Advertisement

Journal of Geodesy

, Volume 86, Issue 3, pp 221–239 | Cite as

Methodology for the combination of sub-daily Earth rotation from GPS and VLBI observations

  • T. ArtzEmail author
  • L. Bernhard
  • A. Nothnagel
  • P. Steigenberger
  • S. Tesmer
Original Article

Abstract

A combination procedure of Earth orientation parameters from Global Positioning System (GPS) and Very Long Baseline Interferometry (VLBI) observations was developed on the basis of homogeneous normal equation systems. The emphasis and purpose of the combination was the determination of sub-daily polar motion (PM) and universal time (UT1) for a long time-span of 13 years. Time series with an hourly resolution and a model for tidal variations of PM and UT1-TAI (dUT1) were estimated. In both cases, 14-day nutation corrections were estimated simultaneously with the ERPs. Due to the combination procedure, it was warranted that the strengths of both techniques were preserved. At the same time, only a minimum of de-correlating or stabilizing constraints were necessary. Hereby, a PM time series was determined, whose precision is mainly dominated by GPS observations. However, this setup benefits from the fact that VLBI delivered nutation and dUT1 estimates at the same time. An even bigger enhancement can be seen for the dUT1 estimation, where the high-frequency variations are provided by GPS, while the long term trend is defined by VLBI. The estimated combined tidal PM and dUT1 model was predominantly determined from the GPS observations. Overall, the combined tidal model for the first time completely comprises the geometrical benefits of VLBI and GPS observations. In terms of root mean squared (RMS) differences, the tidal amplitudes agree with other empirical single-technique tidal models below 4 μas in PM and 0.25 μs in dUT1. The noise floor of the tidal ERP model was investigated in three ways resulting in about 1 μas for diurnal PM and 0.07 μs for diurnal dUT1 while the semi-diurnal components have a slightly better accuracy.

