Abstract
The Rosborough approach was developed in the 1980s for the modeling of orbit perturbations of altimeter satellites. It is a formalism that is rooted in the so-called time-wise approach, in which gravitational functionals are described as an along-orbit time series. Nevertheless, through a transformation of the orbital variables, the along-orbit functional can be mapped back onto the sphere. As such, the Rosborough formulation is a so-called space-wise approach at the same time. Both the conventional time-wise and the space-wise approaches have been improved and optimized over the past decade. When we explore the utility of the Rosborough approach in this contribution, we do not expect improved solutions for this particular GOCE-based case study. However, we aim to show the special characteristics of the Rosborough approach for processing the GOCE gradiometry data. In particular, we show that this approach can successfully deal with the problems that come with real data like bandwidth limitation and mispointing. Based on the first 71 days of the GOCE gravity gradients, we obtain solutions up till spherical harmonic degree 200. Compared to a high-quality gradiometric-only time-wise model, our solution shows a similar performance with just 8 cm geoid RMS difference in the relevant bandwidth. Moreover, relative contributions from the individual components are provided for the geographically mean gravity gradient components \(T_{xx}\), \(T_{yy}\) and \(T_{zz}\), and for the geographically variable gravity gradient components \(T_{xx}\) and \(T_{yy}\). It is shown that the spatially variable components provide a direct access to understanding the mapping of time-variable error effects on the sphere. For instance, the known geomagnetic equator effect comes out clearly in the variable components of gravity gradients, as do track-specific errors. In conclusion, it is demonstrated that the Rosborough approach is a complementary method to the conventional approaches for GOCE data processing.
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References
Albertella A, Migliaccio F, Reguzzoni M, Sansò F (2004) Wiener filters and collocation in satellite gradiometry. In: Sansò F (ed) International association of geodesy symposia, V Hotine-Marussi symposium on mathematical geodesy, vol 127. Springer, Berlin, pp 32–38. doi:10.1007/978-3-662-10735-5_5
Balmino G (1993) Orbit choice and the theory of radial orbit error for altimetry. In: Rummel R, Sansò F (eds) Satellite altimetry in geodesy and oceanography. Lecture notes in earth sciences, vol 50. Springer, Berlin, pp 244–315. doi:10.1007/BFb0117930
Bosch W (1996) Geoid and orbit corrections from crossover satellite altimetry. Tech. Rep , DGFI internal technical report
Bouman J, Rispens S, Gruber T, Koop R, Schrama E, Visser P, Tscherning CC, Veicherts M (2009) Preprocessing of gravity gradients at the GOCE high-level processing facility. J Geodesy 83(7):659–678. doi:10.1007/s00190-008-0279-9
Brockmann JM, Schuh WD, Krasbutter I, Gruber T (2012) TIM\_RL01 gravity field determination with reprocessed EGG\_NOM\_2 data. Tech. Rep. ESA GO-TN-HPF-GS-0301. https://earth.esa.int/c/document_library/get_file?&folderId=85857&name=DLFE-1908.pdf. Accessed 4 Jan 2015
Brockmann JM, Zehentner N, Höck E, Pail R, Loth I, Mayer-Gürr T, Schuh WD (2014) EGM\_TIM\_RL05: an independent geoid with centimeter accuracy purely based on the GOCE mission. Geophys Res Lett 41(22):8089–8099. doi:10.1002/2014GL061904
Cai L, Zhou Z, Hsu H, Gao F, Zhu Z, Luo J (2013) Analytical error analysis for satellite gravity field determination based on two-dimensional fourier method. J Geodesy 87(5):417–426. doi:10.1007/s00190-013-0615-6
Cesare S (2008) GOCE-performance requirements and budgets for the gradiometric mission. Tech. Rep, Thales Alenia Space, Torino
Colombo O (1989) Advanced techniques for high-resolution mapping of the gravitational field. In: Sansò F, Rummel R (eds) Theory of satellite geodesy and gravity field determination. Lecture notes in earth science, vol 25. Springer, New York, pp 335–369
