GRACE Follow-On Mission Research Articles

Changes in the Water Surface Level of the Baltic Sea from Satellite Altimetry and Gravity Missions

ABSTRACT Satellite altimetry provides high-accuracy geometrical measurements of sea level changes. We analyze altimetry time series representing sea surface height anomalies over the mean sea surface provided by the TOPEX/Poseidon, Jason-1, Jason-2, and Jason-3 satellite missions to estimate the annual rate of sea level rise. Then, we compare the results with satellite gravimetric data from GRACE and GRACE Follow-On missions and surface water temperature data, employing statistical analyses to examine the interrelationships and correlations between them. We carry out the main analyses for the period 2001–2021 with a division into 5-year periods for six different areas of the Baltic Sea. The altimetric results show that between 2001 and 2021, the water level of the Baltic Sea rose by 5.8 mm/year on average. About 72% of the changes detected by altimetry missions can be explained by satellite gravimetry from GRACE and GRACE Follow-On, which means that the mass component is responsible for most of the observed sea level change, whereas the remaining 28% can be greatly explained by thermal expansion due to the water temperature rise.

Laboratory demonstration of an off-axis optical bench design for future gravity missions.

The inter-satellite laser ranging interferometer is one of the core components of future gravity missions to achieve high ranging precision. This work builds a preliminary breadboard of the off-axis optical bench design, which integrates the merits of the off-axis optical bench design of GRACE Follow-On mission and other on-axis designs. The study finds that the displacement noise between two optical benches has been reduced to 20nm/Hz at a frequency of 10 mHz, and the differential wavefront sensing noise has been suppressed to 10-5rad/Hz at 1kHz as well. In addition, the tilt-to-length coupling noise related to the piston effect is restricted within 30μm/rad, and the relative parallelism error of the transmitting beam and receiving beam is less than 4.5%. The results show that this off-axis optical bench design is an important candidate for China's future gravity missions.

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).

Spatial downscaling of GRACE-derived groundwater storage changes across diverse climates and human interventions with Random Forests

The Gravity Recovery and Climate Experiment (GRACE) satellites launched in 2002, which were followed by the GRACE Follow-On mission in 2018, represented a significant advancement in global groundwater storage monitoring. However, the inherent limitation of a relatively low spatial resolution confines its applicability primarily to large river basins and aquifers. This study introduces a novel statistical downscaling approach using Random Forests (RF) to enhance the spatial resolution from 3° × 3° to 0.25° × 0.25° for GRACE-derived groundwater storage (GWS) changes. Focusing on sub-Saharan Africa, the Middle East, and South Asia across diverse climates and human interventions, the analysis spans from February 2003 to December 2022. Predictors encompass hydrological fluxes and their accumulation, including IMERG precipitation, GLEAM evapotranspiration, and GLDAS runoff, alongside GLDAS soil moisture and MODIS NDVI. RF models show robust performance across 114 aquifers, with a Pearson’s correlation coefficient (CC) exceeding 0.92 for training sets and 0.85 for validation sets. Validation against in-situ groundwater level observations from wells in India reveals satisfactory performance, with positive Spearman’s CC values between in-situ groundwater levels and downscaled terrestrial water storage anomaly (TWSA) for a majority of dug and bore wells. This study concludes with the generation of monthly downscaled GWS changes (0.25° × 0.25°) spanning from February 2003 to December 2022. These datasets serve as a foundation for facilitating finer-scale hydrological studies and formulating local groundwater management strategies.

HUST-Grace2024: a new GRACE-only gravity field time series based on more than 20 years of satellite geodesy data and a hybrid processing chain

