Geoscience Reference
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Fig. 4.10 Geodetic height
calculated. The leveled height, with corrections applied, can be converted to the
geodetic height.
4.4 Relationship and Transformation Between Different
Height Systems
4.4.1 Relationship Between Orthometric Height, Normal
Height, and Geodetic Height
From the previous discussion, we know that the same surface point has at least five
different values of height due to different reference surfaces for heights. In other
words, height is relative to a reference surface. Its precision depends on the
precision of both the observed quantity and the reference surface used. The rela-
tionship between different reference surfaces for heights will now be described.
The Earth's surface points project on the ellipsoid in two ways: the Helmert's
projection and Pizzett's projection, as shown in Fig.
4.11
.
According to Helmert's projection, a point P on the Earth's surface is directly
projected onto the ellipsoid along the normal (P
0
P
H). In Pizzett's projection,
the same point P is projected along the plumb line onto the geoid (P
0
P
¼
H
O
). The
point on the geoid is then projected once again along the normal to the ellipsoid
(P
0
0
P
0
¼
¼
N).
As is known, the geoid and the reference ellipsoid surface are usually neither
coincident with nor parallel to each other, so there is an angle
between the plumb
line and the normal, called the deflection of the vertical. Using these two different
projection methods will achieve different results, although the difference is quite
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