利用广义三角帽方法评估GRACE反演中国大陆地区水储量变化的不确定性
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摘要
在无真实观测值的情况下,本文利用广义三角帽方法评估了五种GRACE时变重力场模型(CSR、GFZ、GRGS、HUST发布的球谐系数解和JPL发布的Mascon解)反演中国大陆地区2003—2013年水储量变化的不确定性.研究结果表明,CSR、GFZ、JPL、HUST和GRGS反演月水储量变化不确定性的区域平均RMS分别为14.4mm、26.3mm、25.3mm、26.6mm和56.1mm,其中GRGS的结果未恢复泄漏信号;在季和年尺度上,模型的不确定性均小于月尺度;扣除周期和趋势信号后,各模型反演结果更为一致.除长江流域外,CSR在13个流域的不确定性均小于其他模型,GRGS反演各流域水储量变化的不确定性通常较大,且可能高估了温带大陆性气候地区水储量的波动;CSR和JPL的不确定性受流域周边水文特征、气候类型、流域面积和形状的影响相对较小,不确定性变化范围分别为2.3～17.1mm和5.6～22.5mm,GFZ和HUST受影响较大,不确定性变化范围分别为5.5～35.1mm和4.0～40.6mm.本文的研究结果为GRACE产品不确定性评估提供了新的途径,为GRACE时变重力场模型的选取提供参考.
It remains a challenging problem to assess the uncertainties in GRACE-derived terrestrial water storage(TWS)changes due to insufficient observations in many areas globally.Particularly,China has a complicated terrain covering a range of climate settings,aquifers and levels of human interventions.Therefore,it is very important to evaluate the performance of GRACE observations from different processing centers for GRACE applications in China.Due to the absence of ground truth observations,this study analyzed the relative uncertainties in GRACE-derived TWS changes from five solutions over mainland China based on a generalized three-cornered hat(TCH)method,including Stokes coefficients from the Center of Space Research(CSR),the German Research Center for Geoscience(GFZ),the Groupe de Recherches de geodesie spatiale(GRGS)and the Huazhong University of Science and Technology(HUST)as well as the Jet Propulsion Laboratory(JPL)GRACE mascon solution.The results showed that the averaged uncertainties(in terms of root-mean-square,RMS)of derived monthly TWS changes over mainland China for CSR,GFZ,JPL,HUST and GRGS were 14.4 mm,26.3 mm,25.3 mm,26.6 mm and 56.1 mm,respectively;compared to the monthly scale,the uncertainties of each solution were lower at seasonal and annual scales for both the original and nonseasonal terms;the inverted TWS changes were more consistent at the nonseasonal term(after removing the trend and seasonal cycles from the original signals).At the basin scale,except for the Yangtze River basin,CSR showed the lowest uncertainties for the 13 river basins over mainland China,while GRGS showed relative large uncertainties.In addition,GRGS-based TWS showed larger variability than other GRACE solutions and two hydrological models(Global Land Data Assimilation System,GLDAS and WaterGAP Global Hydrology Model,WGHM)in the temperate continental climate region;CSR and JPL were less affected by the surrounding hydrological conditions,climate settings,size and geometry of the basins,with the uncertainties varying from2.3～17.1 mm and 5.6～22.5 mm,respectively.Whereas GFZ and HUST were influenced more by these factors,with the ranges of the uncertainties were 5.5～35.1 mm and 4.0～40.6 mm,respectively.It should be noted that GRGS-derived TWS changes were not restored because of the difficulty in quantifying signal loss resulted from regularization for end-users. High uncertainty in GRGS suggests serious signal loss in regularized GRACE solution in the study region.Therefore,more independent data or models are necessary for validation before using the GRGS solution.This study provides a new way to assess the uncertainty in GRACE products and will be helpful for choosing proper models for specific studies.
