Height Reference Systems

• Introduction
• The German height reference system
• The European height reference system 
• Geoid and Gravity field modelling 

Geoid and gravity field modelling 

Geoid and gravity field models 

Heights indicate the vertical distance of points above a height reference surface. In dependence on the measuring techniques employed and the theoretical fundamentals referred to with the computation of the heights, different types of heights and the pertaining height reference surface are distinguished.

Heights can basically be divided into heights referring to the earth’s gravitational field, and heights above a geometrically conditioned reference surface, i.e. the ellipsoid. The geoid as a natural reference surface constitutes the equipotential surface of the earth’s gravitational field, which optimally approximates the mean sea level. Within the global frame the geoid deviates by up to ±100m from the ellipsoid, which is caused by the irregular distribution of mass in the earth’s interior. The height of the geoid designated as geoid undulation or geoid height above the ellipsoid (so called quasigeoid heights) can be derived from gravity field models. To compute the gravity field models globally distributed measurements of the functionals of the earth’s gravity field are required. Considerable progress was and is still being made with the determination of the global gravity field and its temporal changes as a result of the satellite gravity field missions CHAMP, GRACE and GOCE.

Height reference surfaces in Germany 

The official heights of the DHHN92 (German Mean Height Network 1992) are based on normal heights after the theory of Molodenski. The corresponding height reference surface, i.e. the quasigeoid, is also named NHN surface (Normal Höhen Null - Normal Height Zero). In the case of positioning by means of satellite navigation systems such as GPS, GLONASS and GALILEO ellipsoidal heights are determined. The ellipsoid defined in the GRS80 (Geodetic Reference System 1980) is used as geometric reference surface. The difference designated as quasigeoid height or height anomaly of both surfaces varies in Germany between 36 m and 50 m. The gradients of the quasigeoid heights may amount to several cm per km, so that the  influence of the quasigeoid must be considered also in the case of local measurements by means of GPS. 

Quasigeoid heights in m (click to enlarge)

Gradients of quasigeoid heights in mm (click to enlarge)

Quasigeoid models 

Owing to the increasing utilization of satellite-based techniques in practical surveying the need arose to determine a quasigeoid model compatible with the reference systems used in Germany with an accuracy of a few cm. Since the mid90ties BKG has performed extensive work in this field. In cooperation with the Survey Administrations of the Länder a dense network of stations was created by means of GPS measurements and levellings, at which ellipsoidal heights in the ETRS89 and also heights in the DHHN92 are available. Besides terrestrial gravity measurements, global gravity field models, satellite altimeter measurements, and digital terrain models these stations constitute the basis for the determination of the quasigeoid of Germany.

A first solution of the quasigeoid model was established in 1998 for the territory of the new Länder. Under the name "Satellite-Geodetic Nivellitic Quasigeoid (SNG01)" a completed solution was delivered to the Länder. The improved solution GCG05 (German Combined QuasiGeoid 2005) has been available since August 2005, which was determined through the combination of two independent solutions performed by the "Institut für Erdmessung" of the University of Hannover and by the "Bundesamt für Kartographie und Geodäsie".

This model is compatible with the coordinates given in the ETRS89, which were established by the satellite positioning service (SAPOS) of the Länder. For most areas of Germany transformation of the ellipsoidal heights into heights of the DHHN92 can be guaranteed with an accuracy of 1 to 2 cm.

Measurements for modelling of quasigeoid (gravity measurements: red = terrestrial / yellow = from altimeter measurements / blue = Aerogravimetry / black = GPS and Levelling measurements) Click to enlarge

REMARK:
A new quasigeoid GCG2011 - German Combined Quasigeoid 2011 - are available now. Update of these English websites are in preparation.