Engelis T (1987) Radial orbit error reduction and sea surface topography determination using satellite altimetry. Tech. Rep. No. 337, Ohio state University
ESA (1999) Reports for mission selection, the four candidate earth explorer core missions, gravity field and steady-state ocean circulation mission. Tech. Rep. ESA SP-1233
Fuchs MJ, Bouman J (2011) Rotation of GOCE gravity gradients to local frames. Geophys J Int 187(2):743–753. doi:10.1111/j.1365-246X.2011.05162.x
Kaula WM (1966) Theory of satellite geodesy: applications of satellites to geodesy. Blaisdel Publishing company, Waltham
Keller W, You RJ (2014) Adaptation of the torus and Rosborough approach to radial base functions. Stud Geophys Geod 58(2):249–268. doi:10.1007/s11200-013-0157-7
Klees R, Koop R, Visser PNAM, Van den Ijssel J (2000) Efficient gravity field recovery from GOCE gravity gradient observations. J Geodesy 74(7–8):561–571. doi:10.1007/s001900000118
Klokočník J, Wagner CA, Kostelecky J, Jandová M (1995) The filtering effect of orbit correction on geopotential errors. J Geodesy 70(3):146–157. doi:10.1007/BF00943690
Klokočník J, Li H, Mueller H (1990) The German PAF for ERS-1: investigation of radial orbit error for ERS-1 by means of Rosborough’s formulae. Tech. rep., D-PAF/DGFI ERS-D-roe 31600, Deutsche Geodaet. Forschungs Institue, München
Klokočník J, Wagner CA (1994) A test of GEM T2 from GEOSAT crossovers using latitude lumped coefficients. Bull Géodésique 68(2):100–108. doi:10.1007/BF00819386
Koop R (1993) Global gravity field modelling using satellite gravity gradiometry. Tech. Rep. New Series, 38, The Netherlands Geodetic Commission, Delft
Migliaccio F, Reguzzoni M, Sansò F (2004a) Space-wise approach to satellite gravity field determination in the presence of coloured noise. J Geodesy 78(4–5):304–313. doi:10.1007/s00190-004-0396-z
Migliaccio F, Reguzzoni M, Sansò F, Tscherning CC (2004b) The performance of the space-wise approach to GOCE data analysis, when statistical homogenization is applied. Newtons Bull 2:60–65
Migliaccio F, Reguzzoni M, Sansò F, Zatelli P (2004c) GOCE: dealing with large attitude variations in the conceptual structure of the space-wise approach. In: Proceeding of the 2nd international GOCE user workshop. Frascati
Pail R, Bruinsma S, Migliaccio F, Förste C, Goiginger H, Schuh WD, Höck E, Reguzzoni M, Brockmann JM, Abrikosov O et al (2011) First GOCE gravity field models derived by three different approaches. J Geodesy 85(11):819–843. doi:10.1007/s00190-011-0467-x
Pail R, Goiginger H, Mayrhofer R, Schuh WD, Brockmann JM, Krasbutter I, Höck E, Fecher T (2010) GOCE gravity field model derived from orbit and gradiometry data applying the time-wise method. In: Lacoste-Francis H (ed) Proceedings of the ESA living planet symposium. ESA Publication SP-686. ESA/ESTEC
Papoulis A (1984) Signal analysis. McGraw-Hill, New York
Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the earth gravitational model 2008 (EGM2008). J Geophys Res Solid Earth (1978–2012) 117(B4). doi:10.1029/2011JB008916
Peterseim N, Schlicht A, Stummer C, Yi W (2011) Impact of cross winds in polar regions on GOCE accelerometer and gradiometer data. In: Proceedings of the 4th international GOCE user workshop. München
Preimesberger T, Pail R (2003) GOCE quick-look gravity solution: application of the semi-analytic approach in the case of data gaps and non-repeat orbits. Stud Geophys Geod 47(3):435–453. doi:10.1023/A:1024795030800
Reguzzoni M, Tselfes N (2009) Optimal multi-step collocation: application to the space-wise approach for GOCE data analysis. J Geodesy 83(1):13–29. doi:10.1007/s00190-008-0225-x
Reigber C (1989) Gravity field recovery from satellite tracking data. In: Sansò F, Rummel R (eds) Theory of satellite geodesy and gravity field determination. Springer, Berlin, pp 197–234. doi:10.1007/BFb0010552
