GRAVITY ANOMALY ASSESSMENT USING GGMS AND AIRBORNE GRAVITY DATA TOWARDS BATHYMETRY ESTIMATION

Launches of the CHAMP (CHAllenging Minisatellite Payload) and GRACE (Gravity Recovery And Climate Experiment) satellite missions have produced a new generation of global geopotential models (GGMs). The performance of seven recent GGMs has been analyzed using a local geodetic dataset (terrestrial gravity and GPS/levelling points) in Egypt. The results show that the EIGEN‐CG01C model is best at representing the long and medium wavelengths of the gravity field in Egypt. Its average accuracy, in terms of geoid undulations, when compared to known points, is estimated to be 0.36 m. Additionally, four digital terrain models (GTOPO30, SRTM, DTM2002, LDTM) have been investigated, leading to the conclusion that DTM2002 should be utilized in computing the terrain corrections for gravimetric geoid development in Egypt. When combined with local geodetic data, these two global models (EIGEN‐CG01C and DTM2002) will support the production of a precise local geoid model, to be used in conjunction with Global Positioning System‐based surveying and mapping projects in Egypt.

In 2014, the Jeddah Municipality made a call for an estimate of a centimetric precision geoid model to be used for engineering and surveying applications, because the regional geoid model available at that time did not reach a sufficient precision. A project was set up to this end and dedicated sets of gravity and Global Positioning System (GPS)/levelling data were acquired in the framework of this project. In this paper, a thorough analysis of these newly acquired data and of the last available Global Gravity Field Models (GGMs) has been done in order to obtain a geoid undulation estimate with the prescribed precision. In the framework of the Remove–Compute–Restore (RCR) approach, the collocation method was used to obtain the height anomaly estimation that was then converted to geoid undulation. The remove and restore steps of the RCR approach were based on GGMs, derived from the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) and Gravity Recovery and Climate Experiment (GRACE) dedicated gravity satellite missions, which were used to improve the long wavelength components of the Earth’s gravity field. Furthermore, two different quasi-geoid collocation estimates were computed, based on gravity data only and on gravity plus GPS/levelling data (the so-called hybrid estimate). The best solutions were obtained with the hybrid geoid estimate. This was tested by comparison with an independent set of GPS/levelling geoid undulations that were not included in the computed solutions. By these tests, the precision of the hybrid geoid is estimated to be 3.7 cm. This precision proved to be better, by a factor of two, than the corresponding one estimated from the pure gravimetric geoid. This project has been also useful to verify the importance and reliability of GGMs developed from the last satellite gravity missions (GOCE and GRACE) that have significantly improved our knowledge of the long wavelength components of the Earth’s gravity field, especially in areas with poor coverage of terrestrial gravity data. In fact, the geoid models based on satellite-only GGMs proved to have a better performance, despite the lower spatial resolution with respect to high-resolution models (i.e., Earth Gravitational Model 2008 (EGM2008)).

In gravimetry satellite missions GRACE (Gravity Recovery and Climate Experiment) and GRACE-FO (GRACE Follow-On), accelerometer measurements from both satellites are necessary for the gravity field recovery. The accelerometer provides accurate measurements of the non-gravitational forces acting on the spacecraft, such as atmospheric drag, solar radiation pressure and albedo. These measurements are required to separate any non-gravitational effect from the sought-after gravitational perturbations on the spacecraft motion. Therefore, the quality of accelerometer data, denoted as ACC products, significantly affects the quality of gravity field models.Near the end of the GRACE mission, due to the reduced battery capacity, the on-board accelerometer of the GRACE-B was turned off and its measurements were replaced by synthetic accelerometer data, called transplant data. The transplant data are generated by a series of adjustments to the GRACE-A ACC data. A similar approach was also employed for the GRACE-FO mission, when the GRACE-D ACC data degraded and were required to be replaced with synthetic data as well. Using the transplant data in both missions is one of the main challenges of providing high-quality gravity field models.We investigate the feasibility of Machine Learning (ML) algorithms for the recovery of GRACE-B ACC based on GRACE-A measurements and orbital data such as shadow factor and β angle. Taking advantage of ~14 years of GRACE-B measurements, this work aims to develop a model which can predict the missing accelerometer data under different orbital conditions. Two different architectures are implemented to forecast GRACE-B accelerometer data: Multilayer Perceptron (MLP) and Long Short-Term Memory (LSTM). The performance is evaluated using the Root Mean Square Error (RMSE) and by comparing the predicted data with the calibrated real data in the evaluated period. Furthermore, the ML-based ACC products will be compared to the transplant products and their impact on the gravity field will be discussed.

