Journal of Geodesy

, Volume 89, Issue 3, pp 241–258 | Cite as

Levelling co-located GNSS and tide gauge stations using GNSS reflectometry

  • Alvaro Santamaría-Gómez
  • Christopher Watson
  • Médéric Gravelle
  • Matt King
  • Guy Wöppelmann
Original Article

Abstract

The GNSS reflectometry technique provides geometric information on the environment surrounding the GNSS antenna including the vertical distance to a reflecting surface. We use sea-surface reflections of GPS signals, recorded as oscillations in signal-to-noise ratio (SNR), to estimate the GNSS to tide gauge (TG) levelling tie, and thus the ellipsoidal heights of the TG. We develop approaches to isolate SNR data dominated by sea-surface reflections and to remove SNR frequency changes caused by the dynamic sea surface. Comparison with in situ levelling at eight sites reveals mean differences at the centimetre level for satellites above 12\(^{\circ }\) elevation, with four sites showing differences of 3 cm or smaller. These differences include errors in the in situ levelling, in the antenna calibration model and in the TG measurements, and so represent an upper bound on our technique’s error. Data sampling (1 or 30 s) does not significantly affect the results. We detect systematic errors at the decimetre level related to satellite elevations below 12\(^{\circ }\) and to sea-surface height and also differences between results from the L1 and L2 GPS signals larger than 15 cm at two sites. These systematic errors remain unexplained; differences between GPS signals are attributed to receiver-dependent differences in the SNR measurements, while the elevation-dependent error is attributed to unmodelled phase effects such as those caused by tropospheric refraction and sea-surface roughness. Using our approach, we identify a levelling offset of 1.5 cm related to a TG sensor change, illustrating our technique’s value for TG reference monitoring.

Keywords

Reflectometry GNSS SNR Levelling  Tide gauges Site co-location 

Notes

Acknowledgments

A. SG. is a recipient of a FP7 Marie Curie International Outgoing Fellowship (Project Number 330103). M. A. K. is a recipient of an Australian Research Council Future Fellowship (Project Number FT110100207). We acknowledge Kristine M. Larson, Felipe G. Nievinski, the editor and an anonymous reviewer for constructive comments. We acknowledge the Système d’Observation du Niveau des Eaux Littorales (SONEL), Institut National de l’Information Géographique et Forestière (IGN), Geoscience Australia (GA), and Instituto Geográfico Nacional (IGN) for providing the GPS data, and the Service Hydrographique et Oceanographique de la Marine (SHOM), Australian Bureau of Meteorology (BOM), and Puertos del Estado (REDMAR network) for providing the tide gauge data. Google Earth provided the satellite images. Figures 5, 6, 7 and 8 were produced with Gnuplot.

Supplementary material

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Supplementary material 1 (docx 14 KB)
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Supplementary material 4 (png 68092 KB)

