Currently, various satellite processing centers produce extensive data, with different solutions of the same field being available. For instance, the Gravity Recovery and Climate Experiment (GRACE) has been monitoring terrestrial water storage (TWS) since April 2002, while the Center for Space Research (CSR), the Jet Propulsion Laboratory (JPL), the GeoForschungsZentrum (GFZ), and the Groupe de Recherche de Géodésie Spatiale (GRGS) provide individual monthly solutions in the form of Stokes coefficients. The inverted TWS maps (or the regionally averaged values) from these coefficients are being used in many applications; however, as no ground truth data exist, the uncertainties are unknown. Consequently, the purpose of this work is to assess the quality of each processing center by estimating their uncertainties using a generalized formulation of the three-cornered hat (TCH) method. Overall, the TCH results for the study period of August 2002 to June 2014 indicate that at a global scale, the CSR, GFZ, GRGS, and JPL presented uncertainties of 9.4, 13.7, 14.8, and 13.2 mm, respectively. At a basin scale, the overall good performance of the CSR was observed at 91 river basins. The TCH-based results were confirmed by a comparison with an ensemble solution from the four GRACE processing centers.

The selection of a global geopotential model (GGM) for modeling the long-wavelength for geoid computation is imperative not only because of the plethora of GGMs available but more importantly because it influences the accuracy of a geoid model. In this study, we propose using the Gaussian averaging function for selecting an optimal GGM and degree and order (d/o) for the remove-compute-restore technique as a replacement for the direct comparison of terrestrial gravity anomalies and GGM anomalies, because ground data and GGM have different frequencies. Overall, EGM2008 performed better than all the tested GGMs and at an optimal d/o of 222. We verified the results by computing geoid models using Heck and Grüninger’s modification and validated them against GPS/trigonometric data. The results of the validation were consistent with those of the averaging process with EGM2008 giving the smallest standard deviation of 0.457 m at d/o 222, resulting in an 8% improvement over the previous geoid model. In addition, this geoid model, the Ghanaian Gravimetric Geoid 2017 (GGG 2017) may be used to replace second-order class II leveling, with an expected error of 6.8 mm/km for baselines ranging from 20 to 225 km.

This paper analyzes errors in satellite gravity and GPS/trigonometric benchmarks (BMs) in relation to defining the Ghanaian Vertical Datum (GhVD). Results indicate that synthesized gravity introduce approximately 5 mm of error to corrected heights. However, large errors in BMs render them unsuitable for applications, including properly defining the GhVD. Overall, normal-orthometric corrections were of the order of a few millimetres, with comparatively larger Helmert orthometric and normal corrections. Accordingly, the most suitable heights for the GhVD are the normal-orthometric heights, with the geopotential of the Helmert orthometric heights, $62636861.534\pm 2.27$ m ${}^2$ s ${}^{-2}$, suggested as the potential of the GhVD.

This study investigates the uncertainties of digital elevation models (DEMs) using the triple collocation (TC) method. DEMs from satellite missions are important for many geoscience disciplines and for economic benefits and are freely available. Validating DEMs is necessary to select an appropriate model for a given region and application. Provided certain assumptions about the error structure of any three data sets – measuring the same phenomenon – can be made, the TC approach can be used to provide an unbiased and scaled estimate of the error variances of the data sets, without requiring a reference data. We compared the TC approach to the traditional approach of using a reference data set using the Shuttle Radar Topography Mission version 4.1 (SRTM v4.1) DEM, ASTER (the Advanced Spaceborne Thermal Emission and Reflection Radiometer) GDEM (Global DEM) version 2, the 1 arc-minute global relief model (ETOPO1), a DEM compiled by the Survey and Mapping Division of Ghana (SMD DEM), and 545 ground control stations (GCSs). The error estimates for the DEMs via TC were considerably smaller than those obtained from the reference-based approach. As an example, the best performing DEM (SRTM v4.1) recorded a root-mean-square error (RMSE) of 15.601 m using the GCSs as reference, while its TC-derived accuracy was 6.517 m. We note that based on the results of the TC, the estimated error of the GCSs is approximately 14 m. Using a data set with an error of 14 m to validate other data sets is certainly bound to result in unfavorable results. Thus, we have demonstrated in this work that the TC approach is able to provide an unbiased error of DEMs. The approach is important even for regions where GCSs are highly accurate, but more so for regions with low-quality GCSs.