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
Search WWH ::




Custom Search