It remains a challenging problem to assess the uncertainties in GRACE-derived terrestrial water storage(TWS)changes due to insufficient observations in many areas globally.Particularly,China has a complicated terrain covering a range of climate settings,aquifers and levels of human interventions.Therefore,it is very important to evaluate the performance of GRACE observations from different processing centers for GRACE applications in China.Due to the absence of ground truth observations,this study analyzed the relative uncertainties in GRACE-derived TWS changes from five solutions over mainland China based on a generalized three-cornered hat(TCH)method,including Stokes coefficients from the Center of Space Research(CSR),the German Research Center for Geoscience(GFZ),the Groupe de Recherches de geodesie spatiale(GRGS)and the Huazhong University of Science and Technology(HUST)as well as the Jet Propulsion Laboratory(JPL)GRACE mascon solution.The results showed that the averaged uncertainties(in terms of root-mean-square,RMS)of derived monthly TWS changes over mainland China for CSR,GFZ,JPL,HUST and GRGS were 14.4 mm,26.3 mm,25.3 mm,26.6 mm and 56.1 mm,respectively;compared to the monthly scale,the uncertainties of each solution were lower at seasonal and annual scales for both the original and nonseasonal terms;the inverted TWS changes were more consistent at the nonseasonal term(after removing the trend and seasonal cycles from the original signals).At the basin scale,except for the Yangtze River basin,CSR showed the lowest uncertainties for the 13 river basins over mainland China,while GRGS showed relative large uncertainties.In addition,GRGS-based TWS showed larger variability than other GRACE solutions and two hydrological models(Global Land Data Assimilation System,GLDAS and WaterGAP Global Hydrology Model,WGHM)in the temperate continental climate region;CSR and JPL were less affected by the surrounding hydrological conditions,climate settings,size and geometry of the basins,with the uncertainties varying from2.3～17.1 mm and 5.6～22.5 mm,respectively.Whereas GFZ and HUST were influenced more by these factors,with the ranges of the uncertainties were 5.5～35.1 mm and 4.0～40.6 mm,respectively.It should be noted that GRGS-derived TWS changes were not restored because of the difficulty in quantifying signal loss resulted from regularization for end-users. High uncertainty in GRGS suggests serious signal loss in regularized GRACE solution in the study region.Therefore,more independent data or models are necessary for validation before using the GRGS solution.This study provides a new way to assess the uncertainty in GRACE products and will be helpful for choosing proper models for specific studies.
引文
Awange J L,Ferreira V G,Forootan E,et al.2016.Uncertainties in remotely sensed precipitation data over Africa.International Journal of Climatology,36(1):303-323.
Bruinsma S,Lemoine J M,Biancale R,et al.2010.CNES/GRGS10-day gravity field models(release 2)and their evaluation.Advances in Space Research,45(4):587-601.
Chen J L,Wilson C R,Famiglietti J S,et al.2007.Attenuation effect on seasonal basin-scale water storage changes from GRACE time-variable gravity.Journal of Geodesy,81(4):237-245.
Cheng M K,Tapley B D.2004.Variations in the Earth′s oblateness during the past 28years.Journal of Geophysical Research:Solid Earth,109(B9):B09402,doi:10.1029/2004JB003028.
D9ll P,Kaspar F,Lehner B.2003.A global hydrological model for deriving water availability indicators:Model tuning and validation.Journal of Hydrology,270(1-2):105-134.
Famiglietti J S,Lo M,Ho S L,et al.2011.Satellites measure recent rates of groundwater depletion in California′s Central Valley.Geophysical Research Letters,38(3):L03403,doi:10.1029/2010GL046442.
Feng W,Zhong M,Lemoine J M,et al.2013.Evaluation of groundwater depletion in North China using the Gravity Recovery and Climate Experiment(GRACE)data and groundbased measurements.Water Resources Research,49(4):2110-2118.
Ferreira V G,Montecino H D C,Yakubu C I,et al.2016.Uncertainties of the gravity recovery and climate experiment time-variable gravity-field solutions based on three-cornered hat method.Journal of Applied Remote Sensing,10(1):015015,doi:10.1117/1.JRS.10.015015.