Keywords

VLBI GPS Combination Sub-daily ERPs Empirical tidal ERP model Normal equation systems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Altamimi Z, Collilieux X, Legrand J, Garayt B, Boucher C (2007) ITRF2005: a new release of the International Terrestrial Reference Frame based on time series of station positions and Earth orientation parameters. J Geophys Res 112: B9401. doi: 10.1029/2007JB004949 CrossRefGoogle Scholar
  2. Altamimi Z, Collilieux X, Métivier L (2011) ITRF2008: an improved solution of the International Terrestrial Reference Frame. J Geod 85(8): 457–473. doi: 10.1007/s00190-011-0444-4 CrossRefGoogle Scholar
  3. Artz T, Böckmann S, Jensen L, Nothnagel A, Steigenberger P (2010) Reliability and stability of VLBI-derived sub-daily EOP models. In: Behrend D, Baver KD (eds) IVS 2010 General Meeting Proceedings, VLBI2010: From Vision to Reality, 7–13 February 2010, Hobart, NASA/CP-2010-215864, pp 355–359. http://ivscc.gsfc.nasa.gov/publications/gm2010/artz.pdf
  4. Artz T, Böckmann S, Nothnagel A, Steigenberger P (2010) Subdiurnal variations in the Earth’s rotation from continuous Very Long Baseline Interferometry campaigns. J Geophys Res 115: B05404. doi: 10.1029/2009JB006834 CrossRefGoogle Scholar
  5. Artz T, Tesmer S, Nothnagel A (2011) Assessment of periodic sub-diurnal Earth orientation parameter variations at tidal frequencies via transformation of VLBI normal equation systems. J Geod 85(9): 565–584. doi: 10.1007/s00190-011-0457-z CrossRefGoogle Scholar
  6. Baver K (2010) Mark-5 VLBI analysis software Calc/Solve. Web document. http://gemini.gsfc.nasa.gov/solve/
  7. Beutler G, Brockmann E, Gurtner W, Hugentobler U, Mervart L, Rothacher M, Verdun A (1994) Extended orbit modeling techniques at the CODE processing center of the international GPS service for Geodynamics (IGS): theory and initial results. Manuscr Geodaet 19: 367–386Google Scholar
  8. Bianco G, Luceri V, Sciarretta C (2008) The ILRS standard products: A quality assessment, paper presented at 15th International Workshop on Laser Ranging, Electro Optic Syst. Pty. Ltd., Canberra, 15–20 Oct. In: Proceedings of the 15th International Workshop on Laser Ranging, 15–20 October 2006, Canberra, EOS Space Systems Pty Limited. http://cddis.gsfc.nasa.gov/lw15/docs/papers/The%20ILRS%20Standard%20Products,%20A%20Quality%20Assessment.pdf
  9. Bizouard C, Gambis D (2009) The combined solution C04 for Earth orientation parameters consistent with International Terrestrial Reference Frame 2005. In: Drewes H (ed) Geodetic Reference Frames, Springer Berlin Heidelberg, ISBN 978-3-642-00860-3, International Association of Geodesy Symposia, vol 134, pp 265–270. doi: 10.1007/978-3-642-00860-3_41
  10. Böckmann S, Artz T, Nothnagel A, Tesmer V (2007) Comparison and combination of consistent VLBI solutions. In: Boehm J, Pany A, Schuh H (eds) Proceedings of the 18th European VLBI for Geodesy and Astrometry Working Meeting, 12–13 April 2007, Vienna, Geowissenschaftliche Mitteilungen, Heft Nr. 79, Schriftenreihe der Studienrichtung Vermessung und Geoinformation, Technische Universität Wien, ISSN 1811-8380, pp 82–87. http://mars.hg.tuwien.ac.at/~evga/proceedings/S34_Boeckmann.pdf
  11. Böckmann S, Artz T, Nothnagel A, Tesmer V (2010) International VLBI service for geodesy and astrometry: Earth orientation parameter combination methodology and quality of the combined products. J Geophys Res 115: B04404. doi: 10.1029/2009JB006465 CrossRefGoogle Scholar
  12. Boehm J, Werl B, Schuh H (2006) Troposphere mapping functions for GPS and very long baseline interferometry from European Centre for Medium-range Weather Forecasts operational analysis data. J Geophys Res 111: B02406. doi: 10.1029/2005JB003629 CrossRefGoogle Scholar
  13. Brockmann E (1997) Combination of solutions for geodetic and geodynamic applications of the Global Positioning System (GPS). Geod. Geophys. Arb. Schweiz, vol 55Google Scholar
  14. Brosche P, Wuensch J (1994) On the ‘rotational angular momentum’ of the oceans and the corresponding polar motion. Astron Nachr 315(2): 181–188. doi: 10.1002/asna.2103150208 CrossRefGoogle Scholar