References

  1. Amos MJ, Featherstone WE (2009) Unification of New Zealand’s local vertical datums: iterative gravimetric quasigeoid computations. J Geod 83:57–68. doi: 10.1007/s00190-008-0232-y CrossRefGoogle Scholar
  2. Andersen OB, Knudsen P (2009) DNSC08 mean sea surface and mean dynamic topography models. J Geophys Res 114:1–12. doi: 10.1029/2008JC005179 Google Scholar
  3. Anderson KD (2000) Determination of Water Level and Tides Using Interferometric Observations of GPS Signals. J Atmos Oceanic Technol 17:1118–1127. doi: 10.1175/1520-0426(2000)017<1118:DOWLAT>2.0.CO;2
  4. Axelrad P, Larson K, Jones B (2005) Use of the correct satellite repeat period to characterize and reduce site-specific multipath errors. In: Proceedings of the 18th international technical meeting of the Satellite Division of The Institute of Navigation, ION GNSS 2005. pp 2638–2648Google Scholar
  5. Baire Q et al (2013) Influence of different GPS receiver antenna calibration models on geodetic positioning. GPS Solut 18:1–11. doi: 10.1007/s10291-013-0349-1
  6. Benton CJ, Mitchell CN (2011) Isolating the multipath component in GNSS signal-to-noise data and locating reflecting objects. Radio Sci 46:RS6002. doi: 10.1029/2011RS004767 CrossRefGoogle Scholar
  7. Bilich A, Axelrad P, Larson KM (2007) Scientifc utility of the signal-to-noise ratio (SNR) reported by geodetic GPS receivers. Paper presented at the Proceedings of the 20th international technical meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2007), Fort Worth, 25–28 Sept 2007Google Scholar
  8. Bilich A, Larson KM (2007) Mapping the GPS multipath environment using the signal-to-noise ratio (SNR). Radio Sci 42:RS6003. doi: 10.1029/2007rs003652 CrossRefGoogle Scholar
  9. Bourlier C, Pinel N, Fabbro V (2006) Illuminated height PDF of a random rough surface and its impact on the forward propagation above oceans at grazing angles. In: Antennas and propagation, 2006. EuCAP 2006. First European conference on, 6–10 Nov 2006, pp 1–6. doi: 10.1109/EUCAP.2006.4584894
  10. Calafat FM, Chambers DP, Tsimplis MN (2014) On the ability of global sea level reconstructions to determine trends and variability. J Geophys Res 119:1572–1592. doi: 10.1002/2013JC009298 CrossRefGoogle Scholar
  11. Cardellach E, Rius A (2008) A new technique to sense non-Gaussian features of the sea surface from L-band bi-static GNSS reflections. Remote Sens Environ 112:2927–2937. doi: 10.1016/j.rse.2008.02.003 CrossRefGoogle Scholar
  12. Cardellach E, Fabra F, Nogués-Correig O, Oliveras S, Ribó S, Rius A (2011) GNSS-R ground-based and airborne campaigns for ocean, land, ice, and snow techniques: application to the GOLD-RTR data sets. Radio Sci 46:RS0C04. doi: 10.1029/2011RS004683 CrossRefGoogle Scholar
  13. Church J, White N (2011) Sea-level tise from the Late 19th to the Early 21st Century. Surv Geophys 32:585–602. doi: 10.1007/s10712-011-9119-1 CrossRefGoogle Scholar
  14. Dayoub N, Moore P, Penna NT, Edwards SJ (2012) Evaluation of EGM2008 within geopotential space from GPS, tide gauges and altimetry. In: Kenyon S, Pacino MC, Marti U (eds) Geodesy for planet earth. International Association of Geodesy Symposia, vol 136. Springer, Berlin, Heidelberg, pp 323–331. doi: 10.1007/978-3-642-20338-1_39
  15. Elosegui P, Davis JL, Jaldehag RTK, Johansson JM, Niell AE, Shapiro II (1995) Geodesy using the global positioning system: the effects of signal scattering on estimates of site position. J Geophys Res 100:9921–9934CrossRefGoogle Scholar
  16. Featherstone WE, Filmer MS (2012) The north-south tilt in the Australian height datum is explained by the ocean’s mean dynamic topography. J Geophys Res 117:C08035. doi: 10.1029/2012JC007974 Google Scholar