Abstract. To improve the accuracy of monthly temporal gravity field models for the Gravity Recovery and Climate Experiment (GRACE) and the GRACE Follow-On (GRACE-FO) missions, a new series named HUST-Grace2024 is determined based on the updated L1B datasets (GRACE L1B RL03 and GRACE-FO L1B RL04) and the newest atmosphere and ocean de-aliasing product (AOD1B RL07). Compared to the previous HUST temporal gravity field model releases, we have made the following improvements related to updating the background models and the processing chain: (1) during the satellite onboard events, the inter-satellite pointing angles are calculated to pinpoint outliers in the K-band ranging (KBR) range-rate and accelerometer observations. To exclude outliers, the advisable threshold is 50 mrad for KBR range rates and 20 mrad for accelerations. (2) To relieve the impacts of KBR range-rate noise at different frequencies, a hybrid data-weighting method is proposed. Kinematic empirical parameters are used to reduce the low-frequency noise, while a stochastic model is designed to relieve the impacts of random noise above 10 mHz. (3) A fully populated scale factor matrix is used to improve the quality of accelerometer calibration. Analyses in the spectral and spatial domains are then implemented, which demonstrate that HUST-Grace2024 yields a noticeable reduction of 10 % to 30 % in noise level and retains consistent amplitudes of signal content over 48 river basins compared with the official GRACE and GRACE-FO solutions. These evaluations confirm that our aforementioned efforts lead to a better temporal gravity field series. This data set is identified with the following DOI: https://doi.org/10.5880/ICGEM.2024.001 (Zhou et al., 2024).

Research on Inter-Satellite Laser Ranging Scale Factor Estimation Methods for Next-Generation Gravity Satellites

The scale factor serves as a ruler for converting raw phase measurements into physical displacements and significantly impacts the preprocessing of data from the Laser Ranging Interferometer (LRI) in laser ranging systems. In the current GRACE Follow-On (GRACE-FO) mission for low–low tracking gravity satellites, most of the existing LRI scale factor estimation algorithms heavily rely on cross-calibration between instantaneous/biased ranges from the Ka-Band Ranging Interferometer (KBR) and the LRI. However, due to the nonlinearity of the objective function (which includes terms involving the product of scale and time shifts), the scale factor estimation may absorb errors from timing noise. Moreover, future gravity missions or gravity detection tasks may no longer incorporate KBR ranging instruments. To address these challenges, this paper proposes an energy-based method for scale factor estimation using inter-satellite baseline solutions. Comparative analysis indicates that the proposed method effectively disentangles two parameters in the objective function and can be applied in scenarios where KBR data are unavailable, demonstrating promising prospects for practical application. The experimental results show that when the KBR validation residuals are lower than 0.8 mm, the SYSU LRI1B V01 products exhibit residuals below the payload design accuracy thresholds in the frequency band of 2 mHz to 0.1 Hz. Additionally, the stability of the scale factors obtained from the baseline can reach 10−7. Although this is still below the required precision of better than 10−8 for the laser frequency stability in next-generation gravity satellites, advancements in orbit determination technology and the enhanced stability of GPS receivers offer potential for future precision improvements. Currently, this method appears suitable for roughly extracting the scale factor as a stochastic mean over several months or serving as a backup validation strategy for future missions, but it is not well suited to measure day-to-day variations.

Estimation of groundwater storage variations in African river basins: Response to global climate change using GRACE and GRACE-FO among past two decades

Groundwater Storage (GWS) is an important component of the water cycle and a vital resource for supplying water to millions of people as well as sustaining domestic and economic activities, especially in arid and semi-arid regions such as Africa. This study aims to estimate and analyze the recent groundwater changes (ΔGW) for 11 major African basins in light of climate changes and global warming utilizing the data from the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) from January 2003 to December 2021. We proposed a new gap-filling technique to calculate the missing months between GRACE and GRACE-FO missions for the continuous estimation of groundwater changes. Then, we establish a new framework to analyze and investigated the climate parameters that could affect groundwater changes using Empirical Orthogonal Function (EOF) technique. Our analysis reveals that the new gap-filling technique is significantly consistent with the TWS time-series based on the trend line analysis. The lowest GPCC drought index value occurs in the lower Nile basin by approximately −0.93, while the highest occurs in the middle of Africa in Congo basin by approximately −0.02. The precipitation rate is mostly concentrated in mid-Africa while North and South Africa shows a weak rate. Meanwhile, according to the analysis of dependent climate parameters, climate change has had a negative impact on groundwater. However, the long-term effect on the groundwater does not clearly appear because most of Africa is located within semi-arid and arid regions. The effect of rain on groundwater was evident through EOF analysis, which shows GWS EOF Mode-2 (36.28%) and precipitation EOF Mode-1 (78.34%) were found to be in significant agreement in spatio-temporal domains.

