GRACE time-variable gravity and its application to geoscience:Quantitative analysis of relevant literature

The Gravity Recovery and Climate Experiment(GRACE)is the most important gravity satellite to date in human history.Since its launch in 2002,GRACE time-varying gravity has had an unprecedented impact on earth science and has generated revolutionary changes.Because of natural phenomena such as climate warming,glacial melting,sea level rise,and earthquakes,earth science research has become an increasingly popular discipline in recent years.This article summarizes the importance of GRACE time-varying gravity,its application to geoscience,and its development.We analyzed the historical development and current status of GRACE time-varying gravity as well as research hotspots by searching the literature in the core collection databases of the China National Knowledge Infrastructure and the Web of Science over the past 20 years.The CiteSpace and VOSviewer software packages were applied with reference to the principle of literature metrology.Our investigation and analysis of characteristic indexes,such as the numbers of publications,co-occurrence of keywords,and co-citation of documents,uncovered the wide application and promotion of gravity satellites,especially GRACE time-varying gravity,in earth science.The results showed that the number of publications addressing GRACE data and time-varying gravity theory is increasing annually and that the USA,China,and Germany are the main producers.The Chinese Academy of Sciences,the National Aeronautics and Space Administration of the United States,and the Helmholtz Association of German Research Centres rank among the top three institutions in the world in terms of producing the most publications on this topic.We found that GRACE time-varying gravity plays unique roles in measuring changes in terrestrial water storage changes,ice and snow melting and sea level changes,and(co)seismic gravity changes,as well as in promoting other disciplines.

Determination of the degree 120 time-variable gravity field in the Sichuan-Yunnan region using Slepian functions and terrestrial measurements

The terrestrial time-variable gravity measurements are characterized by a high signal-to-noise ratio and sensitivity to the sources of mass change in the Earth's crust.These gravity data have many applications,such as surface deformation,groundwater storage changes,and mass migration before and after earthquakes.Based on repeated terrestrial gravity measurements at 198 gravity stations in the Sichuan-Yunnan region(SYR)from 2015 to 2017,we determine a time series of degree 120 gravity fields using the localized spherical harmonic(Slepian)basis functions.Our results show that adopting the first 6 Slepian basis functions is sufficient for effective localized Slepian modeling in the SYR.The differences between two gravity campaigns at the same time of year show an obvious correlation with tectonic features.The degree 120 timevariable gravity models presented in this paper will benefit the study of the regional mass migration inside the crust of the SYR and supplement the existing geophysical models for the China Seismic Experimental Site.

Seismologic applications of GRACE time-variable gravity measurements

The Gravity Recovery and Climate Experiment（GRACE） has been measuring temporal and spatial variations of mass redistribution within the Earth system since2002. As large earthquakes cause significant mass changes on and under the Earth＇s surface,GRACE provides a new means from space to observe mass redistribution due to earthquake deformations. GRACE serves as a good complement to other earthquake measurements because of its extensive spatial coverage and being free from terrestrial restriction. During its over 10 years mission,GRACE has successfully detected seismic gravitational changes of several giant earthquakes,which include the 2004 Sumatra–Andaman earthquake,2010 Maule（Chile） earthquake,and 2011 Tohoku-Oki（Japan） earthquake. In this review,we describe by examples how to process GRACE timevariable gravity data to retrieve seismic signals,and summarize the results of recent studies that apply GRACE observations to detect co- and post-seismic signals and constrain fault slip models and viscous lithospheric structures. We also discuss major problems and give an outlook in this field of GRACE application.

