C:\excerc\GEOD98e.E13.wpd

Geofysisk Afdeling, Juliane Maries vej 30, 2100 København Ø.

Geodesy Course, Exercise 13.

The purpose of the exercise is to demonstrate the effect of a datum-shift on coordinates, and to show how a datum-shift can be determined in a simple case.

Examples of datum-shifts are found in Torge(1991, Table 5.3).
We also need to use values of parameters for different ellipsoids, such as the GRS80 ellipsoide (see page 57), Hayford (= International) ellipsoide (Torge, equation 3.66a) and the Bessel ellipsoid (Torge p. 221).

(1) Calculate for Buddinge, station 620, the effect of a datumshift on latitude, longitude and altitude using
(Torge, eq. 5.121a,b). Note that this equation has problems with the signs on the coordinate differences. If you can not guess the right sign, you must derive the equation !

The original co-ordinates in ED1950 are for the Hayford ellipsoide. The height of the geoid in this system can for Buddinge be put equal to 3.0 m.

The program TRANS13 can be used for the transformation in 2 steps and the values in Table 5.3 can be used.

(a) Convert from geodetic to Cartesian coordinates in ED1950. (Forward transformation)
(b) The Cartesian coordinates are converted to geodetic coordinates referring to the GRS80 ellipsoid. (Reverse transformation).
Use points with the coordinates ( degrees, minutes and seconds):
Latitude Longitude H, height above the ellipsoide (m).
1 56 00 00.00 10 00 00.00 50.0
2 56 00 00.00 12 00 00.00 10.0
3 --- Buddinge 620 -----
620 55 44 21.86 12 30 3.59 51.67

Note that data and intermediate results can be put into a file and used in the next two steps.

What is the new geoid height in Buddinge?

(3)A point in NAD1927 has the coordinates = 38o, = 261o and height above sea level H = 0 m. The geoid height can be found from Fig. 5.10 and must be used in integer m. Note that the Bessel ellipsoid is used in NAD1927.

Compute the effect of the datum-shift as in (2) using
TRANS13. What is the geoideheight in GRS80 ?

(4) On the Faroe islands are used a datum called Fød1951, which uses the Hayford Ellipsoide.

A point on the islands has the coordinates (no., latitude, longitude, H) in this datum:
14294 61 25 30.04 -6 44 24.76 426.55.
Using Doppler-satellite methods the coordinates have been determined in the geocentric coordinate system WGS84 to
(X,Y,Z)= 3037596.11 -359292.55 5578619.14 (m).
How many of the 7 parameters will it be possible to determine ?

What is the datum-shift ?

(5) The program TRANS13 may also be used for transformation to UTM coordinates. Transform the geodetic coordinates used in (2) from ED50 to UTM (Zone 32) and from GRS80 also to UTM (Zone 32). What besides the Datumshift is the reason for the magnitude of the difference ?

Appendix. Example of the use of TRANS13.

/disk1/cct/dgravsoft/trans13
MAP TRANSFORMATION PROGRAM, VERS. MAY 06, 1992
COPYRIGHT GEOPHYSICAL INSTITUTE, UNIV. COPENHAGEN, 1991, 92

THE PROGRAM TRANSFORM FROM GEOGRAPHICAL COORDINATES TO
PLANE OR 3-D CARTESIAN COORDINATES OR REVERSE
INPUT IDENTIFYING TEXT (MAX. 72 CHAR).
ED50 to Cartesian with Datumshift from table 5.3.
ED50 to Cartesian with Datumshift from table 5.3.
FORWARD TRANSFORMATION (GEO TO XY(Z)) ? (T/F) t
SELECT SPHEROID:
1: SPHERE, 2: CLARKE 1866, 3: HAYFORD 1909, 4: GRS 1980
5: CLARK1880, 6: BESSEL 1841, 7: KRASOVSKY 1940, 8: WGS 1972
9: AUSTRALIAN 1965, 10: AIRY1849, 11: EVEREST 1830
12: HOUGH 1956,: 13: FISHER 1960, 14&15: SPHERE, 16: INPUT 3

ELLIPSOID : HAYFORD 1909 3
1/FLATTENING = 296.9999982
SELECT PROJECTION:
1: U T M, 2: TRANSVERSE MERCATOR, 3: MERCATOR
4: LAMBERT CONFORMAL CONIC (2 STD. PARAL.)
5: POLAR STEREOGRAPHIC (AZIMUTHAL-),
6: SYSTEM 34 JYLLAND, 7: SYSTEM 34 SJAELLAND,
8: SYSTEM 45 BORNHOLM, 9: CARTESIAN (X,Y,Z) 9

;CARTESIAN
IS DATUM SHIFT NECESSARY ? (T/F) t
INPUT DX,DY,DZ (M) -102.0 -102.0 -129.0
INPUT SCALE CHANGE -1.0 2.5E-6
INPUT ROTATIONS IN ARCSEC AROUND X,Y,Z AXES 0.4 -0.2 0.4
AN INPUT RECORD MUST BE ON THE FORM:
(1) NO. LATITUDE, LONGITUDE,DATA(1),..,DATA(N)
(2) NO. Y, X,DATA(1), DATA(2),..,DATA(N)
(3) NO. X, Y, Z, DATA(2),...,DATA(N) (CARTESIAN)
(4) GRID FORM, WITH COORDINATES GIVEN IMPLICITLY
THROUGH A GRID LABEL. IF TRANSFORMATION
FROM (1) TO (3) DATA(1) MUST BE THE HEIGHT

INPUT NUMBER OF DATA ELEMENTS, AND ELEMENT NUMBER USED 1 1
(ALL ELEMENTS WILL BE REPRODUCED, IF OUTPUT TO FILE)
ANGLES IN 1: DDMMSS.S, 2: DDMM.M 3: DD.D, 4: CC.C ? 1
ARE DATA GRIDDED ? (T/F) f
ARE INPUT DATA FROM THE KEY-BOARD (T/F) ? f
INPUT NAME OF FILE WITH DATA TO BE TRANSFORMED ex13ed50.dat
TRANSFORMED DATA TO BE STORED ON FILE ? (T/F) t
INPUT NAME OF FILE HOLDING TRANSFORMED DATA ex13cart.dat
NO. LATITUDE LONGITUDE H X Y Z
1 55 44 21.86 12 30 3.59 51.67 3513652.74 778944.66 5248192.89
2 56 0 0.00 10 0 0.00 0.00 3520618.63 620698.31 5264430.43
3 56 0 0.00 12 0 0.00 0.00 3496808.64 743191.34 5264430.22
Last update 1999-05-13 by cct.