Time Evolution of the Terrestrial Reference Frame
D. Angermann, B. Meisel, M. Krügel, H. Müller, V. Tesmer
Deutsches Geodätisches Forschungsinstitut (DGFI), Marstallplatz 8, D-80539 München, Germany
email : angerman@dgfi.badw.de
Abstract. This paper investigates the time evolution of the terrestrial reference frame (TRF). We
analysed time series of site positions and datum
parameters obtained from VLBI, SLR, GPS and
DORIS solutions with respect to non-linear motions
(e.g. jumps, seasonal signals) and systematic differences. The time series of the translation and
scale parameters were used to identify solution- and
technique-related problems, and to investigate the
contribution of the different techniques to realise the
TRF origin and scale. The position time series reveal
non-linear motions and jumps for many sites, which
have to be considered for future TRF realisations.
Keywords. Terrestrial Reference Frame, ITRF,
VLBI, SLR, GPS, DORIS, analysis of time series
1 Introduction and motivation
Future research, and in particular the new satellite
missions (GRACE, JASON-1, ENVISAT and the future GOCE and GALILEO), will require a highly accurate and consistent global reference frame as a crucial basis to accomplish scientific goals, such as precise orbit determination, measurement of sea level
change, postglacial rebound, plate tectonics, atmosphere dynamics, Earth orientation excitation or for
other geodynamic and geophysical purposes. The
quality of the realised reference frame has important
implications for the ability to study these global and
regional phenomena of the Earth’s system, including
the solid Earth, oceans and the atmosphere.
Since 1988, the International Earth Rotation and
Reference Systems Service (IERS) has been in
charge of the establishment and maintenance of an
International Terrestrial Reference Frame (ITRF), a
realisation of the International Terrestrial Reference
System (ITRS). Conventionally, the ITRS is realised
by the adoption of positions referred to a specific
reference epoch and constant velocities for a set of
global observing sites. The positions and velocities
of these ITRF stations are derived from a combination of individual technique solutions provided by
various analysis centers. The space geodetic techniques used at present are Very Long Baseline Interferometry (VLBI), Satellite and Lunar Laser Ranging
(SLR/LLR), the Global Positioning System (GPS)
and the Doppler Orbitography and Radio positioning Integrated by Satellite (DORIS). Due to the remarkable progress of these space geodetic observation techniques the accuracy and consistency of the
ITRF has steadily increased. The latest realisation
of the ITRS is the ITRF2000, which includes positions and velocities for about 800 stations located at
approximately 500 sites (Altamimi et al., 2002).
In reality the assumption of constant site velocities
is in conflict with non-linear effects caused by several
geophysical phenomena (e.g. seismic or volcanic effects, quasi-periodic signals caused by loading effects). Not completely modelled site motions can
also induce common (global) variations (e.g. translations, scale) of the station networks w.r.t. a crust
fixed frame such as the ITRF2000. In addition, mass
redistributions within the Earth system cause variations of the center of mass (geocenter). These timevarying effects on site positions and datum parameters can produce systematic errors in the individual
solutions, which may also propagate into the ITRF
and consequently degrade its accuracy.
In its function as IERS Combination Research
Center and ITRS Combination Center, DGFI is
deeply involved in the analysis and combination of
different space geodetic observations. The results
have shown that technique- and/or solution-related
systematic effects (biases), which are often poorly
characterised or quantified, are assumed to set the
accuracy limits of the space geodetic observations in
many cases. The analysis of time series is important for gaining insight into the solution characteristics and to identify technique- and/or solution-related
problems. A comparison of position time series at
co-location sites may help to separate and quantify
possible effects, and to aid in understanding the origin of remaining discrepancies. This is of vital importance, so as to provide highly accurate and consistent results, and thus to exploit the full potential of
the space geodetic techniques.
2 Data and processing strategy
The major characteristics of the contributing solutions are described below (summarised in Table 1).
VLBI solution: DGFI has re-analysed 2230 single
24-h VLBI sessions between January 1984 and the
end of 2001. The computations were performed using the software OCCAM 5.0 (Titov et al., 2001).
The models are based on the IERS Conventions 2000
(see http://www.iers.org/iers/products/conv/). For
each daily VLBI session free normal equations with
positions of the telescopes and the Earth Orientation
Parameters were computed. The celestial reference
frame was fixed to ICRF-Ext. 1 (e.g. Ma and Feissel, 1997). The datum was realised applying no-netrotation (NNR) and -translation (NNT) conditions to
all stations in each single session w.r.t. DGFI02R02
(the processing strategy is similar to that described in
Tesmer, 2002).
