Geodetic datum

( Give lat = dare; Ppp date = Shared ) A geodetic datum describes in geodesy and cartography, the location ( position and orientation) and the scale of a two - or three-dimensional coordinate system and geodetic network, as a reference surface, a suitable reference ellipsoid is based on. The linking of the geodetic datum to a coordinate system that projects the data, for example on a two-dimensional map display, is called coordinate reference system (CRS ).

In order to determine real places on earth, reference points must be established. They form the frame of reference (English Reference Frame, RF ) and link the coordinates with the actual measured positions on the earth.

• 6.1 Traditional Land Surveying
• 6.2 Adjustment of the ellipsoid to the Lotrichtungen
• 6.3 geoid, regional and earth ellipsoid
• 6.4 Germany and Austria
• 6.5 Election of the reference ellipsoid
• 6.6 Election of the fundamental point
• 6.7 System of the Danube monarchy and Germany
• 6.8 World Systems GRS 80 and WGS 84
• 6.9 Other systems in Germany and Western Europe
• 6:10 relative to the geoid and Erdschwerpunkt

Definitions

The narrow definition of the geodetic datum includes the coordinate system with its orientation relative to the Earth and the reference body. The geodetic datum is also called geodetic reference system (see below) (English Terrestrial Reference System, TRS). A so-called reference frame realized a geodetic datum on earth.

The extended definition of a geodetic datum includes the reference frame on the ground with a: = Date reference system reference frame ( see below).

In both cases, one also speaks of a horizontal date. Because the amount of information relates only to the reference ellipsoid. The difference to the respective reference levels can exceed 100 m. A vertical datum may include a geoid model. The deviation of the geoid by a reference ellipsoid are referred to as geoid undulation. For a normal heights Quasigeoid is used as a reference surface.

Reference or reference system

Six coordinates create a three -dimensional Cartesian reference system relative to the Earth clearly states: three coordinates for the origin, three for orientation. Since mainly interested points on the earth's surface, to choose an appropriate reference body. In the past, it was sufficient to find a good approximation locally for their own country.

Today it is common to define an ellipsoid, which on average has globally the smallest deviations. The origin of the global system is in the center of the ellipsoid and the center of gravity of the earth, the z- axis perpendicular to the circular equatorial plane in the direction of the Earth's rotation axis.

The semi-major axis ( equatorial diameter ) and flat ( ratio of semi-major axis to the pole diameter ) determine the reference ellipsoid. The mass of the Earth, or more precisely the product of the gravitational constant and the mass is defined to account for space distortions according to the general theory of relativity, as well as the rotational speed of the earth.

Frame of Reference

A reference frame linked to the mathematical coordinate system with the real positions of the earth. Earlier, it was common to distinguish a fundamental point and align all measurements relative to it. For a global system, this method is too imprecise. Instead, a plurality of measurements are averaged to derive a fundamental virtual point.

If the close and the expanded definition of the geodetic data is not clearly separated from each other, confusions are inevitable. In the narrow interpretation, a date can be mathematically converted into another.

The expanded definition includes erroneous readings of the reference frame with a. An exact conversion is excluded.

The representation of the points in a coordinate system, for example on a two-dimensional map, takes place in a coordinate reference system: the coordinate reference system coordinate system date =

Height

The height error of a best-fit reference ellipsoid to the sea surface is relatively a few hundred meters. For higher values ​​, the height correction of the shape of the geoid is derived.

The geoid is not itself part of the date definition.

Examples

Local date

The Potsdam date is based on a Bessel ellipsoid (1841 ) with good adjustment for Germany and the fundamental point Rauenberg as a reference framework.

Global date

The shape of the reference ellipsoid GRS80 the date WGS84 is adjusted with the smallest possible error of the total earth's surface. Its orientation is continuously adjusted so that the average movement of all the fixed points relative to the coordinate system is zero.

There are numerous reference frame to WGS84. The U.S. DOD operates approximately 13 reference stations. In 1994, the accuracy of the WGS G730 was 10 cm, 2002 ( WGS G1150 ) at a few centimeters. The International Terrestrial Reference Frame ( ITRF ) is based on more than 200 stations and different measuring methods. Because of the higher accuracy of the reference frame is to WGS84 not measured independently, but is derived from the ITRF.

The differences between the geodetic datum of the International Terrestrial Reference System and WGS84 are now negligible.

