trafoparsetrs89_v2011en

Transformation parameters between ETRS89-realisations and WGS84-realisations for the Netherlands

Memo RNLN - Hydrographic Service, Leendert Dorst, July 2011

Parameter order: Tx[m], Ty[m], Tz[m], sf-1[ppm], Rx["], Ry["], Rz["]. Sign convention according to IERS [1,2].

Transformations between ETRS89 and ITRF-s have centimeter level accuracy [1,2].

Transformations between ITRF-s have millimeter level accuracy [10].

Transformations between ITRF-s and WGS84-realisations have the volgende accuracy:

- meter level, for WGS84-original [3];

- decimeter level, for WGS84-G730 and WGS84-G873 [4];

- centimeter level, for WGS84-G1150 [5].

All datums use the same ellipsoid, i.e. GRS80/WGS84. GRS80 and WGS84 are equal up to the centimeter.

The following calculations use additions for all seven transformation parameters, to determine a direct set.

This approximation is acceptable if the scale and rotation parameters are small [6].

Two types of realisations of ETRS89 are distinguished: following from an ITRF [7], and measured.

For the Netherlands, measured AGRS-realisations of 1997 [1] and 2004 [9] are available.

The original ETRS89 and the AGRS-realisation of 2008 are connected to ETRF89 and ETRF2000 [13], respectively.

Seven parameter transformations are position independent.

The conversion to three parameter transformations introduces position dependency [2, section 1.2, 1st formula],

see the annex for the MATLAB function. This is necessary for ETRS89-realisations.

This memo uses as a representative position ("barycenter" in [2]): lat=53N, lon=5E, h_ell=40m -> X=3832066m, Y=335262m, Z=5070575m,

i.e. approximately in the middle of Netherlands territory, incl. NL continental shelf, around sea level.

All source values are marked.

Tectonics

Station Kootwijk has the longest set of measurement [16], and is therefore preferred in [1].

The representative position is assumed to follow it motion.

Subsequently: Vx, Vy, Vz.

A: Kootwijk, GPS, m/year size

a. measured in ITRF96 [1]: -0,0132 0,0163 0,0100 0,0232

b. measured in ITRF2000 [7]: -0,0134 0,0165 0,0099 0,0234

standard deviations: 0,0004 0,0001 0,0005 0,0006

c. measured in ITRF2005:

measured in ETRF2005 [8]: -0,0004 0,0002 0,0017

ETRF2005, in ITRF2005 [B.j]: -0,0140 0,0158 0,0095

total: -0,0144 0,0160 0,0112 0,0243

standard deviations: 0,0001 0,0001 0,0001 0,0002

d. measured in ETRF96:

measured in ITRF96 [A.a]: -0,0132 0,0163 0,0100

ITRF96, in ETRF96 [-B.g]: 0,0133 -0,0170 -0,0090

total: 0,0001 -0,0007 0,0010 0,0012

e. measured in ETRF2000:

measured in ITRF2000 [A.b]: -0,0134 0,0165 0,0099

ITRF2000, in ETRF2000 [-B.i]: 0,0133 -0,0167 -0,0090

total: -0,0001 -0,0002 0,0009 0,0009

f. measured in ETRF2000(R05):

measured in ITRF2005 [A.c]: -0,0144 0,0160 0,0112

ITRF2005, in ETRF2000 [B.k]: 0,0134 -0,0167 -0,0104

total: -0,0010 -0,0007 0,0008 0,0015

B: general motion of ETRS89, m/year [2, section 3.2]:

a. ETRF89, in ITRF89 [2, table 4]: 0,0000 0,0000 0,0000 0,00000 -0,00011 -0,00057 0,00071

position specific: -0,0152 0,0159 0,0104

b. ETRF90, in ITRF90 [2, table 4]: 0,0000 0,0000 0,0000 0,00000 -0,00011 -0,00057 0,00071


c. ETRF91, in ITRF91 [2, table 4]: 0,0000 0,0000 0,0000 0,00000 -0,00021 -0,00052 0,00068


d. ETRF92, in ITRF92 [2, table 4]: 0,0000 0,0000 0,0000 0,00000 -0,00021 -0,00052 0,00068


e. ETRF93, in ITRF93 [2, table 4]: 0,0000 0,0000 0,0000 0,00000 -0,00032 -0,00078 0,00067


f. ETRF94, in ITRF94 [2, table 4]: 0,0000 0,0000 0,0000 0,00000 -0,00020 -0,00050 0,00065


g. ETRF96, in ITRF96 [2, table 4]: 0,0000 0,0000 0,0000 0,00000 -0,00020 -0,00050 0,00065


h. ETRF97, in ITRF97 [2, table 4]: 0,0000 0,0000 0,0000 0,00000 -0,00020 -0,00050 0,00065


i. ETRF2000, in ITRF2000 [2, table 4]: 0,0000 0,0000 0,0000 0,00000 -0,00008 -0,00049 0,00079


standard deviations: 0,0000 0,0000 0,0000 0,00000 0,00002 0,00001 0,00003

position specific standard deviations: 0,0002 0,0007 0,0001

j. ETRF2005, in ITRF2005 [2, table 4]: 0,0000 0,0000 0,0000 0,00000 -0,00005 -0,00052 0,00078


standard deviations: 0,0000 0,0000 0,0000 0,00000 0,00001 0,00001 0,00001

position specific standard deviations: 0,0001 0,0003 0,0001

k. ETRF2000, in ITRF2005 [2, table 5]: 0,0002 0,0001 0,0018 -0,00008 -0,00008 -0,00049 0,00079


Advice: use the values measured in Kootwijk for the Netherlands for the motion of ETRF96, ETRF2000, ETRF2000(R05), and ETRF2000(R08).

