Small satellite formations and constellations for observing sub-daily mass changes in the Earth system

Thanks to the unprecedented success of Gravity Recovery and Climate Experiment (GRACE), its successive mission GRACE Follow-On (GFO) has been in orbit since May 2018 to continue measuring the Earth’s mass transport. In order to possibly enhance GFO in terms of mass transport estimates, four orbit configurations of future polar-type gravity mission (FPG) (with the same payload accuracy and orbit parameters as GRACE, but differing in orbit inclination) are investigated by full-scale simulations in both standalone and jointly with GFO. The results demonstrate that the retrograde orbit modes used in FPG are generally superior to prograde in terms of gravity field estimation in the case of a joint GFO configuration. Considering the FPG’s independent capability, the orbit configurations with 89- and 91-degree inclinations (namely FPG-89 and FPG-91) are further analyzed by joint GFO monthly gravity field models over the period of one-year. Our analyses show that the FPG-91 basically outperforms the FPG-89 in mass change estimates, especially at the medium- and low-latitude regions. Compared to GFO & FPG-89, about 22% noise reduction over the ocean area and 17% over land areas are achieved by the GFO & FPG-91 combined model. Therefore, the FPG-91 is worthy to be recommended for the further orbit design of FPGs.

The precise tracking of distance variations between two satellites in low Earth orbit can provide key data for the understanding of the Earth’s system, specifically on seasonal and sub-seasonal water cycles and their impact on water levels. Measured distance variations, caused by local variations in gravitational field, serve as inputs to complex gravity models with which the movement of water on the globe can be identified. Satellite missions GOCE (2009–2013) and GRACE (2002–2017) delivered a significant improvement to our understanding of spatial and temporal gravity variations. Since 2018, GRACE Follow-On has been providing data continuity and features for the first time through the use of a laser interferometer as the technology demonstrator, in addition to a microwave ranging system as the main instrument. The laser interferometer provides an orders-of-magnitude lower measurement noise, and thereby could enable a significant improvement in the measurement of geoids if combined with suitable improvements in auxiliary instrumentation and Earth system modelling. In order to exploit the improved ranging performance, the ESA is investigating the design of a ‘Next Generation Gravity Mission’, consisting of two pairs of satellites with laser interferometers, improved accelerometers and improved platform performance. In this paper, we present the current design of the laser interferometer developed by us, the development status of the individual instrument units and the options available.

When estimating time-variable gravity field models from GRACE Follow-On data, a set of a priori given background force models is introduced in the processing to enable the computation of monthly snapshots of spherical harmonic coefficients representing the state of the Earth’s gravity field. The to-be-estimated spherical harmonic series has to be truncated at a certain point, for GRACE Follow-On commonly at degree and order 96, and one of the background models is usually a model for the gravity field itself, which is used to reduce higher frequency static gravity field signal to avoid aliasing (contained in degrees above 96). In this study we take a look on the influence of different strategies to treat the high degree gravity field signal in monthly gravity field solutions from GRACE Follow-On data. We estimate temporal gravity fields with fixed high degrees of different a priori background gravity field models, and opposed to this, we also co-estimate static spherical harmonic coefficients from degree 97 up to degree and order 160 from 51 months of GRACE Follow-On data along with the monthly snapshots to enable a consistent handling of correlations between time-variable and static gravity field coefficients. The observation noise modelling of the data is handled by an empirical covariance estimation for the noise based on post-fit residuals between the final GRACE Follow-On orbits, that are co-estimated together with the gravity field, and the observations. Since the post-fit residuals, amongst other things, depend on the choice of the background force models they are a potential carrier of a priori information into the final solution. The results show that a formal correlation between the time-variable and static gravity field coefficients is almost non-existent, and also the empirical covariance model has only minor impacts on this correlation. Only a poor choice of the background gravity field requires a prior or co-estimation of the static gravity field.

