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Time-variable gravity field models derived from observations of the Gravity Recovery and Climate Experiment (GRACE) mission, whose science operations phase ended in June 2017 after more than 15 years, enabled a multitude of studies of Earth’s surface mass transport processes and climate change. The German Research Centre for Geosciences (GFZ), routinely processing such monthly gravity fields as part of the GRACE Science Data System, has reprocessed the complete GRACE mission and released an improved GFZ GRACE RL06 monthly gravity field time series. This study provides an insight into the processing strategy of GFZ RL06 which has been considerably changed with respect to previous GFZ GRACE releases, and modifications relative to the precursor GFZ RL05a are described. The quality of the RL06 gravity field models is analyzed and discussed both in the spectral and spatial domain in comparison to the RL05a time series. All results indicate significant improvements of about 40% in terms of reduced noise. It is also shown that the GFZ RL06 time series is a step forward in terms of consistency, and that errors of the gravity field coefficients are more realistic. These findings are confirmed as well by independent validation of the monthly GRACE models, as done in this work by means of ocean bottom pressure in situ observations and orbit tests with the GOCE satellite. Thus, the GFZ GRACE RL06 time series allows for a better quantification of mass changes in the Earth system.

A new synthetic model of the time-variable global gravity field is now available based on realistic mass variability in atmosphere, oceans, terrestrial water storage, continental ice-sheets, and the solid Earth. The updated ESA Earth System Model is provided in Stokes coefficients up to degree and order 180 with a temporal resolution of 6 h covering the time period 1995–2006, and can be readily applied as a source model in future gravity mission simulation studies. The model contains plausible variability and trends in both low-degree coefficients and the global mean eustatic sea level. It depicts reasonable mass variability all over the globe at a wide range of frequencies including multi-year trends, year-to-year variability, and seasonal variability even at very fine spatial scales, which is important for a realistic representation of spatial aliasing and leakage. In particular on these small spatial scales between 50 and 250 km, the model contains a range of signals that have not been reliably observed yet by satellite gravimetry. In addition, the updated Earth System Model provides substantial high-frequency variability at periods down to a few hours only, thereby allowing to critically test strategies for the minimization of temporal aliasing.

The Earth’s time-variable gravity field holds significant research and application value. However, satellite gravimetry missions such as GRACE and GRACE-FO face limitations in spatial resolution when detecting monthly gravity fields, while traditional radar altimeters lack the observational efficiency needed for monthly gravity anomaly inversion. These limitations hinder further exploration and application of the Earth’s time-variable gravity field. Leveraging its advantages, such as rapid global coverage, high revisit frequency, and low cost for constellation formation, spaceborne GNSS-R technology holds the potential to address the observational efficiency gaps of traditional radar altimeters. This study presents the first assessment of the capability of spaceborne GNSS-R interferometric altimetry for high spatial resolution monthly marine gravity anomaly inversion through simulations. The results indicate that under the PARIS Operational scenario of a single GNSS-R satellite (a spaceborne GNSS-R interferometric altimetry scenario proposed by Martin-Neira), a 30′ grid resolution marine gravity anomaly can be inverted with an accuracy of 4.93 mGal using one month of simulated data. For a dual-satellite constellation, the grid resolution improves to 20′, achieving an accuracy of 4.82 mGal. These findings underscore the promise of spaceborne GNSS-R interferometric altimetry technology for high spatial resolution monthly marine gravity anomaly inversion.

A realistically perturbed synthetic de-aliasing model consistent with the updated Earth System Model of the European Space Agency is now available over the period 1995–2006. The dataset contains realizations of (1) errors at large spatial scales assessed individually for periods 10–30, 3–10, and 1–3 days, the S1 atmospheric tide, and sub-diurnal periods; (2) errors at small spatial scales typically not covered by global models of atmosphere and ocean variability; and (3) errors due to physical processes not represented in currently available de-aliasing products. The model is provided in two separate sets of Stokes coefficients to allow for a flexible re-scaling of the overall error level to account for potential future improvements in atmosphere and ocean mass variability models. Error magnitudes for the different frequency bands are derived from a small ensemble of four atmospheric and oceanic models. For the largest spatial scales up to d/o = 40 and periods longer than 24 h, those error estimates are approximately confirmed from a variance component estimation based on GRACE daily normal equations. Future mission performance simulations based on the updated Earth System Model and the realistically perturbed de-aliasing model indicate that for GRACE-type missions only moderate reductions of de-aliasing errors can be expected from a second satellite pair in a shifted polar orbit. Substantially more accurate global gravity fields are obtained when a second pair of satellites in an moderately inclined orbit is added, which largely stabilizes the global gravity field solutions due to its rotated sampling sensitivity.

