Time-variable Gravity Research Articles

Gap filling between GRACE and GRACE-FO missions: assessment of interpolation techniques

We propose a benchmark for comparing gap-filling techniques used on global time-variable gravity field time-series. The Gravity Recovery and Climate Experiment (GRACE) and the GRACE Follow-On missions provide products to study the Earth’s time-variable gravity field. However, the presence of missing months in the measurements poses challenges for understanding specific Earth processes through the gravity field. We reproduce, adapt, and compare satellite-monitoring and interpolation techniques for filling these missing months in GRACE and GRACE Follow-On products on a global scale. Satellite-monitoring techniques utilize solutions from Swarm and satellite laser ranging, while interpolation techniques rely on GRACE and/or Swarm solutions. We assess a wide range of interpolation techniques, including least-squares fitting, principal component analysis, singular spectrum analysis, multichannel singular spectrum analysis, auto-regressive models, and the incorporation of prior data in these techniques. To inter-compare these techniques, we employ a remove-and-restore approach, removing existing GRACE products and predicting missing months using interpolation techniques. We provide detailed comparisons of the techniques and discuss their strengths and limitations. The auto-regressive interpolation technique delivers the best score according to our evaluation metric. The interpolation based on a least-squares fitting of constant, trend, annual, and semi-annual cycles offers a simple and effective prediction with a good score. Through this assessment, we establish a starting benchmark for gap-filling techniques in Earth’s time-variable gravity field analysis.

The persisting conundrum of mantle viscosity inferred from mantle convection and glacial isostatic adjustment processes

Mantle viscosity exerts important controls on the long-term (i.e., >106 years) dynamics of the mantle and lithosphere and the short-term (i.e., 10 to 104 years) crustal motion induced by loading forces including ice melting, sea-level changes, and earthquakes. However, mantle viscosity structures inferred from modeling observations associated with mantle dynamic and loading processes may differ significantly and remain a hotly debated topic over recent decades. In this study, we investigate the effects of mantle viscosity structures on observations of the geoid, mantle structures, and present-day crustal motions and time-varying gravity by considering five representative mantle viscosity structures in models of mantle convection and glacial isostatic adjustment (GIA). These five viscosity models fall into two categories: 1) two viscosity models derived from modeling the geoid in mantle convection models with ∼100 times more viscous lower mantle than the upper mantle, and 2) the other three with less viscosity increase from the upper to lower mantles that are derived from modeling the late Pleistocene and Holocene relative sea level changes and other observations in GIA models. Our convection models use the plate motion history for the last 130 Myrs as the surface boundary conditions and depth- and temperature-dependent viscosity to predict the present-day convective mantle structure of subducted slabs and the intermediate wavelength (degrees 4–12) geoid. Our GIA models using different ice history models (e.g., ICE-6 G and ANU) compute the GIA-induced present-day crustal motions and time-varying gravity. Our calculations demonstrate that while the viscosity models with a higher viscosity in the lower mantle (∼2 × 1022 Pa.s) reproduce the degrees 4–12 geoid and seismic slab structures, they significantly over-predict the geodetic (i.e., GPS and GRACE) observations of crustal motions and time varying gravity. Our calculations also show that while two viscosity models derived from fitting the RSL data with averaged mantle viscosity of ∼1021 Pa.s for the top 1200 km of the mantle reproduce well the geodetic observations independent of ice models, they fail to explain the geoid and seismic slab structures. Therefore, our study highlights the persisting conundrum of mantle viscosity structures derived from different observations. We also discuss a number of possible ways including transient, stress-dependent and 3-D viscosity to resolve this important issue in Geodynamics.

GCMEbox: A MATLAB toolbox for extracting and analyzing common-mode errors from GNSS time series