Improved GRACE-FO kinematic orbit determination with epoch-difference KBR during the GPS flex power period

The flex power technology in satellite navigation systems enhances anti-jamming capabilities but can impact the quality of GPS observations and the accuracy of low Earth orbit determination, such as GRACE Follow-On (GRACE-FO) mission. This study investigates the influence of GPS flex power on Hatch-Melbourne-Wübbena (HMW) linear combinations and GRACE-FO kinematic orbits from January 1 to September 30, 2020. Epoch-differenced K-Band Ranging (KBR) data is introduced in orbit determination during the flex power period to improve both absolute and inter-satellite relative accuracy. The analysis indicates that the influence of early flex power (before February 13, 2020) on HMW combinations and orbits is minimal, whereas the effect of later flex power (after February 14, 2020) is significant: (1) HMW combinations exhibit notable systematic discontinuities even with elevation angles greater than 50 degrees, causing the fixing rate of wide-lane ambiguities to drop from 96 % to 80 %. (2) Kinematic absolute orbits show significant deteriorations of approximately 9 mm and 4 mm in the three-dimensional direction for float and integer ambiguity resolution (FAR and IAR), while relative accuracy of FAR and IAR orbits decreases by 50 % and 46 %, respectively. However, using epoch-differenced KBR (DKBR) data, the accuracy of absolute orbits could be increased by up to 15 % and the accuracy of relative orbits could be improved by at least 69 %, which showcases a positive effect. Thus, this can be considered as an alternative method to improve the accuracy of GRACE-FO orbit during the flex power period.

Residual Patterns in GRACE Follow-On Laser Ranging Interferometry Post-Fit Range Rate Residuals

The novel laser ranging interferometer (LRI) on GRACE Follow-On (GRACE-FO) provides range and range rate measurements for more than 4 years now. Since the launch of the GRACE-FO mission there were few investigations about this measurement system on the level of gravity field recovery and analysis of post-fit residuals. We applied techniques such as along-orbit-analysis or time-argument of latitude diagrams (TAL) to analyse the post-fit range rate residuals as well as the post-fit range acceleration residuals to identify unknown characteristics and systematic effects. The effects are the range rate effect, the panel effect, the Carrier-To-Noise Ratio (CNR) effect and the polar effect. The range rate effect occurs, when the range rate observation ρ̇ of the LRI is around 0 m/s. In the TAL diagram the effect appears as a mesh pattern. The panel effect shows patterns of increased residuals when a specific satellite panel starts or stops being illuminated by the Sun. Increased residuals appear when the laser beam is aligned with the Sun. A CNR drop as well as a fluctuation of the yaw and pitch pointing angles obtained from the LRI steering mirrors is observable. Additionally, when the satellites flying into or out of the Earth shadow this effect coincides with the shadow transition effect. Another effect is the CNR effect which appears as an elliptic shape in the TAL diagram. This pattern occurs when the CNR values drop below the LRI requirements of 70 dB-Hz. All these effects have not been detected in the residuals of the GRACE-FO K-band ranging system (KBR) and therefore further investigation and studies will improve the understanding and applications of LRI technology.

Alternative Approach to Tilt-to-Length Coupling Estimation for Laser Ranging Interferometers in Future Gravity Missions

Tilt-to-length coupling, a non-constant systematic error source caused by satellite attitude variations, has been observed in the laser ranging signals of the GRACE Follow-On mission. This error can be corrected by certain calibration maneuvers performed regularly in orbit. In this paper, we introduce an alternative approach to tilt-to-length coupling estimation for a laser ranging interferometer in future gravity missions, using the ranging signals without any specific calibration maneuvers, which allows daily estimation. An analytical model of laser ranging signals is derived. The tilt-to-length estimation is performed under different conditions using the least squares method as well as the simulated data. The pointing angle noise is found to be the most significant limiting factor. When the pointing angle noise is below 0.3μrad/Hz1/2, the RMS of the estimation error is below 4 nm, much better than the tilt-to-length error of GRACE Follow-On. In the case of low pointing angle noise, the estimation error of an under 1.5 m offset between the center of mass and the interferometer reference point is not obviously different from the case with only a 0.5 mm offset, which provides installation flexibility for the laser ranging interferometer.

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.

