Height Reference Systems (Geoid) and Datum Unification

Illustration of aheight system with heightH above the geoid

Figure. Illustration of a height system with height H above the geoid. Credit: Sjöberg and Bagherbandi (2017).

Height above the sea is defined in a selected height system. A height system
consists of a number of fixed points (benchmarks), which are marked on the ground.
In the future, the height system may be defined as a digital database versus a defined
geoid model without fixed points. The height of each fixed point is carefully
measured (usually by levelling). The height system is also linked to a number of
parameters that define the height of the fundamental benchmark at the zero point of
the system and the epoch of the height calculation that the heights are valid for, as
well as a possible temporal rate of change of height of each benchmark. The fixed
points are then used as starting points to measure height differences to and the
heights of other objects in the surroundings. When the term “height” is used, it usually
means the height above sea level, or, more precisely, the height along the plumb
line above the geoid. The geoid surface is always perpendicular to the plumb line.  Over time, height systems are affected by a number of external factors: fixed points are destroyed or moved because of subsidence or land uplift (Sjöberg and Bagherbandi 2017, Chapter 1). Generally, there are two types of height systems that are the most commonly used height systems for a geodetic vertical datum realization worldwide:

  • Orthometric heights referred to the geoid and
  • Normal heights referred to the quasigeoid (very closely agrees with the geoid except for mountainous regions)

Most European states use quasigeoid for their height systems and the reference surface, while the rest of the world relies on orthometric heights with the geoid as the zero-level (Sjöberg and Bagherbandi 2017, Chapter 7). Separation of quasigeoid  and geoid can be seen in the following figure (see more in Sjöberg and Bagherbandi 2012, Earth Sci Inform (2012) 5:87–91):

Figure. Quasigeoid-to-geoid height difference obtained using EGM2008 model with resolution is 5×5 arc-minute. Unit: metre Credit: Sjöberg and Bagherbandi (2012)

Why we cannot use an Earth Gravitational Model (e.g. EGM2008) directly to determine the geoid?


Today the geoid can be conveniently determined by a set of high-degree spherical harmonics, such as EGM2008 with a resolution of about 5x5 arc-minute. However, such a series will be biased when applied to the continental geoid inside the topographic masses which is closely related with the so-called topographic potential bias (see more Sjöberg and Bagherbandi 2011, DOI: 10.2478/v10156-010-0001-8). Therefore the topographic correction due to the bias should be added to the geoid height obtained from an EGM.

The following figure shows the topographic bias computed using DTM2006.0 model in Himalayas and Tibet:


Figure. Topographic bias calculated using DTM2006.0 model in Himalayas and Tibet.
Unit: metre Credit: Sjöberg and Bagherbandi 2011.

Published by: Mohammad Bagherbandi Page responsible: Gunilla Mårtensson Updated: 2018-11-13
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