  15. Brosche P, Wünsch J, Seiler U, Sündermann J (1989) Periodic changes in Earth’s rotation due to oceanic tides. Astron Astrophys 220(1–2): 318–320Google Scholar
  16. Büllesfeld F (1985) Ein Beitrag zur harmonischen Darstellung des gezeitenerzeugenden Potentials. PhD thesis, Rheinische Friedrich-Wilhelms-Universität Bonn, Deutsche Geodätische Kommission Bayer. Akad. Wiss. München, Reihe C, vol 314. ISBN 3-7696-9364-7Google Scholar
  17. Capitaine N, Wallace PT, Chapront J (2003) Expressions for IAU 2000 precession quantities. Astron Astrophys 412(2): 567–586. doi: 10.1051/0004-6361:20031539 CrossRefGoogle Scholar
  18. Chao BF, Liu HS, Dong DN, Herring TA (1991) Libration in the Earth’s rotation. Geophys Res Lett 18(11): 2007–2010. doi: 10.1029/91GL02491 CrossRefGoogle Scholar
  19. Chao BF, Ray RD, Egbert GD (1995) Diurnal/semidiurnal oceanic tidal angular momentum: Topex/Poseidon models in comparison with Earth’s rotation rate. Geophys Res Lett 22(15): 1993–1996. doi: 10.1029/95GL01788 CrossRefGoogle Scholar
  20. Chao BF, Ray RD, Gipson JM, Egbert GD, Ma C (1996) Diurnal/semidiurnal polar motion excited by oceanic tidal angular momentum. J Geophys Res 101(B9): 20151–20164. doi: 10.1029/96JB01649 CrossRefGoogle Scholar
  21. Clark TA, Corey BE, Davis JL, Herring TA, Elgered G (1985) Precision geodesy using the Mark-III very-long-baseline interferometer system. IEEE Trans Geosci Remote Sens 23: 438–449. doi: 10.1109/TGRS.1985.289433 CrossRefGoogle Scholar
  22. Dach, R, Hugentobler, U, Fridez, P, Meindl, M (eds) (2007) Bernese GPS Software Version 5.0. Astronomical Institute, University of Bern, Bern, SwitzerlandGoogle Scholar
  23. Dow JM, Neilan RE, Rizos C (2009) The International GNSS Service in a changing landscape of Global Navigation Satellite Systems. J Geod 83(3–4): 191–198. doi: 10.1007/s00190-008-0300-3 CrossRefGoogle Scholar
  24. Egbert GD, Bennett AF, Foreman MGG (1994) TOPEX/POSEIDON tides estimated using a global inverse model. J Geophys Res 99(C12): 24821–24852. doi: 10.1029/94JC01894 CrossRefGoogle Scholar
  25. Englich S, Heinkelmann R, Schuh H (2008) Re-assessment of ocean tidal terms in high-frequency Earth rotation variations observed by VLBI. In: Finkelstein A, Behrend D (eds) Proceedings of the Fifth IVS General Meeting “Measuring the Future”, 3 – 6 March 2008, St. Petersburg, Nauka, pp 314–318. ftp://ivscc.gsfc.nasa.gov/pub/general-meeting/2008/pdf/englich.pdf
  26. Ferland R, Piraszewski M (2009) The IGS-combined station coordinates, earth rotation parameters and apparent geocenter. J Geod 83(3–4): 385–392. doi: 10.1007/s00190-008-0295-9 CrossRefGoogle Scholar
  27. Fey A, Gordon D, Jacobs CS (2009) The second realization of the International Celestial Reference Frame by Very Long Baseline Interferometry. IERS Technical Note 35, Verlag des Bundesamtes für Kartographie und Geodäsie, Frankfurt am Main. ISBN 1019-4568. http://www.iers.org/nn_11216/IERS/EN/Publications/TechnicalNotes/tn35.html
  28. Förste C, Schmidt R, Stubenvoll R, Flechtner F, Meyer U, König R, Neumayer H, Biancale R, Lemoine JM, Bruinsma S, Loyer S, Barthelmes F, Esselborn S (2008) The geoforschungszentrum potsdam/groupe de recherche de godsie spatiale satellite-only and combined gravity field models: Eigen-gl04s1 and eigen-gl04c. J Geod 82(6): 331–346. doi: 10.1007/s00190-007-0183-8 CrossRefGoogle Scholar
  29. Fritsche M, Dietrich R, Knöfel C, Rülke A, Vey S, Rothacher M, Steigenberger P (2005) Impact of higher-order ionospheric terms on GPS estimates. Geophys Res Lett 32: L23311. doi: 10.1029/2005GL024342 CrossRefGoogle Scholar
  30. Gipson JM (1996) Very long baseline interferometry determination of neglected tidal terms in high-frequency earth orientation variation. J Geophys Res 101(B12): 28051–28064. doi: 10.1029/96JB02292 CrossRefGoogle Scholar
  31. Gipson JM, Ray RD (2009) A new model of tidal EOP variations from VLBI data spanning 30 years. In: EGU General Assembly 2009, 19–24 April 2009, Vienna, vol 11, p 13096.http://meetingorganizer.copernicus.org/EGU2009/EGU2009-13096.pdf