The climate anomaly in the Amazon River basin (ARB) has a very important influence on global climate change and has always been the focus of scientists from all over the world. To fill the 11-month data gap between Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) missions, we fused the TWSC results from six GRACE solutions by using the generalized three-cornered hat and the least square method to improve the reliability of TWSC results, and then combined Swarm data to construct an uninterrupted long time series of a TWSC-based drought index (GRACE/Swarm-DSI). The drought index was used to detect and characterize the drought events in the ARB between 2003 and 2020. The results show that GRACE/Swarm-DSI has a strong correlation with Self-Calibrating Palmer Drought Severity Index (SCPDSI) (0.6345), Standardized Precipitation Evapotranspiration Index-3 (SPEI-3) (0.5411), SPEI-6 (0.6377) and SPEI-12 (0.6820), and the Nash–Sutcliffe efficiency between GRACE/Swarm-DSI and the above four drought indices are 0.3348, 0.2786, 0.4044 and 0.4627, respectively. Eleven drought events were identified in the ARB during the study period, and the 2005, 2010 and 2016 droughts are the most severe and the longest. The correlation between GRACE/Swarm-DSI and precipitation (PPT) (the correlation coefficient is 0.55 with a 2-month delay) is higher than that of evapotranspiration (ET) (the correlation coefficient is −0.18 with a 12-month delay). It explains that less PPT is the main cause of drought events in the ARB. The influence of PPT is greater in the plains than the one in the mountains and the response time of GRACE/Swarm-DSI to PPT is 1~2 months in most regions. Our results provide a certain reference for the hydrological application of the Swarm model in filling the gap between GRACE and GRACE-FO missions.

The mass changes in the Earth’s surface internally derived from the Gravity Recovery and Climate Experiment (GRACE) and the GRACE Follow-On (GRACE-FO) missions have played an important role in the research of various geophysical phenomena. However, the one-year data gap between these two missions has broken the continuity of this geophysical research. In order to assess the feasibility of using the Swarm time-variable gravity field (TVGF) to bridge the data gap, we compared Swarm with the GRACE/GRACE-FO models in terms of model accuracy, observation noise and inverted terrestrial water storage change (TWSC). The results of the comparison showed that the difference between the degree-error root mean square (RMS) of the two models is small, within degree 10. The correlation between the spherical harmonic coefficients of the two models is also relatively high, below degree 17. The observation noise values of GRACE/GRACE-FO are smaller than those of Swarm. Therefore, the latter model requires a larger filter radius to lower these noise levels. According to the correlation coefficients and the time series map of TWSC in the Amazon River basin, the results of GRACE and Swarm are similar. In addition, the TWSC signals were further analyzed. The long-term trend changes of TWSC derived from GRACE/GRACE-FO and the International Combination Service for Time-variable Gravity Fields (COST-G)-Swarm over the period from December 2013 to May 2020 were −0.72 and −1.05 cm/year, respectively. The annual amplitudes of two models are 15.65 and 15.39 cm, respectively. The corresponding annual phases are −1.36 and −1.33 rad, respectively. Our results verified that the Swarm TVGF has the potential to extract TWSC signals in the Amazon River basin and can serve as a complement to GRACE/GRACE-FO data for detecting TWSC in local areas.

Mass redistribution of the Earth causes variable loading that deforms the solid Earth. While most recent studies using geodetic techniques focus on regions (such as the Amazon basin and the Nepal Himalayas) with large seasonal deformation amplitudes on the order of 1–4 cm due to hydrologic loading, few such studies have been conducted on the regions where the seasonal deformation amplitude is half as large. Here, we use joint GPS and GRACE data to investigate the vertical deformation due to hydrologic loading in the North China Plain, where significant groundwater depletion has been reported. We found that the GPS- and GRACE-derived secular trends and seasonal signals are in good agreement, with an uplift magnitude of 1–2 mm/year and a correlation of 85.0%–98.5%, respectively. This uplift rate is consistent with groundwater depletion rate estimated from GRACE data and in-situ groundwater measurements from earlier report studies; whereas the seasonal hydrologic variation reflects human behavior of groundwater pumping for agriculture irrigation in spring, leading to less water storage in summer than that in the winter season. However, less than 20% of weighted root-mean-squared (WRMS) reductions were detected for all the selected GPS stations when GRACE-derived seasonal deformations were removed from detrended GPS height time series. This discrepancy is probably because the GRACE-derived seasonal signals are large-scale, while the GPS-derived signals are local point measurements.

