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 a...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.展开更多
The Gravity Recovery and Climate Experiment（GRACE） satellite mission provides a unique opportunity to quantitatively study terrestrial water storage（TWS） variations. In this paper,the terrestrial water storage var...The Gravity Recovery and Climate Experiment（GRACE） satellite mission provides a unique opportunity to quantitatively study terrestrial water storage（TWS） variations. In this paper,the terrestrial water storage variations in the Poyang Lake Basin are recovered from the GRACE gravity data from January 2003 to March 2014 and compared with the Global Land Data Assimilation System（GLDAS） hydrological models and satellite altimetry. Furthermore, the impact of soil moisture content from GLDAS and rainfall from the Tropical Rainfall Measuring Mission（TRMM） on TWS variations are investigated. Our results indicate that the TWS variations from GRACE, GLDAS and satellite altimetry have a general consistency. The TWS trends in the Poyang Lake Basin determined from GRACE, GLDAS and satellite altimetry are increasing at 0.0141 km^3/a, 0.0328 km^3/a and 0.0238 km^3/a,respectively during the investigated time period. The TWS is governed mainly by the soil moisture content and dominated primarily by the precipitation but also modulated by the flood season of the Yangtze River as well as the lake and river exchange water.展开更多
North China is a key region for studying geophysical progress. In this study, ground-based and Gravity Recovery and Climate Experiment（GRACE） gravity data from 2009 to 2013 are used to calculate the gravity change r...North China is a key region for studying geophysical progress. In this study, ground-based and Gravity Recovery and Climate Experiment（GRACE） gravity data from 2009 to 2013 are used to calculate the gravity change rate（GCR） using the polynomial fitting method. In general, the study area was divided into the Shanxi rift, Jing-Jin-Ji（Beijing-Tianjin-Hebei Province）, and Bohai Bay Basin（BBB） regions. Results of the distribution of the GCR determined from ground-based gravimetry show that the GCR appears to be ＂negativepositive-negative＂ from west to east, which indicates that different geophysical mechanisms are involved in the tectonic activities of these regions. However, GRACE solutions are conducted over a larger spatial scale and are able to show a difference between southern and northern areas and a mass redistribution of land water storage.展开更多
Mass variations in terrestrial water storage（TWS） obtained from eight years of satellite data from the Gravity Recovery and Climate Experiment（GRACE） are used to describe low frequency TWS through Empirical Orthog...Mass variations in terrestrial water storage（TWS） obtained from eight years of satellite data from the Gravity Recovery and Climate Experiment（GRACE） are used to describe low frequency TWS through Empirical Orthogonal Function（EOF） analysis. Results of the second seasonal EOF mode show the influence of the Meiyu season. Annual variability is clearly shown in the precipitation distribution over China, and two new patterns of interannual variability are presented for the first time from observations, where two periods of abrupt acceleration are seen in 2004 and 2008. GRACE successfully measures drought events in southern China, and in this respect, an association with the Arctic Oscillation and El Nino-Southern Oscillation is discussed. This study demonstrates the unique potential of satellite gravity measurements in monitoring TWS variations and large-scale severe drought in China.展开更多