Güntner A,Stuck J,Werth S,et al.2007.A global analysis of temporal and spatial variations in continental water storage.Water Resources Research,43(5):W05416,doi:10.1029/2006WR005247.
Galindo F J,Palacio J.1999.Estimating the instabilities of Ncorrelated clocks.∥Proceedings of the 31st Annual Precise Time and Time Interval(PTTI)Meeting,Real Instituto y Observatorio de la Armada.Dana Point,CA,285-296.
Galindo F J,Palacio J.2003.Post-processing ROA data clocks for optimal stability in the ensemble timescale.Metrologia,40(3):S237-S244,doi:10.1088/0026-1394/40/3/301.
Gocic M,Trajkovic S.2013.Analysis of changes in meteorological variables using Mann-Kendall and Sen′s slope estimator statistical tests in Serbia.Global and Planetary Change,100:172-182.
Gray J E,Allan D W.1974.A method for estimating the frequency stability of an individual oscillator.∥28th Annual Symposium on Frequency Control.Atlantic City,NJ,USA:IEEE,243-246.
Hu X G,Chen J L,Zhou Y H,et al.2006.Seasonal water storage change of the Yangtze River basin detected by GRACE.Science in China Series D,49(5):483-491.
Khandu,Forootan E,Schumacher M,et al.2016.Exploring the influence of precipitation extremes and human water use on total water storage(TWS)changes in the Ganges Brahmaputra Meghna River Basin.Water Resources Research,52(3):2240-2258.
Koot L,De Viron O,Dehant V.2006.Atmospheric angular momentum time-series:characterization of their internal noise and creation of a combined series.Journal of Geodesy,79(12):663-674.
Lemoine J M,Bruinsma S,Gégout P,et al.2013.Release 3of the GRACE gravity solutions from CNES/GRGS.∥EGU General Assembly Conference Abstracts,11123.
Li Q,Luo Z C,Zhong B,et al.2013.Terrestrial water storage changes of the 2010 southwest China drought detected by GRACE temporal gravity field.Chinese Journal of Geophysics(in Chinese),55(6):1843-1849,doi:10.6038/cjg20130606.
Long D,Shen Y J,Sun A,et al.2014.Drought and flood monitoring for a large karst plateau in Southwest China using extended GRACE data.Remote Sensing of Environment,155:145-160.
Long D,Longuevergne L,Scanlon B R.2015.Global analysis of approaches for deriving total water storage changes from GRACEsatellites.Water Resources Research,51(4):2574-2594.
Long D,Pan Y,Zhou J,et al.2017.Global analysis of spatiotemporal variability in merged total water storage changes using multiple GRACE products and global hydrological models.Remote Sensing of Environment,192:198-216.
Longuevergne L,Scanlon B R,Wilson C R.2010.GRACE Hydrological estimates for small basins:evaluating processing approaches on the High Plains Aquifer,USA.Water Resources Research,46(11):W11517,doi:10.1029/2009WR008564.
Luo Z C,Li Q,Zhong B.2012.Water storage variations in Heihe River basin recovered from GRACE temporal gravity field.Acta Geodaetica et Cartographica Sinica(in Chinese),41(5):676-681.
Luo Z C,Yao C L,Li Q,et al.2016.Terrestrial water storage changes over the Pearl River Basin from GRACE and connections with Pacific climate variability.Geodesy and Geodynamics,7(3):171-179.
Meyrath T,Rebischung P,Van Dam T.2017.GRACE era variability in the Earth′s oblateness:a comparison of estimates from six different sources.Geophysical Journal International,208(2):1126-1138.
Nanteza J,De Linage C R,Thomas B F,et al.2016.Monitoring groundwater storage changes in complex basement aquifers:An evaluation of the GRACE satellites over East Africa.Water Resources Research,52(12):9542-9564.
Partal T,Kahya E.2006.Trend analysis in Turkish precipitation data.Hydrological Processes,20(9):2011-2026.