The GRACE Follow-On (GRACE-FO) satellite mission, a partnership between NASA (US) and GFZ (Germany), successfully completed its nominal five-year prime mission phase in May 2023, and is currently in its extended mission phase. GRACE-FO continues the unique essential climate data record of mass change in the Earth system initiated in 2002 by the GRACE mission (2002-2017). The combined GRACE & GRACE-FO data records now span 23 years and provide foundational observations of monthly to decadal global mass changes and transports in the Earth system derived from temporal variations in the Earth’s gravity field.  In parallel, as part of NASA’s Earth System Observatory (ESO), a continuity mission called GRACE-Continuity (GRACE-C) scheduled for launch end of 2028 is being developed in partnership between NASA (US) and DLR (Germany), leveraging heritage elements considerably in the design.  One departure from heritage, is that the primary ranging instrument on GRACE-C will be a higher precision laser interferometer, capitalizing on the successful demonstration of this technology on GRACE-FO.  In this presentation, we will present updates on GRACE-FO in the context of satellite operations, data processing, and science/applications highlights, along with updates on the development of GRACE-C, which is meanwhile in Phase C and approaching the Critical Design Review in May 2025.  Prospects for achieving gap-free continuity between GRACE-FO and GRACE-C will be presented.

SUMMARY The Combination Service for Time-variable Gravity fields (COST-G) operationally provides combinations of monthly Earth gravity field models derived from observations of the microwave ranging instrument of the GRACE Follow-on (GRACE-FO) satellite mission, applying the quality control and combination methodology originally developed by the Horizon 2020 project European Gravity Service for Improved Emergency Management for the data of the GRACE satellites. In the frame of the follow-up Horizon 2020 project Global Gravity-based Groundwater Product (G3P), the GRACE-FO combination is used to derive global grids of groundwater storage anomalies. To meet the user requirements and achieve optimal signal-to-noise ratio, the combination has been further developed and extended to incorporate: • new time-series based on the alternative accelerometer transplant product generated in the frame of the project by the Institute of Geodesy at the Graz University of Technology, which specifically improves the estimation of the C30 coefficient and also reduces the noise at medium to short wavelengths, and • the new time-series AIUB–GRACE-FO–RL02 of monthly GRACE-FO gravity fields, which is derived at the Astronomical Institute of the University of Bern by applying empirical noise modelling techniques. The COST-G quality control confirms the consistency of the contributing GRACE-FO time-series concerning the signal amplitude of seasonal hydrology in large river basins and the secular mass change in polar regions, but it also indicates rather diverse noise characteristics. The difference in the noise levels is taken into account in the combination process by relative weights derived by variance component estimation on the solution level. The weights are expected to be inverse proportional to the noise levels of the individual gravity field solutions. However, this expectation is violated when applying the weighting scheme as developed for the GRACE combination. The reason is found in the high-order coefficients of the gravity field, which are poorly determined from the low–low range-rate observations due to the observation geometry and suffer from aliasing due to the malfunctioning accelerometer onboard one of the GRACE-FO satellites. Hence, for the final G3P-combination a revised weighting scheme is applied where the gravity field coefficients beyond order 60 are excluded from the determination of the weights. The quality of the combined gravity fields is assessed by comparison of the noise content and the signal-to-noise ratio with the individual time-series. Independent validation is provided by the COST-G validation centre at the GFZ German Research Centre for Geosciences, where orbit fits of the low-flying Gravity and steady-state Ocean Circulation Explorer satellite are performed that confirm the high quality of the combined GRACE-FO gravity fields. By the end of the G3P project, the new combination scheme is implemented by COST-G as the new COST-G–GRACE-FO–RL02 and continued to be used for the operational GRACE-FO combination.

Tracking inter-annual terrestrial water storage variations over Lake Baikal basin from GRACE and GRACE Follow-On missions

The provided gravity fields of the Gravity Recovery and Climate Experiment (GRACE) mission are noisy. In order to restore the true geophysical signal, it is essential to apply an appropriate filter. A filtering minimizes the noise, as well as affects the real signal inducing uncertainty in the final results. To date, to restore the suppressed geophysical signal the majority of studies have relied on determining the scaling factor using a hydrological model. To estimate the magnitude of the leakage effect we use only the filtered GRACE Follow-On (GRACE-FO) gravity fields. We study two different data-driven approaches, i.e. method of (i) scale and (ii) deviation. For the first method, to derive the scale factor a uniform layer approximation is used. The factor depends on the filter kernel used and the basin mask i.e., its shape and size, and is used to counter the attenuation of the basin-confined signal. For the second approach, the restored signal is independent of the river basin size. It attempts to obtain the deviation integral, which is determined from the filtered deviation field and the regional average estimated for the selected area. We analyze the signal leakage for GRACE-FO monthly gravity fields based on recent the Science Data System (SDS) solutions, i.e., the Center for Space Research (CSR), the German Research Center for Geosciences (GFZ) and the NASA’s Jet Propulsion Laboratory (JPL). We use the available GRACE-FO data for 67 months (June 2018 to February 2024) in the form of spherical harmonics up to degree and order 96. For detailed analysis we choose 24 river basins over Europe that are larger than 50,000 km2 and experienced extreme hydrometeorological changes in recent years. To assess the reliability of obtained results we use total water storage (TWS) from GRACE-FO JPL mascon solution and the Global Land Data Assimilation System (GLDAS) hydrological model. For spherical harmonics we find the largest differences between original (Gaussian-filtered) and data-driven fields in the parts of Europe indicating disparate TWS signals within small basins. We observe changes in trend values by ±1-2 mm/yr and amplitudes by up to 5 cm in the western and the northeastern river basins. The regions with extreme values are spatially coherent with the mascon solution results and are underestimated by the hydrological model mostly in the western areas. The estimated true leakage represents up to 30% of total TWS signal and varies from single cm (e.g., Douro, Ebro, Narva) to even 20 cm (e.g., Dniestr, Northern Dvina, Tigris-Euphrates).

We study temporal gravity field determination from GRACE Follow-On satellite-to-satellite tracking data using the inter-satellite link of the K-Band Ranging System (KBR) and kinematic positions of the satellites as observations and pseudo-observations, respectively. In addition, we introduce the range-rate observations collected by the Laser Ranging System (LRI) as further observation group. We compute our solutions with the Celestial Mechanics Approach using next to the kinematic positions either only LRI range-rate observations or combining them with the KBR derived range-rate data by the means of Variance Component Estimation (VCE).The stochastic noise of the KBR and LRI data is modelled with an empirical description of the noise based on the post-fit residuals between the final GRACE Follow-On orbits, that are co-estimated together with the gravity field, and the observations, expressed in position residuals to the kinematic positions and in KBR and/or LRI range-rate residuals. We validate the LRI-only and KBR+LRI monthly solutions by comparing them with the KBR-only derived models from the operational GRACE Follow-On processing at the AIUB, by examining the stochastic behaviour of respective post-fit residuals and by inspecting  areas where a low noise is expected. Last but not least, we investigate the influence of LRI-only and KBR+LRI monthly gravity field solutions in a  combination of monthly gravity fields based on other approaches as it is done by the Combination Service for Time-variable Gravity fields (COST-G) and make use of noise and signal assessment applying the quality control tools routinely used in the frame of COST-G.

Variations in Earth’s rotation, encompassing polar motion (PM) and the length-of-day (LOD) changes, result from a variety of factors influencing mass distribution and movement. These factors include the redistribution of air and water masses within the climate system and the solid Earth, and exchanges of angular momentum between the core and mantle. The ability to differentiate between these diverse sources is crucial for comprehending processes occurring at or near the Earth's surface, as well as within its interior.Fluctuations in the low-degree spherical harmonic coefficients of Earth's gravitational potential are linked to the redistribution of mass on a large scale within and on the planet. Observing changes in these coefficients provides a means to investigate the movement of mass within the Earth system. The degree-2 order-0 coefficient (C20) of geopotential holds particular significance for Earth rotation studies since C20 variations (ΔC20) are directly linked to the corresponding excitations of LOD. ΔC20 can be determined from various methods, of which Satellite Laser Ranging (SLR) measurements have the longest tradition. Launching Gravity Recovery and Climate Experiment (GRACE) in 2002 and GRACE Follow-On (GRACE-FO) in 2018 brought new measurements of changes in the Earth's gravitational field, including estimates of the ΔC20. However, estimates of ΔC20 from GRACE/GRACE-FO have limitations due to orbital geometry, the relatively short distance between the two satellites, and tide-like aliases. In practice, GRACE/GRACE-FO computing centres replace ΔC20 with an estimate from SLR measurements. Combining GRACE/GRACE-FO and SLR observations could enhance the accuracy of determining low-degree coefficients of geopotential, including ΔC20, ΔC21, and ΔS21.In this study, we reassess the excitation of LOD over the period 2002–2023, estimated from five different data sources: SLR, GRACE/GRACE-FO, a combination of SLR+GRACE/GRACE-FO, geodetic observations, and geophysical fluid models. To each of the time series we apply the same processing to isolate long-period, seasonal and non-seasonal short-term fluctuations. For every component, we conduct a comparative analysis aiming to evaluate the consistency among various estimates and identify discrepancies between the series. We show that combining GRACE/GRACE-FO with SLR data improves the consistency between ΔC20-derived and observed LOD excitation for the studied oscillations.

<p>The GRACE mission (2002-2017) delivered temporal gravity field solutions of the Earth for 15 years. It's successor, GRACE follow-on (GRACE-FO) is continuing it's legacy since May 2018. The time series of monthly gravity fields revealed global mass redistribution in in the near surface layer of the Earth with unprecedented accuracy. This assessed a completely new observable in geoscience disciplines and has become a crucial data product for climate research.<br>Despite the groundbreaking success and relevance of the GRACE mission(s) for Earth observation and climate science, no further successor gravity mission is planned, yet. Summarized by the name Next Generation Gravity Mission (NGGM) concepts for future gravimetry missions have been proposed and analyzed for a while. As an outcome of these studies the so called Bender-configuration (two GRACE-like satellite pairs, one in a polar orbit and a second in an inclined orbit around 60° to 70°) is the concept currently favored by the scientific community for a candidate of the next gravity mission to be realized.</p><p><br>However, an other concept still remains interesting due to specific advantages that might contribute to future improvements of gravity missions. In order to emphasize this, we present results of a full closed loop-simulation for a different ll-SST approach, the so called pendulum. It offers a quite similar overall performance with just two satellites. For this configuration the satellites are following each other in orbits with slightly different longitudes of the ascending nodes, thus the inter-satellite measurement direction is varying between along-track and cross-track. This configuration makes an interferometric laser ranging (LRI) quite challenging on the technical level. Nevertheless, the LRI accuracy is not necessarily needed. The relevance of the pendulum configuration has also been shifted into the focus of the French MARVEL mission proposal.</p><p><br>In this contribution we analyze in detail the performance of the pendulum formation with the main parameters being the angle between along-track and cross-track component of the ranging direction at the equator, and the mean distance between the satellites. We conduct the angle variation for different mean ranges and assumed ranging accuracies. As reference, the GRACE and Bender concepts are simulated, as well. The orbit simulations are performed using a derivative of the ZARM/DLR XHPS mission simulator including high precision implementations of non-gravitational accelerations.<br>The different concepts and configurations include complete GRACE-FO like attitude control and realistic environment models. State-of-the-art instrument noise models based on GRACE/-FO are used to generate observation data for accelerometer (ACC), range dependent inter satellite ranging (KBR/LRI), kinematic orbit solution (KOS) and star camera (SCA). For the gravity recovery process we use the classical variational equation approach. As for real GRACE processing, ACC calibration parameter are estimated and KOS and KBR range-rate observations are weighted by VCE.</p>

