# Geodetic date

Geodetic datum: ellipsoid with a clear orientation to the earth

The geodetic datum ( Latin: dare = to give; PPP datum = given) describes the position of a coordinate system in relation to the earth in geodesy , cartography and geographic information . In order to describe the position of objects on the earth by means of coordinates, it must be determined how the coordinate system used is connected to the earth. This includes information about the position of the coordinate origin, the orientation of the axes and the scale of the coordinate system. The geodetic datum forms a coordinate reference system together with the coordinate system .

The type and number of parameters required differ depending on the type and dimension of the coordinate system.

For a three-dimensional coordinate system you need 6 date parameters, 3 for the position of the origin and 3 for the orientation of the axes. For an ellipsoidal coordinate system , the description of the associated reference ellipsoid is also required.

For a height system (one-dimensional coordinate system), the vertical datum is determined by a parameter that describes the level of the height system. It is sufficient to specify the height of a point, which z. B. derived from level observations. The orientation results from the vertical direction in the earth's gravity field.

For a dynamic coordinate reference system, the points of which change their coordinates over time, the specification of a reference epoch is also required.

In practice, when evaluating the measurements of a geodetic network, the geodetic datum is implemented by defining certain survey points (e.g. fixed coordinates). These points are called date points. All points of a geodetic network with their coordinates form the reference frame

## Different definitions

The “narrow definition” of the geodetic datum described above, which only includes the orientation of the coordinate system relative to the earth, is often used in geodesy.

The extended definition of a geodetic datum includes the frame of reference on earth. (see below). This means that the coordinates of all points in a network derived from concrete measurements are considered part of the datum. This equation of date and frame of reference is particularly common in geographic information .

## Cartesian reference system and reference ellipsoid

Six coordinates clearly define a three-dimensional Cartesian reference system relative to the earth: three coordinates for the origin, three for the orientation. The Cartesian coordinate system is not very suitable in practice. Since points on the earth's surface are mainly of interest, a suitable reference body is chosen. In the past it was enough to find a good regional approximation for your own country.

Today it is common to define an ellipsoid that has the smallest global mean deviations. The coordinate origin of the global system lies in the center of the ellipsoid and in the center of gravity of the earth, the z-axis perpendicular to the circular equatorial plane in the direction of the earth's axis of rotation.

The major semiaxis (equator radius) and the flattening (ratio of major semiaxis to the pole radius) determine the reference ellipsoid . The mass of the earth, more precisely: the product of the gravitational constant and mass, is determined in order to take into account spatial distortions according to the general theory of relativity , as well as the rotational speed of the earth.

## Frame of reference

A reference frame links the mathematical coordinate system with real positions on earth. It used to be common practice to mark a fundamental point and align all measurements relative to it. This method is too imprecise for a global system. Instead, a large number of measurements are averaged in order to derive a virtual fundamental point.

If the narrow and the extended definition of the geodetic datum are not clearly separated from one another, confusion cannot be avoided. With the narrow interpretation, one date can be converted into another mathematically precisely .

The extended definition includes incorrect measured values ​​of the reference frame. An exact conversion is therefore impossible.

The points are represented in a coordinate system, for example on a two-dimensional map, in a coordinate reference system: coordinate reference system = date + coordinate system.

## height

Date definitions related to an ellipsoid of revolution are also referred to as geometric datum because the information relates to the reference ellipsoid, not to the geoid . The difference between the two can be over 100 m.

A vertical date is required to indicate heights above sea level . For this purpose, it is sufficient to define the reference height or, in practice, to define the height of at least one point in the network.

Alternatively, an altitude datum can also be described by specifying a reference ellipsoid and an associated geoid or quasigeoid model. Ellipsoidal heights derived from GNSS measurements can thus be converted into physical heights.

## Examples

Examples of locally and globally fitted ellipsoids

### Regional date

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

### Global date

The shape of the reference ellipsoid GRS80 of the datum WGS84 is adapted to the total surface of the earth with the smallest possible error. Its orientation is continuously readjusted so that the mean movement of all fixed points in relation to the coordinate system is zero.

There are numerous reference frames for WGS84. The US-DOD operates around 13 reference stations. In 1994 the accuracy of the WGS G730 was 10 cm , in 2002 (WGS G1150) a few centimeters. The International Terrestrial Reference Frame (ITRF) is based on more than 200 measuring stations and different measuring methods. Due to the higher accuracy, the reference frame for WGS84 is no longer 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 the ITRS89 of the epoch 1989. Since then the coordinate system has been drifting rigidly with the Eurasian plate . Compared to the ITRS, it shifts and rotates about 2 cm per year. The implementation through the ETRF reference framework is based on 92 marketed points in Europe (EUREF A network), condensed by 109 points in Germany (DREF B network) and further points through measurements by the state surveying offices (C network).

Two-dimensional coordinate systems for representing the points on a map are, for example, the Gauß-Krüger coordinate system or the modern UTM coordinate system .

