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 vertical height relationships are shown in Figure 1 below.
The ellipsoid, which is used as part of the definition of a geodetic datum, can be used as a reference surface. The Ellipsoidal Height (h) is the orthogonal distance between a point and the reference ellipsoid. Therefore, it does not take into account the Earth’s gravity field.
The Orthometric Height is the distance (H) along a line of force from the geoid to a given point (P) on the physical surface of the earth (the line is perpendicular to the equipotential surfaces at different levels).
The Normal Height (H*) of a point is computed from its geopotential difference to that of sea level. It takes into account the 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.
Geoid – Earth Gravitational Model (EGM)
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 WGS 84 ellipsoid is between ± 100m. This difference in elevation is the geoid undulation (N).
Global and local geoids differ in several aspects: in the past global geoids considered only the long- and middle-wave parts of the entire earth's gravity field, such as EGM96. Local geoids consider the long-, middle-, and short-wave parts of a smaller region the earth's gravity field, such as CARIB97 that is valid only for the Caribbean Sea. One of the world's best global geoid models is the Earth Gravitational Model (EGM) 20081. EGM2008 offers modeling to degree and order 2159 - thus considering a fuller range of the middle- and short-wave parts than previous global geoids. Global geoids are used when consistent orthometric heights, over long distances (continent or earth surveying), are required
For local engineering applications and cadastre-surveying, global geoids are not as accurate as needed. For such applications, local geoid models are calculated. These can only be 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).
The Annex 15 requirements currently identify the use of EGM96 for WGS84 heighting. This was the best available at the time of adoption when the heighting decisions were made although its accuracy was not sufficient globally to meet the accuracy requirements of Annex 15 and for this reason, whilst the recommendations below refer to the use of EGM96, it also identifies that other models should be used where EGM96 is not sufficiently accurate. For example, the latest global geoid model, EGM2008 may be used as a means to achieve greater accuracy. It was determined using satellite tracking, gravity anomalies and satellite altimetry. Its estimated global accuracy is in the range of ± 0.05 m (oceans) and ± 0.5 m (on land). This accuracy is higher in flat regions than in topographically mountainous terrain but EGM08 meets all requirements and if applied would avoid the need to undertake an assessment of the local accuracy of EGM96.
Figure 1 Vertical Height Relationships
Caution is necessary in the use of Tide-Free models such as EGM96/EGM2008 as opposed to Zero-Tide models such as the European Vertical Reference System (EVRS). Additional error can be introduced owing to the differing assumptions underlying the different models. Additionally, the use of EGM2008 is appropriate where the density of gravity data was adequate in the development of the model to support the full resolution. In specific regions a target of 25cm can easily be achieved. However, in regions where the density of gravity data in developing the model was sparse, comparisons to GPS leveling are on the order of 40cm and will not meet the targeted 25cm accuracy specification. A local geoid may still have to be used in areas where the gravity point density was spatially poor in extent for EGM2008.
European Vertical Reference System
The European Vertical Reference System (EVRS) is an example of a system that has been built to reflect the globalisation of Geographic Information System (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 Recommendations for Determining Heights Relative to EGM-96
The ICAO SARPS mandate that all height information should be published relative to MSL. Orthometric heights very closely approximate the height above MSL. To determine the geoid undulation, the Earth Gravitational Model 1996 (EGM96) should be used but may be replaced by a more accurate geoid model where the accuracy of EGM96 is not sufficient.
The most stringent accuracy requirements covered by the standards are geoid undulations for several on-aerodrome facilities. These accuracy requirements are 0.25m (95% confidence interval) for the measurements. This can be readily achieved for computing ellipsoidal heights using appropriate GNSS equipment. However, achieving these accuracy requirements for geoid undulations is more difficult at the present time. Recommended methodologies for determining the geoid undulations are provided below.
Because the elevation values of a point may not differ significantly between Ellipsoidal height, EGM96 height or any other vertical reference system height the surveyor should ensure that with each elevation value, the vertical reference frame is stored.
2.2 Method 1
When a new feature is surveyed using GNSS means, the primary reference frame for the determination of a coordinate is the ellipsoid. It is common that GNSS sensors (or their processing software) have an EGMxx2 integrated, therefore allowing the direct determination of height above MSL (in EGMxx). When a new survey point is determined by GNSS, the elevation above EGMxx should be directly determined.
If neither the sensor nor the GNSS processing software have the capability to integrate the EGMxx undulation for a surveyed point, the ellipsoidal height should be stored for the required point. The geoid undulation should then be determined by interpolation from EGMxx for the given latitude and longitude of the point.
The same method may also be used for an airborne data acquisition method when the position of the sensor platform is determined by GNSS.
2.3 Method 2
A national geodetic body may have scientifically determined a geoid. Provided this geoid is of sufficient accuracy and is referenced to a horizontal reference frame which allows transformation to WGS 84/ITRF without a loss of accuracy, then, for given values of the latitude and longitude of a point, the geoid undulation should be interpolated directly from the data.
A description of the geoid model used including the parameters required to allow a transformation between the model and EGMxx or any other reference frame should be published by the State aviation authority.
2.4 Method 3
If a national / regional levelling system is free from limiting systematic biases, and the offset between the national tide gauge datum and the geoid is known (ΔH), then geoid undulations should be computed by measuring the height of a point above the levelling datum (H) and the ellipsoid (h). The geoid undulation (N) at that point is then given by the relationship:
N = h – H + ΔH
A realistic estimate of the quality of the heighting network should be obtained from the relevant authorities prior to carrying out the survey work. The accuracy of the heighting network should be documented, together with the data set as metadata.
The method should only be used when the benchmark values are known with sufficient accuracy.
3 Deriving Elevation Information from Existing Sources
Some of the elevation information does not have very stringent quality requirements (distance measuring equipment (DME), minimum altitudes). In many regions, digital terrain models (DTM) exist which may be used for deriving the elevation information. The sources of error in such models should be fully evaluated to ensure the accuracy requirements can be met. The accuracy of the DTM should be at least 1.5 times higher than the data quality requirement of the required feature. The resolution of the DTM should be adequate for the topography to ensure that the highest elevation of the real world is maintained in the digital data set.
The DTM should be available in the same horizontal reference system as the required feature.
For linear or polygonal features, the elevation information should be derived by determining the highest value within the area of interest. For point features, the potential horizontal displacement between the two data sets should be taken into account. 4 Resources
The NASA Goddard Space Flight Center (GSFC) and National Imagery and Mapping Agency (NIMA) Joint Geopotential Model EGM963;
The Earth Gravitational Model 2008 (EGM2008)4;
European Vertical Reference System (EVRS) website.5