High-precision global navigation satellite system (GNSS) time series data contain rich tectonic and non-tectonic motion information. However, such data also have common-mode errors (CME) related to spatiotemporal characteristics. CME will produce bias in accurate and reliable GNSS station positions and velocities estimations, ultimately deciphering erroneous geophysical signals. Currently, CME extraction methods can be divided into three categories: regional stack filtering, reference frame filtering, and statistical signal decomposition. The third method is widely used in geodetic data processing, including GNSS time series analysis, global time-varying gravity signal extraction, interferometric synthetic aperture radar (InSAR) time series analysis, etc. The demand for GNSS time series analysis software with interactive, visualization, and multifunctional features has also increased with the increase in GNSS stations. Therefore, we developed gCMEbox based on MATLAB. The gCMEbox’s primary functions include GNSS time series preprocessing, multiple statistical signal decomposition algorithms for extracting CME, GNSS time series analysis, visualization, velocity field construction, and generation of multiple time series post-processing products. Based on GNSS time series data, this study utilized the gCMEbox for data preprocessing, including format conversion, outlier removal, missing data recovery, etc. By applying statistical signal decomposition methods, gCMEbox successfully extracted CME. The primary objective of this study is to share this toolbox with the scientific community, providing a comprehensive tool for GNSS time series analysis and applications.

An Improved Average Acceleration Approach of Modelling Earth Gravity Field Based on K-Band Range-Rate Observations

The conventional average acceleration approach relies on K-band range observation, containing an unknown bias, which leads to possible degradation of the precision of Earth’s gravity field modelling. It also suffers from correlated errors caused by three-point numerical differentiation. In this study, an improved approach is proposed that makes use of K-band range-rate observations instead and overcoming the influence of correlated errors by introducing a whitening filter. GRACE-Follow On data spanning the period from January 2019 to December 2022 were processed by the proposed approach and a series of time-varying gravity field models was derived, referred to as SSM-AAA-GFO in this paper. This model series is compared comprehensively with three official model series. Results demonstrate that all model series are highly coincident below degree 30 and reflect similar time-varying gravity field signals in both large and small basins. After filtering, SSM-AAA-GFO shows uncertainty, in the form of equivalent water height below 2.5 cm, which is comparable with three official model series. The comparison results confirm the effectiveness of the proposed approach for precisely modelling a time-varying gravity field based on K-band range-rate observations.

Simulation analysis of recovering time-varying gravity fields based on Starlink-like constellation

Simulation analysis of recovering time-varying gravity fields based on Starlink-like constellation

Orbit design for a future geodetic satellite and gravity field recovery

Spherical geodetic satellites tracked by satellite laser ranging (SLR) stations provide indispensable scientific products that cannot be replaced by other sources. For studying the time-variable gravity field, two low-degree coefficients C20 and C30 derived from GRACE and GRACE Follow-On missions are replaced by the values derived from SLR tracking of geodetic satellites, such as LAGEOS-1/2, LARES-1/2, Starlette, Stella, and Ajisai. The subset of these satellites is used to derive the geocenter motion which is fundamental in the realization of the origin of the terrestrial reference frames. LAGEOS satellites provide the most accurate standard gravitational product GM of the Earth. In this study, we use the Kaula theorem of gravitational perturbations to find the best possible satellite height, inclination, and eccentricity for a future geodetic satellite to maximize orbit sensitivity in terms of the recovery of low-degree gravity field coefficients, geocenter, and GM. We also derive the common station-satellite visibility-coverability coefficient as a function of the inclination angle and satellite height. We found that the best inclination for a future geodetic satellite is 35°–45° or 135°–145° with a height of about 1500–1700 km to support future GRACE/MAGIC missions with C20 and C30. For a better geocenter recovery and derivation of the standard gravitational product, the preferable height is 2300–3500 km. Unfortunately, none of the existing geodetic satellites has the optimum height and inclination angle for deriving GM, geocenter, and C20 because there are no spherical geodetic satellites at the heights between 1500 (Ajisai and LARES-1) and 5800 km (LAGEOS-1/2, LARES-2).

Constellation design and performance of future quantum satellite gravity missions