Premoli A,Tavella P.1993.A revisited three-cornered hat method for estimating frequency standard instability.IEEE Transactions on Instrumentation and Measurement,42(1):7-13.
Rodell M,Houser P,Jambor U,et al.2004.The global land data assimilation system.Bulletin of the American Meteorological Society,85(3):381-394.
Sakumura C,Bettadpur S,Bruinsma S.2014.Ensemble prediction and intercomparison analysis of GRACE timevariable gravity field models.Geophysical Research Letters,41(5):1389-1397.
Scanlon B R,Zhang Z Z,Save H,et al.2016.Global evaluation of new GRACE mascon products for hydrologic applications.Water Resources Research,52(12):9412-9429.
Schmidt R,Petrovic S,Güntner A,et al.2008.Periodic components of water storage changes from GRACE and global hydrology models.Journal of Geophysical Research:Solid Earth,113(B8):B08419,doi:10.1029/2007JB005363.
Steffen H,Petrovic S,Müller J,et al.2009.Significance of secular trends of mass variations determined from GRACE solutions.Journal of Geodynamics,48(3):157-165.
Strassberg G,Scanlon B R,Chambers D.2009.Evaluation of groundwater storage monitoring with the GRACE satellite:Case study of the High Plains aquifer,central United States.Water Resources Research,45(5):W05410,doi:10.1029/2008WR006892.
Swenson S,Wahr J.2006.Post-processing removal of correlated errors in GRACE data.Geophysical Research Letters,33(8):L08402,doi:10.1029/2005GL025285.
Swenson S,Yeh P J F,Wahr J,et al.2006.A comparison of terrestrial water storage variations from GRACE with in situ measurements from Illinois.Geophysical Research Letters,33(16):L16401,doi:10.1029/2006GL026962.
Swenson S C,Wahr J M.2011.Estimating signal loss in regularized GRACE gravity field solutions.Geophysical Journal International,185(2):693-702.
Syed T H,Famiglietti J S,Rodell M,et al.2008.Analysis of terrestrial water storage changes from GRACE and GLDAS.Water Resources Research,44(2):W02433,doi:10.1029/2006WR005779.
Tabari H,Marofi S,Aeini A,et al.2011.Trend analysis of reference evapotranspiration in the western half of Iran.Agricultural and Forest Meteorology,151(2):128-136.
Tapley B D,Bettadpur S,Ries J C,et al.2004.GRACE measurements of mass variability in the Earth system.Science,305(5683):503-505.
Tavella P,Premoli A.1994.Estimating the instabilities of Nclocks by measuring differences of their readings.Metrologia,30(5):479.
Valty P,De Viron O,Panet I,et al.2013.Assessing the precision in loading estimates by geodetic techniques in Southern Europe.Geophysical Journal International,194(3):1441-1454.
Watkins M M,Wiese D N,Yuan D N,et al.2015.Improved methods for observing Earth′s time variable mass distribution with GRACE using spherical cap mascons.Journal of Geophysical Research:Solid Earth,120(4):2648-2671.
Werth S,Güntner A,Schmidt R,et al.2009.Evaluation of GRACEfilter tools from a hydrological perspective.Geophysical Journal International,179(3):1499-1515.
Wu Y L,Li H,Zou Z B,et al.2015.Investigation of water storage variation in the Heihe River using the Forward-Modeling method.Chinese Journal of Geophysics(in Chinese),58(10):30507-3516,doi:10.6038/cjg20151007.
Yao C L,Liu L L.2012.Research on wavelet denosing based on improved thresholding method.Engineering of Surveying and Mapping(in Chinese),21(3):18-20,34.
Yi S,Wang Q Y,Sun W K.2016.Basin mass dynamic changes in China from GRACE based on a multibasin inversion method.Journal of Geophysical Research:Solid Earth,121(5):3782-3803.
Yirdaw S Z,Snelgrove K R,Agboma C O.2008.GRACE satellite observations of terrestrial moisture changes for drought characterization in the Canadian Prairie.Journal of Hydrology,356(1-2):84-92.