ITRS-motions

C: earlier ITRF-s, in ITRF2008, m/year [2, table 2] :

a. ITRF89, in ITRF2008: -0,0001 0,0005 0,0032 -0,00008 0,00000 0,00000 -0,00002

b. ITRF90, in ITRF2008: -0,0001 0,0005 0,0032 -0,00008 0,00000 0,00000 -0,00002

c. ITRF91, in ITRF2008: -0,0001 0,0005 0,0032 -0,00008 0,00000 0,00000 -0,00002

d. ITRF92, in ITRF2008: -0,0001 0,0005 0,0032 -0,00008 0,00000 0,00000 -0,00002

e. ITRF93, in ITRF2008: -0,0030 0,0009 0,0040 -0,00008 0,00011 0,00019 -0,00007

f. ITRF94, in ITRF2008: -0,0001 0,0005 0,0032 -0,00008 0,00000 0,00000 -0,00002

g. ITRF96, in ITRF2008: -0,0001 0,0005 0,0032 -0,00008 0,00000 0,00000 -0,00002

h. ITRF97, in ITRF2008: -0,0001 0,0005 0,0032 -0,00008 0,00000 0,00000 -0,00002

i. ITRF2000, in ITRF2008: -0,0001 -0,0001 0,0018 -0,00008 0,00000 0,00000 0,00000

j. ITRF2005, in ITRF2008: -0,0003 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

The transformation parameters of earlier ITRF-s to ITRF2008 increase yearly with these values.

Transformation parameters of ETRS89-realisations to WGS84-realisations

These parameters cannot be direclty entered into PCTrans,

but are necessary to determine how the various realisations relate to each other.

I: ETRS89-original->WGS84-original, for 1990.0:

ITRF89->ITRF90, for 1988.0 [2, table 1]: -0,0050 -0,0240 0,0380 -0,00340 0,00000 0,00000 0,00000

Motion ITRF89->ITRF90, 1988.0->1990.0 [C.a-C.b]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

Tectonics 1989.0->1990.0, in ITRF90 [B.b]: 0,0000 0,0000 0,0000 0,00000 -0,00011 -0,00057 0,00071

ITRF90->WGS84-original [3]: 0,0600 -0,5170 -0,2230 -0,01100 0,01830 -0,00030 0,00700

total: 0,0550 -0,5410 -0,1850 -0,01440 0,01819 -0,00087 0,00771

position specific: -0,0341 -0,8498 -0,2123

II: ETRS89-original->WGS84-G730, for 1994.0:


Motion ITRF89->ITRF92, 1988.0->1994.0 [C.a-C.d]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

Tectonics 1989.0->1994.0, in ITRF92 [B.d]: 0,0000 0,0000 0,0000 0,00000 -0,00105 -0,00260 0,00340

ITRF92->WGS84-G730 [4]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

total: -0,0170 -0,0340 0,0600 -0,00510 -0,00105 -0,00260 0,00340


III.a: ETRS89-original->WGS84-G873, for 1997.0:

ITRF89->ITRF94, for 1988.0 [1;2, table 1]: -0,0230 -0,0360 0,0680 -0,00430 0,00000 0,00000 0,00000

Motion ITRF89->ITRF94, 1988.0->1997.0 [C.a-C.f]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

Tectonics 1989.0->1997.0, in ITRF94 [B.f]: 0,0000 0,0000 0,0000 0,00000 -0,00160 -0,00400 0,00520

ITRF94->WGS84-G873 [4]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

total: -0,0230 -0,0360 0,0680 -0,00430 -0,00160 -0,00400 0,00520


III.b: ETRS89-AGRS1997->WGS84-G873, for 1997.0:

ETRS89-AGRS1997->ITRF96, for 1997.0 [1]: -0,1480 0,0960 0,1220

ITRF96->ITRF94 [2, table 1]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

ITRF94->WGS84-G873 [4]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

total: -0,1480 0,0960 0,1220 0,00000 0,00000 0,00000 0,00000


size

difference IIIb-IIIa: -0,0017 -0,0025 0,0041 0,00509

IV.a: ETRS89-AGRS1997->WGS84-G1150, for 2001.0:

ETRS89-AGRS1997->ITRF96, for 1997.0 [1]: -0,1480 0,0960 0,1220


Motion ITRF96->ITRF2000, 1997.0->2001.0 [C.g-C.i] 0,0000 0,0024 0,0056 0,00000 0,00000 0,00000 -0,00008

Tectonics 1997.0->2001.0, in ITRF2000 [A.b]: -0,0536 0,0660 0,0396

ITRF2000->WGS84-G1150 [5]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

total: -0,2086 0,1584 0,1862 -0,00160 0,00000 0,00000 -0,00008


IV.b: ETRS89-AGRS2004->WGS84-G1150, for 2001.0:

ETRS89-AGRS2004->ETRS89-AGRS1997 [9]: -0,0023 -0,0062 -0,0161

ETRS89-AGRS1997->WGS84-G1150 [IV.a]: -0,2146 0,1564 0,1781

total: -0,2169 0,1502 0,1620

IV.c: ETRS89-AGRS2008->WGS84-G1150, for 2001.0:

ETRS89-AGRS2008->ETRF2000 [13]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

ETRF2000->ITRF2000, for 2000.0 [2, table 5]: -0,0540 -0,0510 0,0480 0,00000 -0,00089 -0,00539 0,00871


ITRF2000->WGS84-G1150 [5]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

total: -0,0674 -0,0345 0,0579 0,00000 -0,00089 -0,00539 0,00871


IV.d: ETRS89-AGRS2010->WGS84-G1150, for 2001.0:

ETRS89-AGRS2010->ETRS89-AGRS2008 [17]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

ETRS89-AGRS2008->WGS84-G1150, for 2001.0 [IV.c]: -0,0674 -0,0345 0,0579 0,00000 -0,00089 -0,00539 0,00871

total: -0,0674 -0,0345 0,0579 0,00000 -0,00089 -0,00539 0,00871


size

difference IV.b-IV.a: -0,0023 -0,0062 -0,0161 0,0174

difference IV.c/d-IV.a: 0,0005 -0,0072 -0,0215 0,0227

difference IV.c/d-IV.b: 0,0028 -0,0010 -0,0054 0,0062

Advice: use the parameter set of the mewest realisation for the Netherlands, in line with the advice of the Kadaster [1].