“Gravity From Space” for Oceans, Land Ice, and Sea Level Rise; Hamburg, Germany, 29–30 September 2010; Twenty‐five scientists met at the University of Hamburg's KlimaCampus to discuss current analyses and future applications of spaceborne gravity measurements to studies of ocean circulation, cryospheric science, and sea level rise. The Challenging Minisatellite Payload (CHAMP), Gravity Recovery and Climate Experiment (GRACE), and Gravity Field and Steady‐State Ocean Circulation Explorer (GOCE) satellites, complemented with radar and laser altimeters, provide the necessary data. Spaceborne gravity measurements provide two important quantities for ocean circulation studies: (1) the time‐averaged geoid, which when subtracted from a time mean sea surface from radar altimetry yields the absolute surface dynamic topography and absolute surface geostrophic currents, and (2) time changes in ocean bottom pressure and total ocean mass. For sea level rise, the difference between the globally averaged trend from altimetry and that from GRACE is used to infer the top‐to‐bottom steric component (the component of sea level rise resulting from expansion of seawater due to temperature and salt), which is observable with data from the Argo system, a network of drifting probes that measure temperature up to 2000 meters in depth, and from expendable bathythermographs (XBT), temperature sensors deployed by ships.

The accuracy of Earth's gravitational field from the Gravity Recovery and Climate Experiment (GRACE) Follow‐On satellite mission is efficiently and rapidly estimated for the first time based on the analytic method. Firstly, the new single and combined analytic error models of cumulative geoid height influenced by four error sources including the intersatellite range‐rate of interferometric laser ranging system, orbital position and velocity of GPS receiver and nonconservative force of accelerometer from GRACE Follow‐On satellites are established using the power spectrum principle, respectively. Secondly, the dependability of analytic error model is validated according to the consistency of the matching accuracy indexes of GRACE key payloads from the single analytic error models and the GRACE Level 1B provided by the American Jet Propulsion Laboratory (JPL), and the conformity of GRACE cumulative geoid height errors from the combined analytic error model and the Earth's gravitational field model EIGEN‐GRACE02S released by the German GeoForschungsZentrum Potsdam (GFZ). Finally, the influences of different matching accuracy indexes of key payloads and orbital altitudes of GRACE Follow‐On satellites on the accuracies of Earth's gravitational field are demonstrated contrastively. At the 360 degree, cumulative geoid height error is 1.231×10−1 m using combined analytic error model based on orbital altitude 250 km, intersatellite range 50 km, intersatellite range‐rate error 1×10−9 m/s, orbital position error 3×10−5 m, orbital velocity error 3×10−8 m/s and nonconservative force error 3×10−13 m/s2. This work not only can provide the theoretical foundation and calculational guarantee for the efficient and rapid determination of the accuracies of current GRACE and future GRACE Follow‐On Earth's gravitational field, but also has some reference significance to the successful execution of the future Gravity Recovery and Interior Laboratory (GRAIL) lunar satellite gravity exploration mission.

The monthly global gravity field solutions derived using the measurements from the GRACE (Gravity Recovery and Climate Experiment) satellites have been continuously improved by the processing centers. One of the improvements in the processing method is a more detailed calibration of the on-board accelerometers in the GRACE satellites. The accelerometer data calibration is usually restricted to the scale factors and biases. It has been assumed that the three different axes are perfectly orthogonal in the GRACE science reference frame. Recently, it was shown by Klinger and Mayer-Gurr (2016) that a fully-populated scale matrix considering the non-orthogonality of the axes and the misalignment of the GRACE science reference frame and the GRACE accelerometer frame improves the quality of the C20 coefficient in the GRACE monthly gravity field solutions. We investigate the effect of the more detailed calibration of the GRACE accelerometer data on the C20 coefficient in the case of the AIUB (Astronomical Institute of the University of Bern) processing method using the Celestial Mechanics Approach. We also investigate the effect of the new calibration parameters on the stochastic parameters in the Celestial Mechanics Approach.