A High-Resolution Earth’s Gravity Field Model SGG-UGM-2 from GOCE,GRACE,Satellite Altimetry,and EGM2008

This paper focuses on estimating a new high-resolution Earth’s gravity field model named SGG-UGM-2 from satellite gravimetry,satellite altimetry,and Earth Gravitational Model 2008(EGM2008)-derived gravity data based on the theory of the ellipsoidal harmonic analysis and coefficient transformation(EHA-CT).We first derive the related formulas of the EHA-CT method,which is used for computing the spherical harmonic coefficients from grid area-mean and point gravity anomalies on the ellipsoid.The derived formulas are successfully evaluated based on numerical experiments.Then,based on the derived least-squares formulas of the EHA-CT method,we develop the new model SGG-UGM-2 up to degree 2190 and order 2159 by combining the observations of the Gravity Field and Steady-State Ocean Circulation Explorer(GOCE),the normal equation of the Gravity Recovery and Climate Experiment(GRACE),marine gravity data derived from satellite altimetry data,and EGM2008-derived continental gravity data.The coefficients of degrees 251–2159 are estimated by solving the block-diagonal form normal equations of surface gravity anomalies(including the marine gravity data).The coefficients of degrees 2–250 are determined by combining the normal equations of satellite observations and surface gravity anomalies.The variance component estimation technique is used to estimate the relative weights of different observations.Finally,global positioning system(GPS)/leveling data in the mainland of China and the United States are used to validate SGG-UGM-2 together with other models,such as European improved gravity model of the earth by new techniques(EIGEN)-6C4,GECO,EGM2008,and SGG-UGM-1(the predecessor of SGG-UGM-2).Compared to other models,the model SGG-UGM-2 shows a promising performance in the GPS/leveling validation.All GOCE-related models have similar performances both in the mainland of China and the United States,and better performances than that of EGM2008 in the mainland of China.Due to the contribution of GRACE data and the new marine gravity anomalies,SGG-UGM-2 is slightly better than SGG-UGM-1 both in the mainland of China and the United States.

Time-varying gravity field model of Sichuan-Yunnan region based on the equivalent mass source model

High-precision time-varying gravity field is an effective way to study the internal mass movement and understanding the spatio-temporal evolution process of the geodynamic system.Compared to the satellite gravity measurement,the repeated terrestrial gravity observation can provide a more high-order signal related to the shallow crust and subsurface.However,the suitable and unified method for gravity model estimation is a key problem for further applications.In this study,we introduce the spherical hexahedron element to simulate the field source mass and forward model the change of gravity field located at the Sichuan-Yunnan region(99—104°E,23—29°N)in the four epochs from 2015 to 2017.Compared to the experimental results based on Slepian or spherical harmonics frequency domain method,this alternative approach is suitable for constructing the equivalent mass source model of regional-scale gravity data,by introducing the first-order smooth prior condition of gravity time-varying signal to suppress the high-frequency component of the signal.The results can provide a higher spatial resolution reference for regional gravity field modeling in the Sichuan-Yunnan region.

Spatial distribution characteristics and mechanism of nonhydrological time-variable gravity in China's Mainland

The purpose of this study is to explore nonhydrological mass transfer in China's Mainland.For this purpose,gravity recovery and climate experiment(GRACE)data were obtained to study the spatial distribution of time variant gravity signals in China's Mainland.Then,from auxiliary hydrological data processed according to the current hydrological model,a new more comprehensive hydrological model of China's Mainland was constructed.Finally,the time variant signals of this new hydrological model were removed from the time variant gravity field computed from GRACE data,thus obtaining a description of the nonhydrological mass transfer of China's Mainland.The physical sources and mechanisms of the resulting mass transfer are then discussed.The improved,more realistic,hydrological model used here was created by selecting the hydrological components with the best correlations in existing hydrological models,by use of correlation calculation,analysis,and comparison.This improved model includes water in soils and deeper strata,in the vegetation canopy,in lakes,snow,and glaciers,and in other water components(mainly reservoir storage,swamps,and rivers).The spatial distribution of the transfer signals due to nonhydrological mass in China's Mainland was obtained by subtracting the combined hydrological model from the GRACE time-variable gravity field.The results show that the nonhydrological signals in China's Mainland collected in GRACE data were mainly positive signals,and were distributed in the Bohai Rim and the northern and eastern parts of the Tibetan Plateau.The above nonhydrological mass transfer signals have been studied further and are discussed.The results show that the nonhydrological mass migration signals in the Bohai Rim region originate primarily from sea level change and marine sediment accumulation.The mass accumulation from Indian plate collision in the Tibetan Plateau appears to be the main reason for the increase in the residual gravity field in that region.

