Geoscience Reference
In-Depth Information
Today, we can readily determine the deviation of a local system or
local
datum
from a global reference system. We have the deviation of
•
size and shape of the reference ellipsoid (
a, f
),
•
translation (
x
0
,y
0
,z
0
), and
•
orientation (three very small Euler angles
ε
1
,ε
2
,ε
3
).
Since GPS is very well established (cf. Hofmann-Wellenhof et al. 2001),
we assume a general knowledge for granted and recapitulate in this topic
only some basic facts.
Part II: Three-dimensional geodesy: a transition
This part considers how the concepts of geodesy in the modern sense of Molo-
densky, Marussi, and Hotine would look shortly before the advent of satel-
lites, but already including electronically measured spatial distances (trilat-
eration). We work with local Cartesian coordinates rotated in a known way
by the astronomically measurable quantities Φ
,
Λ
,A
(astronomical latitude,
longitude, azimuth), considered as Eulerian angles of rotation of the local
with respect to the global axes. However, we have no means to determine
the geocenter. So the situation is somewhat more complicated but still geo-
metrically well defined and transparent. “Local” here means “strictly local”,
varying from point to point together with their plumb lines defined by (Φ
,
Λ).
The main problem with this approach is the impossibility of measuring
precise zenith angles because of atmospheric refraction. We may say that
the vertical dimension is much worse defined than the horizontal dimension.
Finally, we shall consider how terrestrial and GPS data can be combined.
Part III: Local geodetic datum
The way out of the dilemma of the worse vertical dimension is a complete
separation of horizontal and vertical and determining the latter by the dif-
ferential method of astrogeodetic geoid determination. This was a “2+1-
dimensional” rather than a three-dimensional approach, logically more com-
plicated but practically more accurate. In fact, the former (and present)
astrogeodetic methods can be understood much better by deriving them
from the global situation. Thus, today with GPS we are in a much better
position practically as well as theoretically: the classical local datums can be
understood best by their relation with the global geometry. “Local geodetic
system” or “local geodetic datum” is again meant in the sense of “regional”,
e.g., the North-American Datum or the European Datum.
GPS permits to separate the geometry from the gravity field, which con-
tinues to be a challenge for physical geodesy to be solved by a combination
of terrestrial and satellite data.
