Reference Systems. Paolo Zatelli - Alfonso Vitti. Dept. Civil and Environmental Engineering University of Trento

Reference Systems Reference Systems Paolo Zatelli - Alfonso Vitti Dept. Civil and Environmental Engineering University of Trento P. Zatelli - A. Vitti University of Trento - Italy 1 / 34

Reference Systems Outline 1 Reference Systems and Coordinate Systems 2 Terrestrial reference systems and coordinate systems 3 Geoid and ellipsoid 4 Ellipsoid - shape and orientation 5 Global and local systems 6 Reference systems in Italy P. Zatelli - A. Vitti University of Trento - Italy 2 / 34

Reference Systems Reference Systems and Coordinate Systems Position Position is relative. A point position is always relative to other reference points. It is useful to express a point position by means of labels attached to each single point coordinates To determine the point s coordinates, which express the point relative position, a reference system has to be defined. P. Zatelli - A. Vitti University of Trento - Italy 3 / 34

Reference Systems Reference Systems and Coordinate Systems Examples P. Zatelli - A. Vitti University of Trento - Italy 4 / 34

Reference Systems Reference Systems and Coordinate Systems Reference systems and coordinate systems It is often an implicit choice. For example, on a plane, by fixing the Cartesian coordinates of 2 points (4 degrees of freedom), one has fixed also: the origin point (2 constrains) the reference direction (1 constrain) the reference unit (1 constrain) In general, for a reference system it is possible to use different coordinate systems to express points coordinates. In practice, a reference system (RS) is realized by choosing a specific coordinate system (CS) and by fixing a set of points coordinates in that specific CS. P. Zatelli - A. Vitti University of Trento - Italy 5 / 34

Reference Systems Terrestrial reference systems and coordinate systems Terrestrial reference systems and coordinate systems A terrestrial reference system and the associated coordinates should be related to: the Earth s shape the Earth s gravitational field which are themselves related, too. P. Zatelli - A. Vitti University of Trento - Italy 6 / 34

Reference Systems Terrestrial reference systems and coordinate systems Natural coordinates A natural choice is the triplet (H W, Φ, Λ), where: H W is a linear function of the Earth s gravitational field potential W H W = W W 0 γ 0 Φ and Λ are the angles denoting the direction of the force of gravity The values of Φ and Λ depend on the definition of a reference direction. P. Zatelli - A. Vitti University of Trento - Italy 7 / 34

Reference Systems Terrestrial reference systems and coordinate systems Natural coordinates (H W, Φ, Λ) 1 have a strong physical meaning 2 have a weak geometrical meaning 1 advantage H W tells what is up and what is down; Φ and Λ can be obtained by astronomical measurements (marine navigation) 2 disadvantage it is not possible to compute the distance between two points P. Zatelli - A. Vitti University of Trento - Italy 8 / 34

Reference Systems Terrestrial reference systems and coordinate systems Orthometric height H W is replaced by the orthometric height H, the distance from an equi-potential surface of the Earth s gravitational field with W = W 0 (the Geoid). H is measured along the line of force of the gravity field. The use of H balances the geometrical and the physical meaning of such coordinate. P. Zatelli - A. Vitti University of Trento - Italy 9 / 34

Reference Systems Geoid and ellipsoid Geoid It is a reference surface where W = W 0 P. Zatelli - A. Vitti University of Trento - Italy 10 / 34

Reference Systems Geoid and ellipsoid Geodetic coordinates To get coordinates with a full geometrical meaning, an ellipsoid is used as reference surface. The ellipsoid s shape approximates the Geoid s shape (locally or globally). An ellipsoid has an analytical form and its surface is much more simple (smooth and regular) than the Geoid geometrically meaningful coordinates P. Zatelli - A. Vitti University of Trento - Italy 11 / 34

Reference Systems Geoid and ellipsoid Geodetic coordinates The triplet (φ, λ, h) has a weak physical meaning (the ellipsoid is an approximation of the Geoid). P. Zatelli - A. Vitti University of Trento - Italy 12 / 34