Temporal aliasing is currently the largest error contributor to time-variable satellite gravity field models. Therefore, the evolution of sensor technologies has to be complemented by strategies to reduce temporal aliasing errors. The most straightforward way to improve temporal aliasing is through extended satellite constellations because they improve the observation geometry and increase the achievable temporal resolution. Therefore, strategies to optimize the design of larger satellite constellations are investigated in this contribution. A complete constellation modeling procedure is presented, starting from primary design variables (such as the required targeted resolutions) and concluding with concrete orbital elements for the individual satellites. In parallel, it is evaluated if improved instrument sensitivities based on quantum technologies (cold atom interferometry) can be fully exploited in the case of larger constellations. For this, future quantum satellite gravity missions adopting the gradiometry concept (similar to the GOCE mission) and the low-low satellite-to-satellite tracking concept (similar to GRACE/-FO) are simulated on optimized constellations with up to 6 satellites/pairs. The retrieval performance of a 6-pair mission in terms of the global equivalent water height RMS can be improved by a factor of roughly 3 compared to an inclined double-pair mission. 3D-gradiometry intrinsically has a better de-aliasing behavior but has extremely high accuracy requirements for the gradiometer (about 10 µEotvos) and the attitude reconstruction to be of any benefit. All simulations show that when incorporating improved sensor technologies, such as future quantum sensing instruments in extended constellations, temporal aliasing will remain the dominant error source by far, up to five orders of magnitude larger than the instrument errors. Therefore, improving sensor technologies has to go hand in hand with larger satellite constellations and improved space–time parameterization strategies to further reduce temporal aliasing effects.Graphical

Joint analysis of JUICE and Europa Clipper tracking data to study the Jovian system ephemerides and dissipative parameters

Context. Jupiter and its moons form a complex dynamical system that includes several coupling dynamics at different frequencies. In particular the Laplace resonance is fundamental to maintaining the energy dissipation that sustain Io’s volcanic activity and Europa’s subsurface ocean; studying its stability is thus crucial for characterizing the potential habitability of these moons. The origin and evolution of the Laplace resonance is driven by the strong tidal interactions between Jupiter and its Galilean moons, and the future planetary exploration missions JUICE and Europa Clipper could bring new light to this unsolved mechanism. During the Jupiter tours of both missions and JUICE’s Ganymede orbital phase, two-way radiometric range and Doppler data will be acquired between Earth ground stations and the spacecraft, which will be processed to recover the static and time-varying gravity field of the moons. Moreover, range and Doppler data will improve the orbit accuracy of the moons, providing precise measurements of Jupiter’s tidal parameters. Aims. This work presents a covariance analysis of the joint orbit determination of JUICE and Europa Clipper, aimed at quantifying the expected uncertainties on the main parameters that characterize the dynamics of the Jupiter system. Methods. We simulated radio science data from JUICE and Clipper missions under conservative noise assumptions, using a multi-arc approach to estimate the ephemerides and dissipation in the system. Results. Even though JUICE and Europa Clipper will not perform flybys of Io, the strong coupling with Europa and Ganymede will allow an improvement of our knowledge of the Jupiter-Io dissipation parameters thanks to JUICE and Europa Clipper radiometric data. Moreover, the expected uncertainty in Jupiter’s dissipation at the frequency of Callisto could unveil a potential resonance locking mechanism between Jupiter and Callisto.

Long-term analysis of Sentinel-6A orbit determination: Insights from three years of flight data

The Sentinel-6A mission extends the set of satellites dedicated to continuous ocean altimetry measurements, which started with TOPEX/Poseidon in 1992. To utilize these measurements, high-accuracy orbit solutions with radial position errors of less than 1.5cm (RMS) are required. For precise orbit determination (POD), a dedicated GPS/Galileo triple-frequency receiver (PODRIX) is available. Complementary to this, the TriG receiver provides GPS-only observations for POD and radio occultations. Previous research has shown that reduced-dynamic orbit solutions with PODRIX GPS/Galileo measurements meet the mission requirement for radial position accuracy of 1.5 cm (RMS). However, baseline estimation between the PODRIX and TriG antennas still reveals obvious inconsistencies in the along- and cross-track directions. In this study, we present a comprehensive reprocessing of orbit solutions using three years of Sentinel-6A flight data from both receivers covering January 2021 to December 2023. Cross-comparison between both receivers shows that inconsistencies can be removed by applying a yaw bias and a timing error correction. A comparative analysis of macro-models demonstrates strong correlation of cross-track empirical accelerations with the Sun elevation above the orbital plane when using nominal surface properties reported by the manufacturer. Adjusted macro-models improve performance at the expense of requiring increased surface areas or reflectivity coefficients. In addition to improved radiation pressure models, newly estimated antenna patterns and a time-varying gravity field were used in the analysis. The reprocessed data confirm good agreement of the results of both receivers except for a relative timing error of 1.3 μs, and the yaw bias correction of −0.43° removes previously-observed systematic differences in the estimated empirical accelerations. Satellite laser ranging results based on SLRF2020 station coordinates demonstrate a 5—6 mm (1D RMS) accuracy of the GNSS-based POD solutions across the IGb14/IGS20 reference frame transition in November 2022.