Recent studies show that data from the Gravity Recovery and Climate Experiment (GRACE) is promising for basin‐ to global‐scale water cycle research. This study provides varied assessments of errors associated with GRACE water storage estimates. Thirteen monthly GRACE gravity solutions from August 2002 to December 2004 are examined, along with synthesized GRACE gravity fields for the same period that incorporate simulated errors. The synthetic GRACE fields are calculated using numerical climate models and GRACE internal error estimates. We consider the influence of measurement noise, spatial leakage error, and atmospheric and ocean dealiasing (AOD) model error as the major contributors to the error budget. Leakage error arises from the limited range of GRACE spherical harmonics not corrupted by noise. AOD model error is due to imperfect correction for atmosphere and ocean mass redistribution applied during GRACE processing. Four methods of forming water storage estimates from GRACE spherical harmonics (four different basin filters) are applied to both GRACE and synthetic data. Two basin filters use Gaussian smoothing, and the other two are dynamic basin filters which use knowledge of geographical locations where water storage variations are expected. Global maps of measurement noise, leakage error, and AOD model errors are estimated for each basin filter. Dynamic basin filters yield the smallest errors and highest signal‐to‐noise ratio. Within 12 selected basins, GRACE and synthetic data show similar amplitudes of water storage change. Using 53 river basins, covering most of Earth's land surface excluding Antarctica and Greenland, we document how error changes with basin size, latitude, and shape. Leakage error is most affected by basin size and latitude, and AOD model error is most dependent on basin latitude.

Besides the Global Navigation Satellite Systems (GNSS), Satellite and Lunar Laser Ranging (SLR, LLR) and the Doppler distance measurement technique DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite), Very Long Baseline Interferometry (VLBI) is one of the space-geodetic techniques. In addition to the aforementioned, satellite missions such as radar and laser altimetry and geodetically used components of gravity field satellites in particular CHAMP (CHAllenging Mini satellite Payload), GRACE (Gravity Recovery And Climate Experiment), and GOCE (Gravity field and steady-state Ocean Circulation Explorer) can be counted to the space-geodetic techniques. In radio astronomy VLBI is a technique for astrophysics and astrometry. The later has many things in common with geodetic VLBI; only the schedule varies among terrestrial and celestial motivated observing sessions in terms of the number of observed radio sources as well as the number and sequence of observations to radio sources. Together with geodynamics, oceanography, glaciology, meteorology, and climatology, geodesy provides the metric basis for interdisciplinary research within the geosciences.

Trend of China land water storage redistribution at medi- and large-spatial scales in recent five years by satellite gravity observations

The Tibetan Plateau (TP), characterized by its unique regional features and geographical landscape, is a critical area for studying changes in terrestrial water storage (TWS), which are significantly influenced by global warming. In this study, we integrate data from the Global Navigation Satellite System (GNSS) and the Gravity Recovery and Climate Experiment (GRACE) to jointly estimate TWS variations in the TP and examine their spatiotemporal fluctuations in relation to large-scale climate patterns. To evaluate our approach, we conducted two synthetic tests, which showed that the root mean square errors (RMSEs) for the joint inversion were 23–37% lower than those for GNSS inversion, confirming the effectiveness of our method. When applied to real observational data, the joint inversion technique revealed that the spatial patterns and seasonal characteristics of TWS changes closely aligned with independent GRACE and Global Land Data Assimilation System (GLDAS) products, while offering more detailed insights into local hydrological processes. Notably, during the 2015/2016 El Niño event, the central and eastern TP experienced severe drought, primarily driven by precipitation anomalies (~ -150 mm) associated with extreme climate events, leading to a delayed hydrological response to the meteorological drought. Furthermore, we observed significant interannual variability across the TP sub-basins, with a moderate correlation with the El Niño/Southern Oscillation (ENSO) at a one-month lag. Our research highlights the potential of joint inversion using GNSS and GRACE to enhance TWS monitoring in the TP, providing more spatially detailed insights into water storage variability in response to climate change.Supplementary InformationThe online version contains supplementary material available at 10.1038/s41598-025-12635-x.

