Geoscience Reference
In-Depth Information
which is the difference between the potential at the geoid and the potential
at the point
A
, has been introduced as the
geopotential number
of
A
in
Sect. 2.4. It is defined so as to be always positive.
As a potential difference, the geopotential number
C
is independent of
the particular leveling line used for relating the point to sea level. It is the
same for all points of a level surface; it can, thus, be considered as a
natural
measure of height
, even if it does not have the dimension of a length.
The geopotential number
C
is measured in geopotential units (g.p.u.),
where
1 g.p.u. = 1 kgal m = 1000 gal m
.
(4-11)
.
=0
.
98 kgal in (4-10), we get
Using
g
=
gH
.
=0
.
98
H,
C
(4-12)
so that the geopotential numbers in g.p.u. are almost equal to the height
above sea level in meters.
The geopotential numbers were adopted at a meeting of a Subcommission
of the IAG at Florence in 1955. Formerly, the
dynamic heights
were used,
defined by
C
γ
0
,
H
dyn
=
(4-13)
where
γ
0
is normal gravity for an arbitrary standard latitude, usually 45
◦
:
γ
45
◦
=9
.
806 199 203 m s
−
2
= 980
.
6 199 203 gal
(4-14)
for the GRS 1980. Just note and keep in mind that 1 gal = 10
−
2
ms
−
2
and,
accordingly, 1 mgal = 10
−
5
ms
−
2
.
The dynamic height differs from the geopotential number only in the
scale or the unit: The division by the constant
γ
0
in (4-13) merely con-
verts a geopotential number into a length. However, the dynamic height has
no geometrical meaning whatsoever, so that the division by an arbitrary
γ
0
somehow obscures the true physical meaning of a potential difference. Hence,
the geopotential numbers are, for reasons of theory and for practically es-
tablishing a national or continental height system, preferable to the dynamic
heights.
Dynamic correction
It is sometimes convenient to convert the measured height difference ∆
n
AB
of (4-8) into a difference of dynamic height by adding a small correction.
Using Eqs. (4-13) and (4-10) gives
B
1
γ
0
(
C
B
−
C
A
)=
1
γ
0
∆
H
dyn
=
H
dyn
H
dyn
B
−
=
gdn,
(4-15)
AB
A
A