The European reference system ETRS89 is a copy of ITRS89 the epoch 1989. Since the coordinate system drifts rigidly to the Eurasian plate. Compared to the ITRS shifts and twists it by about 2 cm per year. The realization of the reference frame ETRF based on 92 market points in Europe ( EUREF A network), compressed by 109 points in Germany ( DREF B network ) and other points by measurements of the land survey offices ( C-net ).

Two-dimensional coordinate systems to represent the points on a map, for example, the Gauss- Krüger coordinate system or the modern UTM coordinate system.

Height

The Earth Gravitational Model ( EGM96 ) is an example of a current geoid model, which provides the geoid undulation to the height adjustment for the WGS84 EGM96.

History

Classic Land Surveying

Until about 1960, the surveying systems of the individual states were defined by the "classical" state survey that

Thus, the system was determined in terms of position: the plumb line in the fundamental point P0 is perpendicular to the ellipsoid used and whose axis is parallel to the Earth. For the definition of moderate height, the sea level was taken over by P0 as its ellipsoidal height. ¹) The actual measurements are not "geographical " width / length, but the astronomical latitude and longitude.

Adaptation of the ellipsoid to the Lotrichtungen

The key to this adaptation is the so-called perpendicular error: If you found a plumb the vertical, it is not even normal to the ellipsoid. The mountains, valleys and mass disturbances in the substrate can produce angular deviations up to 0.01 °, which is the measurement accuracy surpasses almost 100-fold. However, you can store the ellipsoid as in the Earth's body that the deflections of the vertical in the country's center or the average for the whole country to be zero.

The first method was used in the 19th century, for example, for the country surveys of Prussia and of Austria - Hungary: you put the zero astro- geodetic so in TP Rauenberg (near Berlin ) and at Vienna decides that its perpendicular direction and perpendicular to the ellipsoid was. At the respective fundamental point of all measurement points within the network were geometrically connected, so that their coordinates to this day refer indirectly to this zero points. In Europe Network for Western and Central Europe, however, the second method was chosen so that the ED50 coordinates de facto, to a central point in Munich.

Geoid, regional and earth ellipsoid

While a reference ellipsoid is adapted to the regional geoid above, the average Erdellipsoid approaches, however, the geoid globally best to, radial Nevertheless, differences between 75 m ( Canada) and -120 m ( Indian Ocean ) remain. The Erdellipsoid was around 1960 exactly known only to about 100 meters, but since then gradually refined and adjusted approximately every 20 years, the current state of knowledge (see GRS 67 and GRS 80).

Most industrialized countries have established their reference ellipsoids in the 19th century and they adjusted by degree measurements and other methods the regional geoid. Therefore, the Ellipsoidachsen differ by 0.5 to 1.5 km from the Erdellipsoid - which means correspondingly large differences in the date parameters.

In contrast, many developing countries have established their land surveying until 1970 and therefore partially taken a good Erdellipsoid as a base.

Germany and Austria

In Germany, the differences between the Bessel ellipsoid and the geoid used here are relatively low, in the lowlands they are constant within a few meters. In Austria, however, the geoid runs because of the influence of the Alps around 43 to 52 meters above the ellipsoid defined by the datum WGS 84.

While such values ​​would be technically useless, giving way to the Ellipsoidsystem introduced by Austria - Hungary MGI - now referred to as Austria date, the geoid by only -2.5 to 3.5 m away from. It is based on the regional bestanschließenden Bessel ellipsoid, which is shifted with respect to a global ellipsoid to 596 m, 87 m and 473 m in the x-, y -, or z-direction. For Germany that fits around 606 m, 23 m and 413 m shifted Bessel ellipsoid best and gives the date of Potsdam.

Choice of the reference ellipsoid

A reference ellipsoid is used as a strictly geometric computing area, which should be regionally best conform to the geoid. In Europe and Asia, the Bessel ellipsoid of 1841 is most commonly used. It was calculated by Bessel by combined adjustment of all the then existing 10 degree measurements, so it is the average curvature of the earth throughout Europe and in South Asia adapts well. As bestanschließendes ellipsoid of Eurasia would have deflections of the vertical, the statistically equal often fall into all four directions. But locally this is not true, especially in the mountains and along the continental margins.

If now a National Survey calculated on this ellipsoid (ie, all geodetic measurements projected onto it ), one must note that the deflections of the vertical in each area Heads of State or surrounding remain as small as possible: the ellipsoid is therefore supported so that it is in the central area of the grid for measuring average Earth curvature realized. Therefore, two neighboring countries can use the same reference ellipsoid, but store something different. The two coordinate systems are similar, but differ by a few hundred meters.