SLR solution: The SLR results presented in this
paper were obtained from a re-analysis of weekly
combined LAGEOS-1 and 2 satellite arcs from
November 1992 until February 2002 with the software package DOGS (DGFI Orbit and Geodetic parameter estimation Software). The processing strategy is similar to that described in the recently published results on the time evolution of an SLR reference frame (Angermann et al., 2002a). Due to
the inhomogeneity of the SLR network, the number of stations and observations varies from arc to
arc. In total 75 SLR stations observed the LAGEOS satellites during this period. We applied
three condition equations to minimise the common rotation of the weekly SLR solutions w.r.t.
ITRF2000. In addition we used weekly SLR solutions computed at ASI (Agencia Spaciale Italiano)
using the software GEODYN. The ASI solutions
are available at the data pool of the IERS SINEX
Combination Campaign (see http://alpha.fesg.tumuenchen.de/iers/sinex/data_pool.html).
GPS solutions: For the analysis of the GPS
time series we used weekly solutions computed
by three IGS Analysis Centers: CODE (Center
for Orbit Determination in Europe), JPL (NASA
Jet Propulsion Laboratory) and SIO (Scripps Institution of Oceanography). The weekly CODE
and JPL solutions were accessed from the ftp
server: ftp://igs.ensg.ign.fr/pub/igs/products, the
weekly SIO solutions from: ftp://lox.ucsd.edu/
pub/combinations. All these solutions are considered as loosely constrained w.r.t. ITRF2000 station
positions. The time span for the GPS solutions covers six to seven years. The analysis centers included,
in total, 150 to 180 stations, each week’s solution
containing between 50 to 150 stations. The GPS
solutions were processed with different software
packages: Bernese GPS Software (CODE), GIPSY
(JPL) and GAMIT (SIO). For more information concerning the solution strategies of the institutions refer
to the respective web pages: http://aiub.unibe.ch
(CODE), http://igscb.jpl.nasa.gov (JPL) and
ftp://lox.ucsd.edu/pub/combinations (SIO).
DORIS solution: For DORIS we used weekly
SINEX files from IGN (Institut Géographique
National) and JPL, available at the Crustal
Dynamics Data Information System (CDDIS,
ftp://cddisa.gsfc.nasa.gov/pub/doris/products/
sinex_series/ignwd03). The solutions were computed using the GIPSY/OASIS software, and data
from October 1992 to May 2002 for all DORIS
satellites. We used those solutions (version 3) that
were obtained applying a free network approach,
and afterwards they were rotated to ITRF2000 (see
description file: ign.wd03.snx.dsc)
Datum definition: In order to realise the datum
of the individual VLBI, SLR, GPS and DORIS solutions in a similar way, we applied 7 parameter
Helmert transformation models (3 translations, 3 rotations, 1 scale) to transform them into a consistent
reference frame, the ITRF2000. A well-known problem related to similarity transformations is the fact
that the results are sensitive to the geometric distribution and to changes w.r.t. the selected transformation
stations. To minimise these effects, we used a subset of "good" and well distributed stations for each
technique (so-called reference stations).
In the case of VLBI typically only 4-6 telescopes
observe simultaneously within one daily session, and
the station configuration often changes from one session to the other. The SLR data are relatively inhomogeneously distributed in space and time. We
defined a subset of 20 reference stations with dense
tracking and a good global distribution. For the transformation of the weekly GPS solutions we used the
55 reference stations identified by the IGS (Ferland,
2002). For the transformation of the DORIS solutions we used 50 reference stations evenly distributed
across the globe. Similar to GPS, the effect of possible changes of the station configuration can be expected to be small.
3 Time evolution of the individual
reference frames
To gain an insight into the characteristics and the
contribution of the individual space techniques to the
realisation of the terrestrial reference frame, we analysed the time series of scale and translation variations
derived from the 7 parameter Helmert transformation
models between the individual space technique solutions and ITRF2000. The time series of these parameters reflect common (global) effects of the station
networks w.r.t. ITRF2000.
Figure 1 shows the time series of scale variations.
