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 NZQM 2010 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. NZQM 2010 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 GPSlevelling 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.