Zhang Z Z,Chao B F,Lu Y,et al.2009.An effective filtering for GRACE time-variable gravity:Fan filter.Geophysical Research Letters,36(17):L17311,doi:10.1029/2009GL039459.
Zhang Z Z,Chao B F,Chen J L,et al.2015.Terrestrial water storage anomalies of Yangtze River basin droughts observed by GRACE and connections with ENSO.Global and Planetary Change,126:35-45.
Zhong M,Duan J B,Xu H Z,et al.2009.Trend of China land water storage redistribution at medi-and large-spatial scales in recent five years by satellite gravity observations.Chinese Science Bulletin,54(5):816-821.
胡小工,陈剑利,周永宏等.2006.利用GRACE空间重力测量监测长江流域水储量的季节性变化.中国科学D辑:地球科学,36(3):225-232.
李琼,罗志才,钟波等.2013.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.地球物理学报,56(6):1843-1849,doi:10.6038/cjg20130606.
罗志才,李琼,钟波.2012.利用GRACE时变重力场反演黑河流域水储量变化.测绘学报,41(5):676-681.
吴云龙,李辉,邹正波等.2015.基于Forward-Modeling方法的黑河流域水储量变化特征研究.地球物理学报,58(10):3507-3516,doi:10.6038/cjg20151007.
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钟敏,段建宾,许厚泽等.2009.利用卫星重力观测研究近5年中国陆地水量中长空间尺度的变化趋势.科学通报,54(9):1290-1294.
Bruinsma S,Lemoine J M,Biancale R,et al.2010.CNES/GRGS10-day gravity field models(release 2)and their evaluation.Advances in Space Research,45(4):587-601.
Chen J L,Wilson C R,Famiglietti J S,et al.2007.Attenuation effect on seasonal basin-scale water storage changes from GRACE time-variable gravity.Journal of Geodesy,81(4):237-245.
Cheng M K,Tapley B D.2004.Variations in the Earth′s oblateness during the past 28years.Journal of Geophysical Research:Solid Earth,109(B9):B09402,doi:10.1029/2004JB003028.
D9ll P,Kaspar F,Lehner B.2003.A global hydrological model for deriving water availability indicators:Model tuning and validation.Journal of Hydrology,270(1-2):105-134.
Famiglietti J S,Lo M,Ho S L,et al.2011.Satellites measure recent rates of groundwater depletion in California′s Central Valley.Geophysical Research Letters,38(3):L03403,doi:10.1029/2010GL046442.
Feng W,Zhong M,Lemoine J M,et al.2013.Evaluation of groundwater depletion in North China using the Gravity Recovery and Climate Experiment(GRACE)data and groundbased measurements.Water Resources Research,49(4):2110-2118.
Ferreira V G,Montecino H D C,Yakubu C I,et al.2016.Uncertainties of the gravity recovery and climate experiment time-variable gravity-field solutions based on three-cornered hat method.Journal of Applied Remote Sensing,10(1):015015,doi:10.1117/1.JRS.10.015015.
Güntner A,Stuck J,Werth S,et al.2007.A global analysis of temporal and spatial variations in continental water storage.Water Resources Research,43(5):W05416,doi:10.1029/2006WR005247.
Galindo F J,Palacio J.1999.Estimating the instabilities of Ncorrelated clocks.∥Proceedings of the 31st Annual Precise Time and Time Interval(PTTI)Meeting,Real Instituto y Observatorio de la Armada.Dana Point,CA,285-296.
Galindo F J,Palacio J.2003.Post-processing ROA data clocks for optimal stability in the ensemble timescale.Metrologia,40(3):S237-S244,doi:10.1088/0026-1394/40/3/301.
Gocic M,Trajkovic S.2013.Analysis of changes in meteorological variables using Mann-Kendall and Sen′s slope estimator statistical tests in Serbia.Global and Planetary Change,100:172-182.