  17. Foreman MGG, Crawford WR, Cherniawsky JY, Galbraith J (2008) Dynamic ocean topography for the northeast Pacific and its continental margins. Geophys Res Lett 35:L22606. doi: 10.1029/2008GL035152 CrossRefGoogle Scholar
  18. Georgiadou Y, Kleusberg A (1988) On carrier signal multipath effects in relative GPS positioning. Map Collect 13:172–179Google Scholar
  19. Holgate SJ et al (2013) New data systems and products at the permanent service for mean sea level. J Coast Res 29:493–504. doi: 10.2112/jcoastres-d-12-00175.1
  20. IOC (2006) Manual on sea-level measurement and interpretation: an update to 2006. IOC manuals and guides no. 14, vol IV, JCOMM technical report no. 31, WMO/TD. No. 1339. Intergovernmental Oceanographic Commission of UNESCO, Paris, p 78 (English)Google Scholar
  21. IOC (2012) Global sea-level observing system (GLOSS) implementation plan—2012. IOC technical series no. 100. UNESCO/IOC, p 41 (English)Google Scholar
  22. ITU (2012) The radio refractive index: its formula and refractivity data. ITU-R recommendation P.453-12, P-series, p 30Google Scholar
  23. Jacobson MD (2010) Snow-covered lake ice in GPS multipath reception—theory and measurement. Adv Space Res 46:221–227. doi: 10.1016/j.asr.2009.10.013 CrossRefGoogle Scholar
  24. Jin S, Cardellach E, Xie F (2014) GNSS remote sensing: theory, methods and applications. Remote sensing and digital image processing, vol 19. Springer, Netherlands. doi: 10.1007/978-94-007-7482-7
  25. Koohzare A, Vaníček P, Santos M (2008) Pattern of recent vertical crustal movements in Canada. J Geodyn 45:133–145. doi: 10.1016/j.jog.2007.08.001 CrossRefGoogle Scholar
  26. Larson K, Nievinski F (2013) GPS snow sensing: results from the EarthScope Plate Boundary Observatory. GPS Solut 17:41–52. doi: 10.1007/s10291-012-0259-7 CrossRefGoogle Scholar
  27. Larson KM, Small EE, Gutmann ED, Bilich AL, Braun JJ, Zavorotny VU (2008) Use of GPS receivers as a soil moisture network for water cycle studies. Geophys Res Lett 35:L24405. doi: 10.1029/2008gl036013 CrossRefGoogle Scholar
  28. Larson KM, Gutmann ED, Zavorotny VU, Braun JJ, Williams MW, Nievinski FG (2009) Can we measure snow depth with GPS receivers? Geophys Res Lett 36:L17502. doi: 10.1029/2009gl039430 CrossRefGoogle Scholar
  29. Larson KM, Braun JJ, Small EE, Zavorotny VU, Gutmann ED, Bilich AL (2010) GPS multipath and its relation to near-surface soil moisture content. selected topics in applied earth observations and remote sensing. IEEE J 3:91–99. doi: 10.1109/jstars.2009.2033612 Google Scholar
  30. Larson KM, Löfgren JS, Haas R (2013a) Coastal sea level measurements using a single geodetic GPS receiver. Adv Space Res 51:1301–1310. doi: 10.1016/j.asr.2012.04.017 CrossRefGoogle Scholar
  31. Larson KM, Ray RD, Nievinski FG, Freymueller JT (2013b) The accidental tide gauge: a GPS reflection case study From Kachemak Bay, Alaska. IEEE Geosci Remote Sens Lett 10:1200–1204. doi: 10.1109/lgrs.2012.2236075 CrossRefGoogle Scholar
  32. Löfgren JS, Haas R, Johansson JM (2011a) Monitoring coastal sea level using reflected GNSS signals. Adv Space Res 47:213–220. doi: 10.1016/j.asr.2010.08.015 CrossRefGoogle Scholar
  33. Löfgren JS, Haas R, Scherneck HG, Bos MS (2011b) Three months of local sea level derived from reflected GNSS signals. Radio Sci 46:RS0C05. doi: 10.1029/2011RS004693 CrossRefGoogle Scholar
  34. Löfgren JS, Haas R (2014) Sea level measurements using multi-frequency GPS and GLONASS observations. EURASIP J Adv Signal Process 2014:50. doi: 10.1186/1687-6180-2014-50 CrossRefGoogle Scholar