Monthly gravity field solution from GRACE range measurements using modified short arc approach

In this paper we present a series of monthly gravity field solutions from Gravity Recovery and Climate Experiment（GRACE） range measurements using modified short arc approach,in which the ambiguity of range measurements is eliminated via differentiating two adjacent range measurements.The data used for developing our monthly gravity field model are same as Tongji-GRACEOl model except that the range measurements are used to replace the range rate measurements,and our model is truncated to degree and order 60,spanning Jan.2004 to Dec.2010 also same as Tongji-GRACE01 model.Based on the comparison results of the C_（2,0）,C_（2,1）,S_（2,1）,and C_（15,15）,S_（15,15）,time series and the global mass change signals as well as the mass change time series in Amazon area of our model with those of Tongji-GRACE01 model,we can conclude that our monthly gravity field model is comparable with Tongji-GRACE01 monthly model.

WHU-Grace01s:A new temporal gravity field model recovered from GRACE KBRR data alone

A new temporal gravity field model called WHU-Grace01s solely recovered from Gravity Recovery and Climate Experiment （GRACE） K-Band Range Rate （KBRR） data based on dynamic integral approach is presented in this paper. After meticulously preprocessing of the GRACE KBRR data, the root mean square of its post residuals is about 0.2 micrometers per second, and seventy-two monthly temporal solutions truncated to degree and order 60 are computed for the period from January 2003 to December 2008. After applying the combi- nation filter in WHU-Grace01s, the global temporal signals show obvious periodical change rules in the large-scale fiver basins. In terms of the degree variance, our solution is smaller at high degrees, and shows a good consistency at the rest of degrees with the Release 05 models from Center for Space Research （CSR）, GeoForschungsZentrum Potsdam （GFZ） and Jet Pro- pulsion Laboratory 0PL）. Compared with other published models in terms of equivalent water height distribution, our solution is consistent with those published by CSR, GFZ, JPL, Delft institute of Earth Observation and Space system （DEOS）, Tongji University （Tongji）, Institute of Theoretical Geodesy （ITG）, Astronomical Institute in University of Bern （AIUB） and Groupe de Recherche de Geodesie Spatiale （GRGS}, which indicates that the accuracy of WHU-Grace01s has a good consistency with the previously published GRACE solutions.

Monthly gravity field recovery from GRACE orbits and K-band measurements using variational equations approach

The Gravity Recovery and Climate Experiment（GRACE） mission can significantly improve our knowledge of the temporal variability of the Earth＇s gravity field.We obtained monthly gravity field solutions based on variational equations approach from GPS-derived positions of GRACE satellites and K-band range-rate measurements.The impact of different fixed data weighting ratios in temporal gravity field recovery while combining the two types of data was investigated for the purpose of deriving the best combined solution.The monthly gravity field solution obtained through above procedures was named as the Institute of Geodesy and Geophysics（IGG） temporal gravity field models.IGG temporal gravity field models were compared with GRACE Release05（RL05） products in following aspects：（i） the trend of the mass anomaly in China and its nearby regions within 2005-2010; （ii） the root mean squares of the global mass anomaly during 2005-2010; （iii） time-series changes in the mean water storage in the region of the Amazon Basin and the Sahara Desert between 2005 and 2010.The results showed that IGG solutions were almost consistent with GRACE RL05 products in above aspects（i）-（iii）.Changes in the annual amplitude of mean water storage in the Amazon Basin were 14.7 ± 1.2 cm for IGG,17.1 ± 1.3 cm for the Centre for Space Research（CSR）,16.4 ± 0.9 cm for the GeoForschungsZentrum（GFZ） and 16.9 ± 1.2 cm for the Jet Propulsion Laboratory（JPL） in terms of equivalent water height（EWH）,respectively.The root mean squares of the mean mass anomaly in Sahara were 1.2 cm,0.9 cm,0.9 cm and 1.2 cm for temporal gravity field models of IGG,CSR,GFZ and JPL,respectively.Comparison suggested that IGG temporal gravity field solutions were at the same accuracy level with the latest temporal gravity field solutions published by CSR,GFZ and JPL.