### height

The altitude data for the currently valid altitude reference system DHHN2016 in Germany is the Amsterdam level (NAP). When determining the heights of the DHHN2016, the level was not leveled as far as Amsterdam, but the date was realized on the basis of the heights of 72 points of the previous height reference system DHHN92, which also refers to the Amsterdam level. The sum of the height differences for the 72 date points between DHHN2016 and DHHN92 is zero.

The Earth Gravitational Model 96 (EGM96) is an example of a geoid model that is still widely used internationally. The more recent geoid model recommended by NASA, which provides the geoid undulation for height adjustment for the WGS84 , is the EGM2008.

## history

### Classic land survey

Until around 1960, in the "classic" national surveying, the surveying systems of the individual states were determined by the fact that

1. a reference ellipsoid suitable for the respective area has been selected,
2. on a fundamental point P 0, which is as centrally located as possible, whose geographical coordinates were determined by astronomical measurements , ¹)
3. these were taken over as ellipsoidal coordinates on the ellipsoid
4. and the (existing or future) surveying network was oriented north or south by measuring an astronomical azimuth (direction to a clearly visible fixed point about 20 to 50 km away).

The position of the system was thus determined: the perpendicular direction in the fundamental point P 0 is perpendicular to the ellipsoid used, and its axis is parallel to the earth's axis . For the height definition, the sea ​​level of P 0 was adopted as its ellipsoidal height .
¹) The actual measured variables are not “geographical” latitude / longitude, but astronomical latitude and longitude .

### Adaptation of the ellipsoid to the perpendicular directions

The key for this adaptation is the so-called deviation from the perpendicular : If you determine the perpendicular with a perpendicular, it is by no means normal on the ellipsoid. The mountains, valleys and mass disturbances in the subsurface can produce angular deviations of up to 0.01 °, which exceeds the measurement accuracy almost 100 times. However, the ellipsoid can be positioned in the earth's body in such a way that the vertical deviations in the center of the country or in the average for the whole country become zero.

The first method was chosen in the 19th century, for example, for the national surveys of Prussia and Austria-Hungary: The zero point was set astro-geodetically in the TP Rauenberg (near Berlin ) or near Vienna in such a way that its plumb line was perpendicular to the Ellipsoid. All measurement points of the network were geometrically connected to the respective fundamental point , so that their coordinates relate indirectly to these zero points to this day. In the European network for Western and Central Europe, however, the second method was chosen, so that the ED50 coordinates de facto refer to a central point near Munich .

### Geoid, regional and earth ellipsoid

While a reference ellipsoid is adapted to the regional geoid as above , the mean earth ellipsoid, on the other hand , approximates the geoid best globally . Nevertheless, radial differences between +75 m (Canada) and −120 m (Ind) remain. Around 1960, the earth's ellipsoid was only known to an accuracy of about 100 meters, but has since been gradually refined and adapted to the current state of knowledge about every 20 years (see GRS 67 and GRS 80 ).

Most industrialized nations established their reference ellipsoids in the 19th century and adapted them to the regional geoid using degree measurements and other methods. The ellipsoid axes therefore deviate from the Earth's ellipsoid by 0.5 to 1.5 km - which means correspondingly large differences in the date parameters.

On the other hand, many developing countries did not establish their national surveying until 1970 and therefore partly used a good earth ellipsoid as a basis.

### Germany and Austria

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

While such values ​​would be technically useless, the ellipsoid system MGI introduced by Austria-Hungary - now also known as Datum Austria - deviates from the geoid by only −2.5 to +3.5 m. It is based on the regionally best adjoining Bessel ellipsoid , which is shifted by 596 m, 87 m and 473 m in the x, y and z directions compared to a global ellipsoid. For Germany, the Bessel ellipsoid, shifted by 606 m, 23 m and 413 m, fits best and gives the date Potsdam .

### Choice of the reference ellipsoid

A reference ellipsoid serves as a strictly geometrical calculation surface that should cling to the geoid as best as possible. In Europe and Asia, the Bessel ellipsoid from 1841 is most common. It was calculated by Bessel through a combined adjustment of all 10 degree measurements available at the time , so that it adapts well to the mean curvature of the earth in all of Europe and in South Asia. As the closest ellipsoid of Eurasia it would have vertical deviations that statistically fall equally often in all four cardinal directions. However, this does not apply locally, especially in the mountains and on the continental edges.

If a national survey is now calculated on this ellipsoid (i.e. all geodetic measurements are projected onto it), one must ensure that the vertical deviations in the respective state or surrounding area remain as small as possible: The ellipsoid is therefore positioned in such a way that it is the middle one in the central area of ​​the surveying network Earth curvature realized.
Therefore, two neighboring states can use the same reference ellipsoid, but have slightly different locations. The two coordinate systems are similar, but will differ by a few hundred meters.