Reference Systems Geoid and ellipsoid Geodetic coordinates - Latitude and Longitude latitude φ angle between the ellipsoid s normal in P and the equatorial plane 90 φ +90 or 90 S φ 90 N φ = cost. parallel longitude λ angle between the meridian plane in P and the meridian plane of a reference point, 180 λ +180 or 180 W λ 180 E λ = cost. meridian P. Zatelli - A. Vitti University of Trento - Italy 13 / 34

Reference Systems Geoid and ellipsoid Geodetic coordinates and orthometric height Most of the times, e.g., in Cartography, an hybrid choice is made by using the triplet (φ, λ, H), where: (φ, λ) have a strong geometrical meaning H is a compromise between the physical and the geometrical meanings GPS gives (φ, λ, h), whereas in classical surveys (optical instruments) and in Cartography we use (φ, λ, H). It is necessary to know the so called Geoid undulation to transform from H to h and vice-versa. P. Zatelli - A. Vitti University of Trento - Italy 14 / 34

Reference Systems Geoid and ellipsoid Orthometric and ellipsoid heights - Geoid undulation P. Zatelli - A. Vitti University of Trento - Italy 15 / 34

Reference Systems Geoid and ellipsoid Geoid undulation From red (85.4 m) to magenta (-107.0 m) P. Zatelli - A. Vitti University of Trento - Italy 16 / 34

Reference Systems Ellipsoid - shape and orientation Ellipsoid - shape and orientation An ellipsoidal reference surface is completely defined by fixing: 1 the shape by choosing: the semi-axes a and b, or the semi-major axis a and flattener f = the semi-major axis a and eccentricity e = a b a, or a 2 b 2 a 2 2 the orientation (the position relative the the Earth surface) P. Zatelli - A. Vitti University of Trento - Italy 17 / 34

Reference Systems Ellipsoid - shape and orientation Ellipsoid - shape The semi-major axis a lies on the equatorial plane, the semi-minor axis b is aligned to the Earth s rotation axis: P. Zatelli - A. Vitti University of Trento - Italy 18 / 34

Reference Systems Ellipsoid - shape and orientation Ellipsoid - shape Late 1800 and early 1900 geodetic measures were used to determine an optimal ellipsoid: Name Year a[m] b[m] Used in Everest 1830 6377276 6356079 India Sri Lanka Bessell 1841 6377397 6356079 Cent.Eu. Cile Indon. Airy 1849 6377563 6356257 United Kingdom Clarke 1866 6378206 6356584 N. America Philippines Clarke 1880 6378249 6356515 France Africa Helmert 1907 6378200 6256818 part of Africa International Hayford 1924 6378245 6356912 UTM Italy (Rome1940) Krasovsky 1940 6378245 6356863 Russia Eu. Or. GRS80 1980 6378137 6356752 N.America Global WGS84 1984 6378137 6356752 Global (GPS) P. Zatelli - A. Vitti University of Trento - Italy 19 / 34

Reference Systems Ellipsoid - shape and orientation Ellipsoid - orientation The orientation can be: global local P. Zatelli - A. Vitti University of Trento - Italy 20 / 34

Reference Systems Ellipsoid - shape and orientation Ellipsoid - global orientation the ellipsoid barycenter coincides with the Earth s center of mass the axis z is aligned to the Earth s rotation axis the axis x lies on a specific plane (Greenwich meridian) containing the axis z P. Zatelli - A. Vitti University of Trento - Italy 21 / 34

Reference Systems Ellipsoid - shape and orientation Ellipsoid - local orientation For a given reference point, in general close to the barycenter of the local region: Φ = φ Λ = λ Geoid origin H = h the ellipsoid semi-minor axis is parallel to the Earth s rotation axis These conditions are often imposed by fixing the coordinates of a set of points. P. Zatelli - A. Vitti University of Trento - Italy 22 / 34

Reference Systems Global and local systems Global and local systems Satellite based positioning systems need global reference systems. In the past, the definition of global reference systems was hard and of scarce interest and need. Surveys did not have a global scope. For this reason, there are more than 150 local reference systems. P. Zatelli - A. Vitti University of Trento - Italy 23 / 34

Reference Systems Global and local systems Continental reference systems P. Zatelli - A. Vitti University of Trento - Italy 24 / 34

