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is denoted as
a
01
etc. From those tables, we conclude that there are only three terms larger than
a centimeter. Accordingly, with such results, we can reduce the computational efforts by 30%.
Indeed, we need only the coecients
a
00
, a
10
, a
01
,b
00
,b
10
,b
01
}
, respec-
tively. For fast less accurate computations, we can disregard the coecients
a
01
and
a
01
.The
value of such a term is smaller than 10cm. Obviously, just for mapping purposes this accuracy
is sucient: it is an advantage when you have to compute datum transformations of conformal
coordinates for mega data sets.
{
a
10
,a
01
,b
00
,b
10
,b
01
}
and
{
X
=
=
X
(
x, y, ρ, t
x
,t
y
,t
z
,α,β,γ,s,A
1
,E
2
,a
1
,e
2
)
,
(21.92)
Y
=
=
Y
(
x, y, ρ, t
x
,t
y
,t
z
,α,β,γ,s,A
1
,E
2
,a
1
,e
2
)
,
x
=
=
x
(
X,Y,ρ,t
x
,t
y
,t
z
,α,β,γ,s,A
1
,E
2
,a
1
,e
2
)
,
(21.93)
y
=
=
y
(
X,Y,ρ,t
x
,t
y
,t
z
,α,β,γ,s,A
1
,E
2
,a
1
,e
2
)
.
Finally, we repeat all computations by replacing the “global” reference system of type WGS 84
by the new World Geodetic Datum 2000,
Grafarend and Ardalan
(
1999
). Table
21.8
reviews th
e best e
stimates of type semi-major axis
A
1
, semi-minor axis
A
2
and linear eccentricity
=
A
1
−
A
2
both for the tide-free geoid-of-reference and for the zero-
frequency tide geoid-of-reference. The related data of transformation of type UTM
{
X
84
,Y
84
}
ver-
sus
, originating from a reference system of Bessel type, are collected in Tables
21.9
and
21.10
. Indeed, they document variations of the order of a few decimeter!
{
X
2000
,Y
2000
}
Table 21.3
Difference between Gauss-Krueger conformal coordinates
X
and
X
(trans): Easting
X
(m)
X
(trans)(m)
d
X
(mm)
Point
6324
3,558,357.7304
3,558,357.7333
−
2
.
9
6417
3,473,105.6664
3,473,105.6701
−
3
.
7
6520
3,503,525.3824
3,503,525.3858
−
3
.
4
6725
3,567,188.4423
3,567,188.4454
−
3
.
1
6922
3,529,538.2613
3,529,538.2647
−
3
.
4
7016
3,462,353.7891
3,462,353.7930
−
3
.
9
7220
3,506,195.9031
3,506,195.9068
−
3
.
7
−
3
.
1
7226
3,579,947.1053
3,579,947.1084
7316
3,462,442.3184
3,462,442.3224
−
4
.
0
−
3
.
3
7324
3,556,797.2523
3,556,797.2556
Note that for our numerical computations, we took advantage of
Grafarend
(
1995
),
Grafarend
and Syffus
(
1998e
),
Friedrich
(
1998
), and
Grafarend and Ardalan
(
1999
).
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