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Few studies have used crustal displacements sensed by the Global Positioning System (GPS) to assess the terrestrial water storage (TWS), which causes loadings. Furthermore, no study has investigated the feasibility of using GPS to image TWS over South America (SA), which contains the world’s driest (Atacama Desert) and wettest (Amazon Basin) regions. This work presents a resolution analysis of an inversion of GPS data over SA. Firstly, synthetic experiments were used to verify the spatial resolutions of GPS-imaged TWS and examine the resolving accuracies of the inversion based on checkerboard tests and closed-loop simulations using “TWS” from the Noah-driven Global Land Data Assimilation System (GLDAS-Noah). Secondly, observed radial displacements were used to image daily TWS. The inverted results of TWS at a resolution of 300 km present negligible errors, as shown by synthetic experiments involving 397 GPS stations across SA. However, as a result of missing daily observations, the actual daily number of available stations varied from 60–353, and only 6% of the daily GPS-imaged TWS agree with GLDAS-Noah TWS, which indicates a root-mean-squared error (RMSE) of less than 100 kg/m 2 . Nevertheless, the inversion shows agreement that is better than 0.50 and 61.58 kg/m 2 in terms of the correlation coefficient (Pearson) and RMSE, respectively, albeit at each GPS site.

We derive the expressions for computing the ice density contrast stripping corrections to the topography corrected gravity field quantities by means of the spherical harmonics. The expressions in the spectral representation utilize two types of the spherical functions, namely the spherical height functions and the newly introduced lower-bound ice functions. The spherical height functions describe the global geometry of the upper topographic bound. The spherical lower-bound ice functions combined with the spherical height functions describe the global thickness of the continental ice sheet. The newly derived formulas are utilized in the forward modelling of the gravitational field quantities generated by the ice density contrast. The 30×30 arc-sec global elevation data from GTOPO30 are used to generate the global elevation model (GEM) coefficients. The spatially averaged global elevation data from GTOPO30 and the 2×2 arc-deg ice-thickness data from the CRUST 2.0 global crustal model are used to generate the global lower-bound ice model (GIM) coefficients. The mean value of the ice density contrast 1753 kg/m 3 (i.e., difference of the reference constant density of the continental upper crust 2670 kg/m 3 and the density of glacial ice 917 kg/m 3 ) is adopted. The numerical examples are given for the gravitational potential and attraction generated by the ice density contrast computed globally with a low-degree spectral resolution complete to degree and order 90 of the GEM and GIM coefficients.

The geopotential-value approach is utilized in this study to estimate the average offsets of local vertical datums (LVDs) in New Zealand realized in the system of normal-orthometric heights. The LVD offsets are taken relative to the World Height System (WHS). We adopt the geoidal geopotential value W 0 =62,636,856 m 2 s −2 for a definition of WHS. The conversion of heights between different permanent tide systems is taken into consideration. The geopotential-value approach utilizes Molodensky's theory of the normal heights. The normal-orthometric heights at global positioning system (GPS)-leveling points are thus first converted to the normal heights. The normal to normal-orthometric height correction is computed and applied along the leveling lines using the leveling data, and the gravity disturbances are computed approximately from the EGM08 global geopotential model. The numerical study is conducted for 18 LVDs in the North and South Islands of New Zealand. The LVD offsets are estimated from EGM08 to GPS-leveling data. The estimated average LVD offsets vary between 1 cm (Wellington 1953 LVD) and 37 cm (One Tree Point 1964 LVD).

Validation of recent GOCE/GRACE geopotential models over Khartoum state - SudanThis paper evaluates a number of latest releases of GOCE/GRACE global geopotential models (GGMs) using the GPS-levelling geometric geoid heights, terrestrial gravity data and existing local gravimetric models. We investigate each global model at every 5 degree of spherical harmonics. Our analysis shows that the satellite-only models derived by space-wise and time-wise approaches (SPW_R1, SPW_R2 TIM_R1 and TIM_R2), GOCO01S together with EGM08 (combined model) are very distinct and consistent to the local data, which guarantees one of them to be selected as the best of candidate models and then to be utilized in our further geoid studies. One of Satellite-only models will be employed for acquiring the long wavelength geoid component which is one of major steps in the geoid determination. EGM08 will be used to compensate and restore the missing gravity data points in the un-surveyed parts within the target area. We expect further improvements in geoid studies in Sudan due to the improved medium wavelength part of the gravity field from GOCE mission.

We use Fast Fourier Transform (FFT) and Least-squares modification (LSM) of Stokes formula to compute the approximate geoid over Khartoum State in Sudan. The two methods (FFT and LSM) have been utilised to test their efficiency with respect to EGM08 and the local GPS-levelling data. The FFT method has many advantages, it is fast and it reduces the computational complexity. The modification of Stokes formula is widely used in geoid modelling, however, its implementation based on point-wise summation requires a considerable amount of time. In FFT we combine the terrestrial gravity data and the global geopotential model (GGM) by means of a remove-compute-restore procedure and we successfully apply the modification of the Stokes formula in the least-squares sense. FFT and LSM approximate geoid solutions are evaluated against EGM2008 and the GPS-levelling data. The analysis of the undulation differences shows that the LSM solution is more compatible with EGM08 and GPS-levelling data. The discrepancies of the differences are removed using a 4-parameter model, the standard deviation (STD) of the undulation differences of LSM decreased from 0.41 m to 0.37 m and from 0.48 m to 0.39 m for FFT solution. There is no significant impact to the LSM geoid when adding the additive corrections, while the FFT geoid solution is slightly improved when terrain correction is applied.

A gravimetric geoid model (SAGEO13) is computed for the Kingdom of Saudi Arabia using a rigorous stochastic computational method. The computational methodology is based on a combination of least-squares (LS) modification of Stokes’ formula and the additive corrections for topographic, ellipsoidal, atmospheric, and downward continuation effects on the geoid solution. In this study, we used terrestrial gravity data, a digital elevation model (SRTM3), and seven global geopotential models (GGMs) to compute a new geoid model for Saudi Arabia. The least-squares coefficients are derived based on the optimisation of the input modification parameters. The gravimetric solution and its additive corrections are computed based on the optimum LS coefficients. Compared to GPS-levelling data, SAGEO13 shows a fit of 18 cm (RMS) after using a 4-parameter fitting model.

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