Gray J E,Allan D W.1974.A method for estimating the frequency stability of an individual oscillator.∥28th Annual Symposium on Frequency Control.Atlantic City,NJ,USA:IEEE,243-246.
Hu X G,Chen J L,Zhou Y H,et al.2006.Seasonal water storage change of the Yangtze River basin detected by GRACE.Science in China Series D,49(5):483-491.
Khandu,Forootan E,Schumacher M,et al.2016.Exploring the influence of precipitation extremes and human water use on total water storage(TWS)changes in the Ganges Brahmaputra Meghna River Basin.Water Resources Research,52(3):2240-2258.
Koot L,De Viron O,Dehant V.2006.Atmospheric angular momentum time-series:characterization of their internal noise and creation of a combined series.Journal of Geodesy,79(12):663-674.
Lemoine J M,Bruinsma S,Gégout P,et al.2013.Release 3of the GRACE gravity solutions from CNES/GRGS.∥EGU General Assembly Conference Abstracts,11123.
Li Q,Luo Z C,Zhong B,et al.2013.Terrestrial water storage changes of the 2010 southwest China drought detected by GRACE temporal gravity field.Chinese Journal of Geophysics(in Chinese),55(6):1843-1849,doi:10.6038/cjg20130606.
Long D,Shen Y J,Sun A,et al.2014.Drought and flood monitoring for a large karst plateau in Southwest China using extended GRACE data.Remote Sensing of Environment,155:145-160.
Long D,Longuevergne L,Scanlon B R.2015.Global analysis of approaches for deriving total water storage changes from GRACEsatellites.Water Resources Research,51(4):2574-2594.
Long D,Pan Y,Zhou J,et al.2017.Global analysis of spatiotemporal variability in merged total water storage changes using multiple GRACE products and global hydrological models.Remote Sensing of Environment,192:198-216.
Longuevergne L,Scanlon B R,Wilson C R.2010.GRACE Hydrological estimates for small basins:evaluating processing approaches on the High Plains Aquifer,USA.Water Resources Research,46(11):W11517,doi:10.1029/2009WR008564.
Luo Z C,Li Q,Zhong B.2012.Water storage variations in Heihe River basin recovered from GRACE temporal gravity field.Acta Geodaetica et Cartographica Sinica(in Chinese),41(5):676-681.
Luo Z C,Yao C L,Li Q,et al.2016.Terrestrial water storage changes over the Pearl River Basin from GRACE and connections with Pacific climate variability.Geodesy and Geodynamics,7(3):171-179.
Meyrath T,Rebischung P,Van Dam T.2017.GRACE era variability in the Earth′s oblateness:a comparison of estimates from six different sources.Geophysical Journal International,208(2):1126-1138.
Nanteza J,De Linage C R,Thomas B F,et al.2016.Monitoring groundwater storage changes in complex basement aquifers:An evaluation of the GRACE satellites over East Africa.Water Resources Research,52(12):9542-9564.
Partal T,Kahya E.2006.Trend analysis in Turkish precipitation data.Hydrological Processes,20(9):2011-2026.
Premoli A,Tavella P.1993.A revisited three-cornered hat method for estimating frequency standard instability.IEEE Transactions on Instrumentation and Measurement,42(1):7-13.
Rodell M,Houser P,Jambor U,et al.2004.The global land data assimilation system.Bulletin of the American Meteorological Society,85(3):381-394.
Sakumura C,Bettadpur S,Bruinsma S.2014.Ensemble prediction and intercomparison analysis of GRACE timevariable gravity field models.Geophysical Research Letters,41(5):1389-1397.
Scanlon B R,Zhang Z Z,Save H,et al.2016.Global evaluation of new GRACE mascon products for hydrologic applications.Water Resources Research,52(12):9412-9429.
Schmidt R,Petrovic S,Güntner A,et al.2008.Periodic components of water storage changes from GRACE and global hydrology models.Journal of Geophysical Research:Solid Earth,113(B8):B08419,doi:10.1029/2007JB005363.