### Choice of the fundamental point

This storage takes place in the so-called fundamental point . On a centrally located observatory or a surveying pillar , the stars are used to determine the exact direction of the plumb bob ( astronomical longitude and latitude ) and the reference ellipsoid is “impaled” on it exactly vertically. H. the deviation from the perpendicular is set to zero. For the German national survey this astronomical zero point is in the former TP Rauenberg ( Berlin-Tempelhof ), for Austria near Vienna, both use the Bessel ellipsoid . Switzerland has a completely different system with the zero point at the old Bern observatory (46 ° 57 ′ 3.89 ″ N, 7 ° 26 ′ 19.09 ″ E).

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

### System of the Danube Monarchy and Germany

The Austria-Hungary surveying network and its date MGI have a special history . Initially there were 7 or 8 fundamental points for the individual regions. In the late 19th century, the Hermannskogel (585 m) near Vienna, which was almost in the center of the entire state, was chosen as the common zero point . However, since Austria became a small state, the central to an eastern peripheral location changed , so that the vertical deviations in the west became very large. Fortunately, the geodesist Karl Ledersteger recognized around 1930 that the absolute vertical deviation of the Hermannskogel becomes almost zero if the Albrechtian length difference Ferro-Greenwich is rounded from 17 ° 39'46.02 "to 17 ° 40'00" - which has been the case ever since happens with a double advantage.

Germany has also determined its geodetic datum using a reference ellipsoid and a fundamental point . The Bessel ellipsoid was stored in the trigonometric point Rauenberg and from 1945 onwards was called Potsdam Datum (PD) by the US military . However, the introduction of WGS 84 preceded the Germanization as "Rauenberg date".

In the case of a large extent of the national survey and / or strong plumbing deviations, the deviations between the location and the calculated coordinates can assume considerable proportions. So-called Laplace points can provide significant improvements here by not relating the ellipsoid to a point, but rather fitting it in as a mediator.

### World systems GRS 80 and WGS 84

The successes of satellite geodesy and navigation since the 1960s were decisive for this increase in accuracy . On this basis, the IUGG defined the global reference system GRS80 and its earth ellipsoid with an accuracy of 1 m in 1979 . The USA developed it further into the World Geodetic System as WGS 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. In addition, however, in Mecklenburg-Western Pomerania and Saxony-Anhalt the system of the former GDR with a Gauss-Krüger map on the Krassowski ellipsoid and in Berlin the Soldner map on the Bessel ellipsoid still applies.

At the western and central European level, the European date ED50 was defined in 1950 on the International Ellipsoid 1924 ( Hayford Ellipsoid ). UTM coordinates are also calculated with reference to the ED50.

In order to have a uniform and modern computing surface at European and international level, the surveying authorities of the federal states in Germany are currently converting the reference systems. The date used is the European Terrestrial Reference System 1989 ( ETRS89 ) using the Ellipsoid Geodetic Reference System 1980 ( GRS80 ) . The change from Gauß-Krüger coordinates to UTM coordinates goes hand in hand with the date change from PD to ETRS89.

### Relation to the geoid and the center of gravity

In Austria , due to the influence of the Alps, the geoid is 43 to 52 meters above the earth ellipsoid defined in WGS 84. The large fluctuation of 10 meters decreases in the date Austria to −2.5 to 3.5 meters. This datum of the Austrian Federal Registration Network refers to a Bessel ellipsoid that is shifted in the X, Y, Z directions by 596, 87 and 473 meters.

For Germany's Bessel ellipsoid and the "Potsdam date" the analog shift is 606, 23 and 413 meters in the XYZ direction (international convention of the 3 axes: X / Y is the geocentric equatorial plane, Z the earth axis , X points to the prime meridian which also runs through Greenwich). The Swiss national coordinates refer to the date CH1903 .

## literature

• Bernhard Heckmann: Introduction of the ETRS89 / UTM position reference system when switching to ALKIS. In: Mitteilungen des DVW Hessen-Thüringen, 1/2005, p. 17ff.
• NIMA - National Imagery And Mapping Agency: Department of Defense World Geodetic System 1984. Technical Report, TR 8350.2, 3rd edition, January 2000.
• Defense Mapping Agency: The Universal Grids - Universal Transverse Mercator (UTM) and Universal Polar Stereographic (UPS). DMA Technical Manual, DMATM 8358.2, September 1989.
• Ralf Strehmel: Official reference system for the situation - ETRS89. Surveying Brandenburg, 1/1996 ( PDF ).
• Bernhard Heck: Calculation methods and evaluation models for national surveying. Karlsruhe 1987.

## References

1. DIN series of standards 18709: Terms, abbreviations and symbols in geodesy - Part 6: Geodetic reference systems and reference surfaces Edition 2016-04. Beuth-Verlag Berlin 2016
2. Date Definitions US National Geodetic Survey Date Definitions
3. DIN EN ISO 19111: 2007-10: Geographic information - Spatial referencing by coordinates. Edition 2007-10. Berlin: Beuth Verlag GmbH
4. Working group of the surveying administrations of the federal states of the Federal Republic of Germany: Geodetic Basics ( Memento of January 24, 2016 in the Internet Archive )
5. NASA (Ed.): EGM96 and EGM2008 Geoids . January 6, 2020 ( usna.edu [accessed April 9, 2020]).