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We investigate the benefits of future quantum accelerometers based on cold atom interferometry (CAI) on current and upcoming satellite gravity mission concepts. These mission concepts include satellite‐to‐satellite tracking (SST) in a single‐pair (GRACE‐like) and double‐pair constellation as well as satellite gravity gradiometry (SGG, single satellite, GOCE‐like). Regarding instruments, four scenarios are considered: current‐generation electrostatic (GRACE‐, GOCE‐like), next‐generation electrostatic, conservative hybrid/CAI and optimistic hybrid/CAI. For SST, it is shown that temporal aliasing poses currently the dominating error source in simulated global gravity field solutions independent of the investigated instrument and constellation. To still quantify the advantages of CAI instruments on the gravity functional itself, additional simulations are performed where the impact of temporal aliasing is synthetically reduced. When neglecting temporal aliasing, future accelerometers in conjunction with future ranging instruments can substantially improve the retrieval performance of the Earth's gravity field (depending on instrument and constellation). These simulation results are further investigated regarding possible benefit for hydrological use cases where these improvements can also be observed (when omitting temporal aliasing). For SGG, it is demonstrated that, with realistic instrument assumptions, one is still mostly insensitive to time‐variable gravity and not competitive with the SST principle. However, due to the improved instrument sensitivity of quantum gradiometers compared to the GOCE mission, static gravity field solutions can be improved significantly. Key Points: Quantum instruments may significantly improve the sensitivity of gravity measurementsA higher sensitivity cannot substantially improve current and upcoming satellite gravity missions due to temporal aliasing [ABSTRACT FROM AUTHOR]

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

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. [ABSTRACT FROM AUTHOR]

During gravity field modeling, the conventional acceleration approach rarely incorporates KBR inter-satellite range rate data from the GRACE mission. To propose an improved acceleration method, this study introduces initial orbital position and velocity vectors to be estimated along with a combination of Cowell, KSG, and Adams integrators. In addition to achieving a full-rank design matrix regarding orbit corrections when constructing observation equations, the proposed method is capable of utilizing range rate observations for gravity field estimation. To verify the reliability of this approach, GRACE data from April 2002 to December 2016 was used to calculate a time series of monthly gravity solutions up to a degree and order of 96, referred to as Tongji-Acc RL06 in this paper. The computed time series are compared with the official models (i.e., CSR RL06, GFZ RL06, and JPL RL06) in terms of geoid degree variances, signal contents over distinct areas, and noise levels in desert regions. The investigations lead to the following conclusions: (a) the geoid degree variances indicate that Tongji-Acc RL06 exhibits comparable signal levels (approximately below 20 degrees) to the other three models while demonstrating lower noise at higher degrees (above 40 degrees); (b) the analysis over the globe, typical river basins, and land–ice regions illustrates that the solutions derived using the proposed acceleration method agree well with the official models based on the dynamic approach; (c) especially over the two large-scale river basins (i.e., Amazon and Zambezi) and another two small-scale river basins (i.e., Tennessee and Irrawaddy), Tongji-Acc RL06 significantly improves the SNR values; and (d) in the cases of the Sahara and Karakum deserts, Tongji-Acc RL06 achieves noise reductions of over 55.8% and 61.5% relative to CSR RL06, respectively. In general, the signal and noise analyses demonstrate that the proposed acceleration-based approach can effectively extract gravity field signals from KBR inter-satellite range rate observations with improved SNR, while significantly reducing the high-frequency noise. [ABSTRACT FROM AUTHOR]

Hydrological droughts are events of prolonged water scarcity and cause many devastating impacts. It is, therefore, extremely crucial to understand their spatiotemporal evolution to guide prevention and mitigation policies. The Gravity Recovery and Climate Experiment (GRACE, April 2002–June 2017) and GRACE Follow‐On (GRACE‐FO, June 2018 until the present) missions have been used to study large‐scale droughts of almost two decades. But characterizing droughts during the between missions gap period of 2017 and 2018 has not been well addressed and will be covered here. To bridge the gap, an innovative Bayesian convolutional neural network is developed to reconstruct the missing signals from hydroclimatic inputs. The reconstruction fields and existing signals are then used to explore regions that have experienced consecutive water storage deficits during the 2017–2018 gap. We found many regions of the northern midlatitudes exhibiting moderate to exceptional droughts in terms of water storage deficits, among which parts of Pakistan and Afghanistan, and Iberian Peninsula experienced exceptional droughts lasting for more than 1 year with the maximum deficits (−4.4 ± 0.8 and −7.2 ± 1.1 cm, respectively) being over 50% of the seasonal storage variations. Comparisons with climate indicators show that the identified droughts are predominantly caused by continuous below‐normal precipitation. The recovery process correlates generally well with the accumulation rate of precipitation surpluses (the correlation coefficient (R) can be up to 0.92). Besides, the reconstructed signals, which have R > 0.7 with the testing GRACE(‐FO) data in over 90% of the globe, reliably maintain the data continuity and therefore they are recommended for hydro‐climatological studies. Key Points: The missing terrestrial water storage anomaly signals between the 2017–2018 Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow‐On gap are reconstructed by Bayesian deep learningHydrological droughts overlapping with this gap period are characterized and quantifiedThe northern midlatitudes experienced continuous water storage deficits as a result of precipitation deficiency [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The gravity field recovery from GRACE (Gravity Recovery and Climate Experiment) mission data is contaminated by both observation noise and dynamic force errors, especially the temporal aliasing errors. To reduce their influence, four approaches are widely adopted, namely the estimation of empirical accelerations (ACC approach), the estimation of K-band range-rate parameters (KBR approach), the incorporation of the full variance–covariance matrix of observations into the least-squares adjustment (COV approach), and the time series model-based filtering (FILT approach). Essentially, the ACC and KBR approaches can be grouped into the method of functional model compensation, while the COV and FILT approaches belong to the method of stochastic model compensation. The four approaches are systematically revisited in this paper concerning their connections and differences from both theoretical perspectives and numerical simulations. Results show that all of them can significantly reduce errors in the recovered monthly gravity field models compared to the nominal approach not applying any of the four approaches. Moreover, their performances are quite consistent in the simulation case where only white observation noise is included. When both colored observation noise and temporal aliasing effects are considered, however, their performances are different. The noise reduction ratio can reach up to 87% by the ACC, COV and FILT approaches, while it is 79% in the KBR approach. The discrepancy can be explained by the compromise between noise reduction and signal absorption in the KBR approach due to the lack of constraints on empirical parameters. Moreover, in the spectral domain, ACC and KBR approaches function as high-pass filters, whereas the stochastic method, COV or FILT approach, can competently cope with colored noise in a full-spectrum manner. [ABSTRACT FROM AUTHOR]

