The Geoid and Different Height Systems - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 155

4.3.6 Geopotential Number

The height of a point on the Earth's surface is represented by the difference between
the potential of the geoid W 0 and that of the equipotential surface passing through
this point W, also known as the geopotential number, namely:

ð

C ¼ W 0 W ¼ gdh, ð 4 : 40 Þ

OAB

where OAB is the level line (see Fig. 4.9 ), dh is the difference in height measured
during each setup of leveling, and g is the mean value of gravity along the leveling
lines. With the geoid as the reference surface, geopotential numbers are not
measured in meters but in potential differences kGal m (10 5 cm 2 /s 2 ). On the same
level surface, the geopotential number of every point is equal and its value can be
obtained by multiplying dh by the mean value of gravity (g) for the setup. The
leveling results expressed by geopotential numbers can be conveniently converted
to the orthometric height, normal height, and the dynamic height.
The orthometric, normal, and dynamic height systems all have their respective
advantages and disadvantages. The coexistence of them not only makes the height
systems non-unified, but also increases the difficulty in combined processing of the
leveling data. Obviously, all three height systems have one part in common, the
geopotential number Ð gdh, which is the potential energy that the elevation point
possesses from the location of the point to the geoid. Its relationship with the three
heights is simple and clear; thus, the leveling data can be processed using
geopotential numbers with a unified height.
Although the geopotential number does not have the dimension of a length, it
can be considered as a natural measure for height.

4.3.7 Geodetic Height

Geodetic height (ellipsoidal height) refers to the reference ellipsoid, measured
along the ellipsoidal normal (see Sect. 5.2). In modern geodesy, the reference
ellipsoid surface can be seen as the normal ellipsoid surface because the reference
ellipsoid is consistent with the normal ellipsoid. The distance from a surface point
to the reference ellipsoid along the ellipsoidal normal is defined as the geodetic
height of this point.
As shown in Fig. 4.10 , point P is a point on the Earth's surface. Its projection
onto the ellipsoid along the ellipsoidal normal is P 0 , and the distance PP 0 is the
geodetic height H.
The geodetic height or geodetic height difference between two points on the
Earth's surface can be obtained by satellite positioning survey or trigonometric
leveling. Given the geodetic height of one point, that of the other can be easily