The VLBI scale variations of the daily session solutions have a higher noise level compared to the
weekly solutions of the other techniques, mainly due
to the poor network geometry of single VLBI sessions and due to the fact that the solutions span only
one day. In principle, the VLBI and SLR scale is
in good agreement with ITRF2000 scale, except for
some irregularities in the ASI solution in early 1999.
The DORIS scale has an offset of about 4 ppb w.r.t.
ITRF2000. The three GPS series (CODE, JPL and
SIO) agree well (within 1 ppb) during the last two
years, whereas before 2000 larger discrepancies and
some irregularities exist. The significant jump of
about 2 ppb in the SIO scale in early 2000 was probably caused by a change of the elevation cut-off angle (Herring, 2002). The large scale variations of the
daily VLBI session solutions can be smoothed significantly by a monthly accumulation (see Figure 2).
Through the orbit dynamics satellite methods such
as SLR, GPS and DORIS are sensitive to the center
of mass (geocenter). Therefore these satellite techniques can be used to realise the origin of the terrestrial reference frame. The time series of weekly
translation (origin) variations w.r.t. ITRF2000 derived from the individual solutions are shown in Figure 3. The most stable results were obtained from
SLR. The amplitudes for the annual translation variations of both SLR solutions are almost identical
(see Figure 4). There is also a good agreement with
recently published SLR results (Angermann et al.,
2002b) and with GPS-derived results (e.g. Dong et
al., 2003). The time series for the translation parameters derived from the GPS and DORIS solutions show larger variations compared to SLR, in particular for the z-component. DORIS shows significant annual signals in the x-and y-component, but
GPS only in the y-component. The large z-offset of
DORIS in 1998 was caused by SPOT-4 data problems (Willis, 2003).
4 Site position time series
We analysed the position time series obtained from
the different space technique solutions with respect
to non-linear effects, periodic signals and systematic
differences (biases), and compared the results at colocation sites. For a large number of tracking sites
we observed non-linear effects in the position time
series that conflict with the assumption of constant
velocities.
For many of the tracking stations, especially for
those with long data time series, the instrumentation
changed several times due to system upgrades, antenna and receiver changes, etc. The effects of instrumental changes are illustrated in Figure 5. At GPS
station Onsala a change of the radome in early 1999
caused a jump of about 2 cm in the height component
(Kaniuth and Huber, 2003). Several receiver and antenna changes at GPS station Westford are accompanied by significant jumps in the longitude. Both colocation sites do not show similar effects in the VLBI
position series, indicating that the observed jumps
are a technique-related problem, and not a "real" site
motion caused by geophysical phenomena.
During the last few years the software systems,
models and processing strategies have improved significantly. To achieve consistent results it is necessary to reprocess all data with the latest software
version, state-of-the-art models and the same strategy. In the case of VLBI and SLR all data were
reprocessed in a consistent way. At present, this
is in particular a problem in the case of GPS, as it
requires a tremendous effort to reprocess all GPS
data homogeneously. As a consequence many of the
time series are affected by changes due to inconsistent software, models and processing strategy (e.g.
Rothacher, 2002). An example is the jump in the
time series of the SIO scale, caused by a change of
the elevation cut-off angle (see Figure 1).
A number of stations are located in deformation
zones, which cover about 15% of the Earth’s surface.
In these geodynamically active regions large earthquakes occur quite often, which are accompanied by
seismic deformation processes that may cause nonlinear motions of surrounding stations. In the last
few years numerous GPS projects were initiated to
study the deformations in plate boundary zones. The
effect of large earthquakes on the position time series
is illustrated for three stations (see Figure 6). Earthquakes in Arequipa, Peru in June 2001 caused a jump
of about 50 cm horizontally (Kaniuth et al., 2002),
and the motion of this station after the earthquake
differs significantly from the expected long-term mo-
tion. This change in motion is probably caused by
post-seismic relaxation processes, which also have
been observed after the 1995 Mw 8.0 Antofagasta
earthquake in Northern Chile (Klotz et al., 1999,
Klotz et al., 2001). For two other stations displayed
in Figure 6 (Ankara and Cocos Island) earthquakes
caused significant jumps of a few cm in the position
time series, accompanied by site motions after the
earthquakes that are different from their long term
behaviour.
