The quasigeoid modelling in New Zealand using the boundary element method

Open access

The quasigeoid modelling in New Zealand using the boundary element method

We compile a quasigeoid model at the study area of New Zealand using the boundary element method (BEM). The direct BEM formulation for the Laplace equation is applied to obtain a numerical solution to the linearized fixed gravimetric boundaryvalue problem in points at the Earth's surface. The numerical scheme uses the collocation method with linear basis functions. It involves a discretisation of the Earth's surface which is considered as a fixed boundary. The surface gravity disturbances represent the oblique derivative boundary condition. The geocentric positions of the collocation points are determined combining the digital elevation data and the a priori quasigeoid model (onshore) and the mean sea surface topography (offshore). In our numerical realization, we use the global elevation data from SRTM30PLUS_V5.0, the detailed DTM of New Zealand, the EGM2008 quasigeoid heights, and the mean sea surface topography from the DNSC08 marine database. The gravity disturbances are computed using two heterogeneous gravity data sets: the altimetry-derived gravity anomalies from the DNSC08 gravity database (offshore) and the observed ground gravity anomalies from the GNS Science gravity database (onshore). The transformation of gravity anomalies to gravity disturbances is realized using the quasigeoid heights calculated from the EGM2008 global geopotential model. The new experimental quasigeoid model NZQM2010 is compiled at the study area of New Zealand bounded by the parallels of 34 and 47.5 arc-deg southern latitude and the meridians of 166 and 179 arc-deg eastern longitude. The least-squares analysis is applied to combine the gravimetric solution with GPS-levelling data using a 7-parameter model. NZQM2010 is validated using GPS-levelling data and compared with the existing regional and global quasigeoid models NZGeoid2009 and EGM2008. The validation at GPS-levelling testing network in New Zealand shows a similar STD fit of all investigated quasigeoid models with the geometric height anomalies computed from GPS-levelling data between 7 cm (NZGeoid2009) and 8 cm (NZQM2010 and EGM2008). The inaccuracies of the compiled quasigeoid models in New Zealand are expected to be mainly due to the presence of large systematic errors and inconsistencies of levelling networks throughout the country. Another source of the inaccuracy is an insufficient coverage and a low accuracy of gravity data especially over large parts of the South Island.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • Amos M. J. Featherstone W. E. 2009: Unification of New Zealand's local vertical datums: iterative gravimetric quasigeoid computations. J. Geod. 83 1 57-68.

  • Andersen O. B. Knudsen P. 2009: DNSC08 mean sea surface and mean dynamic topography models. J. Geophys. Res. 114 C1100.

  • Andersen O. B. Knudsen P. Berry P. 2009: The DNSC08GRA global marine gravity field from double retracked satellite altimetry. J. Geod. 84 191-199.

  • Aoyama Y. Nakano J. 1999: RS/6000 SP: Practical MPI Programming. IBM Poughkeepsie New York.

  • Backus G. E. 1968: Application of a non-linear boundary-value problem for Laplace's equation to gravity and geomagnetic intensity surveys. Q. J. Mech. Appl. Math. 2 195-221.

  • Becker J. J. Sandwell D. T. Smith W. H. F. Braud J. Binder B. Depner J. Fabre D. Factor J. Ingalls S. Kim S.-H. Ladner R. Marks K. Nelson S. Pharaoh A. Sharman G. Trimmer R. vonRosenburg J. Wallace G. Weatherall P. 2009: Global Bathymetry and Elevation Data at 30 Arc Seconds Resolution: SRTM30_PLUS revised for Marine Geodesy.

  • Bjerhammar A. Svensson L. 1983: On the geodetic boundary-value problem for a fixed boundary surface - satellite approach. Bull. Géod. 57 382-393.

  • Blick G. Crook C. Grant D. 2005: Implementation of a semi-dynamic datum for New Zealand. In: Sansò F. (Ed.) A Window on the Future of Geodesy. Springer Berlin Germany 38-43.

  • Brebbia C. A. Telles J. C. F. Wrobel L. C. 1984: Boundary Element Techniques Theory and Applications in Engineering. Springer-Verlag New York.

  • Burša M. Kouba J. Kumar M. Müller A. Raděj K. True S. A. Vatrt V. Vojtíšková M. 1999: Geoidal geopotential and world height system. Stud. Geoph. Geod. 43 327-337.

  • Burša M. Kouba J. Müller A. Raděj K. True S. A. Vatrt V. Vojtíšková M. 2001: Determination of geopotential differences between local vertical datums and realization of a World Height System. Stud. Geoph. Geod. 45 127-132.

