The Geoid and Different Height Systems - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 129

Chapter 4
The Geoid and Different Height Systems
Theory of the Earth's shape (theory of the Earth's gravity field) provides the basis
for determining the geodetic datums. The shape of the Earth can be defined in a
number of ways. The true shape of the Earth is generally perceived as the natural
surface of the Earth, i.e., the continental surface and idealized equilibrium sea and
lake surfaces. Geodetic field operations are conducted on this surface. The mission
of geodesy, however, does not involve acquisition of successive expressions of the
Earth's surface, which should be the research domain of disciplines like cartogra-
phy, aerial or space photogrammetry, and topography. The shape of the Earth in
geodesy refers to the figure abstracted mathematically or physically from the true
shape of the Earth, including the geoid, reference ellipsoid, and normal ellipsoid.
The geoid can be understood as the physical shape of the Earth. A reference
ellipsoid can be interpreted as the mathematical shape of the Earth, and a normal
ellipsoid is the mathematical and physical shape of the Earth. The reference
ellipsoid or normal ellipsoid is a close approximation of the geoid. Therefore, the
shape of the Earth studied in geodesy primarily refers to the shape of the geoid. The
geoid also serves as a reference surface for height determination of a given point on
the Earth's surface. Since the geoid is the level (equipotential) surface of the Earth's
gravity field, processing of leveling data should take into account the properties of
the theory of the Earth's gravity field. The different vertical datums or reference
lines chosen will constitute different height systems.
This chapter deals with the basic concepts of the theory of the Earth's gravity
field, discusses the definition of height system, and establishes the relations of
transformation between different height systems.