Federal Agency for Cartography and Geodesy

D-A-CH-Geoid and European Alps Geoid

Improved cross-border height determination in the region of the European Alps

“Why does the mountain ‘Zugspitze’ have two heights — when there is only one sea level?”

“How big are the differences of the height numbers between Germany, Austria and Switzerland?”

Have you ever asked yourself these questions? Or do you have to work with different height systems for a cross-border project? With our web application you can transform heights between the current national references frames of the countries Germany, Austria and Switzerland.

Height systems in Europe

The national height systems in Europe are based on precise leveling measurements. Depending on the country, these observations are referenced to the mean water level of different seas and time periods. Therefore, heights of individual countries are not directly comparable in general, as their zero levels differs (Fig. 1). The EVRS is the foundation for unified height determination in Europe and is continuously developed further. Even so, the national heights are still statutorily used in land surveying.

Picture shows a map of transformation parameters (mean differences) from national heights in Europe to EVRF2019 in centimeters, as well as the associated reference tide gauges Mean height differences EVRF2019 minus national heights Fig. 1: Transformation parameters (mean differences) from national heights in Europe to EVRF2019 in centimeters, as well as the associated reference tide gauges

Different theoretical bases for the calculation of the height information cause further local deviations along the borders (see also Fig. 2):

Example Zugspitze: 47;42112° North / 10;98623° East 

DE: "m ü. NHN“(Amsterdam, DHHN2016)normal heights2962,08 m
AT: "m ü. A.“(Triest, MGI)normal-orthometric heights2962,33 m
Difference 25 cm

Example Bad Säckingen (close to Laufenburg): 47;549034° North / 7;955177° East

DE: "H. ü. NHN“(Amsterdam, DHHN2016)normal heights300,48 m
CH: "m ü. M.“(Marseille, LN02)forced uncorrected heights300,79 m
Difference 31 cm1

1The frequently encountered information of 27 cm for Laufenburg refers to the outdated German height reference “above NN” (“Normal zero”, normal-orthometric heights in the System DHHN12).

Phase 1: "D-A-CH-Geoid“ project and test area Lake Constance

The "D-A-CH-Geoid“ project aimed at harmonizing the basis for height determination in the Alpine countries. It was a joint initiative of the federal and state authorities responsible for land surveying in the German-speaking Alpine region:

The Memorandum of Understanding (link in German) of October 19, 2017, aimed to promote the cooperation in the field of regional gravity field modeling, to exchange and improve the underlying data and models, and to facilitate cross-border height determination for users of geodetic coordinates.

In their countries, the partners are significantly involved or responsible for determining and making available the national geodetic spatial reference. In this function, they examine the regional course of the physical height reference surface and determine the corresponding geoid or quasigeoid models for ther national territory. On the basis of these models, users of satellite positioning services can determine height above sea level with respect to the national height system.

The following work was successfully completed in the first phase (among others):

  1. Improved regional geoid model in a focus area around Lake Constance
    • Exchange and revision of the base data for the calculation of the geoid models: gravity data, digital elevation models, control points for validation
    • Comparative studies on geoid modeling in high mountains

  2. Improved height transformation between the “D-A-CH countries”
    • Extensive comparative investigations and validation between the national height reference surfaces (geoid models and other height transformation grids) and the national and European heights along the borders
    • Derivation of a consistent height transformation model for the “D-A-CH countries” accurate to a few centimeters
    • Development of a corresponding web application

 Fig. 2 gives an overview of the height differences along the borders of the “D-A-CH countries”.

Picture shows a map of height differences between the official height systems along the borders of the “D-A-CH- countries” in centimeters Height differences between the official height systems along the borders of the “D-A-CH countries” in centimeters Fig. 2: Height differences between the official height systems along the borders of the “D-A-CH countries” in centimeters. The colored points indicate the exact values from cross-border leveling, the surface plot refers to the differences of the height reference surfaces (geoid models): [DE] GCG2016; [AT] Austrian Geoid 2008 + Höhengrid; [CH] CHLN02. Sign convention “country 1 -> country 2”: The quoted values are to be added to the heights of country 1 in order to obtain heights of country 2.

Phase 2: The "D-A-CH-Geoid“ becomes the "European Alps Geoid“ (EAlpG)

The calculation of the height reference surface for the D-A-CH countries is not limited to the national borders. The underlying data (gravity data, elevation models) are also required for an adjacent area in the neighboring countries. At the same time, France, Italy and Slovenia also have a share in the Alpine region.

Together with the responsible national bodies for the integrated geodetic spatial reference, we have been working to expand the initiative to the entire Alpine region and the neighboring lowlands. This means that the “European Alps Geoid” also includes parts of Croatia, Hungary, Slovakia and the Czech Republic. An extended memorandum of understanding as a basis for the cooperation between the participating institutions was concluded on May 12, 2022.