Accelerometer data from coplanar orbits of Challenging Minisatellite Payload (CHAMP) and Gravity Recovery and Climate Experiment (GRACE) satellites were used to study the complex altitude and latitude variations of the thermosphere mass density response to geomagnetic activity during 1–10 December 2008 near 09 LT. Helium number densities near 500 km altitude were extracted from the CHAMP and GRACE measurements and clearly show the presence of a winter hemisphere helium bulge. This recent extreme solar minimum indicates that wintertime helium concentrations exceed NRLMSISE‐00 model estimates by 30%–70% during quiet geomagnetic activity after adjusting F10.7 input into MSIS. The perturbation in mass density from quiet to active conditions is found to be less enhanced in the winter hemisphere at the higher GRACE altitudes (25%) than at the lower CHAMP altitudes (60%) and is attributed to dynamic behavior in the helium/oxygen transition. The investigation revealed the maximum storm time density perturbation to occur near the He/O transition region with a much weaker maximum near the O/N2 transition region. The altitude of maximum density perturbation occurs where the perturbation in the weighted pressure scale height is equal and opposite to the perturbation in the weighted mean molecular weight scale height. The altitude structure of density scale height perturbation is significantly influenced by the changes in the molecular weight scale height and can account for 50% of the change in mass density scale height in a region correspondingly close to the He/O transition during the 2008 solar minimum period.

The terrestrial water resources in Shaanxi–Gansu–Ningxia (SGN) region are relatively scarce, and its climate change is unstable. Research on the deformation driven by terrestrial water load is of great significance to the dynamic maintenance of reference station networks. In this paper, data derived from Gravity Recovery and Climate Experiment (GRACE) and Global Navigation Satellite System (GNSS) from 2010 to 2014 were combined to monitor the spatiotemporal characteristics of surface vertical deformation caused by terrestrial water load change. The single scale factor was calculated by comparing CPC, WGHM, and GLDAS hydrological model to restore filtering leakage signal. The singular spectrum analysis (SSA) method was used to extract the principal component of temporal vertical deformation, and its spatial distribution was analyzed. At the same time, in order to study the relationship between the terrestrial water load deformation from GRACE and that from GNSS, the first-order term correction, the Atmosphere and Ocean De-aliasing Level-1B product (GAC) correction, and the first-order load LOVE number correction for GRACE were adopted in this paper. In addition, a quantitative comparative analysis of both the monitoring results was carried out. The results show that the time-variable characteristics of surface vertical deformation characterized by the filtered three hydrological models were consistent with those of GRACE. The correlation coefficient and Nash–Sutcliffe efficiency coefficient (NSE) values were the highest in the GLDAS model and the GRACE model, respectively; the former index is 0.93, while the latter is 0.85. The crustal vertical deformation from terrestrial water load showed a declining rate from 2010 to 2014. Its spatial change rate showed an obvious ladder distribution, with the surface subsidence rate gradually decreasing from south to north. In addition, weighted root mean square (WRMS) contribution rate of the crustal vertical deformation resulting from GRACE with GAC correction between the different GNSS stations ranged from 18.52% to 54.82%. The correlation coefficient between them was close to 0.70. After deducting the mass load impact of GRACE only, the WRMS contribution rate of the corresponding stations decreased from −8.42% to 21.18%. The correlation coefficient between them reduced noticeably. Adding GAC back can increase the comparability with GRACE and GNSS in terms of monitoring the crustal vertical deformation. The annual amplitude and phase of surface vertical deformation resulting from GRACE with GAC correction were close to those of GNSS. The research results can help to explore the motion mechanism between water migration and surface deformation, which is of benefit in the protection of the water ecological environment in the region.

In the last 5 years, Lake Victoria water level has seen a dramatic fall that has caused alarm to water resource managers. Since the lake basin contributes about 20% of the lakes water in form of discharge, with 80% coming from direct rainfall, this study undertook a satellite analysis of the entire lake basin in an attempt to establish the cause of the decline. Gravity Recovery And Climate Experiment (GRACE), Tropical Rainfall Measuring Mission (TRMM) and CHAllenging Minisatellite Payload (CHAMP) satellites were employed in the analysis. Using 45 months of data spanning a period of 4 years (2002–2006), GRACE satellite data are used to analyse the variation of the geoid (equipotential surface approximating the mean sea level) triggered by variation in the stored waters within the lake basin. TRMM Level 3 monthly data for the same period of time are used to compute mean rainfall for a spatial coverage of .25°×.25° (25×25 km) and the rainfall trend over the same period analyzed. To assess the effect of evaporation, 59 CHAMP satellite’s occultation for the period 2001 to 2006 are analyzed for tropopause warming. GRACE results indicate an annual fall in the geoid by 1.574 mm/year during the study period 2002–2006. This fall clearly demonstrates the basin losing water over these period. TRMM results on the other hand indicate the rainfall over the basin (and directly over the lake) to have been stable during this period. The CHAMP satellite results indicate the tropopause temperature to have fallen in 2002 by about 3.9 K and increased by 2.2 K in 2003 and remained above the 189.5 K value of 2002. The tropopause heights have shown a steady increase from a height of 16.72 m in 2001 and has remained above this value reaching a maximum of 17.59 km in 2005, an increase in height by 0.87 m. Though the basin discharge contributes only 20%, its decline has contributed to the fall in the lake waters. Since rainfall over the period remained stable, and temperatures did not increase drastically to cause massive evaporation, the remaining major contributor is the discharge from the expanded Owen Falls dam.