GRACE detection of the medium-to far-field coseismic gravity changes caused by the 2004 Mw9.3 Sumatra-Andaman earthquake

Large earthquakes cause observable changes in the Earth’s gravity field, which have been detected by the Gravity Recovery and Climate Experiment (GRACE). Since most previous studies focus on the detection of near-field gravity effects, this study provides the results from the medium- to far-field gravity changes caused by the 2004 Sumatra-Andaman earthquake that are recorded within GRACE monthly solutions. Utilizing a spherical-earth dislocation model we documented that large-scale signals predominate in the global field of the coseismic gravity changes caused by the earthquake. After removing the near-field effects, the coseismic gravity changes show a negative anomaly feature with an average magnitude of -0.18×10-8 m·s-2 in the region ranging ～40° from the epicenter, which is considered as the 'medium ffield' in this study. From the GRACE data released by Center for Space Research from August 2002 to December 2008, we retrieved the large-scale gravity changes smoothed with 3 000 km Gaussian ffilter. The results show that the coseismic gravity changes detected by GRACE in the medium field have an average of (-0.20±0.06)×10-8 m·s-2, which agrees with the model prediction. The detection confirms that GRACE is sensitive to large-scale medium-field coseismic gravitational effects of mega earthquakes, and also validates the spherical-earth dislocation model in the medium field from the perspective of satellite gravimetry.

GRACE time-varying gravity field solutions based on PANDA software

The conventional dynamic approach for gravity filed modelling has been implemented in the PANDA(Position and Navigation Data Analyst) software. A variant of the so-called ’two-step’ method for gravity field modelling is adopted for this purpose, where the GRACE(Gravity Recovery and Climate Experiment)orbits are derived from the GPS(Global Positioning System) data in a first step followed by a simultaneous determination of dynamic orbit and gravity filed from the GPS-derived orbits and K-band rangerate measurements in a second step. In this way, the monthly gravity field solutions complete to degree and order 96 are produced for the period Jan. 2005 to Dec. 2010. Their performance is assessed by comparing them with the official solutions, i.e., CSR RL05, GFZ RL05 a and JPL RL05. A comparison in the spectral domain in terms of geoid heights reveals that the obtained solutions present the smallest degree amplitudes at degree 30-75. A further analysis of mass changes in the spatial domain demonstrates that the main signals observed from the obtained solutions are in great agreement with those from the official solutions. Remarkably, the correlation coefficients of mass changes in large river basins from the official solutions with respect to those from the obtained solutions are all above 0.97. These results demonstrate that the obtained solutions are comparable to the official solutions.

Earth gravity field solution with combining CHAMP and GRACE data

Satellite gravity data fusion with multi-type and huge-amount is one of the hot topics in physical geodesy. After a brief review of dynamic approach, the CHAMP-only and GRACE-only gravity fields by using HL-SST and LL-SST data from 2003 to 2009 are recovered respectively. An combination strategy of CHAMP and GRACE data by using Helmert variance component estimation （VCE） is proposed based on normal equation level fusion. Three gravity field models with 150° and order by CHAMP-only data, GRACE-only data and combining CHAMP and GRACE data from 2003 to 2009 are recovered. The comparisons between our recovered models and those latest released models were performed. The external accuracy validations using marine gravity anomalies from DTU13 products and height anomalies from GPS/leveling data are also conducted in this paper. The results show that long-term CHAMP data do contribute to the accuracy improvement of gravity field solution. The accuracy of the combined model using CHAMP and GRACE data is better than those of the individuals and comparative to the models published by international groups.