Long-term droughts significantly impact surface and groundwater resources in India,however,observed changes in major river basins have not been well explored.Here we use Standardized Precipitation Index(SPI)and Standa...Long-term droughts significantly impact surface and groundwater resources in India,however,observed changes in major river basins have not been well explored.Here we use Standardized Precipitation Index(SPI)and Standardized Precipitation Evapotranspiration Index(SPEI)at three different time scales(24,48,and 60 months)to identify long-term droughts in India for the observed record of 1951-2015.Drought characteristics(extent,events,frequency,and intensity)are analyzed for different river basins in India.Increasing trend in the areal extent of droughts is observed in two methods with three time scales in the maximum area(63.66%)in India.We use the data from the Gravity Recovery and Climate Experiment(GRACE)to estimate the changes in the terrestrial water storage(TWS)during the period 2002-2015.We identify that major long-term droughts in India occurred from 1966 to 1969,1972,1986-1987,and 2002-2004.The all-India average TWS shows a negative trend from 2002 to 2015 with prominent decline in north Indian river basins and positive trend in south Indian river basins.SPI and SPEI at longer time scales are positively associated with TWS indicating the adverse impacts of droughts on surface and groundwater resources in such a populated region.展开更多
地球重力场的变化是导致陆地水储量变化的重要因素之一,利用GRACE(Gravity Recovery and Climate Experiment)重力场恢复与气候实验重力卫星数据,结合GLDAS(Global Land Data Assimilation Systems)全球陆面数据同化系统和实测地下水位...地球重力场的变化是导致陆地水储量变化的重要因素之一,利用GRACE(Gravity Recovery and Climate Experiment)重力场恢复与气候实验重力卫星数据,结合GLDAS(Global Land Data Assimilation Systems)全球陆面数据同化系统和实测地下水位数据,反演和田地区克里雅河流域11年间四季和田地区的陆地水储量动态变化,模拟计算地下水等效水高变化趋势,构建了地下水水位估算模型。研究结果表明:和田地区春、夏两季的陆地水储量呈现出增加趋势,而秋、冬两季出现亏损状态;GRACE地球重力卫星所反演的陆地水储量比GLDAS同化系统所模拟的水资源变化更为剧烈,但2类数据的动态变化拟合度很高;GLDAS水资源等效水高二阶微分、GLDAS水资源变化倒数一阶微分、GRACE陆地水储量变化倒数变化、地下水储量变化一阶微分的敏感程度最高,构建的多元逐步回归模型明显优于线性函数,且水位深度越浅,该估算模型的适用性越高。展开更多
重力恢复与气候实验(gravity recovery and climate experiment,GRACE)卫星已成为观测冰盖质量变化的主要手段之一,但不同机构发布的GRACE数据在估计格陵兰冰盖质量变化上存在较大差异,在研究长期变化趋势时会产生很大不一致性。针对此...重力恢复与气候实验(gravity recovery and climate experiment,GRACE)卫星已成为观测冰盖质量变化的主要手段之一,但不同机构发布的GRACE数据在估计格陵兰冰盖质量变化上存在较大差异,在研究长期变化趋势时会产生很大不一致性。针对此问题,先分析了用不同GRACE数据估算的格陵兰冰盖质量变化数据之间的差异,再用三角帽(three-cornered hat,TCH)方法对其进行不确定性分析,并通过数据融合消除了不同数据间的不一致性。展开更多
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 measureme...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.展开更多
文章利用重力恢复与气候实验卫星(Gravity Recovery and Climate Experiment,GRACE)时变重力场球谐系数文件,联合全球陆面数据同化系统(Global Land Data Assimilation System,GLDAS)水文模型反演安徽省2003—2016年地下水储量的时空变...文章利用重力恢复与气候实验卫星(Gravity Recovery and Climate Experiment,GRACE)时变重力场球谐系数文件,联合全球陆面数据同化系统(Global Land Data Assimilation System,GLDAS)水文模型反演安徽省2003—2016年地下水储量的时空变化。通过奇异谱分析(Singular Spectrum Analysis,SSA)地下水时间序列,结合热带降雨测量任务(Tropical Rainfall Measuring Mission,TRMM)降雨数据对地下水储量变化规律进行分析。结果表明,安徽省地下水储量在2011年和2014年前后发生较大变化,在2003—2011年的变化率为0.37 cm/a,2011—2014年的下降速率为-0.2 cm/a,2014—2016年的增长速率为1.9 cm/a;进一步与降雨数据关联,发现降雨量是影响安徽省地下水储量年际变化和季节性变化的主要因素。在空间上,安徽省呈现自东北向西南逐渐缓和的趋势,最大亏损出现在皖北地区,为-7.52 mm/a,在西南地区的最大盈余达到8.38 mm/a。展开更多
The occurrence of earthquakes is closely related to the crustal geotectonic movement and the migration of mass,which consequently cause changes in gravity.The Gravity Recovery And Climate Experiment(GRACE)satellite da...The occurrence of earthquakes is closely related to the crustal geotectonic movement and the migration of mass,which consequently cause changes in gravity.The Gravity Recovery And Climate Experiment(GRACE)satellite data can be used to detect gravity changes associated with large earthquakes.However,previous GRACE satellite-based seismic gravity-change studies have focused more on coseismic gravity changes than on preseismic gravity changes.Moreover,the noise of the north–south stripe in GRACE data is difficult to eliminate,thereby resulting in the loss of some gravity information related to tectonic activities.To explore the preseismic gravity anomalies in a more refined way,we first propose a method of characterizing gravity variation based on the maximum shear strain of gravity,inspired by the concept of crustal strain.The offset index method is then adopted to describe the gravity anomalies,and the spatial and temporal characteristics of gravity anomalies before earthquakes are analyzed at the scales of the fault zone and plate,respectively.In this work,experiments are