For 15 years, the Gravity Recovery and Climate Experiment (GRACE) mission have monitored total water storage (TWS) changes. The GRACE mission ended in October 2017, and 11 months later, the GRACE Follow-On (GRACE-FO) mission was launched in May 2018. Bridging the gap between both missions is essential to obtain continuous mass changes. To fill the gap, we propose a new approach based on a remove–restore technique combined with an autoregressive (AR) prediction. We first make use of the Global Land Data Assimilation System (GLDAS) hydrological model to remove climatology from GRACE/GRACE-FO data. Since the GLDAS mis-models real TWS changes for many regions around the world, we further use least-squares estimation (LSE) to remove remaining residual trends and annual and semi-annual oscillations. The missing 11 months of TWS values are then predicted forward and backward with an AR model. For the forward approach, we use the GRACE TWS values before the gap; for the backward approach, we use the GRACE-FO TWS values after the gap. The efficiency of forward–backward AR prediction is examined for the artificial gap of 11 months that we create in the GRACE TWS changes for the July 2008 to May 2009 period. We obtain average differences between predicted and observed GRACE values of at maximum 5 cm for 80% of areas, with the extreme values observed for the Amazon, Alaska, and South and Northern Asia. We demonstrate that forward–backward AR prediction is better than the standalone GLDAS hydrological model for more than 75% of continental areas. For the natural gap (July 2017–May 2018), the misclosures in backward–forward prediction estimated between forward- and backward-predicted values are equal to 10 cm. This represents an amount of 10–20% of the total TWS signal for 60% of areas. The regional analysis shows that the presented method is able to capture the occurrence of droughts or floods, but does not reflect their magnitudes. Results indicate that the presented remove–restore technique combined with AR prediction can be utilized to reliably predict TWS changes for regional analysis, but the removed climatology must be properly matched to the selected region. [ABSTRACT FROM AUTHOR]

Temporal gaps within the Gravity Recovery and Climate Experiment (GRACE) (gap: 20 months), between GRACE and GRACE Follow-On (GRACE-FO) missions (gap: 11 months), and within GRACE-FO record (gap: 2 months) make it difficult to analyze and interpret spatiotemporal variability in GRACE- and GRACE-FO-derived terrestrial water storage (TWSGRACE) time series. In this study, an overview of data and approaches used to fill these gaps and reconstruct the TWSGRACE record at the global scale is provided. In addition, the study provides an innovative approach that integrates three machine learning techniques (deep-learning neural networks [DNN], generalized linear model [GLM], and gradient boosting machine [GBM]) and eight climatic and hydrological input variables to fill these gaps and reconstruct the TWSGRACE data record at both global grid and basin scales. For each basin and grid cell, the model performance was assessed using Nash–Sutcliffe efficiency coefficient (NSE), correlation coefficient (CC), and normalized root-mean-square error (NRMSE), a leader model was selected based on the model performance, and variables that significantly control leader model outputs were defined. Results indicate that (1) the leader model reconstructed the TWSGRACE with high accuracy over both grid and local scales, particularly in wet and low anthropogenically active regions (grid scale: NSE = 0.65 ± 0.20, CC = 0.81 ± 0.13, and NSE = 0.56 ± 0.16; basin scale: NSE = 0.78 ± 0.14, CC = 0.89 ± 0.07, and NRMSE = 0.43 ± 0.14); (2) no single model was flawless in reconstructing the TWSGRACE over all grids or basins, so a combination of models is necessary; (3) basin-scale models outperform grid-scale models; (4) the DNN model outperforms both GLM and GBM at the basin scale, whereas the GBM outperforms at the grid scale; (5) among other inputs, the Global Land Data Assimilation System (GLDAS)-derived TWS controls the model performance on both basin and grid scales; and (6) the reconstructed TWSGRACE data captured extreme climatic events over the investigated basins and grid cells. The developed approach is robust, effective, and could be used to accurately reconstruct TWSGRACE for any hydrologic system across the globe. [ABSTRACT FROM AUTHOR]

Since Kepler, Newton and Huygens in the seventeenth century, geodesy has been concerned with determining the figure, orientation and gravitational field of the Earth. With the beginning of the space age in 1957, a new branch of geodesy was created, satellite geodesy. Only with satellites did geodesy become truly global. Oceans were no longer obstacles and the Earth as a whole could be observed and measured in consistent series of measurements. Of particular interest is the determination of the spatial structures and finally the temporal changes of the Earth's gravitational field. The knowledge of the gravitational field represents the natural bridge to the study of the physics of the Earth's interior, the circulation of our oceans and, more recently, the climate. Today, key findings on climate change are derived from the temporal changes in the gravitational field: on ice mass loss in Greenland and Antarctica, sea level rise and generally on changes in the global water cycle. This has only become possible with dedicated gravity satellite missions opening a method known as satellite gravimetry. In the first forty years of space age, satellite gravimetry was based on the analysis of the orbital motion of satellites. Due to the uneven distribution of observatories over the globe, the initially inaccurate measuring methods and the inadequacies of the evaluation models, the reconstruction of global models of the Earth's gravitational field was a great challenge. The transition from passive satellites for gravity field determination to satellites equipped with special sensor technology, which was initiated in the last decade of the twentieth century, brought decisive progress. In the chronological sequence of the launch of such new satellites, the history, mission objectives and measuring principles of the missions CHAMP, GRACE and GOCE flown since 2000 are outlined and essential scientific results of the individual missions are highlighted. The special features of the GRACE Follow-On Mission, which was launched in 2018, and the plans for a next generation of gravity field missions are also discussed. [ABSTRACT FROM AUTHOR]

The present study aimed to understand the effect of filtering on global and regional terrestrial water storage (TWS) signal derived from Gravity Recovery and Climate Experiment (GRACE) satellite data obtained from Centre for Space Research (CSR), Jet Propulsion Laboratory (JPL) and GeoForschungsZentrum (GFZ). Our results show that the CSR and GFZ solutions were compatible after processing, while for JPL solutions were more challenging to eliminate data noises using filtering techniques. Concerning the effect of changing the Gauss filtering radius on TWS, differences were found to be at a maximum ±5 cm in annual amplitude and ±1 cm/yr in trend sections; mostly apparent in regions where the signal was anomalous. Various destriping methods may led to data misinterpretation, loss of available TWS signal or confusion. Finally, new releases of CSR (RL06) showed an improvement compared to former versions particularly for solutions for the specific time of year chosen in this study. [ABSTRACT FROM AUTHOR]