  32. Hefty J, Rothacher M, Springer T, Weber R, Beutler G (2000) Analysis of the first year of Earth rotation parameters with a sub-daily resolution gained at the CODE processing center of the IGS. J Geod 74(6): 479–487. doi: 10.1007/s001900000108 CrossRefGoogle Scholar
  33. Herring TA, Dong D (1991) Current and future accuracy of Earth rotation measurements. In: Carter WE (ed) Proceedings of the Chapman conference on Geodetic VLBI: Monitoring Global Change, NOAA Technical Report NOS 137 NGS 49, Washington, pp 306–324Google Scholar
  34. Herring TA, Dong D (1994) Measurement of diurnal and semidiurnal rotational variations and tidal parameters of Earth. J Geophys Res 99(B9): 18051–18071. doi: 10.1029/94JB00341 CrossRefGoogle Scholar
  35. Kouba J (2003) Testing of the IERS2000 sub-daily Earth rotation parameter model. Stud Geophys Geod 47: 725–739. doi: 10.1023/A:1026338601516 CrossRefGoogle Scholar
  36. Letellier T (2004) Etude des ondes de marée sur les plateux continentaux. PhD thesis, Université de Toulouse III, école Doctorale des Sciences de l’Univers, de l’Environnement et de l’EspaceGoogle Scholar
  37. Lyard F, Lefevre F, Letellier T, Francis O (2006) Modelling the global ocean tides: modern insights from FES2004. Ocean Dyn 56(5–6): 394–415. doi: 10.1007/s10236-006-0086-x CrossRefGoogle Scholar
  38. Ma C, Sauber JM, Clark TA, Ryan JW, Bell LJ, Gordon D, Himwich WE (1990) Measurement of horizontal motions in Alaska using very long baseline interferometry. J Geophys Res 95(B13): 21991–22011. doi: 10.1029/JB095iB13p21991 CrossRefGoogle Scholar
  39. MacMillan D (1995) Atmospheric gradients from very long baseline interferometry observations. Geophys Res Lett 22(9): 1041–1044. doi: 10.1029/95GL00887 CrossRefGoogle Scholar
  40. Mathews P, Herring T, Buffett B (2002) Modeling of nutation and precession: new nutation series for nonrigid Earth and insights into the Earth’s interior. J Geophys Res 107(B9): 2068. doi: 10.1029/2001JB000390 CrossRefGoogle Scholar
  41. McCarthy D, Petit G (2004) IERS Conventions 2003. IERS Technical Note 32, Verlag des Bundesamtes für Kartographie und Geodäsie, Frankfurt am Main. http://www.iers.org/IERS/EN/Publications/TechnicalNotes/tn32.html
  42. Nothnagel A, Pilhatsch M, Haas R (1995) Investigations of thermal height changes of geodetic VLBI telescopes. In: Lanotte R, Nianco G (eds) Proceedings of the 10th Working Meeting on European VLBI for Geodesy and Astrometry, 24–26 May 1995, Matera, Agenzia Spatiale Italiana, Matera, pp 121–133Google Scholar
  43. Pearlman MR, Degnan JJ, Bosworth JM (2002) The international laser ranging service. Adv Space Res 30(2): 135–143. doi: 10.1016/S0273-1177(02)00277-6 CrossRefGoogle Scholar
  44. Petit G, Luzum B (2010) IERS Conventions 2010. IERS Technical Note 35, Verlag des Bundesamtes für Kartographie und Geodäsie, Frankfurt am Main. ISSN 1019-4568. http://www.iers.org/IERS/EN/Publications/TechnicalNotes/tn36.html
  45. Petrov L (2007) The empirical Earth rotation model from VLBI observations. Astron Astrophys 467(1): 359–369. doi: 10.1051/0004-6361:20065091 CrossRefGoogle Scholar
  46. Petrov L, Ma C (2003) Study of harmonic site position variations determined by Very Long Baseline Interferometry. J Geophys Res 108: 2190. doi: 10.1029/2002JB001801 CrossRefGoogle Scholar
  47. Ray J, Dong D, Altamimi Z (2004) IGS reference frames: status and future improvements. GPS Solut 8(4): 251–266. doi: 10.1007/s10291-004-0110-x CrossRefGoogle Scholar
  48. Ray JR (1996) Measurements of length of day using the Global Positioning System. J Geophys Res 101(B9): 20141–20149. doi: 10.1029/96JB01889 CrossRefGoogle Scholar
  49. Ray RD, Steinberg DJ, Chao BF, Cartwright DE (1994) Diurnal and semidiurnal variations in the Earth’s rotation rate induced by oceanic tides. Science 264(5160): 830–832. doi: 10.1126/science.264.5160.830 CrossRefGoogle Scholar