The activities will as well be embedded in a pan-European initiative for a European Height Reference Surface within the framework of EUREF, the scientific sub-commission for Europe within the IAG. As a contribution to the EUREF Working Group "European Unified Height Reference”, the EAlpG will be one of many cornerstones for the first official realization of a unified European height reference surface connected to the EVRS. The metadata about the national height reference frames and transformation products will also be used in to modernize the information system for the European coordinate reference systems CRS-EU.

The image illustrates the tentative region for the "European Alps Geoid" cooperation: Terrain (bottom) as well as gravity anomlies (middle) and geoid heights (top) from a global model with limited resolution. Tentative region for the "European Alps Geoid" cooperation Fig. 3: The image illustrates the tentative region for the "European Alps Geoid" cooperation: Terrain (bottom) as well as gravity anomlies (middle) and geoid heights (top) from a global model with limited resolution.

Background information

Modern height determination

Geodesy deals with the measurement and calculation of exact coordinates on the Earth's surface. In the past, this was done using distance and angle measurements with optical instruments, today using satellite navigation systems (GNSS), e.g. GPS, Glonass, Galileo etc. While you can determine your position to within a few meters with a handheld GPS or mobile phone, in geodesy you can achieve accuracies of a few centimeters with special techniques (for moving objects) or even millimeters (for long-term measurements).

What GPS cannot provide is an elevation in relation to the regional sea level. The spatial coordinates, e.g. expressed in geographical longitude, latitude and ellipsoidal height, relate to a global reference ellipsoid and are purely geometric. The difference between ellipsoid and sea level due to the irregularly shaped gravity field of the Earth varies around ±100 m globally. In Germany, it ranges between 36 m and 50 m.

On the other hand, the sea-level related height systems of the countries are still determined by a classic method, the so-called geometric leveling. These measurements are based on long-term readings of tide gauges and are influenced by the gravitational field. A level instrument is basically a highly accurate telescope with a sensitive spirit level.

In order to be able to use GPS for height measurements, one therefore needs a correction model, i.e., a height reference surface, which indicates the local distance of the zero level surface from the reference ellipsoid. In geodesy, this reference surface is called geoid. Its shape cannot be measured directly; it needs to be calculated by combination of local gravity observations, digital terrain models and global gravity field models. By means of such a geoid model, ellipsoidal heights from GNSS can then be transformed into sea-level related heights (Fig. 4).

Picture shows a schematic overview of heights and reference surfaces Schematic overview of heights and reference surfaces Fig. 4: Schematic overview of heights and reference surfaces

“After all, not all sea levels are equal – why the Zugspitze does in fact have two heights”

The surface of an ocean “at rest” would follow the gravity field of the Earth. However, oceans are highly dynamic and respond to a multitude of influences. Salinity, temperature, wind, coastal shape etc. cause currents and force the oceans to deviate from its ideal shape at every coastal location and even in the long-time mean.

Countries connect their leveling to one or more usually nearby tide gauges depending on their geographic location. The elevation value for a certain point on the Earth's surface, e.g. a mountain peak, then differs from country to country.

Simply speaking, German heights refer to the North Sea, those of Austria and Switzerland to the Mediterranean Sea (see Fig. 1 and the numerical example above).

This means that heights and the associated height reference surfaces (geoid models) are never absolute. They follow a convention (definition) for the zero level.

For example, Belgium is the only country in Europe whose heights do not refer to the mean tidal water level, but to the lowest tidal water level (Lowest Astronomical Tide, LAT).

“Why does the height difference change along the border?"

Different definitions when calculating the height information (e.g. taking into account the local gravitational field or the tides) lead to further differences. Between experts, it is spoken of height types. The height differences between individual countries can therefore also vary along the border.

With the transition of the German height reference from “Normalnull” to “Normalhöhennull” at the beginning of the 1990s, the height differences to the neighboring countries also changed slightly!

Further information can be found on the explanatory pages (standard level or expert level) of the D-A-CH transformation application.

“But there are unified European heights, right?"

The national leveling data are submitted to and processed at the UELN, depending on availability. The results are released as realizations of the EVRS with respect to Amsterdam level (NAP).

However, due to the diversity of the height networks, the EVRS is not yet as important as, for example, the ETRS89 for position determination, where all national solutions are based on the same metrological principles (satellite navigation systems). Users expect zero height to be connected to their local mean sea level.

Some countries now relate their heights to the Amsterdam level, i.e. their heights are now in principle compatible with the EVRS (e.g. Baltic States, Poland). For Germany this has always been true for historical reasons (with the exception of the GDR).

Other countries, like Austria and Switzerland, have decided to keep the habituial height definition for end users, e.g., engineering surveys.


Rülke et al. (2013): Unification of European height system realizations. Journal of Geodetic Science 2(4):343-354, DOI: 10.2478/v10156-011-0048-1

Further references can be found at the end of the explanatory pages (standard level or expert level) of the D-A-CH transformation application.