An increasing number of studies suggest that climate change causes variation in the terrestrial water cycle. It is known that the precipitation as the source of water storage change on land and ocean is directly influenced by sea surface temperature (SST). At scales larger than, say, 350 km, such water storage variation can be monitored by the satellite gravimetry mission, the Gravity Recovery and Climate Experiment (GRACE). How the water cycle changes inter‐annually in the boreal region and how the hydrological variables such as precipitation, evaporation, run‐off and terrestrial water storage relate to El Nino Southern Oscillation Index (ENSO) are still unanswered questions. We explore the teleconnection patterns of the boreal hydrological cycle and climate change indicated by ENSO over 2003–2014. We use monthly total water storage changes derived from GRACE, precipitation, run‐off and evaporation on a 1° × 1° grid, land surface temperature anomalies on a 0.5° × 0.5° grid and global SST anomalies with 5° resolution. We apply canonical correlation analysis to link all the hydrological variables to ENSO through SST to identify the implicit relationship between the hydrological cycle on land and ENSO. We identify significant correlations larger than 0.6 between Nino 3.4 and each hydrological variable via SST. The associated spatial patterns indicate a clear ENSO signature in boreal catchments, especially Ob and Yenisei. ENSO correlates to abnormal increase of temperature in Ob, Yenisei and Lena. A notable ENSO‐related increase of precipitation is found over Ob and a decrease over Lena and Yenisei. The negative water balance of Lena and Yenisei reveals a teleconnection between boreal water cycle and ENSO. In addition, the ENSO‐associated modes from terrestrial variables are investigated with aid of cross wavelet coherency. The phase shifts obtained by cross correlation analysis and wavelet coherency maps indicate the response of boreal hydrological cycle with a 1–2 month lag to ENSO. [ABSTRACT FROM AUTHOR]

Ocean tides produce significant gravitational perturbations that affect near‐Earth orbiting spacecraft. The gravitational potential induced by tidal mass redistribution is routinely modeled for global gravity analysis and orbit determination, although generally by assuming a spherical Earth and a uniform seawater density. The inadequacy of these simplifications is here addressed. We have developed an accurate yet efficient algorithm to compute the ocean tidal geopotential, allowing for Earth's elliptical shape and variable seawater density. Using this new computation, we find that (1) the effect of ellipticity is several percent of the tide signal over mid to high‐latitude regions, which is comparable to elevation error in the state‐of‐the‐art ocean tide models; (2) the effect of seawater density variations on the potential is as large as 2–3 cm in water‐height equivalent, primarily in deep water where density increases 2%–3% from compressibility. Our analysis of new Gravity Recovery and Climate Experiment Follow‐On (GRACE‐FO) laser ranging interferometer measurements reveals evident errors when ellipticity and density variations are ignored. When accounted for, the GRACE‐FO residual tidal gravity perturbations are reduced by half, depending on the adopted tide model; only the remaining half likely represents actual model elevation error. The use of a spherical surface and a uniform seawater density is no longer tenable given the precision of gravity measurements from GRACE and GRACE‐FO satellites. Plan Language Summary: Ocean tide involves periodic mass redistribution and changes global Earth gravity fields. The gravitational attraction by ocean tidal mass has been routinely modeled for analyzing Earth‐orbiting spacecraft data and computing Earth's gravity field changes. Generally, the spherical Earth and a uniform seawater density are assumed for mass change by ocean tide. The Earth ellipticity and seawater density variation have not yet been adequately discussed in the literature on time‐variable gravity and orbit analysis. We present new results from the analysis of actual Gravity Recovery and Climate Experiment Follow‐On (GRACE‐FO) laser ranging interferometer measurements and report that the use of spherical Earth and uniform seawater density is no longer tenable given the precision of gravity measurements from GRACE and GRACE‐FO satellites. We recommend the GRACE and GRACE‐FO processing centers to revise their computations of the ocean tide's gravitational potential using the algorithm and computer code in this study. Key Points: New algorithm to compute global geopotential from ocean tidal mass change considering the ellipticity and seawater density changeThe ellipticity and density effects (often neglected in orbit & gravity analysis) were found to be as large as tidal elevation model errors.New GRACE Follow‐On laser ranging interferometer data observed these systematic errors by the ellipticity and seawater density change. [ABSTRACT FROM AUTHOR]

Gravitationally consistent solutions of the Sea Level Equation from leakage‐corrected monthly‐mean GFZ RL06 Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow‐On (GRACE‐FO) Stokes coefficients reveal that barystatic sea level averaged over the whole global ocean was rising by 1.72 mm a−1 during the period April 2002 until August 2016. This rate refers to a truely global ocean averaging domain that includes all polar and semienclosed seas. The result corresponds to 2.02 mm a−1 mean barystatic sea level rise in the open ocean with a 1,000 km coastal buffer zone as obtained from a direct spatial integration of monthly GRACE data. The bias of +0.3 mm a−1 is caused by below‐average barystatic sea level rise in close proximity to coastal mass losses induced by the smaller gravitational attraction of the remaining continental ice and water masses. Alternative spherical harmonics solutions from CSR, JPL, and TU Graz reveal open‐ocean rates between 1.94 and 2.08 mm a−1, thereby demonstrating that systematic differences among the processing centers are much reduced in the latest release. We introduce in this paper a new method to approximate spatial leakage from the differences of two differently filtered global gravity fields. A globally constant and time‐invariant scale factor required to obtain full leakage from those filter differences is found to be 3.9 for GFZ RL06 when filtered with DDK3, and lies between 3.9 and 4.4 for other processing centers. Spatial leakage is estimated for every month in terms of global grids, thereby providing also valuable information of intrabasin leakage that is potentially relevant for hydrologic and hydrometeorological applications. Plain Language Summary: Satellite gravimetry as realized with the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow‐On (GRACE‐FO) missions is measuring tiny variations in the Earth's gravity field that are directly caused by divergent horizontal mass transports such as the melting of ice sheets and the corresponding discharge of melt water into the ocean basins. Between April 2002 and August 2016, this mass inflow caused sea level to rise by 1.72 mm each year as quantified from the latest GRACE reprocessing performed at our institute. The indirect observation principle of GRACE limits the spatial resolution so that highly localized mass loss signals are smeared out into the larger surrounding area, and possibly even from land into the ocean. We propose here a new method to quantify this so‐called spatial leakage from the difference of gravity fields smoothed with slightly different spatial filters. A scale factor is obtained from exploiting the availability of two independent methods to estimate the mass component of sea level rise: The first method spatially integrates over the global gravity fields in all regions away from the coasts, and the second method utilizes a (leakage‐corrected) mass distribution over the continents to calculate the gravitationally consistent distribution of water masses in all ocean basins. We estimate this scale factor as 3.9. Key Points: Mean barystatic sea level rise is biased high by 0.3 mm a−1 when estimated with a 1,000 km coastal buffer zoneFractional spatial leakage in monthly GRACE gravity fields is quantified with two differently strong DDK filtersFractional leakage is scaled by a factor of 3.9 to make results from the Sea Level Equation consistent with open‐ocean integrations [ABSTRACT FROM AUTHOR]

Satellite gravimetry began with the launch of the satellites Sputnik 1 and 2 in 1957. During the following 43 years, more and more details were discovered and the models of the Earth's gravity could be refined. Methods improved and more and more satellite orbits and ground stations were added in the analysis, employing more advanced and precise measuring techniques. A new era started with the dedicated gravimetry missions CHAMP (2000–2010), GRACE (2002–2017), and GOCE (2009–2013). The methods of satellite-to-satellite tracking and satellite gradiometry resulted in a substantial improvement of our knowledge of the Earth's gravity field in terms of accuracy and its spatial and temporal variations. There are three basic ways of using gravity and geoid models in Earth sciences and geodesy. First, in solid Earth physics, the highs and lows of the field are investigated in comparison with an idealized Earth, e.g., a hydrostatic equilibrium figure. In particular, in South America, Africa, Himalaya and Antarctica the gravity field is known much better now, due to GOCE and lead to an improved understanding of the continental crust and lithosphere. Second, in oceanography, the geoid serves as surface in equilibrium, a hypothetical ocean at rest. The ocean topography is the deviation of the actual ocean surface, measured by satellite altimetry, from this reference. The ocean topography serves as a new and independent input to ocean circulation modeling and leads to an improved understanding of ocean transport of mass, heat, and nutrients. Similarly, geodetic heights of the land surface will soon be referred to the geoid, leading to globally consistent heights and enabling the removal of existent systematic deformations and offsets of national and continental height systems. Third, the GRACE time series of monthly gravity models, reflecting seasonal, inter-annual and long-term gravity changes, became one of the most valuable data sources of climate change studies. [ABSTRACT FROM AUTHOR]

We examined the first‐ever laser ranging interferometer (LRI) measurements of inter‐satellite tracking acquired by Gravity Recovery and Climate Experiment (GRACE) Follow‐On satellites. Through direct along‐orbit analysis of instantaneous inter‐satellite measurements, we demonstrate the higher sensitivity of LRI (than K‐band microwave ranging [KBR]) to anomalies associated with the Earth static gravity field at high spatial resolutions of 100–200 km. We found that LRI captures gravitational signals as small as 0.1 nm/s2 at 490 km altitude, improved by 1 order of magnitude from KBR. This allows LRI to uniquely detect un‐/mis‐modeled short‐wavelength gravitational perturbations. We employed all LRI data in 2019 to validate various state‐of‐the‐art global static gravity field models and show that LRI measurements, even over 1 month, can distinguish subtle differences among the models computed from ~15 years of GRACE KBR and ~4 years of Gravity Field and Steady‐State Ocean Circulation Explorer (GOCE) gradiometry data. Ultra‐precise LRI measurements will be yet another critical data set for future gravity field model development. Key Points: We examined the first‐ever measurements of inter‐satellite laser ranging interferometer (LRI) from GRACE Follow‐On satellitesLRI measures static gravity perturbations as small as 100 km by more than 1 order of magnitude better than microwave‐based measurementsLaser data are accurate enough to detect subtle errors in global gravity field models from ~15 years of GRACE and ~4 years of GOCE data [ABSTRACT FROM AUTHOR]

GRACE satellites have detected regional‐scale preseismic, coseismic, and postseismic gravity changes associated with great earthquakes during the GRACE era (2002‐2017). Earthquakes also excite global‐scale transient gravity changes associated with free oscillations that may be discerned for a few days. In this study, we examine such global gravity changes due to Earth's free oscillations and quantify how they affect GRACE measurements. We employ the normal mode formalism to synthesize the global gravity changes after the 2004 Sumatra earthquake and simulate the (gravitational) free oscillation signals manifested in the GRACE K‐band ranging (KBR) measurements. Using the Kaula orbit perturbation theory, we show how GRACE inter‐satellite distances are perturbed through a complex coupling of eigenfrequencies of the normal modes with the Earth's rotation rate and the GRACE satellites' orbital frequency. It is found that a few gravest normal modes can generate range‐rate perturbations as large as 0.2 μm/s, which are comparable to actual errors of GRACE KBR ranging and accelerometer instruments. Wavelet time‐frequency analysis of the GRACE KBR residual data in December 2004 reveals the existence of a significant transient signal after the 2004 Sumatra earthquake. This transient signal is characterized by a frequency of ~0.022 mHz that could be potentially associated with the largest excitation due to the "football" mode of the Earth's free oscillation. However, the results are also affected by low‐frequency noise of the GRACE accelerometers. Improved space‐borne gravitational instrumentation may open new opportunities to study the Earth's interior and earthquakes independently from global seismological analysis. Key Points: Earth's free oscillations excited by great earthquakes cause transient global gravity changes that perturb the GRACE orbital trajectoryWe develop an analytic model of inter‐satellite range perturbation caused by the Earth's free oscillationsWavelet analysis of GRACE data reveals a candidate for football mode excited by 2004 Sumatra earthquake but obscured by accelerometer error [ABSTRACT FROM AUTHOR]