Site displacements are also caused by solid Earth
tides, ocean tidal loading and atmospheric loading, etc. In principle, these effects can mostly be
corrected by models (see IERS Conventions 2000,
http://www.iers.org/iers/products/conv/). In practice,
there are still deficiencies in the models, which can
cause quasi-periodic variations in the position time
series. Precise positioning of globally distributed
GPS sites reveals that during February to March, the
Northern Hemisphere compresses (and the Southern
Hemisphere expands), so that sites near the North
Pole move downward by 3.0 mm, and sites near the
equator move northwards by 1.5 mm. As a response
of an elastic Earth to increased winter loading of
soil moisture, snow cover, and atmosphere, the opposite pattern of deformation occurs during August
and September (Blewitt et al., 2001).
5 Conclusions
The time series of the datum parameters and site positions are influenced by remaining technique- and
solution-related problems, that have to be separated
from "real" geophysical signals. The results confirm
that SLR is the best technique to realise the origin of
the terrestrial reference frame. VLBI and SLR realise
the scale consistent with ITRF2000. Improvements
to the GPS and DORIS solutions seem to be necessary in order to use them for TRF datum realisation.
The observed non-linear effects in the position
time series are in conflict with the assumption of constant site velocities. This can produce errors and systematic effects (biases) in the individual solutions,
which may degrade the accuracy and consistency of
the ITRF. Hence a better realisation of the terrestrial
reference frame may require the estimation of nonlinear components in site positions.
Acknowledgments We thank the reviewers Chris
Rizos and Pascal Willis for their constructive comments. The research was supported by the programme Geotechnologien of BMBF and DFG, Grant
03F0336C; the publication no. is GEOTECH-38.
References
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New Release of the International Terrestrial Reference
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Angermann, D., M. Gerstl, R. Kelm, H. Müller, W. Seemüller,
M. Vei (2002a). Time Evolution of SLR Reference Frame.
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108, No. B4, 2200, doi: 10.1029/2002JB002035.
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Geodesy in the New Millennium, IAG Symposia, J. Adam
and K.-P. Schwarz (eds), Vol. 125, pp. 3–8, Springer.
Herring, T. (2002). Personal Communication.
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effects on height estimates in the EUREF network. Mitt.
Bundesamt für Kartographie und Geodäsie, 29, pp. 97-102.
Kaniuth, K., H. Müller, W. Seemüller (2002). Displacement
of the space geodetic observatory Arequipa due to recent
earthquakes. Zeitschrift für Vermessungswesen, Heft 4,
pp. 238–243, Witwer.
Klotz, J., D. Angermann, G.W. Michel, R. Porth, C. Reigber,
J. Reinking, J. Viramonte, R. Perdomo, V.H. Rios,
S. Barientos, R. Barriga, O. Cifuentes (1999). GPS-derived
deformation of the Central Andes including the 1995
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Antofagasta Mw=8.0 Earthquake.
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Klotz, J., G. Khazaradze, D. Angermann, C. Reigber,
R. Perdomo, O. Cifuentes (2001). Earthquake cycle dominates contemporary crustal deformation in Central and
Southern Andes. Earth and Planetary Science Letters, 193,
pp. 437–446, Elsevier.
Ma, C., M. Feissel (1997). Definition and Realisation of the
International Celestial Reference System by Astrometry of
Extragalactic Objects. IERS Technical Note 23, Paris.
Rothacher, M. (2002). Estimation of station heights with
GPS. In: Vertical Reference Systems, IAG Symposia, H.
Drewes, A. Dodson, L. Fortes, L. Sanchez, P. Sandoval
(eds), Vol. 124, pp. 81–90, Springer.
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VLBI (DGFI)
5
Table 1: Summary of solutions used for this study.
Technique Analysis
Center
DORIS
IGN/JPL
GPS
CODE
GPS
JPL
GPS
SIO
SLR
ASI
SLR
DGFI
VLBI
DGFI
0
0
-5
6
Data Time Span Number of
Stations
GIPSY / OASIS 1992.8-2002.8
80
Bernese
1996.0-2002.2
163
GIPSY
1996.0-2002.2
180
GAMIT
1995.0-2002.2
157
GEODYN
1999.0-2003.0
35
DOGS
1992.9-2002.2
75
OCCAM
1984.0-2002.0
56
4
Scale (session/monthly)
2
4
0
2
-2
[ppb]
SLR (DGFI, ASI)
GPS (CODE, JPL, SIO)
-5
5
Software
0
8
-2
6
-4
-350
-300
-250
-200
-150
time [jd2000]
4
0
1.1.93
1.1.96
1.1.99
1.1.02
Fig. 1: Time series of scale variations [ppb].