The GWR model-based regional downscaling of GRACE/GRACE-FO derived groundwater storage to investigate local-scale variations in the North China Plain

Groundwater storage and depletion fluctuations in response to groundwater availability for irrigation require understanding on a local scale to ensure a reliable groundwater supply. However, the coarser spatial resolution and intermittent data gaps to estimate the regional groundwater storage anomalies (GWSA) prevent the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GARCE-FO) mission from being applied at the local scale. To enhance the resolution of GWSA measurements using machine learning approaches, numerous recent efforts have been made. With a focus on the development of a new algorithm, this study enhanced the GWSA resolution estimates to 0.05° by extensively investigating the continuous spatiotemporal variations of GWSA based on the regional downscaling approach using a regression algorithm known as the geographically weighted regression model (GWR). First, the modified seasonal decomposition LOESS method (STL) was used to estimate the continuous terrestrial water storage anomaly (TWSA). Secondly, to separate GWSA from TWSA, a water balance equation was used. Third, the continuous GWSA was downscaled to 0.05° based on the GWR model. Finally, spatio-temporal properties of downscaled GWSA were investigated in the North China Plain (NCP), China's fastest-urbanizing area, from 2003 to 2022. The results of the downscaled GWSA were spatially compatible with GRACE-derived GWSA. The downscaled GWSA results are validated (R = 0.83) using in-situ groundwater level data. The total loss of GWSA in cities of the NCP fluctuated between 2003 and 2022, with the largest loss seen in Handan (−15.21 ± 7.25 mm/yr), Xingtai (−14.98 ± 7.25 mm/yr), and Shijiazhuang (−14.58 ± 7.25 mm/yr). The irrigated winter-wheat farming strategy is linked to greater groundwater depletion in several cities of NCP (e.g., Xingtai, Handan, Anyang, Hebi, Puyang, and Xinxiang). The study's high-resolution findings can help with understanding local groundwater depletion that takes agricultural water utilization and provide quantitative data for water management.

Evaluating different predictive strategies for filling the global GRACE/-FO terrestrial water storage anomalies gap

The Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) missions provide unprecedented approaches for tracking terrestrial water storage anomalies (TWSA). However, evaluating long-term hydrologic states requires continuous TWSA without the ∼11-month gap between the two GRACE missions. Trend prediction is a challenging problem for TWSA gap-filling. There are three common methods for handling trends in previous efforts, i.e., de-trending the TWSA, adding back the long-term or piecewise trends of GRACE/-FO to the detrended predictions, or not performing such trend replacement. However, a single global application of one of these methods will not produce optimal results. Therefore, we designed a framework to select the optimal trend replacement strategy for each grid in this study. Based on this framework, we better filled the gap (excluding Antarctica) using machine learning techniques adopting the Global Land Data Assimilation System (GLDAS) Noah TWSA, precipitation, and temperature as inputs. The median gridwise Nash-Sutcliffe efficiency of the result generated by our framework improves by 0.08 compared to the result of a single long-term trend replacement strategy. Furthermore, we quantitatively evaluated the impact of three predictive strategies on the results: selection of leader machine learning technique, selection of optimal trend replacement strategy, and selection of most relevant inputs. The results indicate that the selection of trend replacement strategy has the greatest influence, followed by the selection of machine learning technique and then the selection of inputs. In addition, we found that in areas with abundant surface water, utilizing surface water anomalies as an additional predictor benefits the results. Our study is expected to provide suggestions for better TWSA predictive strategies.

Tilt-to-Length Coupling Analysis of an Off-Axis Optical Bench Design for NGGM

A new off-axis optical design alternative to that of the GRACE Follow-on mission for future NGGM missions is considered. In place of the triple-mirror assembly of the GRACE Follow-on mission, a laser retro-reflector is instead generated by means of lens systems. The receiving (RX) beam and transmitting (TX) beam are enforced to be anti-parallel by a control loop with differential wavefront sensing (DWS) signals as readout, and a fast-steering mirror is employed to actuate the pointing of the local beam. The tilt-to-length (TTL) coupling noise of the new off-axis optical bench layout is carefully studied in the present work. Local TTL originated from piston noise as well as assembly and alignment errors of optical components are studied. Effort is also made to have an in depth understanding of global TTL due to relative attitude jitter between spacecraft. The margin of TTL noise in the position noise budget for laser ranging is examined. With an open loop control of the offset between the reference point of the optical bench and the centre of mass of a satellite, the TTL noise of the new off-axis optical bench design may be suppressed efficiently.

