Terrestrial reference frame solution with the Vienna VLBI Software VieVS and implication of tropospheric gradient estimation

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1 Terrestrial reference frame solution with the Vienna VLBI Software VieVS and implication of tropospheric gradient estimation H. Spicakova, L. Plank, T. Nilsson, J. Böhm, H. Schuh Abstract The Vienna VLBI Software (VieVS) has been developed at the Institute of Geodesy and Geophysics of TU Vienna since 28. In this paper we present the determination of the Vienna Terrestrial Reference Frame (VieTRF1) with VieVS using all suitable VLBI sessions from. to 211., and we compare it to the IVS combined solution (VTRF28). We focus on horizontal tropospheric gradients which influence the TRF determination and we show the effect of tropospheric gradients on station height and north-south components. The necessity of using absolute constraints when estimating tropospheric gradients in sessions before 199 is visible from the coordinate time series. Keywords VieVS, TRF, tropospheric gradients 1 Introduction A Terrestrial Reference Frame (TRF) is a set of points (e.g. geodetic markers) on the Earth surface with precisely determined coordinates in a specific coordinate system. The International VLBI Service for Geodesy and Astrometry (IVS) provides a solution of the Terrestrial Reference Frame based on Very Long Baseline Interferometry (VLBI) observations. The recent realization (VTRF28) is an IVS combined solution computed from normal equation systems (NEQs) provided by seven IVS analysis centers including data from to 29. (Böckmann et al., 21). We present in this paper a new TRF solution called VieTRF1 computed with the software VieVS (Böhm et al., 211) and make comparisons with respect to VTRF28. We focus on the estimation of horizontal tropospheric gradients in the VLBI analysis. The extension of atmosphere above the equator is larger than in the polar regions. This atmospheric bulge is responsible for a systematic effect in the measured time delay mainly in north-south direction because the path of the radio wave through the atmosphere is larger if an antenna in the Hana Spicakova, Lucia Plank, Tobias Nilsson, Johannes Böhm and Harald Schuh Vienna University of Technology, Institute of Geodesy and Geophysics, Gußhausstraße 27-29, A-14 Wien, Austria northern hemisphere observes in south direction than if it would observe towards north. We investigate the optimum parametrization for the gradient estimation in the VLBI analysis and how much station coordinates are affected if we would neglect this phenomenon. 2 VieTRF1 VieTRF1 is a terrestrial reference frame including 62 stations (see Fig. 1) estimated by a combination of datum-free NEQs of 358 VLBI sessions from. to 211. produced by the Vienna VLBI Software VieVS. We included only sessions with more than two stations and if the a posteriori sigma of unit weight obtained from a single-session adjustment was less than two. In Table 1 selected modeling and parametrization options are summarized. With VieVS it is possible to create datum-free NEQs containing station coordinates, Earth orientation parameters (EOP), source coordinates, clock parameters, zenith wet delays (zwd), and tropospheric gradients. These are stored in an internal format for further use with a module vie glob which allows stacking of the NEQs and estimating parameters from multiple VLBI sessions in a so-called global solution. For VieTRF1 we fixed the source coordinates to ICRF2 values (Fey et al., 29). All Earth orientation parameters, together with clock parameters, zwd and tropospheric gradients were session-wise reduced from the NEQs. We also reduced session-wise coordinates of stations which participated in less than 1 sessions (mainly stations occupied with mobile antennas) which usually had observing time of less than three years, what is not sufficient to estimate reliable velocities. Exceptions were stations placed in a vicinity of another station with longer observation history, where the velocities were constrained to each other (Richmond - Miami2, Wettzell - Tigowtzl, Kashima - Kashima34, Hobart26 - Hobart12, and Yebes - Yebes4m). The resulting single-session NEQs containing positions and velocities were than stacked. The datum definition was done by applying no-net-translation and no-net-rotation conditions w.r.t. VTRF28 on 22 stations with a long time history and good global distribution (i.e., Algopark, BR-VLBA, DSS45, FD-VLBA, Fortleza, HartRAO, Hobart26, Kashim34, Kashima, Kokee, LA-VLBA, Matera, MK-VLBA, 118