  50. Rothacher M, Beutler G, Herring TA, Weber R (1999) Estimation of nutation using the Global Positioning System. J Geophys Res 104(B3): 4835–4860. doi: 10.1029/1998JB900078 CrossRefGoogle Scholar
  51. Rothacher M, Beutler G, Weber R, Hefty J (2001) High-frequency variations in Earth rotation from Global Positioning System data. J Geophys Res 106(B7): 13711–13738. doi: 10.1029/2000JB900393 CrossRefGoogle Scholar
  52. Rothacher M, Drewes H, Nothnagel A, Richter B (2010) Integration of space geodetic techniques as a basis for the global geodetic-geophysical observing system (GGOS-D): an overview. In: Flechtner F, Gruber T, Güntner A, Mandea M, Rothacher M, Schöne T, Wickert J (eds) System Earth via Geodetic-Geophysical Space Techniques. Springer, Berlin, pp 529–537. doi: 10.1007/978-3-642-10228-8_43
  53. Rothacher M, Angermann D, Artz T, Bosch W, Böckmann S, Drewes H, Gerstl M, Kelm R, König D, König R, Meisel B, Müller H, Nothnagel A, Panafidina N, Richter B, Rudenko S, Schwegmann W, Seitz M, Steigenberger P, Tesmer V, Thaller D (2011) GGOS–D: Homogeneous reprocessing and rigorous combination of space geodetic observations. J Geod. doi: 10.1007/s00190-011-0475-x
  54. Scherneck H, Haas R (1999) Effect of horizontal displacements due to ocean tide loading on the determination of polar motion and UT1. Geophys Res Lett 26(4): 501–504. doi: 10.1029/1999GL900020 CrossRefGoogle Scholar
  55. Schlüter W, Behrend D (2007) The International VLBI Service for Geodesy and Astrometry (IVS): current capabilities and future prospects. J Geod 81(6): 379–387. doi: 10.1007/s00190-006-0131-z CrossRefGoogle Scholar
  56. Schmid R, Steigenberger P, Gendt G, Ge M, Rothacher M (2007) Generation of a consistent absolute phase center correction model for GPS receiver and satellite antennas. J Geod 81(12): 781–798. doi: 10.1007/s00190-007-0148-y CrossRefGoogle Scholar
  57. Seiler U, Wünsch J (1995) A refined model for the influence of ocean tides on UT1 and polar motion. Astron Nachr 316(6): 419–423. doi: 10.1002/asna.2103160610 CrossRefGoogle Scholar
  58. Skurikhina E (2001) On computation of antenna thermal deformation in VLBI data processing. In: Behrend D, Rius A (eds) Proceedings of the 15th Workshop Meeting on European VLBI for Geodesy and Astrometry, 07–08 September 2001, Barcelona, Institut d’Estudis Espacials de Catalunya, Consejo Superior de Investigaciones Cient-ficas, Barcelona. pp 124–130. http://www.ieec.fcr.es/hosted/15wmevga/proceedings/skurikhina/skurikhina.html
  59. Springer TA (2000) Modeling and validating orbits and clocks using the Global Positioning System. Geod.-Geophys. Arb. Schweiz, vol 60Google Scholar
  60. Steigenberger P (2009) Reprocessing of a global GPS network. PhD thesis, Technische Universität München, Deutsche Geodätische Kommission Bayer. Akad. Wiss. München, Reihe C, vol 640. ISBN 978-3-7696-5052-5. http://129.187.165.2/typo3_dgk/docs/c-640.pdf
  61. Steigenberger P, Rothacher M, Dietrich R, Fritsche M, Rülke A, Vey S (2006) Reprocessing of a global GPS network. J Geophys Res 111: B05402. doi: 10.1029/2005JB003747 CrossRefGoogle Scholar
  62. Thaller D, Krügel M, Rothacher M, Tesmer V, Schmid R, Angermann D (2007) Combined Earth orientation parameters based on homogeneous and continuous VLBI and GPS data. J Geod 81(6–8): 529–541. doi: 10.1007/s00190-006-0115-z CrossRefGoogle Scholar
  63. Vennebusch M, Böckmann S, Nothnagel A (2007) The contribution of very long baseline interferometry to ITRF2005. J Geod 81(6–8): 553–564. doi: 10.1007/s00190-006-0117-x CrossRefGoogle Scholar
  64. Watkins MM, Eanes RJ (1994) Diurnal and semidiurnal variations in Earth orientation determined from LAGEOS laser ranging. J Geophys Res 99(B9): 18073–18080. doi: 10.1029/94JB00805 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • T. Artz
    • 1
  • L. Bernhard
    • 1
  • A. Nothnagel
    • 1
  • P. Steigenberger
    • 2
  • S. Tesmer
    • 1
  1. 1.Institute of Geodesy and GeoinformationBonnGermany
  2. 2.Institut für Astronomische und Physikalische GeodäsieTechnische Universität MünchenMunichGermany

Personalised recommendations