Advertisement

Journal of Geodesy

, Volume 88, Issue 6, pp 601–615 | Cite as

Realization of a consistent set of vertical reference surfaces in coastal areas

  • D. C. SlobbeEmail author
  • R. Klees
  • B. C. Gunter
Original Article

Abstract

We present a combined approach for the realization of the (quasi-)geoid as a height reference surface and the vertical reference surface at sea (chart datum). This approach, specifically designed for shallow seas and coastal waters, provides the relation between the two vertical reference surfaces without gaps down to the coast. It uses a regional hydrodynamic model, which, after vertical referencing, provides water levels relative to a given (quasi-)geoid. Conversely, the hydrodynamic model is also used to realize a (quasi-)geoid by providing corrections to the dynamic sea surface topography, which are used to reduce radar altimeter-derived sea surface heights to the (quasi-)geoid. The coupled problem of vertically referencing the hydrodynamic model and computing the (quasi-)geoid is solved iteratively. After convergence of the iteration process, the vertically referenced hydrodynamic model is used to realize the chart datum. In this way, consistency between the chart datum and (quasi-)geoid is ensured. We demonstrate the feasibility and performance of this approach for the Dutch mainland and North Sea. We show that in the Dutch part of the North Sea, the differences between modeled and observed instantaneous and mean dynamic sea surface topography is 8–10 and 5.8 cm, respectively. On land, we show that the methodology provides a quasi-geoid which has a lower standard deviation (SD) than the European Gravimetric Geoid 2008 (EGG08) and the official Netherlands quasi-geoid NLGEO2004-grav when compared to GPS-levelling data. The root mean square at 81 GPS-levelling points is below 1.4 cm; no correction surface is needed. Finally, we show that the chart datum (lowest astronomical tide, LAT) agrees with the observed chart datum at 92 onshore tide gauges to within 21.5 cm (SD).

Keywords

Vertical reference surfaces Quasi-geoid Lowest astronomical tide Hydrodynamic model 

Notes

Acknowledgments

The authors gratefully acknowledge funding from the Netherlands Vertical Reference Frame (NEVREF) Project. Gravity data were kindly provided by the British Geological Service; the Geological Survey of Northern Ireland; the Nordic Geodetic Commission; Bundesamt für Kartographie und Geodäsie (Germany); Institut für Erdmessung (Germany); the Bureau Gravimétrique International (International Gravity Bureau) IAG service (France); the Banque de données Gravimétriques de la France; and the Bureau de Recherches Géologiques et Minières (France). Tide gauge data were kindly provided by the Vlaamse Hydrografie, Agentschap voor Maritieme Dienstverlening en Kust, afdeling Kust (Belgium); Danish Coastal Authority; Danish Meteorological Institute; Danish Maritime Safety Administration; Service Hydrographique et Océanographique de la Marine (France); Bundesamt für Seeschifffahrt und Hydrographie (Germany); Marine Institute, Ireland; Rijkswaterstaat (the Netherlands); Norwegian Hydrographic Service; Swedish Meteorological and Hydrological Institute; and U.K. National Tidal and Sea Level Facility (NTSLF) hosted by POL. P. A. M Berry is acknowledged for providing retracked ERS-1 radar altimeter data and O.B. Andersen for providing the mean sea surface heights and altimeter-derived gravity anomaly grids to the community. In addition, the authors gratefully acknowledge the support of the Proudman Oceanographic Laboratory (POL) for providing the results of the Atlantic—European North West Shelf—Ocean Physics Hindcast to the community and their help in answering some questions. We also acknowledge the valuable comments of three anonymous reviewers.