Transformation parameters of ITRS-realisations to WGS84-G873

These parameters are necessary to implement ITRS-realisations in PCTrans.

V.a: realisation ITRF89:

ITRF89->ITRF94 [1; 2, table 1]: -0,0230 -0,0360 0,0680 -0,00430 0,00000 0,00000 0,00000

Motion ITRF89->ITRF94 [C.a-C.f]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

ITRF94->WGS84-G873 [4]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

total: -0,0230 -0,0360 0,0680 -0,00430 0,00000 0,00000 0,00000

V.b: realisation ITRF90:

ITRF90->ITRF89 [2, table 1]: 0,0050 0,0240 -0,0380 0,00340 0,00000 0,00000 0,00000

Motion ITRF90->ITRF89 [C.b-C.a]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

ITRF89->WGS84-G873 [V.a]: -0,0230 -0,0360 0,0680 -0,00430 0,00000 0,00000 0,00000

total: -0,0180 -0,0120 0,0300 -0,00090 0,00000 0,00000 0,00000

V.c: realisation ITRF91 [like V.b]:

ITRF91->ITRF89 [2, table 1]: 0,0060 0,0200 -0,0540 0,00370 0,00000 0,00000 0,00000

Motion ITRF91->ITRF89 [C.c-C.a]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

ITRF89->WGS84-G873 [V.a]: -0,0230 -0,0360 0,0680 -0,00430 0,00000 0,00000 0,00000

total: -0,0170 -0,0160 0,0140 -0,00060 0,00000 0,00000 0,00000

V.d: realisation ITRF92 [like V.b]:

ITRF92->ITRF89 [2, table 1]: 0,0170 0,0340 -0,0600 0,00510 0,00000 0,00000 0,00000

Motion ITRF92->ITRF89 [C.d-C.a]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

ITRF89->WGS84-G873 [V.a]: -0,0230 -0,0360 0,0680 -0,00430 0,00000 0,00000 0,00000

total: -0,0060 -0,0020 0,0080 0,00080 0,00000 0,00000 0,00000

realisation ITRF93:

V.e: for 1994.0:

ITRF93->ITRF89, for 1988.0 [2, table 1]: 0,0190 0,0410 -0,0530 0,00390 0,00039 -0,00080 0,00096

Motion ITRF93->ITRF89, 1988.0->1994.0 [C.e-C.a]: -0,0174 0,0024 0,0048 0,00000 0,00066 0,00114 -0,00030

ITRF89->WGS84-G873 [V.a]: -0,0230 -0,0360 0,0680 -0,00430 0,00000 0,00000 0,00000

total: -0,0214 0,0074 0,0198 -0,00040 0,00105 0,00034 0,00066

V.f: for 1995.0:

ITRF93->WGS84-G873, for 1994.0 [V.e]: -0,0214 0,0074 0,0198 -0,00040 0,00105 0,00034 0,00066


total: -0,0243 0,0078 0,0206 -0,00040 0,00116 0,00053 0,00061

V.g: for 1996.0:

ITRF93->WGS84-G873, for 1994.0 [V.e]: -0,0214 0,0074 0,0198 -0,00040 0,00105 0,00034 0,00066


total: -0,0272 0,0082 0,0214 -0,00040 0,00127 0,00072 0,00056

V.h: realisation ITRF94 [4] : 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

V.i: realisation ITRF96 [like V.b]:

ITRF96->ITRF89 [2, table 1]: 0,0230 0,0360 -0,0680 0,00430 0,00000 0,00000 0,00000

Motion ITRF96->ITRF89 [C.g-C.a]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

ITRF89->WGS84-G873 [V.a]: -0,0230 -0,0360 0,0680 -0,00430 0,00000 0,00000 0,00000

total: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

V.j: realisation ITRF97 [like V.b]:

ITRF97->ITRF89 [2, table 1]: 0,0230 0,0360 -0,0680 0,00430 0,00000 0,00000 0,00000

Motion ITRF97->ITRF89 [C.h-C.a]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

ITRF89->WGS84-G873 [V.a]: -0,0230 -0,0360 0,0680 -0,00430 0,00000 0,00000 0,00000

total: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

realisation ITRF2000 [10]:

V.k: for 2001.0:

ITRF2000->ITRF89, for 1997.0 [2, table 1]: 0,0300 0,0420 -0,0870 0,00590 0,00000 0,00000 0,00000

Motion ITRF2000->ITRF89, 1997.0->2001.0 [C.i-C.a]: 0,0000 -0,0024 -0,0056 0,00000 0,00000 0,00000 0,00008

ITRF89->WGS84-G873 [V.a]: -0,0230 -0,0360 0,0680 -0,00430 0,00000 0,00000 0,00000

total: 0,0070 0,0036 -0,0246 0,00160 0,00000 0,00000 0,00008

V.l: for 2002.0:

ITRF2000->WGS84-G873, for 2001.0 [V.k]: 0,0070 0,0036 -0,0246 0,00160 0,00000 0,00000 0,00008


total: 0,0070 0,0030 -0,0260 0,00160 0,00000 0,00000 0,00010

V.m: for 2003.0:

ITRF2000->WGS84-G873, for 2001.0 [V.k]: 0,0070 0,0036 -0,0246 0,00160 0,00000 0,00000 0,00008


total: 0,0070 0,0024 -0,0274 0,00160 0,00000 0,00000 0,00012

V.n: for 2004.0:

ITRF2000->WGS84-G873, for 2001.0 [V.k]: 0,0070 0,0036 -0,0246 0,00160 0,00000 0,00000 0,00008


total: 0,0070 0,0018 -0,0288 0,00160 0,00000 0,00000 0,00014

V.o: for 2005.0:

ITRF2000->WGS84-G873, for 2001.0 [V.k]: 0,0070 0,0036 -0,0246 0,00160 0,00000 0,00000 0,00008


total: 0,0070 0,0012 -0,0302 0,00160 0,00000 0,00000 0,00016

V.p: for 2006.0:

ITRF2000->WGS84-G873, for 2001.0 [V.k]: 0,0070 0,0036 -0,0246 0,00160 0,00000 0,00000 0,00008


total: 0,0070 0,0006 -0,0316 0,00160 0,00000 0,00000 0,00018

V.q: for 2007.0:

ITRF2000->WGS84-G873, for 2001.0 [V.k]: 0,0070 0,0036 -0,0246 0,00160 0,00000 0,00000 0,00008


total: 0,0070 0,0000 -0,0330 0,00160 0,00000 0,00000 0,00020


V.r: for 2006.0:


Motion ITRF2005->ITRF89, 2000.0->2006.0 [C.j-C.a]: -0,0012 -0,0030 -0,0192 0,00048 0,00000 0,00000 0,00012

ITRF89->WGS84-G873 [V.a]: -0,0230 -0,0360 0,0680 -0,00430 0,00000 0,00000 0,00000

total: 0,0058 0,0000 -0,0482 0,00248 0,00000 0,00000 0,00018

V.s: for 2007.0:

ITRF2005->WGS84-G873, for 2006.0 [V.r]: 0,0058 0,0000 -0,0482 0,00248 0,00000 0,00000 0,00018


total: 0,0056 -0,0005 -0,0514 0,00256 0,00000 0,00000 0,00020

V.t: for 2008.0:

ITRF2005->WGS84-G873, for 2006.0 [V.r]: 0,0058 0,0000 -0,0482 0,00248 0,00000 0,00000 0,00018


total: 0,0054 -0,0010 -0,0546 0,00264 0,00000 0,00000 0,00022

V.u: for 2009.0:

ITRF2005->WGS84-G873, for 2006.0 [V.r]: 0,0058 0,0000 -0,0482 0,00248 0,00000 0,00000 0,00018


total: 0,0052 -0,0015 -0,0578 0,00272 0,00000 0,00000 0,00024

V.v: for 2010.0:

ITRF2005->WGS84-G873, for 2006.0 [V.r]: 0,0058 0,0000 -0,0482 0,00248 0,00000 0,00000 0,00018


total: 0,0050 -0,0020 -0,0610 0,00280 0,00000 0,00000 0,00026


V.x: for 2009.0:


Motion ITRF2008->ITRF89, 2000.0->2009.0 [-C.a]: 0,0009 -0,0045 -0,0288 0,00072 0,00000 0,00000 0,00018

ITRF89->WGS84-G873 [V.a]: -0,0230 -0,0360 0,0680 -0,00430 0,00000 0,00000 0,00000

total: 0,0059 -0,0024 0,0290 0,00366 0,00000 0,00000 0,00024

V.y: for 2010.0:

ITRF2008->WGS84-G873, for 2009.0 [V.x]: 0,0059 -0,0024 0,0290 0,00366 0,00000 0,00000 0,00024


total: 0,0060 -0,0029 0,0258 0,00374 0,00000 0,00000 0,00026

V.z: for 2011.0:

ITRF2008->WGS84-G873, for 2009.0 [V.x]: 0,0059 -0,0024 0,0290 0,00366 0,00000 0,00000 0,00024


total: 0,0061 -0,0034 0,0226 0,00382 0,00000 0,00000 0,00028

V.aa: for 2012.0:

ITRF2008->WGS84-G873, for 2009.0 [V.x]: 0,0059 -0,0024 0,0290 0,00366 0,00000 0,00000 0,00024


total: 0,0062 -0,0039 0,0194 0,00390 0,00000 0,00000 0,00030

V.bb: for 2013.0:

ITRF2008->WGS84-G873, for 2009.0 [V.x]: 0,0059 -0,0024 0,0290 0,00366 0,00000 0,00000 0,00024


total: 0,0063 -0,0044 0,0162 0,00398 0,00000 0,00000 0,00032

V.cc: for 2014.0:

ITRF2008->WGS84-G873, for 2009.0 [V.x]: 0,0059 -0,0024 0,0290 0,00366 0,00000 0,00000 0,00024


total: 0,0064 -0,0049 0,0130 0,00406 0,00000 0,00000 0,00034

V.dd: for 2015.0:

ITRF2008->WGS84-G873, for 2009.0 [V.x]: 0,0059 -0,0024 0,0290 0,00366 0,00000 0,00000 0,00024


total: 0,0065 -0,0054 0,0098 0,00414 0,00000 0,00000 0,00036

Transformation parameters of WGS84-realisations to WGS84-G873

These parameters are necessary to implement WGS84-realisations in PCTrans.

