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Gravity Recovery and Climate Experiment (GRACE) satellite gravimetry and Global Navigation Satellite System (GNSS) surface displacement measurements offer complementary advantages for monitoring terrestrial water storage (TWS) changes. We propose a new joint inversion model based on the combination of GRACE‐based geopotential difference (GPD) observations using the mascon method and GNSS vertical displacements through the Green's function method to obtain reliable TWS changes in Brazil. The performance of the jointly inverted TWS changes is assessed through closed‐loop simulations and comparisons with hydrometeorological data (precipitation‐P, evapotranspiration‐ET, and runoff‐R) using water budget closure (P‐ET‐R) and river water level observations from satellite altimetry. The simulation results indicate that the joint inversion results exhibit higher accuracy and reliability than GRACE GPD‐based mascon (GPD‐mascon) and GNSS solutions, and the standard deviations (STDs) of joint results decrease by ∼6.98 and ∼37.5 mm compared to those from GPD‐mascon and GNSS solutions. The joint inversion of real GRACE and GNSS data demonstrates notably lower uncertainty than that of GPD‐mascon solutions and exhibits significant improvement than GNSS‐only solutions. The STDs and correlation coefficients between monthly R time series derived from three inversion methods (joint inversion, GPD‐mascon and GNSS solutions, combined with P and ET through water budget closure) and in situ observations are 19.607 mm and 0.912, 20.879 mm and 0.904, and 31.370 mm and 0.778, respectively. The joint estimates also yield better correlation with river water level observations compared to GPD‐mascon and GNSS solutions. Furthermore, at the weekly time scale, the joint inversion results show better consistency with P‐ET‐R data than those from GPD‐mascon and GNSS solutions. Plain Language Summary The migration and redistribution of surface mass changes (e.g., TWS changes) can induce changes in the Earth's gravity field and surface deformation field. The remote sensing‐based Gravity Recovery and Climate Experiment (GRACE) satellite gravimetry and ground‐based Global Navigation Satellite System (GNSS) displacement measurement complement each other in spatio‐temporal resolution, spectral sensitivity, and spatial coverage for retrieving TWS changes. We present a novel joint inversion model that estimates reliable monthly and weekly TWS changes in Brazil through the joint adjustment of GRACE‐based geopotential differences (GPDs) and GNSS vertical displacements based on the mascon method and Green's function method in the spatial domains at the observation level. Compared to the GRACE‐only (GPD‐mascon) and GNSS‐only solutions, the joint inversion can recover more reliable TWS changes in Brazil through closed‐loop simulation tests. In addition, the joint inversion results based on the measured data present better consistency with hydrometeorological variables and river water level time series than GPD‐mascon and GNSS solutions. The proposed approach provides an effective estimation strategy to combine multi‐source geodetic data (e.g., GRACE/GRACE‐FO and GNSS) for recovering reliable TWS changes, which can provide crucial data support for studying water cycles and extreme climate events. Key Points A novel joint inversion model is established from joint adjustment of Gravity Recovery and Climate Experiment (GRACE)‐based geopotential differences and Global Navigation Satellite System (GNSS) vertical displacements Joint inversion demonstrates superior performances compared to GRACE‐ and GNSS‐only solutions through closed‐loop simulations Joint inversion results show better consistency with in situ data than GRACE‐ and GNSS‐only solutions at monthly and weekly scales in Brazil

The accurate estimation of the zero-height geopotential level in a local vertical datum (LVD) is critical for linking traditional height reference systems to a global height system. In this paper, we investigate the theoretical and practical challenges involved in determining the offset between the North American vertical datum (NAVD) and the global vertical datum (GVD). Drawing on the classical theory of the vertical system in physical geodesy, we define the vertical datum offset and derive rigorous formulas for its calculation. We examine various factors that affect the determination of the offset, including the global gravitational models (GGMs), geodetic reference system, tide system, tilt error, and omission error. Using terrestrial gravity data and gravity anomalies from multiple GGMs in conjunction with Global Navigation Satellite System (GNSS) and orthometric heights, we estimate the vertical offset between the NAVD and GVD. Our results indicate that the geopotential difference approach and the geodetic boundary value problem (GBVP) approach yield consistent results. When the normal gravity geopotential of the geodetic reference system is selected as the gravity geopotential of the global height datum, the NAVD is approximately 0.04 m higher than the GVD relative to the GRS80 ellipsoid, and 0.97 cm higher than the GVD relative to the WGS84 ellipsoid. When the Gauss–Listing geopotential value is chosen as the gravity geopotential of the global height datum, the NAVD is roughly 1.45 m higher than the GVD relative to the GRS80 ellipsoid, and approximately 0.52 m higher than the GVD relative to the WGS84 ellipsoid.