Satellite laser ranging (SLR) observations are routinely applied toward the estimation of dynamic oblateness, C20, which is the largest globally integrated component of Earth's time‐variable gravity field. Since 2002, GRACE and GRACE Follow‐On have revolutionized the recovery of higher spatial resolution features of global time‐variable gravity, with SLR continuing to provide the most reliable estimates of C20. We quantify the effect of various SLR processing strategies on estimating C20 and demonstrate better signal recovery with the inclusion of GRACE‐derived low‐degree gravity information in the forward model. This improved SLR product modifies the Antarctic and Greenland Ice Sheet mass trends by −15.4 and −3.5 Gt/year, respectively, as compared to CSR TN11, and improves global mean sea level budget closure by modifying sea level rise by +0.08 mm/year. We recommend that this new C20 product be applied to RL06 GRACE data products for enhanced accuracy and scientific interpretation. Key Points: New satellite laser ranging C20 solution reveals larger Antarctic and Greenland ice mass losses and mass‐driven sea level riseThe new C20 result improves closure of the global mean sea level budget and agreement with an independent Antarctic ice mass assessmentWe recommend this new product for replacing the GRACE C20 values for science applications [ABSTRACT FROM AUTHOR]

Considering the unstable inversion of ill‐conditioned intermediate matrix required in each integral arc in the short‐arc approach presented in Chen et al. (2015, https://doi.org/10.1002/2014JB011470), an optimized short‐arc method via stabilizing the inversion is proposed. To account for frequency‐dependent noise in observations, a noise whitening technique is implemented in the optimized short‐arc approach. Our study shows that the optimized short‐arc method is able to stabilize the inversion and eventually prolong the arc length to 6 hr. In addition, the noise whitening method is able to mitigate the impacts of low‐frequency noise in observations. Using the optimized short‐arc approach, a refined time series of Gravity Recovery and Climate Experiment (GRACE) monthly models called Tongji‐Grace2018 has been developed. The analyses allow us to derive the following conclusions: (a) During the analyses over the river basins (i.e., Amazon, Mississippi, Irrawaddy, and Taz) and Greenland, the correlation coefficients of mass changes between Tongji‐Grace2018 and others (i.e., CSR RL06, GFZ RL06, and JPL RL06 Mascon) are all over 92% and the corresponding amplitudes are comparable; (b) the signals of Tongji‐Grace2018 agree well with those of CSR RL06, GFZ RL06, ITSG‐Grace2018, and JPL RL06 Mascon, while Tongji‐Grace2018 and ITSG‐Grace2018 are less noisy than CSR RL06 and GFZ RL06; (c) clearer global mass change trend and less striping noise over oceans can be observed in Tongji‐Grace2018 even only using decorrelation filtering; and (d) for the tests over Sahara, over 36% and 19% of noise reductions are achieved by Tongji‐Grace2018 relative to CSR RL06 in the cases of using decorrelation filtering and combined filtering, respectively. Key Points: The optimized short‐arc approach greatly reduces the condition number of the final normal equation for estimating gravity field parametersThe noise whitening method is able to mitigate the impacts of low‐frequency noise in observations on gravity field modelingTongji‐Grace2018 monthly models based on the optimized short‐arc approach greatly reduce the noise and improve the signal‐to‐noise ratio [ABSTRACT FROM AUTHOR]

The role of continental water in polar motion excitation can be illustrated by determining Hydrological Angular Momentum calculated from terrestrial water storage (TWS). In this paper we compare global and regional changes in TWS computed using Coupled Model Intercomparison Project Phase 5 climate models, Global Land Data Assimilation System (GLDAS) land hydrology models and observations from the Gravity Recovery and Climate Experiment (GRACE) satellite mission. We also compare hydrological excitation functions derived from models with those obtained from the GRACE mission and the hydrological signal in observed polar motion excitation (the so-called geodetic residuals). The results confirm that GLDAS models of seasonal and non-seasonal TWS change are more consistent with GRACE data than climate models; on the other hand, none of the considered models are fully consistent with GRACE data or geodetic residuals. In turn, GRACE observations are most consistent with the non-seasonal hydrological signal in observed excitation. A detailed study of the contribution of different TWS components to the hydrological excitation function shows that soil moisture dominates. [ABSTRACT FROM AUTHOR]

We develop a transfer function to determine in situ line‐of‐sight gravity difference (LGD) directly from Gravity Recovery and Climate Experiment (GRACE) range‐acceleration measurements. We first reduce GRACE data to form residual range‐acceleration referenced to dynamic orbit computed with a reference gravity field and nonconservative force data. Thus, the residuals and the corresponding LGD data reflect time‐variable gravity signals. A transfer function is designed based on correlation‐admittance spectral analysis. The correlation spectrum shows that residual range‐acceleration and LGD are near‐perfectly correlated for frequencies >5 cycles‐per‐revolution. The admittance spectrum quantifies that the LGD response to range‐acceleration is systematically larger at lower frequencies, due to the increased contribution of centrifugal acceleration. We find that the correlation and admittance spectra are stationary (i.e., are independent of time, satellite altitude, and gravity strength) and, therefore, can be determined a priori with high fidelity. We determine the spectral transfer function and the equivalent time domain filter. Using both synthetic and actual GRACE data, we demonstrate that in situ LGD can be estimated via the transfer function with an estimation error of 0.15 nm/s2, whereas the actual GRACE data error is around 1.0 nm/s2. We present an application of LGD data to surface water storage changes in large basins such as Amazon, Congo, Parana, and Mississippi by processing 11 years of GRACE data. Runoff routing models are calibrated directly using LGD data. Our technique demonstrates a new way of using GRACE data by forward modeling of various geophysical models and in‐orbit comparison with such GRACE in situ data. Key Points: In situ gravimetric observables can be computed from combination of GPS and KBR data of the GRACE satellite missionWe develop a transfer function for accurate estimation of LOS gravity difference directly from level‐1B residual KBR range‐acceleration dataThe in‐orbit comparison between in situ gravimetric data and models is a simple and powerful approach for hydrological model evaluations [ABSTRACT FROM AUTHOR]