carried out on the Tibetan Plateau and its surrounding areas,and the following findings are obtained:First,from the observation scale of the fault zone,we detect the occurrence of large-area gravity anomalies near the epicenter,oftentimes about half a year before an earthquake,and these anomalies were distributed along the fault zone.Second,from the observation scale of the plate,we find that when an earthquake occurred on the Tibetan Plateau,a large number of gravity anomalies also occurred at the boundary of the Tibetan Plateau and the Indian Plate.Moreover,the aforementioned experiments confirm that the proposed method can successfully capture the preseismic gravity anomalies of large earthquakes with a magnitude of less than 8,which suggests a new idea for the application of gravity satellite data to earthquake research.展开更多
[目的]研究科尔沁沙地水储量变化对该区域的生态环境和经济建设等的影响,为当地水资源的保护和可持续利用提供参考。[方法]利用CSR(center for space research)提供的2003.07~2010.12 GRACE(gravity recovery and climate experiment)Re...[目的]研究科尔沁沙地水储量变化对该区域的生态环境和经济建设等的影响,为当地水资源的保护和可持续利用提供参考。[方法]利用CSR(center for space research)提供的2003.07~2010.12 GRACE(gravity recovery and climate experiment)Release-05数据,采用去相关与高斯平滑滤波(平滑半径300 km)相结合的滤波方法,以及尺度因子法进行了重力信号改正和信号泄露恢复,反演了科尔沁沙地陆地水储量长时间序列的变化,该结果与CPC(climate prediction center)水文模型反演结果进行了对比分析;结合GLDAS(global land data assimilation system)水文模型计算的土壤含水量变化,给出了科尔沁沙地地下水储量的时空变化;并利用监测点水井数据和给水度信息对地下水反演结果进行了初步验证。[结果] 2003年7月至2010年12月科尔沁沙地陆地水储量减少速率为-13.2±2.6 mm/a;地下水下降速率为-13.5± 1.9 mm/a。[结论]干旱和农业灌溉是导致科尔沁沙地地表水减少和地下水位降低的重要原因之一。展开更多
The complex geographical environment in China makes its gravity signals miscellaneous.This work gives a comprehensive representation and explanation in secular trend of gravity change in different regions,the key feat...The complex geographical environment in China makes its gravity signals miscellaneous.This work gives a comprehensive representation and explanation in secular trend of gravity change in different regions,the key features of which include positive trend in inner Tibet Plateau and South China and negative trend in North China plain and high mountain Asia（HMA）.We also present the patterns of amplitudes and phases of annual and semiannual change.The mechanism underlying the semiannual period is explicitly discussed.The displacement in three directions expressed in terms of geo-potential spherical coefficients and load Love numbers are given.A case study applied with these equations is presented.The results show that Global Positioning System（GPS） observations can be used to compare with Gravity Recovery and Climate Experiment（GRACE） derived displacement and the vertical direction has a signal-noise-ratio of about one order of magnitude larger than the horizontal directions.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.42174097,41974093,and 41774088).
文摘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.
基金supported by the National Natural Science Foundation of China(NSFC)Projects(11173050 and 11373059)
文摘The Gravity Recovery and Climate Experiment（GRACE） satellite mission provides a unique opportunity to quantitatively study terrestrial water storage（TWS） variations. In this paper,the terrestrial water storage variations in the Poyang Lake Basin are recovered from the GRACE gravity data from January 2003 to March 2014 and compared with the Global Land Data Assimilation System（GLDAS） hydrological models and satellite altimetry. Furthermore, the impact of soil moisture content from GLDAS and rainfall from the Tropical Rainfall Measuring Mission（TRMM） on TWS variations are investigated. Our results indicate that the TWS variations from GRACE, GLDAS and satellite altimetry have a general consistency. The TWS trends in the Poyang Lake Basin determined from GRACE, GLDAS and satellite altimetry are increasing at 0.0141 km^3/a, 0.0328 km^3/a and 0.0238 km^3/a,respectively during the investigated time period. The TWS is governed mainly by the soil moisture content and dominated primarily by the precipitation but also modulated by the flood season of the Yangtze River as well as the lake and river exchange water.
