The Geoid and Different Height Systems - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 151

Fig. 4.9 Effects of
non-parallel level surface
on leveling

X
OAB ʔ

X
BNO ʔ

h 0 ,

h 6¼

X
OAB ʔ

X
BNO ʔ

h 0 h þ ¼ w 6¼ 0 : ð 4 : 29 Þ

So, similarly to errorless leveling, the error of closure of leveling loops w still
cannot be zero. Such closing error of leveling loops caused by unparallel level
surfaces is called theoretical misclosure.
The height of a point should be single-valued and be independent of the leveling
routes. So, in dealing with leveling results, the properties of the theory of the
Earth's shape must be taken into consideration; the height system must be defined
reasonably and corrections applied. These corrections should be very small so that
they could be neglected in dealing with low-order leveling results.

4.3.3 Orthometric Height

Referenced to the geoid, the orthometric height (H o ) is the length between the geoid
(reference surface) and a point on the Earth's surface measured along the plumb
line. As shown in Fig. 4.9 , the height differences between each level surface
measured from point B along the plumb line is expressed by H, then H O , the

ʔ

orthometric height of point B is:

ð

X
CB ʔ

H O ¼ ʔ

H 1 þ ʔ H 2 þ¼ H ¼ dH : ð4:30Þ

CB

Since the level surface is an equipotential surface, the potential energy differ-
ence between two infinite close level surfaces in Fig. 4.9 is given by: