Estimating signal loss in regularized GRACE gravity field solutions

Gravity Recovery and Climate Experiment (GRACE) satellite gravimetry can monitor surface mass variations with a spatial resolution of ~300km and a temporal resolution of 1 month. GRACE intersatellite geopotential difference (GPD) is a type of in-situ gravimetric observables with explicit geophysical interpretation, which can directly reflect surface mass variations. The intersatellite GPDs are estimated from GRACE Level-1B (RL03) data (including KBR range-rate measurements (KBR1B), satellite orbits (GNV1B), accelerometer measurements (ACC1B), and satellite attitude measurements (SCA1B)) based on an improved energy balance equation, and the orbit and background model errors are reduced using empirical parameters based on the remove-compute-restore (RCR) technique. Background models used for estimating GRACE intersatellite GPDs are consistent with GRACE Level-2 Processing Standards Document (for Level-2 Product RL06). GRACE intersatellite GPD data are processed over the period from April 2002 to July 2016 with a sampling rate of 5s along the satellite orbits (orbit height is ~450km), and stored on a monthly basis. There are total 155 months of data files over the period from April 2002 to July 2016, and the other 17 months of data are not available due to the instrument failure or other influencing factors. Each data file includes the positions of GRACE satellites A and B in Earth-centered Earth-fixed (ECEF) coordinate system, intersatellite geopotential differences after deducting the mean gravity field model GGM05C (i.e., the disturbance potential difference TAB=TB-TA), and the corresponding quality flags. GRACE intersatellite GPD data are validated through the estimation of monthly gravity field solutions and regional surface mass variations. The estimates inferred from GPD data are compared with GRACE official monthly solutions and mascon solutions, such as the products published by the Center for Space Research (CSR), Jet Propulsion Laboratory (JPL), German Research Center for Geosciences (GFZ), and Goddard Space Flight Center (GSFC). It is demonstrated that the differences between GPD-inferred results and the official released models are within the range of the differences among those official models.  GRACE intersatellite GPD dataset enriches the GRACE data products, and can be applied to directly invert the monthly gravity field models, global and regional surface mass variations, which is helpful to study the terrestrial water cycle, ice sheets and mountain glacier mass balance, sea level change, and ocean bottom pressure variations, etc.

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.

In areas dominated by Glacial Isostatic Adjustment (GIA), the free-air gravity anomaly rate can be converted to uplift rate to good approximation by using a simple spectral relation. We provide quantitative comparisons between gravity rates derived from monthly gravity field solutions (GFZ Potsdam, CSR Texas, IGG Bonn) from the Gravity Recovery and Climate Experiment (GRACE) satellite mission with uplift rates measured by GPS in these areas. The band-limited gravity data from the GRACE satellite mission can be brought to very good agreement with the point data from GPS by using scaling factors derived from a GIA model (the root-mean-square of differences is 0.55 mm yr-1 for a maximum uplift rate signal of 10 mm yr-1). The root-mean-square of the differences between GRACE derived uplift rates and GPS derived uplift rates decreases with increasing GRACE time period to a level below the uncertainty that is expected from GRACE observations, GPS measurements and the conversion from gravity rate to uplift rate. With the current length of time-series (more than 8 yr) applying filters and a hydrology correction to the GRACE data does not reduce the root-mean-square of differences significantly. The smallest root-mean-square was obtained with the GFZ solution in Fennoscandia and with the CSR solution in North America. With radial gravity rates in excellent agreement with GPS uplift rates, more information on the GIA process can be extracted from GRACE gravity field solutions in the form of tangential gravity rates, which are equivalent to a rate of change in the deflection of the vertical scaled by the magnitude of gravity rate vector. Tangential gravity rates derived from GRACE point towards the centre of the previously glaciated area, and are largest in a location close to the centre of the former ice sheet. Forward modelling showed that present day tangential gravity rates have maximum sensitivity between the centre and edge of the former ice sheet, while radial gravity rates are most sensitive in the centre of the former ice sheet. As a result, tangential gravity rates offer constraints on a two-layer mantle viscosity profile that are different from radial gravity rates, which can be exploited in future GIA studies.

The Gravity Recovery and Climate Experiment (GRACE) processing centers at the GeoForschungsZentrum Potsdam (GFZ) and the University of Texas Center for Space Research (UTCSR) provide time series of monthly gravity field solutions covering the period since mission launch in March 2002. Although the achieved accuracy still remains an order of magnitude below the mission's baseline goal, these time series have successfully been used to study terrestrial phenomena such as water storage variations. Over the oceans, the monthly gravity field solutions can be converted into estimates of the fluctuating ocean bottom pressure (OBP), which is the sum of atmospheric and oceanic mass variations. The GRACE products may be validated against in situ OBP observations which are available from a ground truth site in the tropical northwest Atlantic Ocean. Large differences are observed between the in situ and GRACE‐derived OBP which are investigated by comparing the tidal and nontidal ocean models used at GFZ and UTCSR for dealiasing short‐term (<2 months) mass variations from satellite measurements. Results show that the barotropic nontidal and tide models need improvement at periods shorter than 1 day and longer than 2 weeks. On a global scale the monthly OBP fields from GRACE generally overestimate the variability compared to ocean general circulation models, especially in tropical regions. This may be attributed to continuing deficiencies in GRACE data processing. Nevertheless, there is some initial evidence that GRACE possesses the potential to observe large‐scale averages of bottom pressure fluctuations.

The Earth’s time-variable gravity field is of great significance to study mass change within the Earth’s system. Since 2002, the NASA-DLR Gravity Recovery and Climate Experiment (GRACE) and its successor GRACE follow-on mission provide observations of monthly changes in the Earth gravity field with unprecedented accuracy and resolution by employing low-low satellite-to-satellite tracking (LLSST) measurements. In addition to LLSST, monthly gravity field models can be acquired from satellite laser ranging (SLR) and high-low satellite-to-satellite tracking (HLSST). The monthly gravity field solutions HLSST+SLR were derived by combining HLSST observations of low earth orbiting (LEO) satellites with SLR observations of geodetic satellites. Bandpass filtering was applied to the harmonic coefficients of HLSST+SLR solutions to reduce noise. In this study, we analyzed the performance of the monthly HLSST+SLR solutions in the spectral and spatial domains. The results show that: (1) the accuracies of HLSST+SLR solutions are comparable to those from GRACE for coefficients below degree 10, and significantly improved compared to those of SLR-only and HLSST-only solutions; (2) the effective spatial resolution could reach 1000 km, corresponding to the spherical harmonic coefficient degree 20, which is higher than that of the HLSST-only solutions. Compared with the GRACE solutions, the global mass redistribution features and magnitudes can be well identified from HLSST+SLR solutions at the spatial resolution of 1000 km, although with much noise. In the applications of regional mass recovery, the seasonal variations over the Amazon Basin and the long-term trend over Greenland derived from HLSST+SLR solutions truncated to degree 20 agree well with those from GRACE solutions without truncation, and the RMS of mass variations is 282 Gt over the Amazon Basin and 192 Gt in Greenland. We conclude that HLSST+SLR can be an alternative option to estimate temporal changes in the Earth gravity field, although with far less spatial resolution and lower accuracy than that offered by GRACE. This approach can monitor the large-scale mass transport during the data gaps between the GRACE and the GRACE follow-on missions.

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.

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.

Land water storage plays a fundamental role in the West African water cycle and has an important impact on climate and on the natural resources of this region. However, measurements of land water storage are scarce at regional and global scales and especially in poorly instrumented endorheic regions, such as most of the Sahel, where little useful information can be derived from river flow measurements and basin water budgets. The Gravity Recovery and Climate Experiment (GRACE) satellite mission provides an accurate measurement of the terrestrial gravity field variations from which land water storage variations can be derived. However, their retrieval is not straightforward, and different methods are employed, which results in different water storage GRACE products. On the other hand, water storage can be estimated by land surface modeling forced with observed or satellite‐based boundary conditions, but such estimates can be highly model dependent. In this study, land water storage by six GRACE products and soil moisture estimations by nine land surface models (run within the framework of the African Monsoon Multidisciplinary Analysis Land Surface Intercomparison Project (ALMIP)) are evaluated over West Africa, with a particular focus on the Sahelian area. The water storage spatial distribution, including zonal transects, its seasonal cycle, and its and interannual variability, are analyzed for the years 2003–2007. Despite the nonnegligible differences among the various GRACE products and among the different models, a generally good agreement between satellite and model estimates is found over the West Africa study region. In particular, GRACE data are shown to reproduce well the water storage interannual variability over the Sahel for the 5 year study period. The comparison between satellite estimates and ALMIP results leads to the identification of processes needing improvement in the land surface models. In particular, our results point out the importance of correctly simulating slow water reservoirs as well as evapotranspiration during the dry season for accurate soil moisture modeling over West Africa.

The aim of the MOCAST+ (MOnitoring mass variations by Cold Atom Sensors and Time measures) project, which was carried out during the years 2020–2022, was the investigation of the performance of a gravity field mission based on the integration of atomic clocks and cold atom interferometers. The idea was that the combined observations of the two sensors would be beneficial for the detection and monitoring of geophysical phenomena which have an impact on the time-variable part of the Earth gravity field models. Several different mission scenarios were simulated, considering different satellite configurations such as a Gravity Recovery and Climate Experiment (GRACE)-class formation and a Bender-class formation with either two or three in-line satellites along each orbit. Moreover, different atomic species (rubidium and strontium), different inter-satellite distances, different noise power spectral densities, and different observation rates were taken into account. For the gravity field estimation from the simulated data, the space-wise approach was exploited. The results showed that, as it could be expected, the Bender configuration provides significantly better monthly gravity field solutions, as compared to a ‘nominal’ configuration with two or three satellites in a GRACE-class formation. In this way, and pushing the quantum sensors technology to its limits, it is in fact possible to obtain results which are comparable with those from GRACE at low harmonic degrees, and are better at higher degrees with positive effects in the detectability of localized time variable phenomena, as well as in the determination of the static gravity field at a higher maximum spherical harmonic degree than the one achieved by Gravity Field and Steady-State Ocean Circulation Explorer (of course considering an equivalent mission life-time).

On the computation of mass-change trends from GRACE gravity field time-series

Aimed at mapping time variations in the Earth’s gravity field, the Gravity Recovery and Climate Experiment (GRACE) satellite mission is applicable to access terrestrial water storage (TWS), which mainly includes groundwater, soil moisture (SM), and snow. In this study, SM and accumulated snow water equivalent (SWE) are simulated by the Global Land Data Assimilation System (GLDAS) land surface models (LSMs) and then used to isolate groundwater anomalies from GRACE-derived TWS in Pennsylvania and New York States of the Mid-Atlantic region of the United States. The monitoring well water-level records from the U.S. Geological Survey Ground-Water Climate Response Network from January 2005 to December 2011 are used for validation. The groundwater results from different combinations of GRACE products (from three institutions, CSR, GFZ and JPL) and GLDAS LSMs (CLM, NOAH and VIC) are compared and evaluated with in-situ measurements. The intercomparison analysis shows that the solution obtained through removing averaged simulated SM and SWE of the three LSMs from the averaged GRACE-derived TWS of the three centers would be the most robust to reduce the noises, and increase the confidence consequently. Although discrepancy exists, the GRACE-GLDAS estimated groundwater variations generally agree with in-situ observations. For monthly scales, their correlation coefficient reaches 0.70 at 95% confidence level with the RMSE of the differences of 2.6 cm. Two-tailed Mann-Kendall trend test results show that there is no significant groundwater gain or loss in this region over the study period. The GRACE time-variable field solutions and GLDAS simulations provide precise and reliable data sets in illustrating the regional groundwater storage variations, and the application will be meaningful and invaluable when applied to the data-poor regions.

Global hydrological and land surface models are increasingly used for tracking terrestrial total water storage (TWS) dynamics, but the utility of existing models is hampered by conceptual and/or data uncertainties related to various underrepresented and unrepresented processes, such as groundwater storage. The gravity recovery and climate experiment (GRACE) satellite mission provided a valuable independent data source for tracking TWS at regional and continental scales. Strong interests exist in fusing GRACE data into global hydrological models to improve their predictive performance. Here we develop and apply deep convolutional neural network (CNN) models to learn the spatiotemporal patterns of mismatch between TWS anomalies (TWSA) derived from GRACE and those simulated by NOAH, a widely used land surface model. Once trained, our CNN models can be used to correct the NOAH‐simulated TWSA without requiring GRACE data, potentially filling the data gap between GRACE and its follow‐on mission, GRACE‐FO. Our methodology is demonstrated over India, which has experienced significant groundwater depletion in recent decades that is nevertheless not being captured by the NOAH model. Results show that the CNN models significantly improve the match with GRACE TWSA, achieving a country‐average correlation coefficient of 0.94 and Nash‐Sutcliff efficient of 0.87, or 14% and 52% improvement, respectively, over the original NOAH TWSA. At the local scale, the learned mismatch pattern correlates well with the observed in situ groundwater storage anomaly data for most parts of India, suggesting that deep learning models effectively compensate for the missing groundwater component in NOAH for this study region.

Currently, various satellite processing centers produce extensive data, with different solutions of the same field being available. For instance, the Gravity Recovery and Climate Experiment (GRACE) has been monitoring terrestrial water storage (TWS) since April 2002, while the Center for Space Research (CSR), the Jet Propulsion Laboratory (JPL), the GeoForschungsZentrum (GFZ), and the Groupe de Recherche de Geodesie Spatiale (GRGS) provide individual monthly solutions in the form of Stokes coefficients. The inverted TWS maps (or the regionally averaged values) from these coefficients are being used in many applications; however, as no ground truth data exist, the uncertainties are unknown. Consequently, the purpose of this work is to assess the quality of each processing center by estimating their uncertainties using a generalized formulation of the three-cornered hat (TCH) method. Overall, the TCH results for the study period of August 2002 to June 2014 indicate that at a global scale, the CSR, GFZ, GRGS, and JPL presented uncertainties of 9.4, 13.7, 14.8, and 13.2 mm, respectively. At a basin scale, the overall good performance of the CSR was observed at 91 river basins. The TCH-based results were confirmed by a comparison with an ensemble solution from the four GRACE processing centers.

Gravity Recovery and Climate Experiment (GRACE) satellite mission is ground-breaking information hotspot for the evaluation of groundwater storage. The present study aims at validating the sensitivity of GRACE data to groundwater storage variation within a basaltic aquifer system after its statistical downscaling on a regional scale. The basaltic aquifer system which covers 82.06% area of Maharashtra state in India, is selected as the study area. Five types of basaltic aquifer systems with varying groundwater storage capacities, based on hydrologic characteristics, have been identified within the study area. The spatial and seasonal trend analysis of observed in situ groundwater storage anomalies (ΔGWSano) computed from groundwater level data of 983 wells from the year 2002 to 2016, has been performed to analyze the variation in groundwater storages in the different basaltic aquifer system. The groundwater storage anomalies (ΔGWSDano) have been derived from GRACE Release 05 (RL05) after removing the soil moisture anomaly (ΔSMano) and canopy water storage anomaly (ΔCNOano) obtained from Global Land Data Assimilation System (GLDAS) land surface models (NOAH, MOSAIC, CLM and VIC). The artificial neural network technique has been used to downscale the GRACE and GLDAS data at a finer spatial resolution of 0.125°. The study shows that downscaled GRACE and GLDAS data at a finer spatial resolution is sensitive to seasonal groundwater storage variability in different basaltic aquifer systems and the regression coefficient R has been found satisfactory in the range of 0.696 to 0.818.

Abstract. Accurate estimation of terrestrial water storage (TWS) at a high spatiotemporal resolution is important for reliable assessments of regional water resources and climate variability. Individual components of TWS include soil moisture, snow, groundwater, and canopy storage and can be estimated from the Community Atmosphere Biosphere Land Exchange (CABLE) land surface model. The spatial resolution of CABLE is currently limited to 0.5∘ by the resolution of soil and vegetation data sets that underlie model parameterizations, posing a challenge to using CABLE for hydrological applications at a local scale. This study aims to improve the spatial detail (from 0.5 to 0.05∘) and time span (1981–2012) of CABLE TWS estimates using rederived model parameters and high-resolution meteorological forcing. In addition, TWS observations derived from the Gravity Recovery and Climate Experiment (GRACE) satellite mission are assimilated into CABLE to improve TWS accuracy. The success of the approach is demonstrated in Australia, where multiple ground observation networks are available for validation. The evaluation process is conducted using four different case studies that employ different model spatial resolutions and include or omit GRACE data assimilation (DA). We find that the CABLE 0.05∘ developed here improves TWS estimates in terms of accuracy, spatial resolution, and long-term water resource assessment reliability. The inclusion of GRACE DA increases the accuracy of groundwater storage (GWS) estimates and has little impact on surface soil moisture or evapotranspiration. Using improved model parameters and improved state estimations (via GRACE DA) together is recommended to achieve the best GWS accuracy. The workflow elaborated on in this paper relies only on publicly accessible global data sets, allowing the reproduction of the 0.05∘ TWS estimates in any study region.