  35. Löfgren JS, Haas R, Scherneck HG (2014) Sea level time series and ocean tide analysis from multipath signals at five GPS sites in different parts of the world. J Geodyn. doi: 10.1016/j.jog.2014.02.012 Google Scholar
  36. Madsen KS, Høyer JL, Tscherning CC (2007) Near-coastal satellite altimetry: sea surface height variability in the North Sea-Baltic Sea area. Geophys Res Lett 34:L14601. doi: 10.1029/2007GL029965 CrossRefGoogle Scholar
  37. Martin Miguez B, Le Roy R, Woeppelmann G (2008a) The use of radar tide gauges to measure variations in sea level along the French coast. J Coast Res 24:61–68. doi: 10.2112/06-0787.1 CrossRefGoogle Scholar
  38. Martin Miguez B, Testut L, Woppelmann G (2008b) The Van de Casteele test revisited: an efficient approach to tide gauge error characterization. J Atmos Oceanic Technol 25:1238–1244. doi: 10.1175/2007jtecho554.1 CrossRefGoogle Scholar
  39. Nievinski F, Larson K (2014a) Forward modeling of GPS multipath for near-surface reflectometry and positioning applications. GPS Solut 18:309–322. doi: 10.1007/s10291-013-0331-y CrossRefGoogle Scholar
  40. Nievinski FG, Larson KM (2014b) Inverse modeling of GPS multipath for snow depth estimation—part I: formulation and simulations. IEEE Trans Geosci Remote Sens 52:6555–6563. doi: 10.1109/TGRS.2013.2297681
  41. Nievinski FG, Larson KM (2014c) Inverse modeling of GPS multipath for snow depth estimation—part II: application and validation. IEEE Trans Geosci Remote Sens 52:6564–6573. doi: 10.1109/TGRS.2013.2297688
  42. Nievinski FG, Larson KM (2014d) An open source GPS multipath simulator in Matlab/Octave. GPS Solut 18:1–9. doi: 10.1007/s10291-014-0370-z
  43. Penna NT, Featherstone WE, Gazeaux J, Bingham RJ (2013) The apparent British sea slope is caused by systematic errors in the levelling-based vertical datum. Geophys J Int 194:772–786. doi: 10.1093/gji/ggt161 CrossRefGoogle Scholar
  44. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2001) Numerical recipes in Fortran 77: the art of scientific computing, vol 1, 2nd edn. Cambridge University Press, New YorkGoogle Scholar
  45. Pugh DT (1996) Tides, surges and mean sea-level (reprinted with corrections). Wiley, ChichesterGoogle Scholar
  46. Roussel N, Frappart F, Ramillien G, Desjardins C, Gegout P, Pérosanz F, Biancale R (2014) Simulations of direct and reflected waves trajectories for in situ GNSS-R experiments. Geosci Model Dev Discuss 7:1001–1062. doi: 10.5194/gmdd-7-1001-2014 CrossRefGoogle Scholar
  47. Sánchez L (2012) Towards a vertical datum standardisation under the umbrella of global geodetic observing system. J Geod Sci 2:325–342. doi: 10.2478/v10156-012-0002-x Google Scholar
  48. 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 81:781–798. doi: 10.1007/s00190-007-0148-y CrossRefGoogle Scholar
  49. Small EE, Larson KM, Braun JJ (2010) Sensing vegetation growth with reflected GPS signals. Geophys Res Lett 37:L12401. doi: 10.1029/2010gl042951 Google Scholar
  50. Watson C, White N, Church J, Burgette R, Tregoning P, Coleman R (2011) Absolute calibration in Bass Strait, Australia: TOPEX, Jason-1 and OSTM/Jason-2. Mar Geod 34:242–260. doi: 10.1080/01490419.2011.584834 CrossRefGoogle Scholar
  51. Woodworth PL, Hughes CW, Bingham RJ, Gruber T (2012) Towards worldwide height system unification using ocean information. J Geod Sci 2:302–318. doi: 10.2478/v10156-012-0004-8 Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Alvaro Santamaría-Gómez
    • 1
    • 2
  • Christopher Watson
    • 2
  • Médéric Gravelle
    • 1
  • Matt King
    • 2
  • Guy Wöppelmann
    • 1
  1. 1.LIENSs, University of La Rochelle - CNRSLa RochelleFrance
  2. 2.School of Land and FoodUniversity of TasmaniaHobartAustralia

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