Abstract: In order to derive high‐precision static Gravity Recovery and Climate Experiment (GRACE)‐only gravity field solutions, the following strategies were implemented in this study: (1) a refined accelerometer calibration model that treats monthly accelerometer scales as a third‐order polynomial and daily accelerometer biases as a fifth‐order polynomial was developed to calibrate accelerometer measurements; (2) the errors of the acceleration and attitude data were estimated together with the geopotential coefficients and accelerometer parameters on the basis of the weighted least squares adjustments; (3) a nearly complete observation series of GRACE mission was used to decrease the condition number of normal equation; and (4) the GRACE data collected in lower orbit altitude were also included to decrease the condition number. Our results show that (1) the refined accelerometer calibration model with much less parameters performs as well as previous methods (i.e., solving daily scales and hourly biases or estimating biases along with bias rates every 2 hr). However, it provides a system of more stable normal equation and less high‐frequency noise in gravity field solutions; (2) high‐frequency noise in the gravity field solution is reduced by modeling the errors of the acceleration and attitude data; (3) the geopotential coefficients at all degrees is greatly enhanced by using longer GRACE time series (especially the data by the end of 2010); and (4) due to lower orbit altitude, the GRACE data collected since 2014 lead to a significant improvement of the gravity field solution as the satellites are more sensitive to higher‐frequency signal. Using the refined strategies, an unconstrained static solution (named Tongji‐Grace02s) up to degree and order 180 was derived. For further suppressing the high‐frequency noise, a regularization strategy based on the Kaula rule is applied to the degrees and orders beyond 80, leading to a regularized model Tongji‐Grace02k. To validate the quality of the derived models, both Tongji‐Grace02s and Tongji‐Grace02k were compared to the latest GRACE‐only models (i.e., GGM05S, ITU_GRACE16, ITSG‐Grace2014s, and ITSG‐Grace2014k) and validated using independent data (i.e., Global Navigation Satellite Systems (GNSS)/Leveling data and DTU13 oceanic gravity data). Compared to other models, much less spatial noise in terms of global gravity anomalies with respect to the state‐of‐the‐art model EIGEN6C4 and far higher accuracy at high degrees are achieved by Tongji‐Grace02s. The same conclusions can be drawn for Tongji‐Grace02k when the same analyses were applied to the regularized solutions ITSG‐Grace2014k and Tongji‐Grace02k. Validations with independent data confirm that Tongji‐Grace02s has the least noise among the unconstrained GRACE‐only models and Tongji‐Grace02k is the one with the best accuracy among the regularized GRACE‐only solutions. For the tests up to degree and order 180 using GNSS/Leveling data, the improvements of Tongji‐Grace02s with respect to ITSG‐Grace2014s reach 13% over Canada and 23% in Mexico. Even better, no less than 58% of improvement is achieved by both Tongji‐Grace02s relative to ITSG‐Grace2014s and Tongji‐Grace02k with respect to ITSG‐Grace2014k in the validation based on DTU13 data. [ABSTRACT FROM AUTHOR]

Temporal variations of geoid heights are vitally important in geodesy and Earth science. They are essentially needed for dynamic and kinematic updates of the static geoid model. These temporal variations, which substantially differ for different geographic locations, can successfully be determined using the Gravity Recovery And Climate Experiment (GRACE) mission data. So far, statistical decomposition methods, e.g. the Principal Component Analysis/Empirical Orthogonal Function (PCA/EOF) method, have not been implemented for the analysis and modelling of temporal mass variations within the Earth’s system over the area of Poland. The aim of this contribution is to analyse and model temporal variations of geoid heights obtained from GRACE mission data over the area of Poland using the PCA/EOF method. Temporal variations of geoid heights were obtained from the latest release, i.e. release five, of monthly GRACE-based Global Geopotential Models. They can reach the level of 10 mm. The PCA modes and their corresponding EOF loading patterns were estimated using two different algorithms. The results obtained revealed that significant part of the signal of temporal variations of geoid heights over Poland can be obtained from the first three PCA modes and EOF loading patterns. They demonstrate the suitability of the PCA/EOF method for analysing and modelling temporal variations of geoid heights over the area investigated. [ABSTRACT FROM AUTHOR]

Abstract: West African regions along the Niger River experience climate and land cover changes that affect hydrological processes and therewith the distribution of fresh water resources (WR). This study provides an investigation of long‐term changes in terrestrial water storages (TWS) of the Niger River basin and its subregions by analyzing a decade of satellite gravity data from the Gravity Recovery and Climate Experiment (GRACE) mission. The location of large trends in TWS maps of differently processed GRACE solutions points to rising groundwater stocks. Soil moisture data from a global land surface model allow separating the effect of significantly increasing amount of WR from that of TWS variations. Surface water variations from a global water storage model validated with observations from altimetry data were applied to estimate the groundwater component in WR. For the whole Niger, a rise in groundwater stocks is estimated to be 93 ± 61 km3 between January 2003 and December 2013. A careful analysis of uncertainties in all data sets supports the significance of the groundwater rise. Our results confirm previous observations of rising water tables, indicating that effects of land cover changes on groundwater storage are relevant on basin scales. Areas with rising water storage are stocking a comfortable backup to mitigate possible future droughts and to deliver water to remote areas. This has implications for Niger water management strategies. Increasing groundwater recharges may be accompanied by reduction in water quality. This study helps to inform authority's decision to mitigate its negative impacts on local communities. [ABSTRACT FROM AUTHOR]

Many geoscience disciplines push for ever higher requirements on accuracy, homogeneity and time- and space-resolution of the Earth's gravity field. Apart from better instruments or new observables, alternative satellite formations could improve the signal and error structure compared to Grace. One possibility to increase the sensitivity and isotropy by adding cross-track information is a pair of satellites flying in a pendulum formation. This formation contains two satellites which have different ascending nodes and arguments of latitude, but have the same orbital height and inclination. In this study, the semi-analytical approach for efficient pre-mission error assessment is presented, and the transfer coefficients of range, range-rate and range-acceleration gravitational perturbations are derived analytically for the pendulum formation considering a set of opening angles. The new challenge is the time variations of the opening angle and the range, leading to temporally variable transfer coefficients. This is solved by Fourier expansion of the sine/cosine of the opening angle and the central angle. The transfer coefficients are further applied to assess the error patterns which are caused by different orbital parameters. The simulation results indicate that a significant improvement in accuracy and isotropy is obtained for small and medium initial opening angles of single polar pendulums, compared to Grace. The optimal initial opening angles are $$45^\circ $$ and $$15^\circ $$ for accuracy and isotropy, respectively. For a Bender configuration, which is constituted by a polar Grace and an inclined pendulum in this paper, the behaviour of results is dependent on the inclination (prograde vs. retrograde) and on the relative baseline orientation (left or right leading). The simulation for a sun-synchronous orbit shows better results for the left leading case. [ABSTRACT FROM AUTHOR]