Choice of the fundamental point

This storage takes place in the so-called fundamental point. On a central observatory or a surveying pillars the exact plumb determined ( Astronomical length and width) and the reference ellipsoid by means of the stars on " impaled " exactly vertical, ie the deflection of the vertical is set to zero. For the German State Survey is this astronomical zero in the former TP Rauenberg (Berlin- Tempelhof ) for Austria in Vienna, both use the Bessel ellipsoid. Switzerland has a very different system with the zero point at the old observatory in Bern (46 ° 57 ' 3.89? N, 7 ° 26' 19:09? ).

In the so-called European network the states of Western Europe from 1950 and those of Central Europe from 1970 their measurement results as a "black box" introduced and agreed to a joint calculation to the respective national borders. This led to the ED50 and ED79 systems, which refer to a fictitious center in Munich. Later, the European network was 84 recalculated on the global ellipsoid WGS and stiffened by means of satellite geodesy; it is recalculated as ETRF every few years and refers to the Erdschwerpunkt ( geocenter ).

System of the monarchy and Germany

One story has the geodetic network Austria -Hungary and his date MGI. First, there were 7 or 8 Fundamental points for each region. In the late 19th century was chosen as the common zero Hermannskogel ( 585 m) in Vienna, which was almost in the center of the entire state. However, since Austria became a small state, is converted the central to the eastern edge location, so that the deflections of the vertical were very big in the West. Fortunately, recognized the astronomer Charles Steger leather around 1930 that the absolute vertical deflection of the Hermannskogel is almost zero when the length difference Albrecht'sche Ferro - Greenwich 17 ° 39'46, 02 is rounded " to 17 ° 40'00 " - which has since happens with double advantage.

Germany also has its geodetic datum defined by reference ellipsoid and fundamental point. The Bessel ellipsoid was stored in the trigonometric point Rauenberg and from 1945 by the U.S. military as Potsdam designated date (PD). The Eindeutschung as "Rough mountain - date " but came 84 before the introduction of the WGS.

With a large extent of land surveying and / or strong deflections of the vertical deviations between the calculated location and coordinates can assume considerable proportions. Here, so-called Laplace points for significant improvements in care by the ellipsoid not related to a point, but is fit for mediation.

World Systems GRS 80 and WGS 84

The decisive factor for this increase in accuracy were the successes of satellite geodesy and navigation since the 1960s. On the basis of the defined IUGG 1979, the Global Reference System GRS80 and its Erdellipsoid to 1 meter. The U.S. developed it to the World Geodetic System WGS further than 84

Other systems in Germany and Western Europe

A large part of the German national surveys still uses the Bessel ellipsoid with the Gauss -Krüger coordinate system for plane metric coordinates. But also qualifies in Mecklenburg- Vorpommern and Saxony- Anhalt, nor the system of the former GDR with a Gauss - Krüger projection on the Krasovsky ellipsoid and in Berlin the Soldner - illustration on the Besselellipsoid.

In western and central European level was defined in 1950 by the European date ED50 at the International ellipsoid 1924 ( Hayford ellipsoid ). UTM coordinates can also be calculated with reference to the ED50.

In order to have at European and international level on a uniform and modern computing area, set the surveying authorities of the countries in Germany is currently the reference systems. One uses the date the European Terrestrial Reference System 1989 ( ETRS89 ) using the ellipsoid Geodetic Reference System 1980 ( GRS80 ). The change from Gauss -Krüger coordinates to UTM coordinates dates with the date change of PD associated to ETRS89.

Respect to the geoid and Erdschwerpunkt

In Austria, due to the influence of the Alps, the geoid 43 to 52 meters above Erdellipsoid defined in WGS 84. However, the large variation of 10 meters is reduced in date Austria to -2.5 up to 3.5 m. This date of the Austrian Federal signaling network refers to a Bessel ellipsoid, which is shifted in the X, Y, Z direction by 596, 87 and 473 meters.

For Germany Bessel ellipsoid and the " Potsdam Datum " is the analog shift 606, 23 and 413 meters in XYZ direction ( International Convention on the 3 axes: X / Y is the geocentric equatorial plane, Z is the Earth's axis, X has the prime meridian; which also passes through Greenwich ). The Swiss coordinates refer to the date CH1903.