不同模型的地表质量异常一阶项、二阶项估计
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摘要
为了合理补充重力场恢复与气候试验卫星(Gravity Recovery and Climate Experiment, GRACE)时变重力场的一阶斯托克斯系数(C_(10)、C_(11)、S_(11))和替换二阶斯托克斯系数(C_(20)),介绍了相关GRACE-OBP算法及其改进的算法,比较了相应的Chamber Model和4个Sun Model的一阶系数及其计算的地表质量异常,同时比较了基于卫星激光测距观测的Cheng Model与4个Sun Model的C_(20)及其地表质量异常。结果表明,GRACE-OBP算法的一阶系数、卫星激光测距观测的C_(20)及其地表质量异常与改进的GRACE-OBP算法在趋势项上有很大差异,但周年项差异相对较小。利用不同截断阶数和不同机构的GRACE时变重力场模型,对其趋势项和周年项都有一定影响,且对趋势项影响更大。因此,在计算陆地水储量变化时,建议使用改进的GRACE-OBP算法的估计结果,使用较理想的、截断阶数较高的GRACE时变重力模型。
In order to suitably supplement the degree one Stokes coefficients(C_(10), C_(11), S_(11)) in the Gravity Recovery and Climate Experiment(GRACE) time-variable gravity data and substitute the C_(20) coefficient, we review two commonly applied methods based on different combination models of GRACE data and an Ocean Bottom Pressure(OBP) model, which we call Chambers model and Sun model. We compare the results of the degree one coefficients and derive global surface mass anomalies from the two methods, respectively. We also do the similar comparison for the C_(20) coefficient and derived global surface mass anomalies from Satellite Laser Ranging(SLR) based estimates and the Sun model. There are obvious differences, particularly in the trend rates of the degree one coefficients, C_(20) and the derived mass anomalies between the Sun model and both the Chambers model and SLR estimates. However, there are relatively small differences for annual signals. As the GRACE gravity models are released by different institutions applying different data processing and may also have different maximum degrees, the choice of GRACE data additionally affects the annual signals and especially the trend rates. Therefore, for the derivation of terrestrial water storage changes from GRACE, the results of degree one coefficients and C_(20) from the Sun model are recommended to be used together with the best GRACE time variable gravity data with the highest maximum degree available.
In order to suitably supplement the degree one Stokes coefficients(C_(10), C_(11), S_(11)) in the Gravity Recovery and Climate Experiment(GRACE) time-variable gravity data and substitute the C_(20) coefficient, we review two commonly applied methods based on different combination models of GRACE data and an Ocean Bottom Pressure(OBP) model, which we call Chambers model and Sun model. We compare the results of the degree one coefficients and derive global surface mass anomalies from the two methods, respectively. We also do the similar comparison for the C_(20) coefficient and derived global surface mass anomalies from Satellite Laser Ranging(SLR) based estimates and the Sun model. There are obvious differences, particularly in the trend rates of the degree one coefficients, C_(20) and the derived mass anomalies between the Sun model and both the Chambers model and SLR estimates. However, there are relatively small differences for annual signals. As the GRACE gravity models are released by different institutions applying different data processing and may also have different maximum degrees, the choice of GRACE data additionally affects the annual signals and especially the trend rates. Therefore, for the derivation of terrestrial water storage changes from GRACE, the results of degree one coefficients and C_(20) from the Sun model are recommended to be used together with the best GRACE time variable gravity data with the highest maximum degree available.