References

  1. Andersen OB (2010) The DTU10 global gravity field and mean sea surface—improvements in the Arctic. http://www.space.dtu.dk/english/Research/Scientific_data_and_models/Global_Marine_Gravity_Field, Second international symposium of the gravity field of the Earth (IGFS2), Fairbanks, Alaska
  2. Andersen OB, Knudsen P (2000) The role of satellite altimetry in gravity field modelling in coastal areas. Phys Chem Earth 25(1):17–24. doi: 10.1016/S1464-1895(00)00004-1 CrossRefGoogle Scholar
  3. Andersen OB, Knudsen P, Berry P (2010) The DNSC08GRA global marine gravity field from double retracked satellite altimetry. J Geod 84(3):191–199. doi: 10.1007/s00190-009-0355-9 CrossRefGoogle Scholar
  4. Carrère L, Lyard F (2003) Modeling the barotropic response of the global ocean to atmospheric wind and pressure forcing—comparisons with observations. Geophys Res Lett 30(6):n/a-n/a, doi: 10.1029/2002GL016473
  5. Crombaghs M, de Bruijne A (2004) NLGEO2004—een nieuw geoïdemodel voor Nederland. Technical report, Adviesdienst Geo-informatie en ICT, Report AGI-GAP-2004-25, Delft, 41 pGoogle Scholar
  6. Dee DP, Uppala SM, Simmons AJ, Berrisford P, Poli P, Kobayashi S, Andrae U, Balmaseda MA, Balsamo G, Bauer P, Bechtold P, Beljaars ACM, van de Berg L, Bidlot J, Bormann N, Delsol C, Dragani R, Fuentes M, Geer AJ, Haimberger L, Healy SB, Hersbach H, Hólm EV, Isaksen L, Kållberg P, Köhler M, Matricardi M, McNally AP, Monge-Sanz BM, Morcrette JJ, Park BK, Peubey C, de Rosnay P, Tavolato C, Thépaut JN, Vitart F (2011) The ERA-Interim reanalysis: configuration and performance of the data assimilation system. QJ R Meteor Soc 137(656):553–597. doi: 10.1002/qj.828 CrossRefGoogle Scholar
  7. Deng X (2003) Improvement of Geodetic Parameter Estimation in Coastal Regions from Satellite Radar Altimetry. Phd, Curtin University of Technology, Department of Spatial SciencesGoogle Scholar
  8. Deng X, Featherstone WE, Hwang C, Berry PAM (2002) Estimation of contamination of ERS-2 and POSEIDON satellite radar altimetry close to the coasts of Australia. Mar Geod 25(4):249–271CrossRefGoogle Scholar
  9. Denker H (2013) Regional gravity field modeling: theory and practical results. In: Xu G (ed) Sciences of Geodesy—II, Springer, Berlin, Heidelberg, pp 185–291. doi: 10.1007/978-3-642-28000-9_5
  10. Denker H, Roland M (2005) Compilation and evaluation of a consistent marine gravity data set surrounding europe. In: A window on the future of geodesy. Springer, Berlin, Heidelberg, pp 248–253. doi: 10.1007/3-540-27432-4_42
  11. Farahani HH, Ditmar P, Klees R, Liu X, Zhao Q, Guo J (2013a) The static gravity field model DGM-1S from GRACE and GOCE data: computation, validation and an analysis of GOCE mission’s added value. J Geod 87(9):843–867. doi: 10.1007/s00190-013-0650-3 CrossRefGoogle Scholar
  12. Farahani HH, Ditmar P, Klees R, Liu X, Zhao Q, Guo J (2013b) Validation of static gravity field models using GRACE K-band ranging and GOCE gradiometry data. Geophys J Int 194:751–771. doi: 10.1093/gji/ggt149 CrossRefGoogle Scholar
  13. Forsberg R, Hehl K, Mayer U, Gidskehaug A, Bastos L (1997) Development of an airborne geoid mapping system for coastal oceanography (AGMASCO). In: Proceedings of international symposium on gravity geoid and marine geodesy, Japan, pp 130–142Google Scholar
  14. General Bathymetric Chart of the Oceans (GEBCO) (2012) General bathymetric chart of the oceans (GEBCO). http://www.gebco.net/. Accessed Mar 7, 2013
  15. Gerritsen H, de Vries H, Philippart M (1995) The Dutch continental shelf model. In: Lynch DR, Davies AM (eds) Quantitative skill assessment for coastal ocean models, Coastal Estuarine Stud., vol 47, AGU, Washington, DC, pp 425–467. doi: 10.1029/CE047p0425
  16. Gommenginger C, Thibaut P, Fenoglio-Marc L, Quartly G, Deng X, Gómez-Enri PJ, Challenor YG (2011) Retracking altimeter waveforms near the coasts. In: Vignudelli S, Kostianoy AG, Cipollini P, Benveniste J (eds) Coastal altimetry, 1st edn. Springer, Berlin, Heidelberg, pp 61–101CrossRefGoogle Scholar
  17. González Á (2010) Measurement of areas on a sphere using Fibonacci and latitude–longitude lattices. Math Geosci 42(1):49–64. doi: 10.1007/s11004-009-9257-x CrossRefGoogle Scholar
  18. Gunter BC (2004) Computational methods and processing strategies for estimating earth’s gravity field. PhD thesis, The University of Texas at Austin. http://repositories.lib.utexas.edu/handle/2152/1318
