Abstract
The NZGeoid2009 is currently the official quasigeoid model of New Zealand. It was computed to unify 13 separate local vertical datums (LVDs) in New Zealand. This study intends primarily to compute an improved gravimetric quasigeoid model in New Zealand. The computation of a gravimetric quasigeoid model depends on four input data sets namely the gravity data, DTM, GGM and GPS/levelling data. The accuracy of the input data sets plays an important role in the quality of the final gravimetric solution.
Therefore, the second objective has been devoted to analysing the levelling networks and investigating recent global geopotential models (GGMs). The joint adjustment approach is used to refine and readjust the levelling networks as well as for the unification of 13 separate local vertical datums (LVDs) in the North and South islands. The unification of LVDs has been done in two steps. The levelling networks in the North and South islands are jointly adjusted at first by fixing two tide gauges in Dunedin and Wellington. The gravity anomalies along levelling lines are generated from EGM2008. The cumulative normal to normal-orthometric height correction is computed from levelling and gravity anomaly data. The average offsets of these fixed points are then estimated relative to the World Height System (WHS). The average offset at Wellington and Dunedin are found to be 10.6 and 27.5 cm, respectively. These offsets are added to the newly derived orthometric and normal heights at the levelling networks for each island. The investigation of the recently released GGMs is conducted for a number of 11 GGMs (9 satellite-only and 2 combined models) by testing them using the newly adjusted levelling heights combined to GPS points. Among all tested satellite-only models, the GRACE/GOCE model GOCO-02S has the best RMS fit with GPS/levelling data of 56 cm when using the maximum degree/order 250 of spherical harmonic coefficients.
Three methods are reviewed for the gravimetric geoid/quasigeoid modelling and therefore three regional corresponding models have been computed, namely NZGM2010, NZQM2010 and OTG12. NZGM2010 geoid model is compiled using the method of least-squares modification of Stokes formula with additive corrections (widely known as the KTH method). The least-squares modified Stokes formula combines the terrestrial gravity and GGM in the context of the KTH method to provide an approximate estimator of the gravimetric solution. Hence, four additive corrections that account for the effects of topography, atmosphere, ellipsoidal approximation and downward continuation of the gravity data are applied to the approximate gravimetric solution. NZQM2010 quasigeoid model is computed using the boundary element method (BEM) based on the collocation and linear basis functions. The Earth's surface is discretised and considered as a constant boundary. The gravity disturbances derived from gravity anomaly data represent the oblique derivation boundary.
OTG12 quasigeoid model is computed using a new methodology based on the discretized-integral-equation (DIE) approach. The new method is successfully analysed and tested. The computation of OTG12 has been implemented in two steps. Step 1 involves testing the performance of DIE approaches when the gravity data is corrected for the residual terrain model (RTM) and reference gravity field. Four DIE approaches, namely the Poisson integral, Green integral, Point mass, and Radial multipole are tested and discretised at the locations of the gravity data at a constant depth below the Bjerhammar sphere to estimate the optimal depth. The optimal depth is based on the minimum RMS of residual between the observed and predicted gravity data. The investigation of DIE approaches revealed a good performance of Green's integral approach.
Step 2 involves the computation of the quasigeoid model (OTG12) using the remove-compute-restore (RCR) computation procedure. The near-zone contribution is computed using Green integral approach based on results from Step 1. The far-zone contribution is computed using the Earth Gravitational Model 2008 (EGM2008) coefficients from degree 251 up to degree 2160 of spherical harmonics. The reference gravity field is obtained using GOCO-02S global gravitational model coefficients complete to degree 250 of spherical harmonics. The comparison of OTG12 with the newly adjusted GPS-levelling data revealed that three gravimetric solutions (OTG12, NZGM2010 and NZGeoid2009) have similar accuracy (12 cm), and NZQM2010 (15cm) after applying the 3-parameter correction model.
Finally, the relative offset between the datums at Dunedin and Wellington tide gauges is extensively investigated by comparing the newly adjusted GPS-levelling data with the regional gravimetric solutions, EGM08 and the mean dynamic topography (MDT) models. Analysis reveals an existence of systematic discrepancies that can be attributed to the systematic errors within the gravimetric solutions.