Tx
Tz
4
4
2
2
2
0
0
0
-2
-2
-2
-4
4
-4
4
SLR (DGFI,ASI)
GPS (CODE, JPL, SIO)
DORIS (IGN)
Ty
4
-4
10
2
2
0
0
-2
-2
-4
4
-4
4
30
2
2
20
0
0
-2
-2
5
0
10
0
-10
-4
1.1.93
1.1.96
1.1.99
1.1.02
-4
1.1.93 1.1.96
1.1.99
1.1.93
1.1.02
1.1.96
1.1.99
1.1.02
Fig. 3: Time series of weekly translation variations [cm].
Tx
SLR (DGFI,ASI)
0
50
0.1
Ty
0.2
40
30
30
10
Annual Amplitude
ASI: 4,1 ± 1,2 mm
DGFI: 3,1 ± 0,6 mm
50
40
30
20
10
40
Seasonal Signal
not significant
30
20
20
10
10
0
0
50
50
40
30
0.1
Annual Amplitude
5,9 ± 1,8 mm
40
30
Tz
0.2
0
50
0.1
0.2
40
Annual Amplitude
ASI: 3,7 ± 2,3 mm
DGFI: 4,5 ± 1,3 mm
30
Annual Amplitude
ASI: 4,5 ± 1,1 mm
DGFI: 3,0 ± 0,6 mm
0
50
0
GPS (CODE, JPL, SIO)
0
50
40
20
20
10
0
400
Annual Amplitude
SIO: 5,2 ± 1,4 mm
JPL: 7,8 ± 1,7 mm
CODE: 3,6 ± 0,9 mm
300
200
100
Annual Amplitude
SIO: 9,8 ± 9,2 mm
JPL: 19,1 ± 4,1 mm
CODE: 5,0 ± 2,6 mm
0
400
Annual Amplitude
4,7 ± 1,4 mm
300
Seasonal Signal
not significant
200
20
20
10
10
0
0
0
-100
-50
0
Fig. 2: VLBI scale variations obtained from daily session
and accumulated monthly solutions. The normal equations
of the daily sessions for the year 1999 were accumulated
monthly with the DGFI combination software DOGS-CS.
2
DORIS (IGN)
DORIS (IGN)
-4
0.1
0.2
Frequency [1/weeks]
100
0
0
0.1
0.2
Frequency [1/weeks]
0
0.1
0.2
Frequency [1/weeks]
Fig. 4: Fourierspectrum of the translation parameter time series
Onsala, Sweden
1995
3
1996
1997
1998
1999
2000
Westford, USA
2001
2
1995
1996
1995
1996
1997
1998
1999
2000
2001
1.5
2
Longitude [cm]
Height [cm]
1
1
0
-1
0.5
0
- 0.5
-1
-2
-3
ROGUE SNR-8000
Radome: DUTD
-2
GPS (ONSA): CODE, JPL, SIO
1995
5
- 1.5
ASHTECH Z-XII3
Radome: OSOD
1996
1997
1998
1999
2000
2001
2
GPS (WES2): CODE, JPL, SIO
1997
1998
1999
2000
2001
1.5
Longitude [cm]
Height [cm]
1
0
0.5
0
- 0.5
-1
- 1.5
-5
-2
VLBI (7213): DGFI
VLBI (7209): DGFI
Fig. 5: The effect of instrumental changes on the position time series is shown for two co-location sites.
GPS solutions: CODE, JPL, SIO
North [cm]
Arequipa (AREQ), Peru
Ankara (ANKR), Turkey
3
3
0
2
2
- 10
1
1
- 20
0
0
- 30
-1
-1
- 40
-2
-2
- 50
-3
-3
10
3
0
2
June 23, 2001: 8,2 Ms
East [cm]
- 10
Height [cm]
Cocos Island (COCO), Australia
10
5
Aug. 17, 1999:
7,8 Ms
- 20
4
Dec. 11, 1999:
7,5 Ms
1
0
- 30
3
2
-1
- 40
0
- 50
-2
-1
- 60
-3
-2
5
5
5
0
0
0
-5
1996
June 18, 2000:
8,0 Ms
1
1998
2000
2002
-5
1996
1998
2000
2002
-5
1996
1998
2000
2002
Fig. 6: The effect of large earthquakes on the position time series is shown for three stations.