2 Vienna Terrestrial Reference Frame VieTRF1 119 WESTFORD HRAS 85 RICHMOND MOJAVE12 WETTZELL ONSALA6 HAYSTACK OVRO 13 KAUAI KWAJAL26 GILCREEK VNDNBERG KASHIMA ALGOPARK HATCREEK HARTRAO MEDICINA SESHAN25 DSS45 DSS65 PIETOWN DSS15 NRAO85 3 NOTO HOBART26 KASHIM34 MATERA LA VLBA YLOW7296 TRYSILNO SANTIA12 FD VLBA OHIGGINS FORTLEZA NL VLBA GGAO718 SC VLBA HN VLBA KOKEE MIZNAO1 BR VLBA KP VLBA MK VLBA OV VLBA URUMQI CRIMEA NYALES2 NRAO2 MIAMI2 YEBES TIGOWTZL TSUKUB32 SYOWA TIGOCONC CTVASTJ SVETLOE PARKES VERAMZSW ZELENCHK BADARY YEBES4M HOBART12 5 mm Fig. 2 Horizontal and vertical position differences at epoch Sessions 2. between VieTRF1 and VTRF28. Only differences for stations participating in more than 3 sessions are plotted. Fig. 1 Overview of participation of stations in VLBI sessions used for VieTRF1 determination. Helmert parameters 22 datum stations NL-VLBA, NRAO85 3, NyAles2, Onsala6, Richmond, SCVLBA, Seshan25, Westford, and Wettzell). Figure 2 shows the differences in vertical and horizontal components between VieTRF1 and VTRF28 at epoch 2. for 46 stations which participated in more than 3 sessions. Larger differences can be observed mainly at three stations. At Zelenchukskaya ((Zc), Russia) and Badary ((Bd), Russia) it is probably due to the fact, that these stations started their observations in 26. and 27.4, respectively, so that VTRF28 includes only two years of data for Zelenchukskaya and a few months for Badary. For VieTRF1 the time span was longer by two years and we can assume, that the estimation of positions for these two stations is therefore more stable. The third station HRAS 85 ((Hr), Texas, USA) observed only in the early years within networks with poor geometry and stopped observations in 199. In that time unusual apparent station motions of HRAS 85 were an often discussed open question which never could be answered. In terms of RMS the agreement between these TRFs is 6.8 mm for the height components and 7. mm for the horizontal differences over all 46 stations at epoch 2.. By excluding Hr, Zc, and Bd from the comparison the RMS decreases to 1.8 mm for height as well as horizontal components. Another comparison was done in terms of Helmert parameters for the transformation from VieTRF1 to VTRF28 at epoch 2.. In Table 2 the results for two different sets of stations are listed. The first column shows the Helmert parameters for the transformation between stations used for datum definition. In the second column a network with all stations participating in more than 3 sessions (see Fig. 2), except stations Hr, Zc and Bd, is used. The differences between these two networks are very small and for both sets of stations we see a good agreement between VieTRF1 and VTRF28 as the Helmert parameters are not significantly different from zero. Tx [mm] Ty [mm] Tz [mm] Rx [mas] Ry [mas] Rz [mas] Scale [mm].1 ±.44.3 ± ± ±.2 -. ±.2. ±.2.15 ±.42 stations participated in > 3 sessions (see Figure 2) except Hr, Zc, Bd.23 ± ± ± ±.1.3 ± ±.1.26 ±.38 Table 2 Helmert parameters for the transformation between VieTRF1 and VTRF28 (VTRF28-VieTRF1) at epoch Horizontal Tropospheric Gradients The azimuth-dependent part of the neutral atmosphere delay Lazim measured by VLBI antennas can be expressed by: Lazim (α, ε ) = mg (ε ) [Gn cos(α ) + Ge sin(α )] (1) where ε is the elevation angle, α the azimuth angle, Gn and Ge the components of the horizontal gradient vector, and mg is the gradient mapping function. To test the hypothesis that atmosphere asymmetry causes a systematic effect on the estimated station coordinates, we ran three test solutions (Tab. 3): 1. In the first solution we fixed the asymmetric part to zero and neglected the atmosphere gradients in the VLBI analysis. 2. The asymmetric part was a priori set to zero, and the components Gn and Ge of the horizontal gradient vector were estimated in the least-squares analysis with relative constraints (.5 mm/6 h) to stabilize the NEQs. 3. The parametrization was identical to solution 2 with additional absolute constraints (.5 mm) applied on Gn and Ge. In Figure 3 session-wise estimated gradients at station Westford from. till 211. are plotted. Gradients from solu-