The current high-degree global geopotential models EGM2008 and EIGEN-6C4 resolve gravity field structures to $$\sim $$ 10 km spatial scales over most parts of the of Earth's surface. However, a notable exception is continental Antarctica, where the gravity information in these and other recent models is based on satellite gravimetry observations only, and thus limited to about $$\sim $$ 80-120 km spatial scales. Here, we present a new degree-2190 global gravity model (GGM) that for the first time improves the spatial resolution of the gravity field over the whole of continental Antarctica to $$\sim $$ 10 km spatial scales. The new model called SatGravRET2014 is a combination of recent Gravity Recovery and Climate Experiment (GRACE) and Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite gravimetry with gravitational signals derived from the 2013 Bedmap2 topography/ice thickness/bedrock model with gravity forward modelling in ellipsoidal approximation. Bedmap2 is a significantly improved description of the topographic mass distribution over the Antarctic region based on a multitude of topographic surveys, and a well-suited source for modelling short-scale gravity signals as we show in our study. We describe the development of SatGravRET2014 which entirely relies on spherical harmonic modelling techniques. Details are provided on the least-squares combination procedures and on the conversion of topography to implied gravitational potential. The main outcome of our work is the SatGravRET2014 spherical harmonic series expansion to degree 2190, and derived high-resolution grids of 3D-synthesized gravity and quasigeoid effects over the whole of Antarctica. For validation, six data sets from the IAG Subcommission 2.4f 'Gravity and Geoid in Antarctica' (AntGG) database were used comprising a total of 1,092,981 airborne gravimetric observations. All subsets consistently show that the Bedmap2-based short-scale gravity modelling improves the agreement over satellite-only data considerably (improvement rates ranging between 9 and 75 % with standard deviations from residuals between SatGravRET2014 and AntGG gravity ranging between 8 and 25 mGal). For comparison purposes, a degree-2190 GGM was generated based on the year-2001 Bedmap1 (using the ETOPO1 topography) instead of 2013 Bedmap2 topography product. Comparison of both GGMs against AntGG consistently reveals a closer fit over all test areas when Bedmap2 is used. This experiment provides evidence for clear improvements in Bedmap2 topographic information over Bedmap1 at spatial scales of $$\sim $$ 80-10 km, obtained from independent gravity data used as validation tool. As a general conclusion, our modelling effort fills-in approximation-some gaps in short-scale gravity knowledge over Antarctica and demonstrates the value of the Bedmap2 topography data for short-scale gravity refinement in GGMs. SatGravRET2014 can be used, e.g. as a reference model for future gravity modelling efforts over Antarctica, e.g. as foundation for a combination with the AntGG data set to obtain further improved gravity information. [ABSTRACT FROM AUTHOR]

A gravity field model is computed from the four accurate gravitational gradient components of GOCE (Gravity field and steady-state Ocean Circulation Explorer), combined with the analysis of the kinematic orbits, and some moderate constraint (or stabilization) in the polar areas where no observation from GOCE is available due to the orbit geometry. The normal matrix of each component is computed individually in order to study its contribution to the combined solution. The results show that the contribution of V is the largest, with an average value of 32.74% of the total solution; the second and the third largest are V and V, with average values of 28.04% and 26.08%, respectively; the component V contributes 11.81%. Validation with external data shows that each component has its characteristic value and that the information content of the component V is not negligible and should be included for gravity field recovery. The orbit part as derived from high-low satellite-to-satellite tracking (SST-hl) to the GPS contributes mostly to the coefficients below degree and order (d/o) 20, and to non-zonal coefficients from d/o 20 to 80. The mean value of the contribution of the polar stabilization is the smallest with a value of 0.22%, nevertheless it is important. In addition to the contribution analysis in terms of the normal matrices, each individual component of the gradiometer has been combined with SST and polar stabilization, to give a set of single component gravity field models. These partially combined solutions are compared to the fully combined solution in terms of geoid differences. They show that the partially combined solution with V is closest to the complete solution. Even closer is a combination with V and V. In addition to the GOCE-only solution, a GOCE-GRACE (Gravity Recovery And Climate Experiment) combined gravity field model is derived and the information content of GOCE and an available set of normal equations of GRACE are investigated. Results show that, as expected, GRACE dominates the solution below degree 90 and GOCE above degree 140. [ABSTRACT FROM AUTHOR]

Recently, four global geopotential models (GGMs) were computed and released based on the first 2 months of data collected by the Gravity field and steady-state Ocean Circulation Explorer (GOCE) dedicated satellite gravity field mission. Given that GOCE is a technologically complex mission and different processing strategies were applied to real space-collected GOCE data for the first time, evaluation of the new models is an important aspect. As a first assessment strategy, we use terrestrial gravity data over Switzerland and Australia and astrogeodetic vertical deflections over Europe and Australia as ground-truth data sets for GOCE model evaluation. We apply a spectral enhancement method (SEM) to the truncated GOCE GGMs to make their spectral content more comparable with the terrestrial data. The SEM utilises the high-degree bands of EGM2008 and residual terrain model data as a data source to widely bridge the spectral gap between the satellite and terrestrial data. Analysis of root mean square (RMS) errors is carried out as a function of (i) the GOCE GGM expansion degree and (ii) the four different GOCE GGMs. The RMS curves are also compared against those from EGM2008 and GRACE-based GGMs. As a second assessment strategy, we compare global grids of GOCE GGM and EGM2008 quasigeoid heights. In connection with EGM2008 error estimates, this allows location of regions where GOCE is likely to deliver improved knowledge on the Earth's gravity field. Our ground truth data sets, together with the EGM2008 quasigeoid comparisons, signal clear improvements in the spectral band ~160-165 to ~180-185 in terms of spherical harmonic degrees for the GOCE-based GGMs, fairly independently of the individual GOCE model used. The results from both assessments together provide strong evidence that the first 2 months of GOCE observations improve the knowledge of the Earth's static gravity field at spatial scales between ~125 and ~110 km, particularly over parts of Asia, Africa, South America and Antarctica, in comparison with the pre-GOCE-era. [ABSTRACT FROM AUTHOR]