Analysis of limitations on recovery of gravity field based on satellite gravity gradient data

Although satellite gravity gradient data plays a great role in determining short-wavelength part of static gravity field model,accuracy of the long-wavelength part of gravity field model recovered by them are poor,which leads to only a few applications in time-variable gravity investigation.The reason is that some factors limit the accuracy of the gravity field recovered using gradient data,including accuracy of the gravity gradient observations,measurement bandwidth(MBW)of gradiometer,satellite inclination,etc.This paper aims at analyzing the influence of these limitations on gravity field recovery and discusses the possibility of time-variable gravity field detection by using gravity gradient observations.Firstly,for arbitrary satellite orbit inclination,we give the frequency distributions of all the components of gravity gradients(i.e.Txx;Tyy;Tzz;Txy;Txz and Tyz,).The results show that the maximum frequency of each component of the gravity gradients is the same,i.e.l=Ts(l is degree of the gravity field model,Ts is the orbital periods),and it is not influenced by the inclination of the satellite orbits.Secondly,the paper gives a theory proof to explain why only the low orders of the coefficients are influenced by polar gaps.Big polar gaps are experimented by a numerical test with inclination of 45°.Finally,considering that the measurement bandwidth can be expanded and accuracy of gradient observations can be improved by superconducting gravity gradiometer(SGG)compared to gradiometer used in Gravity field and steadystate Ocean Circulation Explorer(GOCE),the possibility of detecting time-variable gravity using gravity gradient observations is discussed.The results show that the SGG creates errors in MBW with magnitude of 0.014 m E,which is smaller than the magnitude of the time-variable gravity gradient signals(i.e.,0.02 m E)derived from Gravity Recovery and Climate Experiment(GRACE)gravity field models.This indicates the potential of SGG in time-variable gravity detection.

Progress in satellite gravity recovery from implemented CHAMP,GRACE and GOCE and future GRACE Follow-On missions

Firstly, the Earth＇s gravitational field from the past Challenging Minisatellite Payload （CHAMP） mission is determined using the energy conservation principle, the combined error model of the cumulative geoid height influenced by three instrument errors from the current Gravity Recovery and Climate Experiment （GRACE） and future GRACE Follow-On missions is established based on the semi-analytical method, and the Earth＇s gravitational field from the executed Gravity Field and Steady-State Ocean Circulation Explorer （GOCE） mission is recovered by the space-time-wise approach. Secondly, the cumulative geoid height errors are 1.727 × 10^-1 m, 1.839 × 10^-1 m and 9.025 × 10^ -2 m at degrees 70,120 and 250 from the implemented three-stage satellite gravity missions consisting of CHAMP, GRACE and GOCE, which preferably accord with those from the existing earth gravity field models involving EIGEN-CHAMP03S, EICEN-GRACE02S and GO_CONS GCF 2 DIR R1. The cumulative geoid height error is 6.847 × 10 ^-2 m at degree 250 from the future GRACE Follow-On mission. Finally, the complementarity among the four-stage satellite gravity missions including CHAMP, GRACE, GOCE and GRACE Follow-On is demonstrated contrastively.

Comparison of Present SST Gravity Field Models

Taking the main land of Europe as the region to be studied, the potential of the new satellite gravity technique: satellite-to-satellite tracking (SST) and improving the accuracy of regional gravity field model with the SST models are investigated. The drawbacks of these models are discussed. With GPM98C as the reference, the gravity anomaly residuals of several other models, the latest SST global gravity field models (EIGEN series and GGM series), were computed and compared. The results of the comparison show that in the selected region, some systematic errors with periodical properties exist in the EIGEN and GGM’s S series models in the high degree and order. Some information that was not shown in the classic gravity models is detected in the low and middle degree and order of EIGEN and GGM’s S series models. At last, the effective maximum degrees and orders of SST models are suggested.

Accuracy Analysis for SST Gravity Field Model in China

Taking China as the region for test, the potential of the new satellite gravity technique, satellite-to-satellite tracking for improving the accuracy of regional gravity field model is studied. With WDM94 as reference, the gravity anomaly residuals of three models, the latest two GRACE global gravity field model (EIGEN_GRACE02S, GGM02S) and EGM96, are computed and compared. The causes for the differences among the residuals of the three models are discussed. The comparison between the residuals shows that in the selected region, EIGEN_GRACE02S or GGM02S is better than EGM96 in lower degree part (less than 110 degree). Additionally, through the analysis of the model gravity anomaly residuals, it is found that some systematic errors with periodical properties exist in the higher degree part of EIGEN and GGM models, the results can also be taken as references in the validation of the SST gravity data.