Evaluating the Use of Seasonal Surface Displacements and Time‐Variable Gravity to Constrain the Interior of Mars

AbstractThe mass transport of volatiles on Mars represents a seasonally changing load on the surface of the planet. Like on Earth, as mass is redistributed across the planet, the surface responds in a complex manner becoming displaced downwards or upwards. The magnitude and extent of displacement depend on the properties of the load and mechanical properties of the planetary interior. Based on new estimates of the height variation of the seasonal polar caps (SPCs), we predict local surface displacements of up to tens of millimeters with a strong degree 1 signal throughout the Martian year. The long‐wavelength portion of the displacement is potentially observable, with a magnitude of a few millimeters, located away from the SPC where one could realistically measure it with a landed or orbital mission. We also model the direct contribution of this process to observable time variable gravity, where we find the zonal coefficients to be in line with previous measurements, although with a smaller magnitude. Future measurements of this displacement could be used to help elucidate the composition of the interior of Mars using this process as a probe into the Martian interior. Furthermore, more refined measurements of time‐variable gravity would be a powerful tool in constraining the pole‐to‐pole volatile cycle present on Mars.

A New Order Tracking Method for Fault Diagnosis of Gearbox under Non-Stationary Working Conditions Based on In Situ Gravity Acceleration Decomposition

Rotational speed measuring is important in order tracking under non-stational working conditions. However, sometimes, encoders or coded discs are not easy to mount due to the limited measurement environment. In this paper, a new in situ gravity acceleration decomposition method (GAD) is proposed for rotational speed estimation, and it is applied in the order tracking scene for fault diagnosis of a gearbox under non-stationary working conditions. In the proposed method, a MEMS accelerometer is locally embedded on the rotating shaft or disc in the tangential direction. The time-varying gravity acceleration component is sensed by the in situ accelerometer during the rotation of the shaft or disc. The GAD method is established to exploit the gravity acceleration component based on the linear-phase finite impulse response (FIR) filter and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) methods. Then, the phase signal of time-varying gravity acceleration is derived for rotational speed estimations. A motor–shaft–disc experimental setup is established to verify the correctness and effectiveness of the proposed method in comparison to a mounted encoder. The results show that both the estimated average and instantaneous rotational speed agree well with the mounted encoder. Furthermore, both the proposed GAD method and the traditional vibration-based tacholess speed estimation methods are applied in the context of order tracking for fault diagnosis of a gearbox. The results demonstrate the superiority of the proposed method in the detection of tooth spalling faults under non-stationary working conditions.

A novel dynamic scale factor designed for recovering global TWS changes

For time-variable satellite gravity solutions of GRACE and GRACE-FO in terms of spherical harmonics coefficients, the Scale Factor (SF) is often used to recover the close to “true” signal of Terrestrial Water Storage (TWS) anomalies. However, the conventional SF method has some limitations that may hinder its effectiveness, including: (1) their dependency on input hydrological models that may lead to divergent estimations of SFs; (2) the arbitrary choice of filter strength, which may not be representative in different regions; (3) limited consideration of SF in the temporal dynamics (the conventional SF was fixed value) for monthly varied TWS. Here, we propose a new Dynamic SF method to overcome these limitations and increase accuracy of the restored global TWS changes. This method involves: (1) the Bayesian Three-Cornered Hat (BTCH) method is applied to merge three sets of hydrological products into an optimal hydrological dataset to be used for estimating a unique SF, (2) the anisotropic DDK3 filter (found to be numerically optimal) is applied to suppress the correlated noise, and (3) an iterative Kalman filter process is formulated and implemented to estimate monthly Dynamic SF corresponding to monthly global TWS fields. The Dynamic SF outperformed an ordinary SF method in terms of the Root Mean Squared Error (RMSE), the Mean Absolute Error (MAE), and the Signal to Noise Ratio (SNR), which were found to be improved by 30.8%, 32.2%, and 41.3%, respectively. Moreover, the recovered TWS using the Dynamic SF method showed a good agreement with the GRACE/GRACE-FO RL06 mascon solutions of the CSR and that of JPL regarding the long-term trend, seasonal, and interannual variations.