基金supported by the National Natural Science Foundation of China(41304060)the national key basic research and development plan(2013CB733304)
文摘North China is a key region for studying geophysical progress. In this study, ground-based and Gravity Recovery and Climate Experiment（GRACE） gravity data from 2009 to 2013 are used to calculate the gravity change rate（GCR） using the polynomial fitting method. In general, the study area was divided into the Shanxi rift, Jing-Jin-Ji（Beijing-Tianjin-Hebei Province）, and Bohai Bay Basin（BBB） regions. Results of the distribution of the GCR determined from ground-based gravimetry show that the GCR appears to be ＂negativepositive-negative＂ from west to east, which indicates that different geophysical mechanisms are involved in the tectonic activities of these regions. However, GRACE solutions are conducted over a larger spatial scale and are able to show a difference between southern and northern areas and a mass redistribution of land water storage.
基金supported by China National Science Funds(41474064,41504066)
文摘Mass variations in terrestrial water storage（TWS） obtained from eight years of satellite data from the Gravity Recovery and Climate Experiment（GRACE） are used to describe low frequency TWS through Empirical Orthogonal Function（EOF） analysis. Results of the second seasonal EOF mode show the influence of the Meiyu season. Annual variability is clearly shown in the precipitation distribution over China, and two new patterns of interannual variability are presented for the first time from observations, where two periods of abrupt acceleration are seen in 2004 and 2008. GRACE successfully measures drought events in southern China, and in this respect, an association with the Arctic Oscillation and El Nino-Southern Oscillation is discussed. This study demonstrates the unique potential of satellite gravity measurements in monitoring TWS variations and large-scale severe drought in China.
文摘Long-term droughts significantly impact surface and groundwater resources in India,however,observed changes in major river basins have not been well explored.Here we use Standardized Precipitation Index(SPI)and Standardized Precipitation Evapotranspiration Index(SPEI)at three different time scales(24,48,and 60 months)to identify long-term droughts in India for the observed record of 1951-2015.Drought characteristics(extent,events,frequency,and intensity)are analyzed for different river basins in India.Increasing trend in the areal extent of droughts is observed in two methods with three time scales in the maximum area(63.66%)in India.We use the data from the Gravity Recovery and Climate Experiment(GRACE)to estimate the changes in the terrestrial water storage(TWS)during the period 2002-2015.We identify that major long-term droughts in India occurred from 1966 to 1969,1972,1986-1987,and 2002-2004.The all-India average TWS shows a negative trend from 2002 to 2015 with prominent decline in north Indian river basins and positive trend in south Indian river basins.SPI and SPEI at longer time scales are positively associated with TWS indicating the adverse impacts of droughts on surface and groundwater resources in such a populated region.
文摘地球重力场的变化是导致陆地水储量变化的重要因素之一,利用GRACE(Gravity Recovery and Climate Experiment)重力场恢复与气候实验重力卫星数据,结合GLDAS(Global Land Data Assimilation Systems)全球陆面数据同化系统和实测地下水位数据,反演和田地区克里雅河流域11年间四季和田地区的陆地水储量动态变化,模拟计算地下水等效水高变化趋势,构建了地下水水位估算模型。研究结果表明:和田地区春、夏两季的陆地水储量呈现出增加趋势,而秋、冬两季出现亏损状态;GRACE地球重力卫星所反演的陆地水储量比GLDAS同化系统所模拟的水资源变化更为剧烈,但2类数据的动态变化拟合度很高;GLDAS水资源等效水高二阶微分、GLDAS水资源变化倒数一阶微分、GRACE陆地水储量变化倒数变化、地下水储量变化一阶微分的敏感程度最高,构建的多元逐步回归模型明显优于线性函数,且水位深度越浅,该估算模型的适用性越高。
基金sponsored by National Natural Science Foundation of China(41474017)National Key Basic Research Program of China(973 Program+3 种基金2012CB957703)sponsored by National Natural Science Foundation of China(41274035)State Key Laboratory of Geodesy and Earth's Dynamics(SKLGED2013-3-2-Z,SKLGED2014-1-3-E)State Key Laboratory of Geo-Information Engineering(SKLGIE2014-M-1-2)
文摘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.