Large, confined aquifer systems play a vital role in sustaining human settlements and industries in many regions. Understanding the sustainability of these water resources requires the evaluation of groundwater storage change. Direct in‐situ observation of groundwater storage is limited by the distribution and availability of groundwater level and aquifer storativity data. Here, we use and compare two auxiliary methods, applied at basin and sub‐basin scales, to assess groundwater storage changes in the Great Artesian Basin (GAB), one of the World's largest confined aquifer systems. The first, the groundwater budget, derives storage change as the residual of fluxes in and out of the GAB, assuming they are all accounted for and accurately estimated. The second uses time‐variable gravity data from GRACE satellites to estimate temporal changes in groundwater mass, assuming that all other components of the terrestrial water mass change detected by GRACE are correctly subtracted. Despite the depletion observed during the 20th century, groundwater storage is mostly stable during 2002–2022. An increase in storage is detected in the Surat sub‐basin, a major recharge area. This increase is attributed to an over‐representation of large recharge events during the study period and/or storage recovery following rehabilitation of free‐flowing bores. The approach consisting in disaggregating GRACE data assumes that water storage changes in confined aquifers is dominated by changes in the GAB, and as such, it may overestimate the increase in the GAB by incorrectly attributing the increase occurring in overlying aquifers to the GAB. In contrast, the recharge estimates used in the groundwater budgets do not account for flood recharge and might underestimate storage increase in the GAB. Plain Language Summary Monitoring groundwater storage in large, confined aquifers is often impossible as it requires large groundwater level and lithological data sets that are often unavailable. However, monitoring is crucial for assessing and managing the sustainability of this resource and manage it appropriately. This study uses and compares two auxiliary methods, applied at basin and sub‐basin scales, to assess groundwater storage changes in the Great Artesian Basin (GAB), one of the World's largest confined aquifer systems. The groundwater budget approach estimates water storage changes by adding up the amounts of groundwater that goes in and out of the aquifer system. The satellite gravimetry approach uses the temporal changes of Earth's gravity field to infer changes in groundwater mass. Both methods agree that, despite the depletion observed during the 20th century, groundwater storage in the GAB was mostly stable during 2002–2022. An increase in groundwater storage is detected near major recharge areas. It is attributed to an over‐representation of large recharge events during the study period and/or groundwater storage recovery following capping of free‐flowing bores. Key Points GRACE and groundwater budgets agree that water storage in the Great Artesian Basin was stable for the period 2002–2022 Increased storage in the Surat sub‐basin is attributed to bore rehabilitation and/or increased recharge during the study period Within the Surat sub‐basin, increased storage may be overestimated by GRACE and/or underestimated by the groundwater budgets

The development of optical clocks has experienced significant acceleration in recent years, positioning them as one of the most promising quantum optical sensors for next-generation gravimetric missions (NGGMs). This study investigates the feasibility of retrieving the temporal gravity field via improved optical clocks through a closed-loop simulation. It evaluates optical clock capabilities in temporal gravity field inversion by considering the clock noise characteristics, designing satellite formations, and simulating the performance of optical clocks. The results indicate that optical clocks exhibit higher sensitivity to low-degree gravity field signals. However, when the optical clock noise level drops below 1 × 10 −19 / τ (τ being the averaging time in seconds) in the satellite-to-ground (SG) mode or below 1 × 10 −20 / τ in the satellite-to-satellite (SS) mode, atmospheric and oceanic (AO) errors become the dominant source of error. At this noise level, optical clocks can detect time-variable gravity signals up to approximately degree 30. Compared to existing gravity measurement missions such as GRACE-FO, optical clocks exhibit consistent results in detecting signals below degree 20. If the orbital altitude is reduced to 250 km, the performance of optical clocks across all degrees aligns with the results of GRACE-FO. Furthermore, the study reveals that lowering the orbital altitude of satellite-based optical clocks from 485 to 250 km improves results by an average of 33%. Switching from the SS mode to the SG mode results in an average improvement of 51%, while each order-of-magnitude improvement in clock precision enhances results by an average of 60%. In summary, these findings highlight the tremendous potential of optical clock technology in determining Earth’s temporal gravity field and provide crucial technological support for NGGMs.

The primary objective of the gravity recovery and climate experiment follow-on (GRACE-FO) satellite mission, due for launch in August 2017, is to continue the GRACE time series of global monthly gravity field models. For this, evolved versions of the GRACE microwave instrument, GPS receiver, and accelerometer will be used. A secondary objective is to demonstrate the effectiveness of a laser ranging interferometer (LRI) in improving the satellite-to-satellite tracking measurement performance. In order to investigate the expected enhancement for Earth science applications, we have performed a full-scale simulation over the nominal mission lifetime of 5 years using a realistic orbit scenario and error assumptions both for instrument and background model errors. Unfiltered differences between the synthetic input and the finally recovered time-variable monthly gravity models show notable improvements with the LRI, on a global scale, of the order of 23 %. The gain is realized for wavelengths smaller than 240 km in case of Gaussian filtering but decreases to just a few percent when anisotropic filtering is applied. This is also confirmed for some typical regional Earth science applications which show randomly distributed patterns of small improvements but also degradations when using DDK4-filtered LRI-based models. Analysis of applied error models indicates that accelerometer noise followed by ocean tide and non-tidal mass variation errors are the main contributors to the overall GRACE-FO gravity model error. Improvements in these fields are therefore necessary, besides optimized constellations, to make use of the increased LRI accuracy and to significantly improve gravity field models from next-generation gravity missions.