SDUST2020MGCR: a global marine gravity change rate model determined from multi-satellite altimeter data

Abstract. Investigating the global time-varying gravity field mainly depends on GRACE/GRACE-FO gravity data. However, satellite gravity data exhibit low spatial resolution and signal distortion. Satellite altimetry is an important technique for observing the global ocean and provides many consecutive years of data, which enables the study of high-resolution marine gravity variations. This study aims to construct a high-resolution marine gravity change rate (MGCR) model using multi-satellite altimetry data. Initially, multi-satellite altimetry data and ocean temperature–salinity data from 1993 to 2019 are utilized to estimate the altimetry sea level change rate (SLCR) and steric SLCR, respectively. Subsequently, the mass-term SLCR is calculated. Finally, based on the mass-term SLCR, the global MGCR model on 5′ × 5′ grids (SDUST2020MGCR) is constructed by applying the spherical harmonic function method and mass load theory. Comparisons and analyses are conducted between SDUST2020MGCR and GRACE2020MGCR resolved from GRACE/GRACE-FO gravity data. The spatial distribution characteristics of SDUST2020MGCR and GRACE2020MGCR are similar in the sea areas where gravity changes significantly, such as the eastern seas of Japan, the western seas of the Nicobar Islands, and the southern seas of Greenland. The statistical mean values of SDUST2020MGCR and GRACE2020MGCR in global and local oceans are all positive, indicating that MGCR is rising. Nonetheless, differences in spatial distribution and statistical results exist between SDUST2020MGCR and GRACE2020MGCR, primarily attributable to spatial resolution disparities among altimetry data, ocean temperature–salinity data, and GRACE/GRACE-FO data. Compared with GRACE2020MGCR, SDUST2020MGCR has higher spatial resolution and excludes stripe noise and leakage errors. The high-resolution MGCR model constructed using altimetry data can reflect the long-term marine gravity change in more detail, which is helpful in studying seawater mass migration and its associated geophysical processes. The SDUST2020MGCR model data are available at https://doi.org/10.5281/zenodo.10701641 (Zhu et al., 2024).

Assessment of the Added Value of the GOCE GPS Data on the GRACE Monthly Gravity Field Solutions

The time-varying gravity field models derived from the Gravity Recovery and Climate Experiment (GRACE) satellite mission suffer from pronounced longitudinal stripe errors in the spatial domain. A potential way to mitigate such errors is to combine GRACE data with observations from other sources. In this study, we investigate the impacts on GRACE monthly gravity field solutions of incorporating the GPS data collected by the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission. To that end, we produce GRACE/GOCE combined monthly gravity field solutions through combination on the normal equation level and compare them with the GRACE-only solutions, for which we have considered the state-of-the-art ITSG-Grace2018 solutions. Analysis in the spectral domain reveals that the combined solutions have a notably lower noise level beyond degree 30, with cumulative errors up to degree 96 being reduced by 31%. A comparison of the formal errors reveals that the addition of GOCE GPS data mainly improves (near-) sectorial coefficients and resonant orders, which cannot be well determined by GRACE alone. In the spatial domain, we also observe a significant reduction by at least 30% in the noise of recovered mass changes after incorporating the GOCE GPS data. Furthermore, the signal-to-noise ratios of mass changes over 180 large river basins were improved by 8–20% (dependent on the applied Gaussian filter radius). These results demonstrate that the GOCE GPS data can augment the GRACE monthly gravity field solutions and support a future GOCE-type mission for tracking more accurate time-varying gravity fields.

Crustal Apparent Density Variations in the Middle Segment of the North Tianshan Mountains and Their Tectonic Significance

In this study, we collected mobile gravity observations in the middle segment of the North Tianshan Mountains from August 2016 to July 2022 and carried out classical adjustment calculations under the constraint of the absolute gravity datum to obtain the spatiotemporal variation pattern of the local gravity field. We used equivalent source inversion to obtain the spatiotemporal variation characteristics of crustal apparent density. We also extracted the coseismic deformation field from SAR data, using the 2016 Hutubi earthquake as an example, and constructed a model of the seismogenic fault. The gravity monitoring network in the study area performed well in resolving the earthquake source parameters. Both the time-varying gravity field and equivalent apparent density variation pattern show prominent zoning characteristics with a smoothly evolving spatial distribution over time. The variation trends of the gravity field and equivalent apparent density are in line with the orientation of tectonic structures, and their anomalous signals can be detected before and after an earthquake. The constructed seismogenic structure of the 2016 Hutubi earthquake indicates a typical thrust earthquake, probably occurring on a north-dipping blind fault beneath a region with intense crustal deformation. The subsurface tectonic system reflected by this earthquake can be informatively extended to the entire middle segment of the North Tianshan Mountains by subsurface configuration. Our findings can serve as a reference for analyzing the source characteristics of the time-varying gravity field and interpreting anomalous pre-seismic signals, and aid in understanding earthquake preparation zones and the mode of crustal tectonic movements.

