One goal of modern geodesy is the global unification of vertical datums so that height data from them can be properly integrated. This thesis studies the unification of the 13 disparate levelling- and tide-gauge-based vertical datums in New Zealand (NZ). It proposes a new NZ-wide single vertical datum based on a gravimetric quasigeoid model to unify the existing local vertical datums. This will also include methods to transform height data in terms of the existing datums to the new datum and vice versa. After defining and comparing the main types of height system and vertical datum used around to world, the system of heights used in NZ was shown to be normal-orthometric. Consequently, datum unification was achieved using a quasigeoid model, as opposed to a geoid model. The quasigeoid was computed by combining the GRACE-based GGM02 and EGM96 global geopotential models with land gravity data (40,737 observations) and a 56-m resolution digital elevation model (DEM). Marine gravity data came from a least-squares collocation combination of 1,300,266 crossover-adjusted ship track observations and gravity anomalies derived from multi-mission satellite altimetry. / To ensure that the best quasigeoid was computed for the NZ datasets, a number of computation processes were compared and contrasted. The Hammer chart, fast Fourier transform (FFT) and prism integration methods of computing terrain corrections (TCs) were compared. This showed that the prism integration TC is the most realistic in NZ. The mean Helmert gravity anomalies, required for numerical integration of Stokes’s formula, were computed via refined Bouguer anomalies with the prism TCs, and reconstruction with heights from the DEM used to ‘reconstruct’ more representative mean anomalies. In addition, five deterministic modifications to Stokes’s formula were compared. There was little difference between three of them, so the Featherstone et al. (1998) modification ( 0 y = 1.5°, M = 40) was chosen because it is theoretically better than its predecessors. The global geopotential, gravimetric geoid, sea surface topography and geodetic boundary-value problem approaches to vertical datum unification were then contrasted. As none was likely to be effective in NZ, a new iterative quasigeoid approach was adopted. This procedure computes an initial quasigeoid from existing data on the various local vertical datums to estimate the vertical datum offsets from co-located GPS-levelling data. These offsets were then subsequently applied to the gravity observations by way of additional reductions to the initially computed quasigeoid to reduce gravity anomaly biases caused by the vertically offset datums. These adjusted gravity anomalies were then used to compute a new quasigeoid model, and the process repeated until the computed offsets between the local vertical datums (or equivalently two quasigeoid solutions) converged, which took only two iterations. / The computed offsets were then compared with spirit-levelled height differences among adjoining datums, where these were available, giving an average agreement of 7 cm. Since the local vertical datums are effectively unified, the new national vertical datum for NZ will comprise the iteratively computed gravimetric quasigeoid model, accompanied by local vertical datums. This approach is implemented to give a new national vertical datum for NZ. When used with the appropriate offset, this enables the transformation of heights in terms of the national vertical datum to the 13 precise-levelling datums and the ellipsoidal national geodetic datum, NZ Geodetic Datum 2000.

This study is devoted to the determination of a high resolution gravimetric geoid model for Uganda based on the optimal combination of terrestrial and satellite gravity anomalies using the method of Least Squares Modification of Stokes’ formula with additive corrections. Specifically the study investigates the current status of the existing Uganda Vertical Network relative to the requirements of a modern height datum and includes a detailed evaluation and validation of terrestrial gravity data, several digital elevation models and some recent global geopotential models. Finally a new height datum based on a gravimetric quasigeoid model and Global Navigation Satellite Systems (GNSS)/levelling is proposed. In this thesis, the Uganda Gravimetric Geoid Model 2014 (UGG2014) is computed from several datasets which, include 7839 terrestrial gravity data points from the International Gravimetric Bureau, the 3 arc second Shuttle Radar Topography Mission digital elevation model and a recent Gravity field and steady-state Ocean Circulation Explorer-only global geopotential model. To compensate for the missing gravity data in the target area, the surface gravity anomalies extracted from the World Gravity Map 2012 were used. Outliers in the terrestrial gravity data were detected using the cross-validation technique which, also estimated the accuracy of the remaining terrestrial gravity data as 9 mGal. Based on 12 GNSS/levelling data points distributed over Uganda, the root mean square fit of UGG2014 before and after the 4-parameter fit is 16 cm and 9 cm, respectively. The study has revealed that the heights of the Uganda Vertical Network are normal-orthometric heights for which the quasigeoid is the closest approximation to the zero reference surface. Consequently, the Uganda Gravimetric Quasigeoid Model 2014 (UGQ2014) was derived from the UGG2014 with the quasigeoid-geoid separation computed from the Earth Gravitational Model 2008 complete to degree/order 2160 of spherical harmonics. The root mean square fit of UGQ2014 versus GNSS/levelling is 15 cm and 8 cm before and after the 4-parameter fit, respectively, which shows that the quasigeoid model fits GNSS/levelling better than the geoid model. Thus a new height datum based on UGQ2014 and GNSS/levelling was determined as a practical solution to the determination of heights directly from GNSS. Evaluated with 4 independent GNSS/levelling points, the root mean square fit of the new height datum is 5 cm better than using the quasigeoid model alone. With an average parts-per-million of 29 in the relative test, the new height datum satisfies the precision and accuracy requirements of third order precise levelling. Overall, the results show that UGG2014 and UGQ2014 agree considerably better with GNSS/levelling than any other recent regional/global gravimetric geoid models. Therefore, both gravimetric solutions are a significant step forward in the modelling of a “1-cm geoid” over Uganda given the poor quality and quantity of the terrestrial gravity data used for computation. / <p>QC 20150831</p>