Reference Systems Reference systems in Italy Reference systems in Italy The first national reference system was defined and realized in late 1800: Bessel ellipsoid orientated in three different points (Genova, Monte Mario, and Castanea delle Furie), with three different reference systems cartographic proiection: modified Flamsteed block adjusted triangulation network (1908-1919) P. Zatelli - A. Vitti University of Trento - Italy 25 / 34

Reference Systems Reference systems in Italy Cadastral reference system Not in use anymore Bessel ellipsoid orientation: Genova, Istituto Idrografico della Marina φ = 44 25 08.235 λ = 0 azimuth to Monte del Telegrafo α = 117 31 08.91 IGM and cadastral triangulation networks P. Zatelli - A. Vitti University of Trento - Italy 26 / 34

Reference Systems Reference systems in Italy Italian reference system - Rome1940 It is the official system in use in Italy International ellipsoid (Hayford) oriented in Roma Monte Mario (astronomical definition 1940) φ = 41 55 25.51 λ = 0 (12 27 00.88 da Greenwich) azimuth to Monte Soratte α = 6 35 00.88 h = H = 0 Genova tide gauge block adjusted triangulation network (1908-1919) using an interim reference system with successive system transformation (distortions) P. Zatelli - A. Vitti University of Trento - Italy 27 / 34

Reference Systems Reference systems in Italy Continental ref. system European Datum 1950 (ED50) It is a system created to homogenize the European small and medium scale cartography: International ellipsoid (Hayford) European mean orientation (1950) longitude origin: Greenwich P. Zatelli - A. Vitti University of Trento - Italy 28 / 34

Reference Systems Reference systems in Italy Global reference systems There are two types of system currently in use: celestial reference systems, defined by positions of extragalactic radio sources and satellites orbits terrestrial reference systems, defined by fixing the coordinates of reference points on the Earth s surface The Earth is not a rigid body the position of objects and points on the Earth s surface are not fixed coordinates need to be updated and the reference systems refer to a specific date. P. Zatelli - A. Vitti University of Trento - Italy 29 / 34

Reference Systems Reference systems in Italy IERS Terrestrial Reference System (ITRS) Defined by the International Earth Rotation and Reference System Service the origin point coincides with the Earth s center of mass the axis Z passes through the Conventional International Origin (CIO) the axis X is direct toward the Greenwich meridian the axis Y completes the triad of axes The IERS periodically publishes the ITRFYY (International Terrestrial Reference Frame and YY indicates the year) which is a realization at a given date of the ITRS. The ITRFYY compromises a set of coordinates and velocities of a set of reference points obtained by processing measures coming from different geodetic observing techniques (VLBI, DORIS, LLR, SLR, GPS). P. Zatelli - A. Vitti University of Trento - Italy 30 / 34

Reference Systems Reference systems in Italy ITRS derived reference system Europe: EUREF ETRS89 ITRF89 and subsequent ETRFYY Italy: IGM IGM95 Italian realization of ETRS89 Italy: IGM RDN ETRF2000 P. Zatelli - A. Vitti University of Trento - Italy 31 / 34

Reference Systems Reference systems in Italy Global reference system WGS84 It is a Cartesian system with an associated reference ellipsoid. It is the reference system in which the transmitted GPS orbits are given and hence it is the system used by any GPS device. P. Zatelli - A. Vitti University of Trento - Italy 32 / 34

Reference Systems Appendice Bibliografia Bibliografia Benciolini B., 2004, Report on refrence systems, personal communication. Surace L., 1998, La georeferenziazione delle informazioni territoriali, Bollettino di geodesia e scienze affini, anno LVII, n. 2, pp. 181-234. For the images http://kartoweb.itc.nl/geometrics/reference surfaces/body.htm For information on exotic reference systems: Photogrammetric Engineering and Remote Sensing (PE&RS) Journal, http://http://www.asprs.org/pe-rs-journal/ P. Zatelli - A. Vitti University of Trento - Italy 33 / 34

Reference Systems Appendice Licenza These slides are c 2009 Paolo Zatelli, available as P. Zatelli - A. Vitti University of Trento - Italy 34 / 34