Vertical Reference Systems

1.1 Vertical Reference System
A vertical (height) reference system can be defined by only two parameters: a point with a known elevation from which vertical differences are calculated, and the reference surface. The different height systems are briefly explained below.

1.2 Ellipsoidal Heights
The ellipsoid, which is used as part of the definition of a geodetic datum, can be used as a reference surface. The ellipsoidal height is the orthogonal distance between a point and the reference ellipsoid. Therefore, it does not take into account the Earth’s gravity field.

1.3 Geoid
The geoid is the equipotential surface of the earth’s gravity field, chosen at a certain level (approximately Mean Sea Level (MSL)) which serves as the reference surface for height measurements. Globally, the difference in elevation between the geoid and the geocentric ellipsoid is between ± 100m.

Global and local geoids differ in their origin: global geoids consider only the long- wave and middle-wave part of the earth’s gravity field, whilst local geoids, in addition, also consider the short-wave part of the gravity field, resulting in higher resolution and, hence, better local accuracy.

Global geoids are used when consistent, orthometric heights, over long distances (continent or earth surveying), are required. Currently, the world’s best global geoid model is the Earth Gravitational Model (EGM) 200812. It was determined using satellite tracking, gravity anomalies and satellite altimetry. Its accuracy is in the range of ± 0.05m (oceans) and ± 0.5m (on land). This accuracy is higher in flat regions than in topographically mountainous terrain, such as the Alps. In aviation, elevation values have long been referenced to MSL; ICAO Annex 15 [Reference 4] requires that EGM-96 is used as the global gravity model as EGM- 2008 was not available when the requirements for a global gravity model requirement were introduced through Amendment 33 in 2004. The accuracy of EGM-96 is sufficient for terrain and obstacle elevations. This is because it meets the accuracy requirements of aviation and because height information is primarily used in context.

For local engineering applications and cadastre-surveying, global geoids are not as accurate as needed. For such applications, local geoid models are calculated, developed using local field measurements. They offer centimetre accuracy over several hundred kilometres, with a high resolution. Local geoids are not suitable for height comparison over large distances since they are based on different origins and reference heights (different equipotential levels).

1.4 Orthometric Heights
The orthometric height is the distance (H) along a line of force from a given point (P) on the physical surface of the earth to the geoid (the line is perpendicular to the equipotential surfaces at different levels).

1.5 Normal Heights
The normal height (H*) of a point is computed from its geopotential difference to that of sea level. It takes into account normal gravity, computed along the plumb line of the point (height difference of a point to the quasi-geoid). The difference between the normal height and the ellipsoidal height is called height-anomaly or quasi-geoid-height.

1.6 Graphical Representation of Different Reference Surfaces

2.1 European Vertical Reference System
The European Vertical Reference System (EVRS) has been built to reflect the globalisation of GIS applications and the need for continental-wide, consistent height information. EVRS is a gravity-related height reference system, i.e. the height values provided are normal heights. The EVRS is a tidal zero system. The EVRS is realised in the European Vertical Reference Frame (EVRF) by the geopotential numbers and normal heights of nodal points of the United European Levelling Network 95/98, extended for Estonia, Latvia, Lithuania and Romania, in relation to the Normaal Amsterdams Peils (NAP). The geopotential number at NAP is zero.

2.2 Modernised National Vertical Reference Frames
Heights in old national frames were usually determined using levelling. The heights are not strictly orthometric heights since the so-called orthometric correction was not taken into account. Whereas this correction will only be very small (millimetres) in flat areas, it can be several centimetres in mountainous terrain (10-30cm per 100km levelling). The orthometric correction can be determined using gravity measurements.

To eliminate inaccuracies, as well as torsion in the vertical reference, national geodetic agencies have started, often in combination with new horizontal reference frames, to rebuild the vertical reference frame, taking into account very accurate geoid or quasi-geoid models. The results are strict orthometric or normal heights which provide the base for a new national height reference frame. This allows the simple combination of GPS measurements (ellipsoidal heights) and levelling since the geoid undulation is precisely known for each horizontal co- ordinate.