VI.a: realisation WGS84-original:

WGS84-original->ITRF90 [3]: -0,0600 0,5170 0,2230 0,01100 -0,01830 0,00030 -0,00700

ITRF90->WGS84-G873 [V.b]: -0,0180 -0,0120 0,0300 -0,00090 0,00000 0,00000 0,00000

total: -0,0780 0,5050 0,2530 0,01010 -0,01830 0,00030 -0,00700

VI.b: realisation WGS84-G730:

WGS84-G730->ITRF92 [4]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

ITRF92->WGS84-G873 [V.d]: -0,0060 -0,0020 0,0080 0,00080 0,00000 0,00000 0,00000

total: -0,0060 -0,0020 0,0080 0,00080 0,00000 0,00000 0,00000

realisation WGS84-G1150:

VI.c: for 2002.0

WGS84-G1150->ITRF2000 [5]: 0,0000 0,0000 0,0000 0,00000 0,00000 0,00000 0,00000

ITRF2000->WGS84-G873, for 2002.0 [V.l]: 0,0070 0,0030 -0,0260 0,00160 0,00000 0,00000 0,00010

total: 0,0070 0,0030 -0,0260 0,00160 0,00000 0,00000 0,00010

VI.d: for 2003.0 [V.m]: 0,0070 0,0024 -0,0274 0,00160 0,00000 0,00000 0,00012

VI.e: for 2004.0 [V.n]: 0,0070 0,0018 -0,0288 0,00160 0,00000 0,00000 0,00014

VI.f: for 2005.0 [V.o]: 0,0070 0,0012 -0,0302 0,00160 0,00000 0,00000 0,00016

VI.g: for 2006.0 [V.p]: 0,0070 0,0006 -0,0316 0,00160 0,00000 0,00000 0,00018

VI.h: for 2007.0 [V.q]: 0,0070 0,0000 -0,0330 0,00160 0,00000 0,00000 0,00020

VI.i: for 2008.0:

WGS84-G1150->WGS84-G873, for 2002.0 [VI.c]: 0,0070 0,0030 -0,0260 0,00160 0,00000 0,00000 0,00010


total: 0,0070 -0,0006 -0,0344 0,00160 0,00000 0,00000 0,00022

VI.j: for 2009.0:

WGS84-G1150->WGS84-G873, for 2002.0 [VI.c]: 0,0070 0,0030 -0,0260 0,00160 0,00000 0,00000 0,00010


total: 0,0070 -0,0012 -0,0358 0,00160 0,00000 0,00000 0,00024

VI.k: for 2010.0:

WGS84-G1150->WGS84-G873, for 2002.0 [VI.c]: 0,0070 0,0030 -0,0260 0,00160 0,00000 0,00000 0,00010


total: 0,0070 -0,0018 -0,0372 0,00160 0,00000 0,00000 0,00026

VI.l: for 2011.0:

WGS84-G1150->WGS84-G873, for 2002.0 [VI.c]: 0,0070 0,0030 -0,0260 0,00160 0,00000 0,00000 0,00010


total: 0,0070 -0,0024 -0,0386 0,00160 0,00000 0,00000 0,00028

VI.m: for 2012.0:

WGS84-G1150->WGS84-G873, for 2002.0 [VI.c]: 0,0070 0,0030 -0,0260 0,00160 0,00000 0,00000 0,00010


total: 0,0070 -0,0030 -0,0400 0,00160 0,00000 0,00000 0,00030

VI.n: for 2013.0:

WGS84-G1150->WGS84-G873, for 2002.0 [VI.c]: 0,0070 0,0030 -0,0260 0,00160 0,00000 0,00000 0,00010


total: 0,0070 -0,0036 -0,0414 0,00160 0,00000 0,00000 0,00032

VI.o: for 2014.0:

WGS84-G1150->WGS84-G873, for 2002.0 [VI.c]: 0,0070 0,0030 -0,0260 0,00160 0,00000 0,00000 0,00010


total: 0,0070 -0,0042 -0,0428 0,00160 0,00000 0,00000 0,00034

VI.p: for 2015.0:

WGS84-G1150->WGS84-G873, for 2002.0 [VI.c]: 0,0070 0,0030 -0,0260 0,00160 0,00000 0,00000 0,00010


total: 0,0070 -0,0048 -0,0442 0,00160 0,00000 0,00000 0,00036

Transformation parameters of ETRS89-realisations to WGS84-G873

These parameters ae necessary to implement ETRS89-realisations in PCTrans.

ETRS89-original:

VII.a: for 1989.0:

ETRS89-original->WGS84-G873, for 1997.0 [III.a]: -0,0230 -0,0360 0,0680 -0,00430 -0,00160 -0,00400 0,00520

Tectonics 1997.0->1989.0, in ITRF94 [B.f]: 0,0000 0,0000 0,0000 0,00000 0,00160 0,00400 -0,00520

total: -0,0230 -0,0360 0,0680 -0,00430 0,00000 0,00000 0,00000

position specific: -0,0395 -0,0374 0,0462

VII.b: for 1990.0:



total: -0,0230 -0,0360 0,0680 -0,00430 -0,00020 -0,00050 0,00065


VII.c: for 1991.0:



total: -0,0230 -0,0360 0,0680 -0,00430 -0,00040 -0,00100 0,00130


VII.d: for 1992.0:



total: -0,0230 -0,0360 0,0680 -0,00430 -0,00060 -0,00150 0,00195


VII.e: for 1993.0:



total: -0,0230 -0,0360 0,0680 -0,00430 -0,00080 -0,00200 0,00260


VII.f: for 1994.0:



total: -0,0230 -0,0360 0,0680 -0,00430 -0,00100 -0,00250 0,00325


VII.g: for 1995.0:



total: -0,0230 -0,0360 0,0680 -0,00430 -0,00120 -0,00300 0,00390


VII.h: for 1996.0:



total: -0,0230 -0,0360 0,0680 -0,00430 -0,00140 -0,00350 0,00455


VII.i: for 1997.0:

total: -0,0230 -0,0360 0,0680 -0,0043 -0,0016 -0,0040 0,0052


ETRS89-AGRS1997:

VII.j: for 1998.0:

ETRS89-AGRS1997->WGS84-G873, for 1997.0 [III.b]: -0,1480 0,0960 0,1220

Tectonics 1997.0->1998.0, in ITRF96 [A.a]: -0,0132 0,0163 0,0100

total: -0,1612 0,1123 0,1320

VII.k: for 1999.0:



total: -0,1744 0,1286 0,1420

VII.l: for 2000.0:



total: -0,1876 0,1449 0,1520

VII.m: for 2001.0:



total: -0,2008 0,1612 0,1620

VII.n: for 2002.0:



total: -0,2140 0,1775 0,1720

VII.o: for 2003.0:



total: -0,2272 0,1938 0,1820

VII.p: for 2004.0:



total: -0,2404 0,2101 0,1920

ETRS89-AGRS2004:

VII.q: for 2005.0:

ETRS89-AGRS2004->ETRS89-AGRS1997 [9]: -0,0023 -0,0062 -0,0161

ETRS89-AGRS1997->WGS84-G1150, for 2001.0 [IV.a]: -0,2086 0,1584 0,1862 -0,00160 0,00000 0,00000 -0,00008


WGS84-G1150->WGS84-G873, for 2005.0 [VI.f] 0,0070 0,0012 -0,0302 0,00160 0,00000 0,00000 0,00016

total: -0,2575 0,2194 0,1795 0,00000 0,00000 0,00000 0,00008


VII.r: for 2006.0:

ETRS89-AGRS2004-WGS84-G873, for 2005.0 [VII.q]: -0,2575 0,2194 0,1795 0,00000 0,00000 0,00000 0,00008


Motion WGS84-G1150->WGS84-G873, 2005.0->2006.0 [VI.g-VI.f] 0,0000 -0,0006 -0,0014 0,00000 0,00000 0,00000 0,00002

total: -0,2709 0,2353 0,1880 0,00000 0,00000 0,00000 0,00010


VII.s: for 2007.0:



Motion WGS84-G1150->WGS84-G873, 2005.0->2007.0 [VI.h-VI.f] 0,0000 -0,0012 -0,0028 0,00000 0,00000 0,00000 0,00004

total: -0,2843 0,2512 0,1965 0,00000 0,00000 0,00000 0,00012


VII.t: for 2008.0:



Motion WGS84-G1150->WGS84-G873, 2005.0->2008.0 [VI.i-VI.f] 0,0000 -0,0018 -0,0042 0,00000 0,00000 0,00000 0,00006

total: -0,2977 0,2671 0,2050 0,00000 0,00000 0,00000 0,00014


ETRS89-AGRS2008:

VII.u: for 2009.0:

ETRS89-AGRS2008->WGS84-G1150, for 2001.0 [IV.c]: -0,0674 -0,0345 0,0579 0,00000 -0,00089 -0,00539 0,00871


WGS84-G1150->WGS84-G873, for 2009.0 [VI.j] 0,0070 -0,0012 -0,0358 0,00160 0,00000 0,00000 0,00024

total: -0,1676 0,0963 0,1013 0,00160 -0,00089 -0,00539 0,00895


VII.v: for 2010.0:

ETRS89-AGRS2008->WGS84-G873, for 2009.0 [VII.u]: -0,1676 0,0963 0,1013 0,00160 -0,00089 -0,00539 0,00895


Motion WGS84-G1150->WGS84-G873, 2009.0->2010.0 [VI.k-VI.j] 0,0000 -0,0006 -0,0014 0,00000 0,00000 0,00000 0,00002

total: -0,1810 0,1122 0,1098 0,00160 -0,00089 -0,00539 0,00897


ETRS89-AGRS2010:

VII.w: for 2011.0:

ETRS89-AGRS2010->WGS84-G1150, for 2001.0 [IV.d]: -0,0674 -0,0345 0,0579 0,00000 -0,00089 -0,00539 0,00871


WGS84-G1150->WGS84-G873, for 2011.0 [VI.l] 0,0070 -0,0024 -0,0386 0,00160 0,00000 0,00000 0,00028

total: -0,1944 0,1281 0,1183 0,00160 -0,00089 -0,00539 0,00899


VII.x: for 2012.0:

ETRS89-AGRS2010->WGS84-G873, for 2011.0 [VII.w]: -0,1944 0,1281 0,1183 0,00160 -0,00089 -0,00539 0,00899


Motion WGS84-G1150->WGS84-G873, 2011.0->2012.0 [VI.m-VI.l] 0,0000 -0,0006 -0,0014 0,00000 0,00000 0,00000 0,00002

total: -0,2078 0,1440 0,1268 0,00160 -0,00089 -0,00539 0,00901


VII.y: for 2013.0:



Motion WGS84-G1150->WGS84-G873, 2011.0->2013.0 [VI.n-VI.l] 0,0000 -0,0012 -0,0028 0,00000 0,00000 0,00000 0,00004

total: -0,2212 0,1599 0,1353 0,00160 -0,00089 -0,00539 0,00903


VII.z: for 2014.0:



Motion WGS84-G1150->WGS84-G873, 2011.0->2014.0 [VI.o-VI.l] 0,0000 -0,0018 -0,0042 0,00000 0,00000 0,00000 0,00006

total: -0,2346 0,1758 0,1438 0,00160 -0,00089 -0,00539 0,00905


VII.aa: for 2015.0:



Motion WGS84-G1150->WGS84-G873, 2011.0->2015.0 [VI.p-VI.l] 0,0000 -0,0024 -0,0056 0,00000 0,00000 0,00000 0,00008

total: -0,2480 0,1917 0,1523 0,00160 -0,00089 -0,00539 0,00907


Checks: transformation parameters of ETRS89-realisations to WGS84-realisations via WGS84-G873

VIII.a: ETRS89-original->WGS84-original, for 1990.0:

ETRS89-original->WGS84-G873 [VII.b]: -0,0230 -0,0360 0,0680 -0,00430 -0,00020 -0,00050 0,00065

WGS84-G873->WGS84-original [-VI.a]: 0,0780 -0,5050 -0,2530 -0,01010 0,01830 -0,00030 0,00700

total: 0,0550 -0,5410 -0,1850 -0,01440 0,01810 -0,00080 0,00765

direct [I]: 0,0550 -0,5410 -0,1850 -0,01440 0,01819 -0,00087 0,00771

difference: 0,0000 0,0000 0,0000 0,00000 -0,00009 0,00007 -0,00006

position specific: 0,0018 0,0011 -0,0014 size 0,0025

VIII.b: ETRS89-original->WGS84-G730, for 1994.0:

ETRS89-original->WGS84-G873 [VII.f]: -0,0230 -0,0360 0,0680 -0,00430 -0,00100 -0,00250 0,00325

WGS84-G873->WGS84-G730 [-VI.b]: 0,0060 0,0020 -0,0080 -0,00080 0,00000 0,00000 0,00000

total: -0,0170 -0,0340 0,0600 -0,00510 -0,00100 -0,00250 0,00325

direct [II]: -0,0170 -0,0340 0,0600 -0,00510 -0,00105 -0,00260 0,00340

difference: 0,0000 0,0000 0,0000 0,00000 0,00005 0,00010 -0,00015

position specific: 0,0027 -0,0040 -0,0018 size 0,0052

VIII.c: ETRS89-AGRS1997->WGS84-G1150, for 2001.0:

ETRS89-AGRS1997->WGS84-G873 [VII.m]: -0,2008 0,1612 0,1620

WGS84-G873->WGS84-G1150, for 2002.0 [-VI.c]: -0,0070 -0,0030 0,0260 -0,00160 0,00000 0,00000 -0,00010

Motion ITRF94->ITRF2000, 2002.0->2001.0: 0,0000 -0,0006 -0,0014 0,00000 0,00000 0,00000 0,00002

total: -0,2078 0,1576 0,1866 -0,00160 0,00000 0,00000 -0,00008

direct [IV.a]: -0,2086 0,1584 0,1862 -0,00160 0,00000 0,00000 -0,00008

difference: -0,0008 0,0008 -0,0004 0,00000 0,00000 0,00000 0,00000

size 0,0012

These differences are caused by the use of different values for tectonics [B].

Advice: neglect these differences, whicha allows for implementation in PCTrans via WGS84-G873.

Difference vector of representative position in WGS84-realisation, with position with equal coordinates in ETRS89-realisation

These vectors have been calculated using PCTrans 4.2.7. Subsequently distance [m] and azimuth [] for ETRS89-realisation, WGS84-G873;

idem for WGS84-G873, WGS84-realisation; and idem for total. The vectors represent the motion of ETRS89 in WGS84.

ETRS89-original, WGS84-original:

IX.a: for 1989.0: 0,07 331 0,31 219 0,29 232

IX.b: for 1990.0: 0,08 348 0,31 219 0,26 232

IX.c: for 1991.0: 0,09 001 0,31 219 0,24 233

IX.d: for 1992.0: 0,11 011 0,31 219 0,22 233

IX.e: for 1993.0: 0,13 018 0,31 219 0,19 233

ETRS89-original, WGS84-G730:

IX.f: for 1994.0: 0,15 023 0,01 171 0,14 025

IX.g: for 1995.0: 0,17 026 0,01 171 0,16 028

IX.h: for 1996.0: 0,19 029 0,01 171 0,18 031

ETRS89-original, WGS84-G873:

IX.i: for 1997.0: 0,21 032 0,00 0,21 032

ETRS89-AGRS1997, WGS84-G873:

IX.j: for 1998.0: 0,24 032 0,00 0,24 032

IX.k: for 1999.0: 0,26 034 0,00 0,26 034

IX.l: for 2000.0: 0,28 035 0,00 0,28 035

IX.m: for 2001.0: 0,30 036 0,00 0,30 036


IX.n: for 2002.0: 0,33 037 0,02 359 0,34 035

IX.o: for 2003.0: 0,35 038 0,02 001 0,37 036

IX.p: for 2004.0: 0,37 038 0,02 004 0,39 036


IX.q: for 2005.0: 0,38 039 0,02 006 0,40 037

IX.r: for 2006.0: 0,41 040 0,02 008 0,43 038

IX.s: for 2007.0: 0,43 040 0,03 010 0,45 039

IX.t: for 2008.0: 0,45 041 0,03 011 0,47 039


IX.u: for 2009.0: 0,47 042 0,03 013 0,49 040

IX.v: for 2010.0: 0,49 042 0,03 015 0,52 040


IX.w: for 2011.0: 0,51 042 0,03 016 0,54 041

IX.x: for 2012.0: 0,54 043 0,03 017 0,56 041

IX.y: for 2013.0: 0,56 043 0,03 019 0,59 042

IX.z: for 2014.0: 0,58 043 0,03 020 0,61 042

IX.aa: for 2015.0: 0,60 043 0,03 021 0,64 042

Conclusion

Use of the transformation "required ETRS89-realisation->WGS84-G873", followed by the transformation

"WGS84-G873-required WGS84-realisation" gives an approximation that has centimeter level accuracy for the Netherlands [VIII].