Over the past 20 years, the Gravity Recovery and Climate Experiment (GRACE), and its successor mission, GRACE‐Follow On (GRACE‐FO) have made significant contributions to time‐variable gravity field modeling. A Chinese low‐low satellite‐to‐satellite tracking gravimetry mission (i.e., Chinese future gravimetry mission) has been confirmed to be selected as the polar‐orbiting satellite gravimetry mission for China, because of the capability to collect gravity data globally. However, the analysis of potential contributions to geosciences from GRACE‐FO coupling with the Chinese future gravimetry mission is still limited. This study combines GRACE‐FO and Chinese future gravimetry missions as the Dual GRACE‐like Polar satellite Constellation (DGPC). By carefully choosing the initial orbit parameters of the Chinese future gravimetry mission with the differential evolution algorithm, the DGPC is expected to mitigate the temporal aliasing effects by improving the temporal resolution of time‐variable gravity solutions (i.e., 1‐day and 3‐day solutions). Regarding the spectral‐domain evaluation, zonal, tesseral, and sectorial coefficients estimated by the DGPC show approximately 6.01%–13.42% noise reductions compared with GRACE‐FO. Regarding the spatial‐domain evaluation, the DGPC can suppress noises of about 39.44% and 31.12% in annual amplitude and long‐term trend, respectively. On this basis, this paper analyzes the effectiveness of the DGPC in potential contributions to geosciences (e.g., hydrology, glaciology, and seismology). Specifically, the DGPC can improve accuracy by about 36.96%, 25.85%, and 33.16% with respect to GRACE‐FO for signals in the subhumid basin, signals of ice‐sheet mass balance over Greenland, and coseismic displacement of the fault zone, respectively. In general, the potential capability for high‐frequency signals recovery of the DGPC would facilitate contributions of satellite gravimetry to geosciences.

Abstract. Time variable gravity fields, reflecting variations of mass distribution in the system Earth is one of the key parameters to understand the changing Earth. Mass variations are caused either by redistribution of mass in, on or above the Earth's surface or by geophysical processes in the Earth's interior. The first set of observations of monthly variations of the Earth gravity field was provided by the US/German GRACE satellite mission beginning in 2002. This mission is still providing valuable information to the science community. However, as GRACE has outlived its expected lifetime, the geoscience community is currently seeking successor missions in order to maintain the long time series of climate change that was begun by GRACE. Several studies on science requirements and technical feasibility have been conducted in the recent years. These studies required a realistic model of the time variable gravity field in order to perform simulation studies on sensitivity of satellites and their instrumentation. This was the primary reason for the European Space Agency (ESA) to initiate a study on ''Monitoring and Modelling individual Sources of Mass Distribution and Transport in the Earth System by Means of Satellites''. The goal of this interdisciplinary study was to create as realistic as possible simulated time variable gravity fields based on coupled geophysical models, which could be used in the simulation processes in a controlled environment. For this purpose global atmosphere, ocean, continental hydrology and ice models were used. The coupling was performed by using consistent forcing throughout the models and by including water flow between the different domains of the Earth system. In addition gravity field changes due to solid Earth processes like continuous glacial isostatic adjustment (GIA) and a sudden earthquake with co-seismic and post-seismic signals were modelled. All individual model results were combined and converted to gravity field spherical harmonic series, which is the quantity commonly used to describe the Earth's global gravity field. The result of this study is a twelve-year time-series of 6-hourly time variable gravity field spherical harmonics up to degree and order 180 corresponding to a global spatial resolution of 1 degree in latitude and longitude. In this paper, we outline the input data sets and the process of combining these data sets into a coherent model of temporal gravity field changes. The resulting time series was used in some follow-on studies and is available to anybody interested.

