Datum Problems - Map Projections: Cartographic Information Systems - page 551

Table 21.8 World Geodetic Datum 2000 (WGS 2000), Grafarend and Ardalan ( 1999 )

“tide-free”

A 1 (m) A 2 (m) (m)

6,378,136.572 6,356,751.920 521,853.58

“zero-frequency”

A 1 (m) A 2 (m) (m)

6,378,136.602 6,356,751.860 521,854.674

Table 21.9 Transformation from conformal coordinates of type Gauss-Krueger (Bessel reference ellipsoid) to
conformal coordinates of type Gauss-Krueger (WGS 84 and WGS 2000, “tide-free geoid”)

Point X 84 (m) Y 84 (m) X 2000 , tf (m) Y 2000 , tf (m)

6324 3,558,357.6411 5,502,059.3874 3,558,357.6374 5,502,059.0228

6417 3,473,105.6872 5,488,314.2616 3,473,105.6989 5,488,313.8979

6520 3,503,525.2908 5,481,082.8581 3,503,525.2906 5,481,082.4948

6725 3,567,188.4302 5,458,730.6878 3,567,188.4259 5,458,730.3259

6922 3,529,538.2090 5,437,066.5340 3,529,538.2071 5,437,066.1735

7016 3,462,353.8528 5,429,412.1301 3,462,353.8552 5,429,411.7702

7220 3,506,195.8794 5,405,925.7956 3,506,195.8790 5,405,925.4371

7226 3,579,947.2236 5,406,962.2314 3,579,947.2185 5,406,961.8728

7316 3,462,442.3282 5,386,837.1695 3,462,442.3306 5,386,836.8123

7324 3,556,797.3245 5,387,475.3087 3,556,797.3209 5,387,474.9514

Table 21.10 Transformation from conformal coordinates of type Gauss-Krueger (Bessel reference ellipsoid) to
conformal coordinates of type Gauss-Krueger (WGS 84 and WGS 2000, “zero-frequency tide geoid”)

Point X 84 (m) Y 84 (m) X 2000 , zf (m) Y 2000 , zf (m)

6324 3,558,357.6411 5,502,059.3874 3,558,357.6372 5,502,059.0320

6417 3,473,105.6872 5,488,314.2616 3,473,105.6990 5,488,313.9072

6520 3,503,525.2908 5,481,082.8581 3,503,525.2906 5,481,082.5041

6725 3,567,188.4302 5,458,730.6878 3,567,188.4256 5,458,730.3353

6922 3,529,538.2090 5,437,066.5340 3,529,538.2070 5,437,066.1830

7016 3,462,353.8528 5,429,412.1301 3,462,353.8553 5,429,411.7796

7220 3,506,195.8794 5,405,925.7956 3,506,195.8790 5,405,925.4467

7226 3,579,947.2236 5,406,962.2314 3,579,947.2182 5,406,961.8824

7316 3,462,442.3282 5,386,837.1695 3,462,442.3308 5,386,836.8219

7324 3,556,797.3245 5,387,475.3087 3,556,797.3207 5,387,474.9610

21-51 Datum Transformation Extended by Form Parameters
of the UMP

Let us refer to Definition 21.2 as the universal Mercator projection of the ellipsoid-of-revolution
E

a 1 ,a 2

in local coordinates, namely ellipsoidal coordinates in a local datum.
Definition 21.2 (Universal Mercator projection, local coordinates).

A conformal transformation of ellipsoidal coordinates of type “surface normal” ellipsoidal longi-
tude λ and “surface normal” ellipsoidal latitude ϕ into Cartesian coordinates

{ x, y } with respect