Disturbances from single event upsets in the GRACE follow-on laser ranging interferometer

The GRACE – Follow On (GRACE-FO) satellite mission (2018-now) hosts the novel Laser Ranging Interferometer (LRI), a technology demonstrator for proving the feasibility of laser interferometry for inter-satellite ranging measurements. The GRACE-FO mission extends the valuable climate data record of changing mass distribution in the system Earth, which was started by the original GRACE mission (2002–2017). The mass distribution can be deduced from observing changes in the distance of two low-earth orbiters employing interferometry of electromagnetic waves in the K-Band for the conventional K-Band Ranging (KBR) and in near-infrared for the novel LRI.This paper identifies possible radiation-induced Single Event Upset (SEU) events in the LRI phase measurement. We simulate the phase data processing within the Laser Ranging Processor (LRP) and use a template-based fitting approach to determine the parameters of the SEU and subtract the events from the ranging data. Over four years of LRI data, 31 of such events were identified and characterized.

Designing Satellite Constellations to Observe Earth’s Time-Varying Gravity from Clock Frequency Comparisons

The nondominated sorting genetic algorithm III (NSGA-III) is used to design nonsymmetric satellite constellations to observe large-scale high-frequency gravity variations that would serve as complementary systems to other dedicated gravity field mapping missions such as the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On missions. The functionality of the NSGA-III method is validated by reproducing optimal surface-coverage satellite constellations from the literature. Then, NSGA-III is used to generate nondominated constellations tuned to detect short-term long-wavelength gravity field variations. The constellations are used to generate subweekly gravity field solutions from clock frequency comparison measurements. The effectiveness of NSGA-III for optimizing nonsymmetric constellations was demonstrated because the constellations obtained from NSGA-III were consistently superior in performance than traditional symmetric constellations. Furthermore, the results showed that the time-varying signals of interest (that is, gravity coefficients through the spherical harmonic degree and order of seven at daily intervals) can be unambiguously resolved by assuming an optical clock with a fractional frequency uncertainty representative of current technology. The ability to monitor these short-term long-wavelength signals on a global scale would observe a spectrum of the gravity field inherently undetectable by GRACE-like missions, and it would provide new insight to the understanding of global mass redistribution processes.

Studying an off-axis optical bench for future gravity missions from the perspective of carrier-to-noise ratio.

The inter-satellite laser ranging heterodyne interferometer is vital for future gravity missions to achieve high ranging accuracy. This paper proposes a novel off-axis optical bench design which integrates merits of the off-axis optical bench design of GRACE Follow-On mission and other on-axis designs. This design makes use of lens systems subtly to restrict the tilt-to-length coupling noise and takes advantage of the DWS feedback loop to maintain the transmitting beam and receiving beam anti-parallel. The critical parameters of the optical components are determined and the carrier-to-noise ratio for a single channel of the photoreceiver is calculated to be more than 100 dB-Hz for the high case. The off-axis optical bench design is a potential candidate for China's future gravity missions.

The impacts of reducing atmospheric and oceanic de-aliasing model error on temporal gravity field model determination

SUMMARYThe Gravity Recovery and Climate Experiment (GRACE) and its successor GRACE Follow-On mission have been estimating temporal gravity field models for various geoscience applications since 2002. While the errors in atmospheric and oceanic de-aliasing (AOD) model are still the key limitation for GRACE-type missions especially taking advantages of improved laser ranging interferometer (LRI), this paper explores the realistic assumption of continuously reducing AOD model error in global scale and regional scale (e.g. ocean, Greenland, Qinghai-Tibet plateau and South America) in the anticipated future. For this, using a realistic orbit scenario and error assumptions both for instrument and background model errors, the 5-yr full-scale simulations are implemented in the context of 26 scenarios with different AOD model errors. Our overall simulation results demonstrate that: (1) when the AOD model errors are reduced in the global scale, the corresponding gain in temporal gravity field determination is significant, with the cumulative geoid height error decrease from 11.28 to 6.25 mm in spectral domain, as well as 26.3–65.2 per cent noise reduction in terms of mean RMS residuals over ocean in spatial domain. (2) When the AOD model errors are reduced in the regional scale, the improvements of temporal gravity field estimations are diverse in different simulation scenarios. The most notable noise reduction, with 22.9–43.9 per cent noise reduction in spatial domain, is observed when the AOD model error decreases in ocean. The limited noise reductions (0.1 per cent and 1.3 per cent respectively in spectral and spatial domain) are observed in the temporal gravity field estimations if the AOD model is refined in other typical regions such as the Qinghai-Tibet plateau, the Greenland and the South America. (3) However, when the satellites passing over the AOD model refined regions, the along-orbit range rate analysis indicates that, there are visible differences by about 50.0 nm s−1 in terms of range rate residuals as well as 11.0–48.5 nm s−1 in terms of the mean RMS of range rate residuals. These results reflect the benefits of reducing AOD model error in both global and regional scale for improving GRACE-type temporal gravity estimation, especially considering the development of LRI technology.

A mass conserving filter based on diffusion for gravity recovery and climate experiment (GRACE) spherical harmonics solutions

SUMMARYOver the past two decades, the GRACE (Gravity Recovery and Climate Experiment) and GRACE Follow-On mission (GRACE-FO) have provided monthly measurements of the gravity field as sets of Stokes coefficients, referred to as spherical harmonics solutions. The variations of the gravity field can be used to infer mass variations on the surface of the Earth, mostly driven by the redistribution of water. However, unconstrained GRACE and GRACE-FO solutions are affected by strong correlated errors, easily identified as stripes along the north–south direction in the spatial domain. Here, we develop a filter based on the principle of diffusion to remove correlated errors and access the underlying geophysical signals. In contrast to many filters developed for this task, diffusion filters allow a spatially variable level of filtering that can be adapted to match spatially variable signal-to-noise ratios. Most importantly, the formalism of diffusion allows the implementation of boundary conditions, which can be used to prevent any flux through the coastlines during the filtering step. As mass conservation is enforced in the filter, global indicators such as trends in the global mean ocean mass are preserved. Compared with traditional filters, diffusion filters ensure the consistency of the solution at global and regional scales for ocean applications. Because leakage errors occurring during the filtering step are suppressed, better agreement is found when comparing diffusion-filtered spherical harmonic solutions with mascon solutions and independent estimates based on altimetry and in situ data.

Inversion of terrestrial water storage changes from GNSS vertical displacements using a priori constraint: A case study of the Yunnan Province, China

Global Navigation Satellite System (GNSS) is an effective means to monitor surface deformations associated with changes in terrestrial water storage (TWS). In this study, we introduced a priori constraint matrix and estimated the regularization parameter through an iterative least-squares method to infer the TWS changes using GNSS vertical displacements from December 2010 to February 2021 in the Yunnan Province (YNP), China. The GNSS-inferred TWS changes were validated through the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GFO) estimates, the Global Land Data Assimilation System (GLDAS) hydrological model, and the meteorological data (i.e., precipitation and Drought Severity Index (DSI)). The results demonstrate that the spatial resolution of TWS changes derived from 45 GNSS stations can reach 2°×2° in the YNP, and the a priori constraint is better than the traditional Laplacian matrix constraint for solving the discrete ill-conditioned problem of GNSS inversion. The GNSS-inferred TWS changes are consistent with the TWS changes derived from GRACE/GFO and GLDAS estimates in the spatio-temporal domains over the YNP, but the GNSS inversion results show stronger amplitudes. Furthermore, the ground-based GNSS observations are more sensitive to the TWS changes, and the correlation between precipitation and GNSS-inferred TWS changes is improved by about 11 % and 5 % compared to GRACE/GFO and GLDAS estimates in the YNP, respectively. The GNSS-inferred DSI can well reveal the two severe drought events in the YNP during the study period, which is consistent with the DSI derived from GRACE/GFO and GLDAS estimates, as well as the published self-calibrating Palmer Drought Severity Index (scPDSI) and the Standardized Precipitation-Evapotranspiration Index (SPEI). The GNSS observations can compensate the limitations of GRACE/GFO observations (e.g., bridging the data gap between GRACE and GFO missions), and help to better investigate the TWS changes in the YNP, which has significant potentials for regional water resource management and extreme climate changes monitoring.