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>

In order to be able to use the operational Moldavian GNSS Positioning System MOLDPOS efficiently for the determination of normal heights in surveying engineering, e.g. during the construction of a road, an accurate quasigeoid model is needed. The main goal of this thesis is to present a new gravimetric quasigeoid model for Moldova (Mold2012), which has been determined by applying the Least Squares Modification of Stokes’ formula with Additive corrections (LSMSA), also called the KTH method. Due to limited coverage of gravity data, the integration area is often limited to a small spherical cap around the computation point, which leads to a truncation error for geoid height. Molodensky et al. (1962) showed that the truncation error can be reduced by the modification of Stokes’ formula, where the measured gravity data are combined with the low-frequency component of the geoid from a Global Gravitational Model (GGM). The LSMSA technique combines the GGM and the terrestrial data in an optimum way. In order to find the most suitable modification approach or cap size it is necessary to compare the gravimetric height anomalies with the GPS/levelling derived height anomalies, and for this purpose we use a GPS/levelling dataset that consists of 1042 points with geodetic coordinates in the MOLDREF99 reference system and normal heights at the same points given in the height system Baltic 77. The magnitude of the additive corrections varies within an interval from -0.6 cm to -4.3 cm over the area of Moldova. The quasigeoid model which results from combining the ITG-Grace02s solution (with n = M = 170, ψ0 = 3° and σΔg = 10 mGal) and the solution obtained from the modified Stokes’ formula together with the additive correction gives the best fit for the GPS/levelling data with a standard deviation (STD) of ±7.8 cm. The evaluation of the computed gravimetric quasigeoid is performed by comparing the gravimetric height anomalies with the GPS/levelling derived height anomalies for 1042 points. However, the above heterogeneous data include outliers, and in order to find and eliminate these, a corrector surface model is used. This surface provides a connection to the local vertical when the GNSS technique is used. After the elimination of the suspicious outliers (170 points) according to a 2-RMS test, a new corrective surface was computed based on the remaining 872 GPS/levelling points, and the STD of residuals became ±4.9 cm. The STD value for the residuals according to the order of the levelling network for the Mold2012 fitted to the local vertical datum is 3.8 cm for the I-order, 4.3 cm for the II-order, 4.5 cm for the III-order and 5.0 cm for the IV-order levelling network. But the STD of the residuals for the 18 control points indicates a better result where the STD is 3.6 cm and RMS is 3.9 cm and the min and max value of residuals is -5.3 cm and 9.0 cm, respectively. As the STD of the differences in height anomaly are not just the standard error of the height anomalies (quasigeoid model), but it contains also the standard errors of GPS heights and of normal heights. Assuming that the latter STDs are 3 cm and 3.5 cm, respectively, the STD of Mold2012 is estimated to 1.7 cm. / <p>QC 20121127</p>

This study work deals with the determination of the gravimetric geoid model for Kazakhstan by using the KTH-method. A number of data sets were collected for this work, such as the gravity anomalies, high-resolution Digital Elevation Model (DEM), Global Geopotential Models (GGMs) and GPS/Levelling data. These data has been optimally combined through the KTH approach, developed at the Royal Institute of Technology (KTH) in Stockholm. According to this stochastic method, Stokes’ formula is being used with the original surface gravity anomaly, which combine with a GGM yields approximate geoid heights. The corrected geoid heights are then obtained by adding the topographic, downward continuation, atmospheric and ellipsoidal corrections to the approximate geoid heights. To compute the geoid model for Kazakhstan as accurately as possible with available data set different numerical tests have been performed: Choice of the best fit geopotential model in the computation area Investigations for the best choice of the initial condition for determination of the least-squares parameters Selection of the best parametric model for reducing the effect of the systematic error and data inconsistencies between computed geoid heights and GPS/Levelling heights.  Finally, 5'x5' Kazakh gravimetric geoid (KazGM2010) has been modelled.