Impact of the combination and replacement of SLR-based low-degree gravity field coefficients in GRACE solutions

GRACE and GRACE Follow-On (FO) missions provide time-variable gravity field models of unprecedented quality that allow for the hydrological, oceanic, and ice mass change studies on a global scale. However, the very low-degree coefficients derived from GRACE and GRACE-FO are of inferior quality due to thermal effects acting on satellites and malfunctioning of the onboard accelerometers. Therefore, C20 and C30 coefficients describing the Earth’s oblateness and the pear shape of the Earth, respectively, are being replaced by values derived from satellite laser ranging (SLR) in the standard GRACE solutions. This study assesses the impact of the replacement of low-degree gravity field coefficients in GRACE/GRACE-FO solutions by SLR data on the trend and seasonal signals of ice mass changes in Greenland and Antarctica. We found that the replacement of the low-degree gravity field coefficients changes the estimates of trends by 4, 8, and 22 Gt/year in Greenland, West, and East Antarctica, respectively, depending on the source of SLR coefficients and period for which the coefficients are replaced. In SLR and GRACE solutions, all coefficients of the same order and the same parity of degrees are strongly correlated. Therefore, replacing only two selected coefficients may lead to a biased solution. Thus, we propose to combine GRACE with SLR solutions up to a degree and order 10 × 10 to properly consider the sensitivity of each of the techniques to gravity field coefficients, instead of replacing two coefficients from SLR in GRACE solutions. The combined solution reduces the residual trend of post-glacial rebound from 1.2 to 0.9 Gt/year and from − 57.8 to − 57.0 Gt/year in Scandinavia and South Canada, respectively, when compared to GRACE/GRACE-FO solutions with the replacement of coefficients. The SLR-GRACE combination reduces the noise in the GRACE/GRACE-FO solutions by 8%, from 38 to 35 Gt, in the Fennoscandia region. In the periods when GRACE is at the end of its mission and observations are disrupted, the weights adjust the contribution from SLR and GRACE based on relative ratio of variances from each techniques. Thus, the combined solutions are more consistent with independent geophysical models of glacial isostatic adjustment, and the combinations are affected by smaller noise than the standard GRACE solutions and properly account for different sensitivities of SLR and GRACE techniques to low-degree time-variable gravity field coefficients.

A high-resolution time-variable terrestrial gravity field model of continental North China

Given the spatial resolution of ~300 km in Gravity Recovery and Climate Experiment (GRACE) measurements, accurately quantifying mass variations at smaller scales proves challenging. Here, we present a high-resolution time-variable gravity field model of continental North China. This model, denoted as IGP-NorthChina2022TG, contains 15 gravity field solutions determined using an innovative approach that relies on terrestrial gravity measurements and Slepian basis functions. IGP-NorthChina2022TG provides degree 150 gravity changes (spatial resolution of ~120 km) on a semi-annual basis from September 2009 to September 2016, in contrast to the monthly degree 60 GRACE solutions. Despite their different temporal resolutions, the good agreement between GRACE and the ground-based results up to degree 60 confirms the robustness and reliability of the proposed method and favors the combination of these two types of measurements. The gravity changes with much finer spatial resolution from IGP-NorthChina2022TG could complement GRACE solutions for sub-regional scale investigations in North China.