Steffen H,Petrovic S,Müller J,et al.2009.Significance of secular trends of mass variations determined from GRACE solutions.Journal of Geodynamics,48(3):157-165.
Strassberg G,Scanlon B R,Chambers D.2009.Evaluation of groundwater storage monitoring with the GRACE satellite:Case study of the High Plains aquifer,central United States.Water Resources Research,45(5):W05410,doi:10.1029/2008WR006892.
Swenson S,Wahr J.2006.Post-processing removal of correlated errors in GRACE data.Geophysical Research Letters,33(8):L08402,doi:10.1029/2005GL025285.
Swenson S,Yeh P J F,Wahr J,et al.2006.A comparison of terrestrial water storage variations from GRACE with in situ measurements from Illinois.Geophysical Research Letters,33(16):L16401,doi:10.1029/2006GL026962.
Swenson S C,Wahr J M.2011.Estimating signal loss in regularized GRACE gravity field solutions.Geophysical Journal International,185(2):693-702.
Syed T H,Famiglietti J S,Rodell M,et al.2008.Analysis of terrestrial water storage changes from GRACE and GLDAS.Water Resources Research,44(2):W02433,doi:10.1029/2006WR005779.
Tabari H,Marofi S,Aeini A,et al.2011.Trend analysis of reference evapotranspiration in the western half of Iran.Agricultural and Forest Meteorology,151(2):128-136.
Tapley B D,Bettadpur S,Ries J C,et al.2004.GRACE measurements of mass variability in the Earth system.Science,305(5683):503-505.
Tavella P,Premoli A.1994.Estimating the instabilities of Nclocks by measuring differences of their readings.Metrologia,30(5):479.
Valty P,De Viron O,Panet I,et al.2013.Assessing the precision in loading estimates by geodetic techniques in Southern Europe.Geophysical Journal International,194(3):1441-1454.
Watkins M M,Wiese D N,Yuan D N,et al.2015.Improved methods for observing Earth′s time variable mass distribution with GRACE using spherical cap mascons.Journal of Geophysical Research:Solid Earth,120(4):2648-2671.
Werth S,Güntner A,Schmidt R,et al.2009.Evaluation of GRACEfilter tools from a hydrological perspective.Geophysical Journal International,179(3):1499-1515.
Wu Y L,Li H,Zou Z B,et al.2015.Investigation of water storage variation in the Heihe River using the Forward-Modeling method.Chinese Journal of Geophysics(in Chinese),58(10):30507-3516,doi:10.6038/cjg20151007.
Yao C L,Liu L L.2012.Research on wavelet denosing based on improved thresholding method.Engineering of Surveying and Mapping(in Chinese),21(3):18-20,34.
Yi S,Wang Q Y,Sun W K.2016.Basin mass dynamic changes in China from GRACE based on a multibasin inversion method.Journal of Geophysical Research:Solid Earth,121(5):3782-3803.
Yirdaw S Z,Snelgrove K R,Agboma C O.2008.GRACE satellite observations of terrestrial moisture changes for drought characterization in the Canadian Prairie.Journal of Hydrology,356(1-2):84-92.
Zhang Z Z,Chao B F,Lu Y,et al.2009.An effective filtering for GRACE time-variable gravity:Fan filter.Geophysical Research Letters,36(17):L17311,doi:10.1029/2009GL039459.
Zhang Z Z,Chao B F,Chen J L,et al.2015.Terrestrial water storage anomalies of Yangtze River basin droughts observed by GRACE and connections with ENSO.Global and Planetary Change,126:35-45.
Zhong M,Duan J B,Xu H Z,et al.2009.Trend of China land water storage redistribution at medi-and large-spatial scales in recent five years by satellite gravity observations.Chinese Science Bulletin,54(5):816-821.
胡小工,陈剑利,周永宏等.2006.利用GRACE空间重力测量监测长江流域水储量的季节性变化.中国科学D辑:地球科学,36(3):225-232.
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