基金supported by the National Key Research and Development Program of China(Grant No.2019YFC1509202)the National Natural Science Foundation of China(Grant Nos.41772350,61371189,and 41701513).
文摘The occurrence of earthquakes is closely related to the crustal geotectonic movement and the migration of mass,which consequently cause changes in gravity.The Gravity Recovery And Climate Experiment(GRACE)satellite data can be used to detect gravity changes associated with large earthquakes.However,previous GRACE satellite-based seismic gravity-change studies have focused more on coseismic gravity changes than on preseismic gravity changes.Moreover,the noise of the north–south stripe in GRACE data is difficult to eliminate,thereby resulting in the loss of some gravity information related to tectonic activities.To explore the preseismic gravity anomalies in a more refined way,we first propose a method of characterizing gravity variation based on the maximum shear strain of gravity,inspired by the concept of crustal strain.The offset index method is then adopted to describe the gravity anomalies,and the spatial and temporal characteristics of gravity anomalies before earthquakes are analyzed at the scales of the fault zone and plate,respectively.In this work,experiments are carried out on the Tibetan Plateau and its surrounding areas,and the following findings are obtained:First,from the observation scale of the fault zone,we detect the occurrence of large-area gravity anomalies near the epicenter,oftentimes about half a year before an earthquake,and these anomalies were distributed along the fault zone.Second,from the observation scale of the plate,we find that when an earthquake occurred on the Tibetan Plateau,a large number of gravity anomalies also occurred at the boundary of the Tibetan Plateau and the Indian Plate.Moreover,the aforementioned experiments confirm that the proposed method can successfully capture the preseismic gravity anomalies of large earthquakes with a magnitude of less than 8,which suggests a new idea for the application of gravity satellite data to earthquake research.
文摘[目的]研究科尔沁沙地水储量变化对该区域的生态环境和经济建设等的影响,为当地水资源的保护和可持续利用提供参考。[方法]利用CSR(center for space research)提供的2003.07~2010.12 GRACE(gravity recovery and climate experiment)Release-05数据,采用去相关与高斯平滑滤波(平滑半径300 km)相结合的滤波方法,以及尺度因子法进行了重力信号改正和信号泄露恢复,反演了科尔沁沙地陆地水储量长时间序列的变化,该结果与CPC(climate prediction center)水文模型反演结果进行了对比分析;结合GLDAS(global land data assimilation system)水文模型计算的土壤含水量变化,给出了科尔沁沙地地下水储量的时空变化;并利用监测点水井数据和给水度信息对地下水反演结果进行了初步验证。[结果] 2003年7月至2010年12月科尔沁沙地陆地水储量减少速率为-13.2±2.6 mm/a;地下水下降速率为-13.5± 1.9 mm/a。[结论]干旱和农业灌溉是导致科尔沁沙地地表水减少和地下水位降低的重要原因之一。
基金supported financially by the National Natural Science Foundation of China(41174063,41331066 and41474059)the CAS/CAFEA International Partnership Program for Creative Research Teams(KZZD-EW-TZ-19)the SKLGED Foundation(2014-1-1-E)
文摘The complex geographical environment in China makes its gravity signals miscellaneous.This work gives a comprehensive representation and explanation in secular trend of gravity change in different regions,the key features of which include positive trend in inner Tibet Plateau and South China and negative trend in North China plain and high mountain Asia（HMA）.We also present the patterns of amplitudes and phases of annual and semiannual change.The mechanism underlying the semiannual period is explicitly discussed.The displacement in three directions expressed in terms of geo-potential spherical coefficients and load Love numbers are given.A case study applied with these equations is presented.The results show that Global Positioning System（GPS） observations can be used to compare with Gravity Recovery and Climate Experiment（GRACE） derived displacement and the vertical direction has a signal-noise-ratio of about one order of magnitude larger than the horizontal directions.