3 12 Spicakova et al. some modeling options VTRF28 a priori ICRF2 fixed C4 5, IERS23 (McCarthy and Petit, 24) IAU2A IERS23 linear model, IERS23 FES24 (Lyard et al., 26) (Petrov and Boy, 24) DAO (MacMillan and Ma, 1997) VMF1 (Bo hm et al., 26) TRF CRF EOP precession/nutation model solid Earth tides pole tides ocean tidal loading atmosphere loading a priori tropospheric gradients mapping functions clock parameters zenith wet delay tropospheric gradients EOP some options for parametrization 6 min piece-wise linear (pwl) offsets (relative constraints: 42 ps) + rate + quadratic term 3 min pwl offsets (relative constraints: 35 ps) 6 h pwl offsets (relative constraints:.5 mm + absolute constraints: 1 mm) 24 h pwl offsets (relative constraints:.1 mas for polar motion and precession/nutation, and.1 ms for UT1) Table 1 Overview of selected modeling and parametrization options used for VLBI data processing for the estimation of the VieTRF1. 4 dr [cm] relative absolute estimation of gradients constraints constraints solution 1 no solution 2 yes, 6-h offsets.5 mm no solution 3 yes, 6-h offsets.5 mm.5 mm Table 3 Overview of the three solutions with different gradient handling dn [cm] north grad. [cm] east grad. [cm] Fig. 4 Difference in station coordinates (height and north com.2 ponent) at station Westford for solution 2 (light grey) and solution 3 (black) w.r.t. solution 1. Bold lines are smoothed values over 1 days Fig. 3 Total session-wise estimated gradients at station West- ford. In light grey gradients from solution 2 are plotted, in black from solution 3. Bold lines are smoothed values over 1 days. tion 2 are plotted in light grey and from solution 3 in black. It can be seen, that before 199 the determination of gradients without applying absolute constraints in the least-squares analysis is very unreliable. This is most probably due to the limited number of observations and the poor network geometry in the early VLBI years. After 199 the values for the north gradients reach systematically negative values, which reflects the atmospheric bulge above the equator since Westford is a station in the northern hemisphere. Figure 4 shows the corresponding estimates of station positions (height and north component) at station Westford for solution 2 (light grey) and solution 3 (black) w.r.t. to station positions estimated in solution 1. The unstable gradient determination in solution 2 in the early years also shows up in the station estimates and can reach a few centimeters. Since 199 there is a good agreement between the station coordinates if gradients were estimated with or without absolute constraints and the difference to solution 1 (neglection of the troposphere asymmetry) reaches several millimeters. Mean values of the es-

4 Vienna Terrestrial Reference Frame VieTRF dr [cm] mm dn [cm] Fig. 5 Global map with mean values over for total tropospheric gradients from solution 2 (light grey) and solution 3 (black). Plotted are stations that participated in more than 2 sessions. timated gradients over from solutions 2 and 3 for all stations participating in more than 2 sessions are shown in Figure 5. At all stations the north-south component of the tropospheric gradient vectors points towards the equator. The unconstrained gradients from solution 2 are larger at all sites in comparison with solution 3, and the largest differences between these two solutions occur at stations Santia12 (Chile) and NRAO85 3 (West Virginia, USA) which observed only in the 9ies. Stations CTVA St. John s (Canada) and Urumqi (China) show also larger differences what is most probably caused by the small number of observations. The corresponding mean values of the estimated station heights and north components are plotted in Figure 6. The stations are sorted on the x-axis by latitude. The estimated positions are plotted w.r.t. the estimates from solution 1. The mean difference in the north component for stations in the southern hemisphere is 2.8 mm between solution 2 and solution 1, and 1.4 mm between solution 3 and solution 1. In the northern hemisphere the mean difference in the north component w.r.t. solution 1 is -.6 mm for solution 2, and -.4 mm for solution 3. In other words, if tropospheric asymmetry is neglected, stations are shifted towards the poles w.r.t. their real positions latitude 45 9 Fig. 6 Mean values over for height and north component of stations participated in more than 2 sessions sorted by latitude. Solution 2 (light grey) and solution 3 (black) are plotted w.r.t. solution 1. shown that handling and estimation of tropospheric gradients in the VLBI analysis has to be done carefully, especially for the early VLBI years where networks with only few stations and a small number of observations do not allow reliable gradient estimation without using absolute constraints. 5 Acknowledgements The authors acknowledge the IVS (Schlüter and Behrend, 27) and all its components for providing VLBI data. Hana Spicakova is grateful to Mondi Austria Privatstiftung for financial support during her Ph.D. study at TU Vienna. Tobias Nilsson works under project SCHUH 113/3-2 Earth Rotation and Global Dynamic Processes, Forschergruppe FOR Conclusions The first determination of a Terrestrial Reference Frame with the recently developed VieVS software (VieTRF1) is presented in this paper and is available at We showed a good agreement with the IVS combined solution even though the time span of data used for the determination of these two TRFs is not identical and there is also a difference in terms of a priori modeling since we corrected for atmosphere loading what was not done for the VTRF28. Each of the seven analysis centers contributing to the VTRF28 has also its own strategy for parametrization and time resolution of the pre-reduced parameters such as the zwd or tropospheric gradients. It was References S. Böckmann, T. Artz, and A. Nothnagel (21). VLBI terrestrial reference frame contributions to ITRF28. Journal of Geodesy 84. pp doi: 1.17/s J. Böhm, B. Werl, and H. Schuh (26). Troposphere mapping functions for GPS and very long baseline interferometry from European Centre for Medium-Range Weather Forecasts operational analysis data. Journal of Geophysical Research 111. B pp. doi: 1.129/25JB3629. J. Böhm, S. Böhm, T. Nilsson, A. Pany, L. Plank, H. Spicakova, K. Teke, and H. Schuh (21). The new Vienna VLBI Software VieVS. Proceedings of the 29 IAG Symposium, Series: International Association of Geodesy Symposia. Vol Geodesy for Planet Earth. Steve Kenyon,

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