  19. Gunter BC, van de Geijn RA (2005) Parallel out-of-core computation and updating of the QR factorization. ACM Trans Math Softw 31(1):60–78. doi: 10.1145/1055531.1055534 CrossRefGoogle Scholar
  20. Haagmans RHN, Husti GJ, Plugers P, Smit JHM, Strang van Hees GL (1988) NAVGRAV Navigation and Gravimetric Experiment at the North Sea. Technical report 32, Netherlands Geodetic Commission, DelftGoogle Scholar
  21. Holt JT, James ID (2001) An s coordinate density evolving model of the northwest European continental shelf, 1. Model description and density structure. J Geophys Res 106:14015–14034. doi: 10.1029/2000JC000304 CrossRefGoogle Scholar
  22. Holt JT, James ID, Jones JE (2001) An s coordinate density evolving model of the northwest European continental shelf, 2. Seasonal currents and tides. J Geophys Res 106:14035–14054. doi: 10.1029/2000JC000303 CrossRefGoogle Scholar
  23. Holt JT, Allen JI, Proctor R, Gilbert F (2005) Error quantification of a high-resolution coupled hydrodynamic ecosystem coastal ocean model: part 1 model overview and assessment of the hydrodynamics. J Mar Syst 57(1–2):167–188. doi: 10.1016/j.jmarsys.2005.04.008 CrossRefGoogle Scholar
  24. Horsburgh KJ, Wilson C (2007) Tide-surge interaction and its role in the distribution of surge residuals in the North Sea. J Geophys Res 112(C8):n/a–n/a. doi: 10.1029/2006JC004033
  25. Hughes CW, Bingham RJ (2008) An oceanographer’s guide to GOCE and the geoid. Ocean Sci 4:15–29CrossRefGoogle Scholar
  26. Huthnance JM, Holt JT, Wakelin SL (2009) Deep ocean exchange with west-European shelf seas. Ocean Sci 6:1061–1092Google Scholar
  27. Hwang C, Hsu HY (2008) Shallow-water gravity anomalies from satellite altimetry: case studies in the east china sea and Taiwan strait. J Chin Inst Eng 31(5):841–851. doi: 10.1080/02533839.2008.9671437 CrossRefGoogle Scholar
  28. Hwang C, Guo J, Deng X, Hsu HY, Liu Y (2006) Coastal gravity anomalies from retracked geosat/GM altimetry: improvement, limitation and the role of airborne gravity data. J Geod 80:204–216. doi: 10.1007/s00190-006-0052-x CrossRefGoogle Scholar
  29. Ihde J, Augath W (2002) The European vertical reference system (EVRS), its relation to a world height system and to the ITRS. Vistas for geodesy in the new millennium, pp 78–83Google Scholar
  30. Iliffe JC, Ziebart MK, Turner JF (2007) A new methodology for incorporating tide gauge data in sea surface topography models. Mar Geod 30(4):271–296. doi: 10.1080/01490410701568384 CrossRefGoogle Scholar
  31. International Hydrographic Organization (1994) Hydrographic dictionary part I, vol I, English. http://www.iho.int/iho_pubs/standard/S-32/S-32-eng.pdf, special publication no. 32, 5th edn
  32. International Hydrographic Organization (2011) Resolutions of the International Hydrographic Organization. www.iho.int, publication M-3, 2nd edn, 2010, updated to August 2011
  33. Klees R, Prutkin I, Tenzer R, Wittwer T (2007) Development of a technique for combining parameters of the Earth’s gravity field for quasi-geoid determination on the territory of the Federal Republic of Germany and Europe. Technical report, Delft University of TechnologyGoogle Scholar
  34. Klees R, Tenzer R, Prutkin I, Wittwer T (2008) A data-driven approach to local gravity field modelling using spherical radial basis functions. J Geod 82:457–471. doi: 10.1007/s00190-007-0196-3 CrossRefGoogle Scholar
  35. Kusche J (2003) A Monte-Carlo technique for weight estimation in satellite geodesy. J Geod 76:641–652. doi: 10.1007/s00190-002-0302-5 CrossRefGoogle Scholar
  36. Leendertse JJ (1967) Aspects of a computational model for long-period water-wave propagation. Rand Corporation for the United States Air Force Project Rand, CaliforniaGoogle Scholar
  37. Myers EP, Wong A, Hess KW, White SA, Spargo E, Feyen J, Yang Z, Richardson P, Auer C, Sellars J, Woolard J, Roman D, Gill S, Zervas C, Tronvig K (2005) Development of a national VDatum, and its application to sea level rise in North Carolina. Downloaded from http://www.thsoa.org/hy05/09_3.pdf, technical paper presented at the U.S. Hydro 2005 conference
  38. Parker B, Milbert D, Hess K, Gill S (2003) National vdatum—the implementation of a national vertical datum transformation database. U.S. Hydrographic conference 2003 proceedings/technical papersGoogle Scholar