  • Burša M. Kenyon S. Kouba J. Raděj K. Vatrt V. Vojtíšková M. Šimek J. 2002: World height system specified by geopotential at tide gauge stations. IAG Symposium Vertical reference system. Cartagena February 20-23 2001 Colombia Proceedings Springer Verlag 291-296.

  • Classens S. Hirt C. Featherstone W. E. Kirby J. F. 2009: Computation of a new gravimetric quasigeoid model for New Zealand. Technical report prepared for Land Information New Zealand by Western Australia Centre for Geodesy.

  • Čunderlík R. Mikula K. 2009: Direct BEM for high-resolution global gravity field modelling. Stud. Geoph. Geod. 54 219-238.

  • Čunderlík R. Mikula K. Mojzeš M. 2008: Numerical solution of the linearized fixed gravimetric boundary-value problem. J. Geod. 82 15-29.

  • Fašková Z. 2008: Numerical Methods for Solving Geodetic Boundary Value Problems PhD Thesis Svf STU Bratislava Slovakia.

  • Fašková Z. Čunderlík R. Mikula K. 2009: Finite element method for solving geodetic boundary value problems. J. Geod. 84 135-144.

  • Grafarend E. W. 1989: The geoid and the gravimetric boundary-value problem. Rep. 18 Dept. Geod. The Royal Institute of Technology Stockholm.

  • Heiskanen W. A. Moritz H. 1967: Physical Geodesy. W. H. Freeman and Co. New York London and San Francisco.

  • Klees R. 1992: Loesung des fixen geodaetischen Randwertproblems mit Hilfe der Randelementmethode. DGK Reihe C Nr. 382 Muenchen.

  • Klees R. 1998: Topics on Boundary Element Methods. In: Sanso F. Rummel R. (Eds.) geodetic boundary value problems in view of the one centimeter geoid. Lecture Notes in Earth Sciences 65 Springer 482-531.

  • Klees R. Van Gelderen M. Lage C. Schwab C. 2001: Fast numerical solution of the linearized Molodensky problem. J. Geod. 75 349-362.

  • Koch K. R. Pope A. J. 1972: Uniqueness and existence for the geodetic boundary value problem using the known surface of the earth. Bull. Géod. 46 467-476.

  • Kotsakis C. Sideris M. G. 1999: On the adjustment of combined GPS/levelling/geoid networks. J. Geod. 73 412-421.

  • Lehmann R. 1997: Studies on the Use of Boundary Element Methods in Physical Geodesy. Publ. German Geodetic Commission Series A No. 113 Munich.

  • Lehmann R. Klees R. 1996: Parallel Setup of Galerkin Equation System for a Geodetic Boundary Value Problem. In: Hackbusch W. Wittum G. (Eds.): "Boundary Elements: Implementation and Analysis of Advanced Algorithms" Notes on Numerical Fluid Mechanics 54 Vieweg Verlag Braunschweig.

  • Lemoine F. G. Kenyon S. C. Factor J. K. Trimmer R. G. Pavlis N. K. Chinn D. S. Cox C. M. Klosko S. M. Luthcke S. B. Torrence M. H. Wang Y. M. Williamson R. G. Pavlis E. C. Rapp R. H. Olson T. R. 1998: EGM-96 - The Development of the NASA GSFC and NIMA Joint Geopotential Model. NASA Technical Report TP-1998-206861.

  • Mayer-Gürr T. 2007: ITG-Grace03s: The latest GRACE gravity field solution computed in Bonn. Presentation at GSTM+SPP 15-17 Oct 2007 Potsdam.

  • Pavlis N. K. Holmes S. A. Kenyon S. C. Factor J. K. 2008: An Earth Gravitational Model to Degree 2160: EGM2008 presented at the 2008 General Assembly of EGU Vienna Austria April 13-18 2008.

  • Rapp R. H. Pavlis N. K. 1990: The development and analysis of geopotential coefficient models to spherical harmonic degree 360. J. Geoph. Res. 95 B13 21885-21911.

  • Sacerdote F. Sansó F. 1989: On the analysis of the fixed-boundary gravimetric boundary-value problem. In: Sacerdote F. Sansó F. (Eds.) Proc. 2nd Hotine-Marussi Symp. Math. Geod. Pisa 1989 Politecnico di Milano 507-516.

  • Schatz A. H. Thomée V. Wendland W. L. 1990: Mathematical Theory of Finite and Boundary Element Methods. Birkhäuser Verlag Basel Boston and Berlin.

Search
Journal information
Impact Factor


CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.312
Source Normalized Impact per Paper (SNIP) 2018: 0.615

Cited By
Metrics
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 186 119 2
PDF Downloads 76 58 3