Long-term ice mass changes in Greenland and Antarctica derived from satellite laser ranging

Time-variable gravity field models obtained from satellite gravimetric techniques allow for the assessment of ice sheet mass changes in remote polar regions, such as Greenland and Antarctica. So far, GRACE has been the primary mission for obtaining the global time-variable gravity field models. However, GRACE was launched in 2002, thus very little is known about the global mass changes before this data, as well as between GRACE and its successor – GRACE Follow-On. We derive a method of gravity field recovery based on Satellite Laser Ranging (SLR) data to geodetic satellites that allows for obtaining direct ice mass change estimates for a period longer by 10 years than that provided by the GRACE missions. The developed method is based on splitting normal equation systems and re-stacking the solutions which allow for stable inversion, reduces the correlations between obtained parameters, stabilizes the ice mass estimates in polar regions, and reduces the noise over oceans by a factor of four. The secular trends obtained from SLR are equal to −113.5 and −82.8 Gt/year, whereas these are −119.1 and −83.3 Gt/year from GRACE and GRACE-FO to degree and order 10 for Greenland and West Antarctica, respectively, for the common period of 2002–2021 and after removing the post-glacial rebound effect. Despite the conformity of the trend and patterns, an underestimation is observed in the solutions expanded to degree and order 10. Therefore, scaling factors between GRACE/GRACE-FO expanded up to a degree and order 10 × 10 and 60 × 60 were derived and applied to SLR solutions to account for the differences in mass estimates due to the truncation of the models. SLR data revealed that in Greenland the smallest ice mass trends are for 1995–2000, 2000–2005, and 2015–2020 which are equal to +54.3, −15.5, and −75.9 Gt/year. The largest ice mass depletion periods took place in 2005–2010, 2010–2015, and recently in 2019–2021 with trends of −213.9, −287.2, and −276.1 Gt/year, respectively. For Greenland and West Antarctica, the period 2010–2015 is characterized by the most enormous ice depletion events, whereas the later 5-year period of 2015–2020 provided a near mass-equilibrium for Antarctica reducing the negative trend and returning to the situation from the ‘90s when no significant ice mass changes were observed.

Height Variations in the Mississippi River Basin From Daily Time-Varying Satellite Gravity Data and Hydrological Model

Height Variations in the Mississippi River Basin From Daily Time-Varying Satellite Gravity Data and Hydrological Model

Geophysical monitoring of the groundwater resources in the Southern Arabian Peninsula using satellite gravity data

In recent decades, geophysical and remote sensing monitoring techniques have advanced to the point where they can be utilized. It is possible to investigate the spatiotemporal mass fluctuations induced by groundwater changes over the Southern Arabian Peninsula (SAP) by combining time-variable gravity data with land surface model outputs and rainfall data. Here are the findings: The average annual precipitation rates for the whole study region were 91.11, 87.6, and 96.61 mm yr−1 during the entire period (2002–2021), period before 2013, and period after 2012, respectively. The southern and eastern parts (Zone I) of the investigated region show modest rainfall rates of 109.6, 105, and 117 mm yr−1 during the whole period, period before 2013, and period after 2012, respectively. The Rub El Khali region (Zone II) is receiving lower precipitation rates of 54.6, 53.3, and 56.5 mm yr−1 throughout the whole period, period before 2013, and period after 2012, respectively. Based on the three distinct gravity solutions, the average Terrestrial Water Storage (ΔTWS) values are computed through the entire period to be − 0.21 ± 0.011, − 0.15 ± 0.013, and − 0.32 ± 0.0107 cm yr−1 for the whole study region, Zone of the southern and eastern regions, and Zone of Rub El Khali, respectively. The whole study region, Zone of the southern and eastern parts, and Zone of Rub El Khali are showing highly negative ΔTWS in the period before 2013, in comparison to slightly negative to slightly positive ΔTWS trends in period after 2012. The average annual change in groundwater storage for the entire study area was calculated at − 0.21 ± 0.011, − 0.29 ± 0.024, and − 0.091 ± 0.038 cm yr−1 throughout the investigated period, period before 2013, and period after 2012, respectively. Zone of Rub El Khali is showing higher negative groundwater storage trend (ΔGWS) averaged at − 0.32 ± 0.104 cm yr−1 throughout the investigated period, whereas Zone of southern and eastern regions is showing lower negative groundwater storage trend of − 0.15 ± 0.013 cm yr−1. Most of the recharge rate occurs in Zone of the southern and eastern regions reaching up to + 0.77 ± 0.092 cm yr−1 by taking the average groundwater withdrawal rate of + 0.92 ± 0.092 cm yr−1 during the whole period. This integrated approach is a valuable and economical method for more effectively assessing the variations of groundwater resources across wide areas.