As the largest component of Earth's time‐variable gravity field, is crucial for understanding regional mass variability and climate changes. However, the estimated by Gravity Recovery and Climate Experiment Follow‐On (GRACE‐FO) is currently unreliable and has been replaced by values derived from the satellite laser ranging (SLR) to ensure the proper scientific application of GRACE‐FO data products. Yet, exploring the reasons for the bias in the estimates has been of great interest, as there is always a concern about the inconsistency between the SLR and GRACE solutions. This study investigates the impact of accelerometer (ACC) data processing methods on the accuracy of estimation by examining the anomalous response characteristics of the GRACE‐FO ACC to the thruster. Firstly, using the statistical analysis method, we identify a correlation between the anomalous response caused by the Roll thrusters and the ACC range mode. From this basis, we make a conjecture about the mechanism of anomalous response generation, and a new thruster firing physical model based on statistical results is proposed to replace the anomalous response and optimize the current ACC data processing flow. From the results of the gravity field recovery, the corrected ACC data improve the accuracy of the estimation of . After multiple months of estimation, the estimate RMSD between the new ACC product and the TN‐14 solutions was , better than the precision of the estimate of the reference solutions. Finally, we discuss the correlation between this ACC processing method and the accuracy of estimation.

The GRACE and GRACE-FO missions have been fundamental in establishing a near-continuous time series of global mass transport since 2002. However, monthly gravity field recovery using these mission data includes errors limiting the spatial and temporal resolution of the estimated gravity field solutions. Besides the noise of the accelerometer instruments, the primary error contributions arise from temporal aliasing errors due to undersampling of signals to be recovered (e.g., hydrology), uncertainties in the de-aliasing models (e.g., non-tidal atmosphere and ocean), and imperfect ocean tide models. Especially the latter will also remain one of the most limiting factors in determining high-resolution temporal gravity fields from Next-Generation Gravity Missions (NGGM).In this context, recent further developments have been made within the research unit, NEROGRAV (New Refined Observations of Climate Change from Spaceborne Gravity Missions), funded by the German Research Foundation (DFG). One of the NEROGRAV projects deals with stochastic modeling of ocean tide background models utilizing covariance information for eight major tidal constituents. The repeatable pattern of the tidal signal enables the extraction of uncertainty information by an ensemble of different ocean tide models. This information can be introduced into the gravity field recovery process as a covariance matrix while expanding the parameter space by additional tidal parameters to be estimated.This presentation provides an overview of the recovered monthly gravity fields from GRACE/GRACE-FO when applying covariance information of ocean tide errors. In addition, realistic simulations have been performed to assess the pure effect of the covariance information on ocean tide errors and the potential of co-estimating ocean tides over a longer period while considering tidal covariance information is addressed. It is shown that the application of ocean tide covariance information contributes to the reduction of temporal aliasing caused by the mismodeling of ocean tide background models.

Accurate monitoring of the Earth's gravity field is crucial for understanding mass redistribution processes related to climate change, hydrology, and geodynamics. The Gravity Recovery and Climate Experiment (GRACE) and its successor, GRACE Follow‐On (GRACE‐FO), have provided invaluable satellite gravimetry data through low‐low satellite‐to‐satellite tracking (LL‐SST). However, the precision of gravity field recovery is significantly affected not only by data gaps in the accelerometer (ACC) measurements, but also by potential failures or limitations in their performance. To mitigate these issues, accelerometer data transplantation has been employed, leveraging the similarity in non‐gravitational accelerations experienced by both satellites. This study presents an in‐depth assessment of transplant noise and evaluates advanced accelerometer configurations, including Cold Atom Interferometry (CAI) accelerometers and hybrid electrostatic‐quantum accelerometer setups for future satellite gravimetry missions. Through closed‐loop LL‐SST simulations, we compare four different accelerometer configurations, ranging from conventional electrostatic accelerometers (EAs) to fully hybrid CAI‐EA setups. Results indicate that a dual hybrid accelerometer configuration offers the highest accuracy in gravity field recovery, while a transplant‐based hybrid approach significantly enhances the performance of non‐gravitational force modeling without requiring additional instrumentation. The findings underscore the potential of quantum accelerometery and transplant methodologies for future satellite gravimetry missions, offering a cost‐effective solution to improve gravity field recovery, while benefitting from new sensor types.