Construction of Earth's gravitational field model from CHAMP,GRACE and GOCE data

The basic principle of spectral combination method is discussed,and the general expressions of the spectral weight and spectral combination of the united-processing of various types of gravimetric data are shown.What＇s more,based on degree error RMS of potential coefficients,the detailed expressions of spectral combination formulae and the corresponding spectral weights in the Earth＇s gravitational field model（EGM） determination using GOCE ＋ GRACE and CHAMP ＋ GRACE ＋ GOCE are derived.The fundamental situation that ulux-champ2013 s,tongji-GRACE01,go-cons-gcf-2-tim-r5 constructed respectively by CHAMP,GRACE,GOCE data and go-cons-gcf-2-dir-r5 constructed by syncretic processing of GRACE,GOCE and LAGEOS data are explained briefly,the degree error RMS,cumulative geoid height error and cumulative gravity anomaly error of these models are calculated.A syncretic model constructed from CHAMP,GRACE and GOCE data,which is expressed by champ ＋ grace ＋ goce,is obtained based on spectral combination method.Experimentation results show that the precision of CHAMP data model is the lowest in satellite-only models,so it is not needed in the determination of syncretic models.The GRACE data model can improve the GOCE data model in medium-long wavelength,so the overall precision of syncretic model can be improved.Consequently,as many types of gravimetric data as possible should be combined together in the data processing in order to strengthen the quality and reliability with widening scope and improve the precision and spatial resolution of the computational results.

GRACE重力卫星运行管理的参考借鉴

低低跟踪重力卫星在全球重力获取、反演应用等方面有着重要的战略作用,我国已布局相关卫星的研制建设。为确保未来我国自主低低跟踪重力卫星系统的高效稳定运行,重点对GRACE及其后续星组GRACE-FO卫星的组织模式和管理机制进行了系统梳理与总结分析。基于我国重力卫星技术发展研究现状,对未来卫星运行管理模式进行了探讨分析,给出了实用的工程运行管理建议,可为后续卫星运行管理提供参考借鉴。

用GRACE卫星跟踪数据反演地球重力场

利用141天GRACE卫星观测资料,包括K波段、星载加速度和卫星轨道数据,反演了80阶地球重力场模型IGGGRACE01S,该模型在半波长为500km的空间分辨率上,确定大地水准面的精度约为0.012m,中长波(<80阶)精度优于重力卫星发射以前研制的重力场模型.与EIGEN_GRACE02S、EIGEN_CHAMP03S和EGM96模型的位系数相比,该模型系数最接近于EIGEN_GRACE02S,与另两个模型差异较大.比较几种模型确定的全球重力异常和大地水准面起伏,结果发现IGGGRACE01S与EIGEN_GRACE02S模型的计算结果比较接近,与EGM96模型结果差异较大,差别较大地区主要在南极等地区.对于中国大陆,比较IGGGRACE01S模型(前72阶)计算的重力异常和NIMA重力异常数据(2.5°×2.5°网格),两者之间的标准偏差为4.8mGal.

利用GRACE时变重力场探测2010年中国西南干旱陆地水储量变化

GRACE(Gravity Recovery And Climate Experiment)卫星计划为监测陆地水储量变化提供了有效技术手段.本文采用2003至2010年共计8年的GRACE月重力场模型反演中国西南区域陆地水储量变化,与GLDAS(Global Land Data Assimilation System)全球水文模型进行对比分析,其结果在时空分布上均符合较好,同时在2009年秋至2010年春该区域陆地水储量均呈现明显减少,与该时段云贵川三省的干旱事件相一致;比较分析了2009年秋至2010年春GRACE反演陆地水储量变化与TRMM(Tropical Rainfall Measuring Mission)合成数据计算的月降雨量的时空分布,两组结果均与西南干旱事件对应时段与区域十分吻合;对近8年的陆地水储量变化与月降雨量数据进行相关性分析,其结果表明陆地水储量变化与降雨量强相关,即降雨量是导致陆地水储量变化的主要因素;分析该区域地表温度变化,结果显示2009年9月至2010年3月地表温度均比历史同期高,地表温度的升高加剧了陆地水储量的减少.