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 : email@example.com 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 Altamimi, Z., P. Sillard, C. Boucher (2002). ITRF2000: A New Release of the International Terrestrial Reference Frame for Earth Science Applications. J. Geophysical Res., 107 (B10), 2214, doi:10.1029/2001JB000561. Angermann, D., M. Gerstl, R. Kelm, H. Müller, W. Seemüller, M. Vei (2002a). Time Evolution of SLR Reference Frame. Adv. in Space Res., Vol. 30/2, pp. 201–206, Elsevier. Angermann, D., H. Müller, M. Gerstl (2002b). Geocenter variations derived from SLR data to LAGEOS 1 and 2. In: Vistas for Geodesy in the New Millennium, IAG Symposia, J. Adam and K.-P. Schwarz (eds), Vol. 125, pp. 30–35. Blewitt, G. D., Lavallee, P. Clarke, K. Nurutdinov (2001). A new global mode of Earth deformation: Seasonal cycle detected. Science, 294 (5550), pp. 2342–2345. Blewitt (2003). Self-consistency in reference frames, geocenter definition, and surface loading of the solid Earth. J. Geophys. Res., Vol. 108, No. B2, 2103, doi: 10.1029/2002JB002082. Dong, D., T. Yunck, M. Heflin (2003). Origin of the International Terrestrial Reference Frame. J. Geophys. Res., Vol. 108, No. B4, 2200, doi: 10.1029/2002JB002035. Ferland, R. (2002). Activities of the International GPS Service IGS Reference Frame Working Group. In: Vistas for 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. Kaniuth, K., and S. Huber (2003). An assessment of radome 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 Pure and Appl. Antofagasta Mw=8.0 Earthquake. Geophysics, 154, pp. 709–730. 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. Tesmer, V. (2002). VLBI Solution DGFI01R01 based on leastsquares estimation using OCCAM5.0 and DOGS-CS. In: IVS 2002 General Meeting Proceedings, N. Vandenberg and N.K. Baver (eds), NASA/CP-2002-210002. Titov, O., V. Tesmer, J. Böhm (2001). OCCAM5.0 Users Guide, AUSLIG Technical Report 7, Canberra. Willis, P. (2003). Personal Communication. 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.