We presented an improved method for estimation of regional surface mass variations from the Gravity Recovery and Climate Experiment (GRACE)-derived precise intersatellite geopotential differences using a priori constraints. An alternative analytic formula was proposed to incorporate the K-band ranging (KBR) range rate into the improved energy balance equation, and precise geopotential differences were estimated from GRACE Level-1B data based on the remove-compute-restore (RCR) technique, which avoids the long-wavelength gravity signals being absorbed by empirical parameters. To reduce the ill condition for inversion of regional mass variations from geopotential differences, a priori information from hydrological models was used to construct the constraint equations, and the optimal regularization parameters were adaptively determined based on iterative least-squares estimation. To assess our improved method, a case study of regional mass variations’ inversion was carried out over South America on 2° × 2° grids at monthly intervals from January 2005 to December 2010. The results show that regional mascon solutions inverted from geopotential differences estimated by the RCR technique using hydrological models as a priori constraints can retain more signal energy and enhance regional mass variation inversion. The spatial distributions and annual amplitudes of geopotential difference-based regional mascon solutions agree well with the official GRACE mascon solutions, although notable differences exist in spatial patterns and trends, especially in small basins. In addition, our improved method can robustly estimate the mascon solutions, which are less affected by the a priori information. The results from the case study have clearly demonstrated the feasibility and effectiveness of the proposed method.

To suppress the correlated noise of Gravity Recovery and Climate Experiment (GRACE) spherical harmonic (SH) solutions, we developed a series of constrained monthly gravity field solutions named WHU‐GRACE‐GPD01s from August 2002 to July 2016 using GRACE‐based geopotential differences. The constrained solutions were estimated using Kaula regularization, and the optimal regularization parameters were adaptively determined from the GRACE data itself through variance component estimation. The performance of the constrained WHU‐GRACE‐GPD01s solutions was validated against the official SH solutions (GFZ, JPL, and CSR RL06) and mass concentration (mascon) solutions (CSR RL06M) at global and regional scales. The results demonstrate that mass changes derived from the constrained solutions and official SH solutions with DDK4 filtering are in good agreement, but the constrained solutions present weaker longitudinal stripes and have a lower noise level at regional scales (e.g., in the Middle Pacific Ocean and Sahara Desert). Furthermore, regional mass changes (e.g., major river basins, Greenland, and Antarctic ice sheet) inferred from the constrained solutions agree with the ones derived from the official SH solutions with DDK4 filtering. The constrained solutions also have a higher signal intensity and smaller spatial leakages as compared to the CSR RL06 SH solutions with spatial filtering (Gaussian filtering plus de‐striping). For the problematic months, the constrained solutions are more reliable than the official SH solutions using spatial filtering or DDK4 filtering, and are closer to CSR RL06M mascon solutions. These validations demonstrate that our constrained solutions are comparable to the official SH solutions and can be used without postprocessing. Key Points The constrained WHU‐GRACE‐GPD01s solutions are estimated based on Kaula regularization using GRACE‐based geopotential differences Optimal regularization parameters are adaptively determined from the GRACE data itself based on variance component estimation Performance of the constrained solutions is validated with comparisons of the official spherical harmonic solutions and mascon solutions

We present a theory and numerical algorithm to directly determine the time-varying along-track geopotential difference and deflection of the vertical at the Gravity Recovery and Climate Experiment (GRACE) satellite altitude. The determination was implemented using the GEOGRACE computer program using the K-band range rate (KBRR) of GRACE from the Level-1B (L1B) product. The method treated KBRR, GPS-derived orbit of GRACE and an initial geopotential difference as measurements used in the least-squares estimation of the geopotential difference and its formal error constrained by the energy conservation principle. The computational procedure consisted of three steps: data reading and interpolation, data calibration and estimations of the geopotential difference and its error. The formal error allowed removal of KBRR outliers that contaminated the gravity solutions. We used the most recent models to account for the gravity changes from multiple sources. A case study was carried out over India to estimate surface mass anomalies from GEOGRACE-derived geopotential differences. The 10-day mass changes were consistent with those from the MASCON solutions of NASA (correlation coefficient up to 0.88). Using the geopotential difference at satellite altitude avoids the errors caused by downward continuation, enabling the detection of small-scale mass changes.