Rosborough GW (1986) Satellite orbit perturbations due to the geopotential. Tech. Rep. CSR-86-1, Center for Space research, University of Texas at Austin
Rosborough GW, Tapley BD (1987) Radial, transverse and normal satellite position perturbations due to the geopotential. Celest Mech 40(3–4):409–421. doi:10.2478/arsa-2013-0004
Rummel R, Yi W, Stummer C (2011) Goce gravitational gradiometry. J Geodesy 85(11):777–790. doi:10.1007/s00190-011-0500-0
Rummel R, van Gelderen M, Koop R, Schrama E, Sansò F, Brovelli M, Migliaccio M, Sacerdote F (1993) Spherical harmonic analysis of satellite gradiometry. Tech. Rep, Nederlandse Commissie Voor Geodesie, Delft
Sharifi MA (2006) Satellite to satellite tracking in the space-wise approach. PhD thesis, University of Stuttgart. http://elib.uni-stuttgart.de/opus/volltexte/2006/2833/pdf/Dissertation_Sharifi.pdf. Accessed 3 Jan 2015
Sharifi MA, Sneeuw N, Ghobadi-Far K (2013b) Analysis of GOCE data based on the Rosborough method. Poster presentation. In: VIII Hotine-Marussi symposium. Rome
Sharifi MA, Safari A, Ghobadi-Far K (2013) Rosborough formulation in satellite gravity gradiometry. Artif Satell 48(1):39–50. doi:10.2478/arsa-2013-0004
Siemes C, Haagmans R, Kern M, Plank G, Floberghagen R (2012) Monitoring GOCE gradiometer calibration parameters using accelerometer and star sensor data: methodology and first results. J Geodesy 86(8):629–645. doi:10.1007/s00190-012-0545-8
Sneeuw N (2000) A semi-analytical approach to gravity field analysis from satellite observations. PhD thesis, University of München. http://mediatum.ub.tum.de/doc/601028/601028.pdf. Accessed 3 Jan 2015
Sneeuw N (2003) Space-wise, time-wise, torus and Rosborough representations in gravity field modelling. Space Sci Rev 108(1–2):37–46. doi:10.1023/A:1026165612224
Sneeuw N, Sharifi MA (2015) Rosborough representation in satellite gravimetry. In: International association of geodesy symposia. Springer, Berlin. doi:10.1007/1345_2015_68
Sneeuw N, Van Gelderen M (1997) The polar gap. In: Sansó F, Rummel R (eds) Geodetic boundary value problems in view of the one centimeter geoid. Lecture notes in earth sciences, vol 65. Springer, Berlin, pp 559–568. doi:10.1007/BFb0011717
Stummer C, Siemes C, Pail R, Frommknecht B, Floberghagen R (2012) Upgrade of the GOCE Level 1b gradiometer processor. Adv Space Res 49(4):739–752. doi:10.1016/j.asr.2011.11.027
Wermuth M (2008) Gravity field analysis from the satellite missions CHAMP and GOCE. PhD thesis, University of München
Wessel P, Smith W (1998) New, improved version of generic mapping tools released. Eos Trans Am Geophys Union (AGU) 79(47):579–579. doi:10.1029/98EO00426
Xu C, Sideris M, Sneeuw N (2008) The torus approach in spaceborne gravimetry. In: Xu P, Liu J, Dermanis A (eds) International assiciation of geodesy symposia, VI Hotine-Marussi symposium on mathematical geodesy, vol 132. Springer, Berlin, pp 23–28. doi:10.1007/978-3-540-74584-6_4
Yi W, Rummel R, Gruber T (2013) Gravity field contribution analysis of GOCE gravitational gradient components. Stud Geophys Geod 57(2):174–202. doi:10.1007/s11200-011-1178-8
Yi W, Rummel R (2014) A comparison of GOCE gravitational models with EGM2008. J Geodyn 73:14–22. doi:10.1016/j.jog.2013.10.004
Acknowledgments
Jan Martin Brockmann is gratefully acknowledged for providing the gradiometric-only time-wise model based on the GOCE reprocessed EGG_NOM_2 data. Some of the figures of the paper were produced using the Generic Mapping Tools (GMT) (Wessel and Smith 1998). The authors would like to thank the editor and the anonymous reviewers for their helpful comments which led to a clearer presentation of our work.
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Ghobadi-Far, K., Sharifi, M.A. & Sneeuw, N. GOCE gradiometry data processing using the Rosborough approach. J Geod 89, 1245–1261 (2015). https://doi.org/10.1007/s00190-015-0849-6
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DOI: https://doi.org/10.1007/s00190-015-0849-6