<p>Spherical harmonic synthesis (SHS) can be used to compute various gravity functions (e.g., geoid undulations, height anomalies, deflections of vertical, gravity disturbances, gravity anomalies, etc.) using the 4pi fully normalised Stokes coefficients from the many freely available Global Geopotential Models (GGMs).  This requires a normal ellipsoid and its gravity field, which are defined by four parameters comprising (i) the second-degree even zonal Stokes coefficient (J2) (aka dynamic form factor), (ii) the product of the mass of the Earth and universal gravitational constant (GM) (aka geocentric gravitational constant), (iii) the Earth’s angular rate of rotation (ω), and (iv) the length of the semi-major axis (a). GGMs are also accompanied by numerical values for GM and a, which are not necessarily identical to those of the normal ellipsoid.  In addition, the value of W<sub>0,</sub> the potential of the geoid from a GGM, needs to be defined for the SHS of many gravity functions. W<sub>0</sub> may not be identical to U<sub>0</sub>, the potential on the surface of the normal ellipsoid, which follows from the four defining parameters of the normal ellipsoid.  If W<sub>0</sub> and U<sub>0</sub> are equal and if the normal ellipsoid and GGM use the same value for GM, then some terms cancel when computing the disturbing gravity potential.  However, this is not always the case, which results in a zero-degree term (bias) when the masses and potentials are different.  There is also a latitude-dependent term when the geometries of the GGM and normal ellipsoids differ.  We demonstrate these effects for some GGMs, some values of W<sub>0</sub>, and the GRS80, WGS84 and TOPEX/Poseidon ellipsoids and comment on its omission from some public domain codes and services (isGraflab.m, harmonic_synth.f and ICGEM).  In terms of geoid heights, the effect of neglecting these parameters can reach nearly one metre, which is significant when one goal of modern physical geodesy is to compute the geoid with centimetric accuracy.  It is also important to clarify these effects for all (non-specialist) users of GGMs.</p>

Owing to the intense tectonic activity and significant seasonal surface mass change, Southwest China is characterized by noticeable vertical land movement. We determined the vertical movement of Southwest China using 10 years of data from 41 continuous global positioning system (GPS) stations, gravity recovery and climate experiment (GRACE), and surface loading model (SLM). The annual variation in hydrological loading is the main factor causing the seasonal oscillation of surface deformation in Southwest China. Seasonal deformations captured by GPS, GRACE, and SLM are consistent to a certain extent, and the correlation coefficients between GPS/GRACE, and GPS/SLM are 0.82 and 0.81, respectively. After deducting the results yielded by GRACE and SLM from the GPS time series, the average reductions in root mean square were 41.3% and 38.0%, respectively. However, some systematic differences were observed among the annual amplitudes and phases of the seasonal deformations among the three products. For example, the average amplitudes estimated by GRACE and SLM were 7.4 mm and 6.1 mm, respectively, which were smaller than the amplitude deduced from GPS (9.7 mm). Furthermore, mean phase delays of 16, 22, and 6 days were observed between GPS/GRACE, GPS/SLM, and GRACE/SLM. The data processing errors and local geophysical signals in GPS and the underestimation of land water storage in GRACE and SLM were jointly responsible for the systemic differences. The simulated data show that the misestimating of hydrological loading can explain approximately 50%, 64%, and 83% of the phase delays between GPS/GRACE, GPS/SLM, and GRACE/SLM, respectively. In addition, we obtained long-term vertical crustal motion rates by subtracting the loading deformation rates estimated by GRACE from the linear rates of the GPS. The vertical crustal motion in this region is block-dependent. The Central Yunnan block and its eastern boundary are uplifted; meanwhile, the Southwest Yunnan block, which features stretching in the horizontal direction, appears to be subsiding. The aforementioned results can provide data support for the study of water resource utilization and geodynamics in Southwest China.