Germany

Geodetic transformation software

The geodetic program  TRANSDATpro can convert coordinates between many Coordinate Reference Systems. The same applies to the Geodetic Development Kit  GeoDLL, which allows the embedding of geodetic functions, e.g. coordinate transformations, into own software. For coordinate transformations with the WGS84 Reference System, continental drift is considered in both tools by applying ITRS epochs. Detailed information about the software and the possibility to download trial versions can be found on the Internet site of KilletSoft. The installation of the software is very easy and can be done with just a few clicks.

Author

Dipl.-Ing. Fred Killet
Escheln 28a
47906 Kempen (Germany)
https://www.killetsoft.de