In large freshwater river basins across the globe, the composite influences of large-scale climatic processes and human activities (e.g., deforestation) on hydrological processes have been studied. However, the knowledge of these processes in this era of the Anthropocene in the understudied hydrologically pristine South Central African (SCA) region is limited. This study employs satellite observations of evapotranspiration (ET), precipitation and freshwater between 2002 and 2017 to explore the hydrological patterns of this region, which play a crucial role in global climatology. Multivariate methods, including the rotated principal component analysis (rPCA) were used to assess the relationship of terrestrial water storage (TWS) in response to climatic units (precipitation and ET). The use of the rPCA technique in assessing changes in TWS is warranted to provide more information on hydrological changes that are usually obscured by other dominant naturally-driven fluxes. Results show a low trend in vegetation transpiration due to deforestation around the Congo basin. Overall, the Congo (r2 = 76%) and Orange (r2 = 72%) River basins maintained an above-average consistency between precipitation and TWS throughout the study region and period. Consistent loss in freshwater is observed in the Zambezi (−9.9 ± 2.6 mm/year) and Okavango (−9.1 ± 2.5 mm/year) basins from 2002 to 2008. The Limpopo River basin is observed to have a 6% below average reduction in rainfall rates which contributed to its consistent loss in freshwater (−4.6 ± 3.2 mm/year) from 2006 to 2012.Using multi-linear regression and correlation analysis we show that ET contributes to the variability and distribution of TWS in the region. The relationship of ET with TWS (r = 0.5) and rainfall (r = 0.8) over SCA provides insight into the role of ET in regulating fluxes and the mechanisms that drive precipitation in the region. The moderate ET–TWS relationship also shows the effect of climate and anthropogenic influence in their interactions. [ABSTRACT FROM AUTHOR]

The Gravity Recovery and Climate Experiment (GRACE) mission has measured total water storage change (TWSC) and interpreted drought patterns in an unparalleled way since 2002. Nevertheless, there are few sources that can be used to understand drought patterns prior to the GRACE era. In this study, we extended the gridded GRACE TWSC to 1993 by combining principal component analysis (PCA), least square (LS) fitting, and multiple linear regression (MLR) methods using climate variables as input drivers. We used the extended (climate-driven) TWSC to interpret drought patterns (1993–2019) over the Amazon basin. Results showed that, in the Amazon area with the resolution of 0.5°, GRACE, GRACE follow on, and Swarm had correlation coefficients of 0.95, 0.92, and 0.77 compared with climate-driven TWSCS, respectively. The drought patterns assessed by the climate-driven TWSC were consistent with those interpreted by the Palmer Drought Severity Index and GRACE TWSC. We also found that the 1998 and 2016 drought events in the Amazon, both induced by strong El Niño events, showed similar drought patterns. This study provides a new perspective for interpreting long-term drought patterns prior to the GRACE period. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The GRACE-derived terrestrial water storage (TWSGRACE) provides measurements of the mass exchange and transport between continents, oceans, and ice sheets. In this study, a statistical approach was used to forecast TWSGRACE data using 10 major African watersheds as test sites. The forecasted TWSGRACE was then used to predict drought events in the examined African watersheds. Using a nonlinear autoregressive with exogenous input (NARX) model, relationships were derived between TWSGRACE data and the controlling and/or related variables (rainfall, temperature, evapotranspiration, and Normalized Difference Vegetation Index). The performance of the model was found to be "very good" (Nash–Sutcliffe (NSE) > 0.75; scaled root mean square error (R*) < 0.5) for 60% of the investigated watersheds, "good" (NSE > 0.65; R* < 0.6) for 10%, and "satisfactory" (NSE > 0.50; R* < 0.7) for the remaining 30% of the watersheds. During the forecasted period, no drought events were predicted over the Niger basin, the termination of the latest (March–October 2015) drought event was observed over the Zambezi basin, and the onset of a drought event (January-March 2016) over the Lake Chad basin was correctly predicted. Adopted methodologies generate continuous and uninterrupted TWSGRACE records, provide predictive tools to address environmental and hydrological problems, and help bridge the current gap between GRACE missions. [ABSTRACT FROM AUTHOR]

In contrast to most of the coseismic gravity change studies, which are generally based on data from the Gravity field Recovery and Climate Experiment (GRACE) satellite mission, we use observations from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) Satellite Gravity Gradient (SGG) mission to estimate the coseismic gravity and gravity gradient changes caused by the 2011 Tohoku-Oki Mw 9.0 earthquake. We first construct two global gravity field models up to degree and order 220, before and after the earthquake, based on the least-squares method, with a bandpass Auto Regression Moving Average (ARMA) filter applied to the SGG data along the orbit. In addition, to reduce the influences of colored noise in the SGG data and the polar gap problem on the recovered model, we propose a tailored spherical harmonic (TSH) approach, which only uses the spherical harmonic (SH) coefficients with the degree range 30–95 to compute the coseismic gravity changes in the spatial domain. Then, both the results from the GOCE observations and the GRACE temporal gravity field models (with the same TSH degrees and orders) are simultaneously compared with the forward-modeled signals that are estimated based on the fault slip model of the earthquake event. Although there are considerable misfits between GOCE-derived and modeled gravity gradient changes (ΔVxx, ΔVyy, ΔVzz, and ΔVxz), we find analogous spatial patterns and a significant change (greater than 3σ) in gravity gradients before and after the earthquake. Moreover, we estimate the radial gravity gradient changes from the GOCE-derived monthly time-variable gravity field models before and after the earthquake, whose amplitudes are at a level over three times that of their corresponding uncertainties, and are thus significant. Additionally, the results show that the recovered coseismic gravity signals in the west-to-east direction from GOCE are closer to the modeled signals than those from GRACE in the TSH degree range 30–95. This indicates that the GOCE-derived gravity models might be used as additional observations to infer/explain some time-variable geophysical signals of interest. [ABSTRACT FROM AUTHOR]

The potential of terrestrial water storage (TWS) inverted from Gravity Recovery and Climate Experiment (GRACE) measurements to investigate water variations and their response to droughts over the Volta, Niger, and Senegal Basins of West Africa was investigated. An altimetry-imagery approach was proposed to deduce the contribution of Lake Volta to TWS as “sensed” by GRACE. The results showed that from April 2002 to July 2016, Lake Volta contributed to approximately 8.8% of the water gain within the Volta Basin. As the signal spreads out far from the lake, it impacts both the Niger and Senegal Basins with 1.7% (at a significance level of 95%). This figure of 8.8% for the Volta Basin is approximately 20% of the values reported in previous works. Drought analysis based on GRACE-TWS (after removing the lake’s contribution) depicted below-normal conditions prevailing from 2002 to 2008. Wavelet analysis revealed that TWS changes (fluxes) and rainfall as well as vegetation index depicted a highly coupled relationship at the semi-annual to biennial periods, with common power covariance prevailing in the annual frequencies. While acknowledging that validation of the drought occurrence and severity based on GRACE-TWS is needed, we believe that our findings shall contribute to the water management over West Africa. [ABSTRACT FROM AUTHOR]