  39. Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the earth gravitational model 2008 (egm2008). J Geophys Res 117(B4):n/a–n/a. doi: 10.1029/2011JB008916
  40. Pineau-Guillou L, Dorst LL (2011) Creation of vertical reference surfaces at sea using altimetry and GPS. Ann Hydrograph 8(777):10-1–10-7. http://www.shom.fr/fr_prod_annales/777/777-ZTL.pdf Google Scholar
  41. Prandle D (1978) Residual flows and elevations in the Southern North Sea. Proc R Soc Lond A 359:189–228. doi: 10.1098/rspa.1978.0039 CrossRefGoogle Scholar
  42. Prandle D, Wolf J (1978) The interaction of surge and tide in the North Sea and River Thames. Geophys J Int 55:203–216. doi: 10.1111/j.1365-246X.1978.tb04758.x CrossRefGoogle Scholar
  43. Ray RD (1999) A global ocean tide model from TOPEX/POSEIDON altimetry: GOT99.2. Technical report, Goddard Space Flight Center, Greenbelt, NASA Tech. Memo 209478, 58 ppGoogle Scholar
  44. Sandwell DT, Smith WHF (2009) Global marine gravity from retracked Geosat and ERS-1 altimetry: ridge segmentation versus spreading rate. J Geophys Res 114(B1):n/a–n/a. doi: 10.1029/2008JB006008.
  45. Schäfer U, Liebsch G, Schirmer U, Ihde J, Olesen AV, Skourup H, Forsberg R, Pflug H, Neumeyer J (2008) Improving gravity field modelling in the German-Danish border region by combining airborne, satellite and terrestrial gravity data. In: IAG International symposium on gravity, geoid and earth observation (Chania, Greece 2008)Google Scholar
  46. Scharroo R (2013) RADS version 3.1: user manual and format specification. Delft University of technology (Accessed June 2013). http://rads.tudelft.nl/rads/radsmanual.pdf
  47. Slobbe DC, Klees R (2014) The impact of the dynamic sea surface topography on the quasi-geoid in shallow coastal waters. J Geod 88:241–261. doi: 10.1007/s00190-013-0679-3 Google Scholar
  48. Slobbe DC, Verlaan M, Klees R, Gerritsen H (2013a) Obtaining instantaneous water levels relative to a geoid with a 2D storm surge model. Cont Shelf Res 52:172–189. doi: 10.1016/j.csr.2012.10.002 CrossRefGoogle Scholar
  49. Slobbe DC, Klees R, Verlaan M, Dorst LL, Gerritsen H (2013b) Lowest astronomical tide in the North Sea derived from a vertically referenced shallow water model, and an assessment of its suggested sense of safety. Mar Geod 36(1):31–71. doi: 10.1080/01490419.2012.743493 Google Scholar
  50. Stelling GS (1984) On the construction of computational methods for shallow water flow problems. PhD thesis, Delft University of Technology, Delft, Rijkswaterstaat communications 35Google Scholar
  51. Tenzer R, Prutkin I, Klees R (2012) A comparison of different integral-equation-based approaches for local gravity field modelling: case study for the Canadian rocky mountains. In: Kenyon S, Pacino MC, Marti U (eds) Geodesy for planet Earth, international association of geodesy symposia, vol 136, Springer, Berlin Heidelberg, pp 381–388. doi: 10.1007/978-3-642-20338-1_46
  52. Turner JF, Iliffe JC, Ziebart MK, Wilson C, Horsburgh KJ (2010) Interpolation of tidal levels in the coastal zone for the creation of a hydrographic datum. J Atmos Ocean Tech 27:605–613. doi: 10.1175/2009JTECHO645.1 CrossRefGoogle Scholar
  53. Verlaan M, Zijderveld A, de Vries H, Kroos J (2005) Operational storm surge forecasting in the Netherlands: developments in the last decade. Philos Trans R Soc Math Phys Eng Sci 363:1441–1453. doi: 10.1098/rsta.2005.1578 CrossRefGoogle Scholar
  54. Wittwer TF (2009) Regional gravity field modelling with radial basis functions. PhD thesis, Delft University of Technology, Nederlandse Commissie voor Geodesie Publikatie 72Google Scholar
  55. Wolf J (1981) Surge-tide interaction in the North Sea and River Thames. In: Peregrine DH (ed) Floods due to high winds and tides. Elsevier, New York, pp 75–94Google Scholar
  56. Ziebart MK, Iliffe JC, Turner JF, Oliveira J, Adams R (2007) VORF—The UK vertical offshore reference frame: enabling real-time hydrographic surveying. In: Proceedings of ION GNSS2007, Fort Worth, Texas, USAGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Delft University of TechnologyDelftThe Netherlands
  2. 2.Daniel Guggenheim School of Aerospace EngineeringGeorgia Institute of TechnologyAtlantaUSA

Personalised recommendations