Considering the efforts to establish Global Reference Systems linked to the geopotential space, new alternatives are sought to address the problems found in the classic national vertical networks. The Brazilian Vertical Reference Frame (BVRF) was materialized in two different segments with independent datums (Imbituba and Santana tide gauges) due to the terrain difficulties for conventional leveling. The 2018 BVRF realization, in the geopotential space, still remains without interoperability between its segments. We analyze alternatives for physical connection based on the new precepts of the International Association of Geodesy (IAG) involving the geopotential space. Some proposed solutions for physical connection based on GPS leveling associated with gravimetry are presented. These solutions were developed with the aim of evidencing the discrepancy between the two BVRF segments, now carried out in terms of geopotential numbers and normal heights. The results indicate differences ranging from about 45 cm to 140 cm between the two segments depending on the strategy employed. Comparisons with previous determinations based on indirect strategies and involving previous BVRF realizations are made.

The study concerns computation of the gravity potential difference between the Kronsztadt86 datum and the global vertical datum. This method is based on the use of ellipsoidal heights from satellite observations, normal heights obtained from the conducted leveling campaign and quasigeoid/ellipsoid separations computed based on the EGM2008 model. The obtained results indicate that there are substantial differences in the estimated value of the parameter ΔW, computed from three different satellite networks: POLREF, EUVN-DA and ASG-EUPOS. The parameter was determined with sufficient accuracy and the applied systematic error model has low efficiency. The computations reveal that the best value of ΔW for the territory of Poland is 0.43 m2s-2.

The possibilities of using gravimetric data obtained from global geopotential models (GGM) for the territory of Bulgaria in the processing of precise levelling measurements for the determination of normal differences and geopotential differences are presented in the article. The researches were carried out on first order levelling lines of the State Levelling Network of the Republic of Bulgaria, situated in different topographic conditions, as well as in conditions of different anomalous gravitational field. The data used for the calculation of the second normal correction and geopotential differences on the levelling lines are data from gravimetric measurements and interpolated gravimetric data for the Bouguer anomalies of EGM2008. Normal differences and geopotential differences were determined using different gravimetric data as well as data for benchmark heights from previous levelling measurements. The differences between the two types of height determinations based on conventional gravimetric data and GGM data are analyzed. The dependence of the series from the different physiographic conditions has been studied. The obtained results for differences on the levelling lines are compared with the regulatory requirements for accuracy in Bulgaria concerning the precise levelling determinations. The applications of gravimetric data from GGM are outlined both for precise height determinations and for detection of gross errors in precise levelling processing. The study for the territory of Bulgaria is based on an idea presented in the publication by Popadyev V. V., Gulyyev D. A. (2017) \"Application of global geopotential models to high- precision levelling processing\", where such studies were made to determine a normal correction on first-order levelling lines.

The aim of this study is to determine the gravity potential difference AW between the Kronsztadt86 local vertical datum in Poland and the global vertical datum. The computation is based on the use of ellipsoidal heights from satellite observations, normal heights obtained from the levelling campaign and quasigeoid/ellipsoid separations computed from the EGM2008 geopotential model. This study is revised version of previous computations by taking into account the influence of vertical movements of Earth's crust, and unification of the tide systems in satellite and levelling networks. Computed value of potential difference between the local and global vertical datum vary from 0.158 m2s-2 to 0.606 m2s-2 which correspond to 2 cm and 6 cm respectively. The results indicate that there are still unexpected differences in the estimated value of the parameter AW, computed from three different satellite networks: POLREF, EUVN-DA and ASG-EUPOS.

In the context of the rapid development of environmental research technologies and techniques to solve scientific and practical problems in different fields of knowledge including geosciences, the study of Earth’s gravity field models is still important today. The results of gravity anomaly modelling calculated by the current geopotential models data were compared with the independent terrestrial gravity data for the two territories located in West Siberia and Kazakhstan. Statistical characteristics of comparison results for the models under study were obtained. The results of investigations show that about 70% of the differences between the gravity anomaly values calculated by recent global geopotential models and those observed at the points in flat areas are within ±10 mGal, in mountainous areas are within ±20 mGal.