This is the best solution for implementation in PCTrans. (PCTrans internally works with WGS84-G873 for consistency with [4].)

References

[1]: memo J. van Buren, Concernstaf Kadaster, "WGS84 ", 9 January 2001.

[2]: memo Claude Boucher and Zuheir Altamimi, "Specifications for reference frame fixing in the analysis of a EUREF GPS campaign",

version 8, 18 May 2011, available at http://etrs89.ensg.ign.fr/memo-V8.pdf. Also see [11] and [12] for ITRF2005 and [14] and [15] for ITRF2008.

[3]: "ITRS and WGS84 ", available at ftp://itrf.ensg.ign.fr/pub/itrf/WGS84.TXT.

[4]: NIMA Technical Report 8350.2; 3rd edition; amendment 1; 3 January 2000, "Department of Defense World Geodetic System 1984 -

Its definition and relationships with local geodetic systems ", available at http://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf.

Also published as [4a] "User's handbook on datum transformations involving WGS84 ", IHO Special Publication 60, 3rd edition,

International Hydrographic Bureau, Monaco, July 2003.

[5]: Addendum to [4]: "Implementation of the WGS84 reference frame G1150 ", 20 January 2002, available at

http://earth-info.nga.mil/GandG/publications/tr8350.2/Addendum%20NIMA%20TR8350.2.pdf.

[6]: notes 1 December 2004.

[7]: "ITRF2000 station positions at epoch 1997.0 and velocities - European permanent GPS stations ",

available at http://itrf.ensg.ign.fr/ITRF_solutions/2000/results/ITRF2000_EUR_GPS_PERM.SSC.txt.

[8]: "ETRF2005 station positions at epoch 2000.0 and velocities - GPS, VLBI, SLR and DORIS stations ", available at

http://etrs89.ensg.ign.fr/pub/ETRF2005.SSC.

[9]: memo Arnoud Pol and Anton Ksters, Rijkswaterstaat-AGI, "Nieuwe ETRS89-cordinaten voor het AGRS.nl", 6 April 2004,

[10]: Claude Boucher, Zuheir Altamimi, Patrick Sillard and Martine Feissel-Vernier, "The ITRF2000", IERS Technical Note 31, 2004,

Contains [10a]: "ITRF2000 workshop recommendations "

and [10b]: Altamimi, Z., P. Sillard and C. Boucher, "ITRF2000, a new release of the International Terrestrial Reference Frame

for Earth science applications ", Journal of Geophysical Research, 107(B10), 2214, doi: 10.1029/2001JB000561, 2002.

available at http://www.iers.org/nn_11216/IERS/Publications/TechnicalNotes/tn31.html

[11]: Transformation Parameters between ITRF2000 and ITRF2005, beschikbaar op http://itrf.ensg.ign.fr/ITRF_solutions/2005/tp_05-00.php.

[12]: Altamimi, Z., X. Collilieux, J. Legrand, B. Garayt, and C. Boucher, "ITRF2005: A new release of the International Terrestrial

Reference Frame based on time series of station positions and Earth Orientation Parameters ", Journal of Geophysical Research,

112, B09401, doi:10.1029/2007JB004949, 2007.

[13]: letter Martijn Rijsdijk 18 June 2009 and email Joop van Buren 29 June 2009.

[14]: Altamimi, Z., X. Collilieux, and L. Metivier, "ITRF2008: an improved solution of the international terrestrial reference frame ",

Journal of Geodesy, doi: 10.1007/s00190-011-0444-4, 2011.

[15]: Transformation Parameters between ITRF2005 and ITRF2008, available at http://itrf.ign.fr/ITRF_solutions/2008/ITRF2008.php.

[16]: internet page "Referentiestations", available at http://www.kadaster.nl/rijksdriehoeksmeting/agrs/referentiestations.html

[17]: yearly report 2010 Subcommittee Geodetic Infrastructure & Reference systems, in: NCG jaarverslag 2010

available at http://www.ncg.knaw.nl/Publicaties/Jaarverslagen/Jaarverslag2010.html

Annex: MATLAB-code

%% translvec: [T_X, T_Y, T_Z] in [m, m, m];

%% paramvec: [T_X, T_Y, T_Z, D, R_X, R_Y, R_Z] in [m, m, m, ppm, arcsec, arcsec, arcsec];

%% xyz: [X, Y, Z] in [m, m, m]

function [paramvec3, paramstdvec3]=seven2three(paramvec7, paramstdvec7, xyz)

translvec=paramvec7(1:3)'; translstdvec=paramstdvec7(1:3)';

sf=paramvec7(4)/1e6; sfstd=paramstdvec7(4)/1e6;

rotatvec=dms2rads([zeros(3,2), paramvec7(5:7)']); rotatstdvec=dms2rads([zeros(3,2),paramstdvec7(5:7)']);

translmat=zeros(3,4);

translmat(1,1)=xyz(1);translmat(1,3)=xyz(3); translmat(1,4)=-xyz(2);

translmat(2,1)=xyz(2);translmat(2,2)=-xyz(3); translmat(2,4)=xyz(1);

translmat(3,1)=xyz(3);translmat(3,2)=xyz(2); translmat(3,3)=-xyz(1);

paramvec3=round(1e4*(translvec+translmat*[sf; rotatvec]))/1e4;

paramcovmat=diag(translstdvec.^2)+translmat*diag([sfstd; rotatstdvec].^2)*translmat';

paramstdvec3=round(1e4*sqrt(diag(paramcovmat)))/1e4;

paramvec3=paramvec3'; paramstdvec3=paramstdvec3';

Documents

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