引文
[1] Tapley B D, Bettadpur S, Ries J C, et al. GRACE Measurements of Mass Variability in the Earth System [J]. Science, 2004, 305: 503-505
[2] Ning Jinsheng, Wang Zhengtao, Chao Nengfang. Research Status and Progress in International Next-Generation Satellite Gravity Measurement Missions [J]. Geomatics and Information Science of Wuhan University, 2016, 41(1):1-8 (宁津生,王正涛,超能芳.国际新一代卫星重力探测计划研究现状与进展[J]. 武汉大学学报·信息科学版, 2016, 41(1):1-8)
[3] Xu Caijun, Gong Zheng. Review of the Post-processing Methods on GRACE Time Varied Gravity Data [J]. Geomatics and Information Science of Wuhan University, 2016, 41(4): 503-510(许才军, 龚正. GRACE时变重力数据的后处理方法研究进展[J]. 武汉大学学报·信息科学版, 2016, 41(4): 503-510)
[4] Wang Xingxing, Li Fei, Hao Weifeng, et al. Comparison of Several Filters in the Rates of Antarctic Ice Sheet Mass Change Based on GRACE RL05 Data [J]. Geomatics and Information Science of Wuhan University, 2016, 41(11): 1 450-1 457(王星星, 李斐, 郝卫峰, 等. GRACE RL05反演南极冰盖质量变化方法比较[J]. 武汉大学学报·信息科学版, 2016, 41(11): 1 450-1 457)
[5] Han S C, Shum C K, Bevis M, et al. Crustal Dilatation Observed by GRACE After the 2004 Sumatra-Andaman Earthquake [J]. Science, 2006, 313: 658-662
[6] Wang Hansheng, Wu P, Xu Houze. A Review of Research in Glacial Isostatic Adjustment [J]. Progress in Geophysics, 2009, 24(6): 1 958-1 967(汪汉胜, Wu P, 许厚泽. 冰川均衡调整(GIA)的研究 [J]. 地球物理学进展,2009, 24(6): 1 958-1 967)
[7] Rodell M, Velicogna I, Famiglietti J S. Satellite-Based Estimates of Groundwater Depletion in India [J]. Nature, 2009, 460(7 258): 999-1 002
[8] Feng W, Zhong M, Lemoine J M, et al. Evaluation of Groundwater Depletion in North China Using the Gravity Recovery and Climate Experiment (GRACE) Data and Ground-Based Measurements [J]. Water Resour Res, 2013, 49: 2 110-2 118
[9] Wang H, Jia L, Steffen H, et al. Increased Water Storage in North America and Scandinavia from GRACE Gravity Data [J]. Nature Geoscience, 2013, 6: 38-42
[10] Li T, Wu P, Wang H, et al. Hydrology Signal from GRACE Gravity Data in the Nelson River Basin, Canada: A Comparison of Two Approaches [J]. Planets and Space, 2018, 70: 41-53
[11] Xiang L, Wang H, Steffen H, et al. Groundwater Storage Changes in the Tibetan Plateau and Adjacent Areas Revealed from GRACE Satellite Gravity Data [J]. Earth and Planetary Science Letters, 2016, 449: 228-239
[12] Wang Hansheng, Wang Zhiyong, Yuan Xudong, et al. Water Storage Changes in Three Gorges Water Systems Area Inferred from GRACE Time-Variable Gravity Data [J]. Chinese Journal of Geophysics, 2007, 50(3): 76-82(汪汉胜,王志勇,袁旭东,等. 基于GRACE时变重力场的三峡水库补给水系水储量变化[J]. 地球物理学报,2007,50(3): 76-82)
[13] Famiglietti J S, Lo M, Ho S L, et al. Satellites Measure Recent Rates of Groundwater Depletion in California’s Central Valley [J]. Geophys Res Lett, 2011, 38: L03403
[14] Scanlon B R, Zhang Z, Save H, et al. Global Mo-dels Underestimate Large Decadal Declining and Rising Water Storage Trends Relative to GRACE Satellite Data [J]. Proceedings of the National Academy of Sciences, 2018, 115(6): E1 080-E1 089
[15] Thomas A C, Reager J T, Famiglietti J S, et al. A GRACE-Based Water Storage Deficit Approach for Hydrological Drought Characterization[J]. Geophys Res Lett, 2014,41:1 537-1 545, doi: 10.1002/2014GL059323
[16] Chen J L, Wilson C R, Tapley B D. Antarctic Regional Ice Loss Rates from GRACE [J]. Earth and Planetary Science Letters, 2008, 266(1-2): 140-148
[17] Matsuo K, Heki K. Time-Variable Ice Loss in Asian High Mountains from Satellite Gravimetry [J]. Earth Planet Sci Lett, 2010, 290: 30-36
[18] Wang H, Wu P. Effects of Lateral Variations in Lithospheric Thickness and Mantle Viscosity on Glacially Induced Surface Motion on a Spherical, Self-Gravitating Maxwell Earth [J]. Earth and Planetary Science Letters, 2006, 244: 576-589
[19] Wang H, Wu P. Effects of Lateral Variations in Lithospheric Thickness and Mantle Viscosity on Glacially Induced Relative Sea Levels and Long Wavelength Gravity Field in a Spherical, Self-Gravitating Maxwell Earth [J]. Earth and Planetary Science Letters, 2006, 249: 368-383
[20] Wang H, Wu P, van der Wal W. Using Postglacial Sea Level, Crustal Velocities and Gravity-Rate-of-Change to Constrain the Influence of Thermal Effects on Mantle Lateral Heterogeneities [J]. J Geodyn, 2008, 46: 104-117
[21] Cazenave A, Dominh K, Guinehut S, et al. Sea Level Budget over 2003-2008: A Reevaluation from GRACE Space Gravimetry, Satellite Altimetry and Argo [J]. Global Planet Change, 2009, 65: 83-88
[22] Chen J, Wilson C, Ries J. Broad-Band Assessment of Degree-2 Gravitational Changes from GRACE and Other Estimates, 2002-2015 [J]. J Geophys Res: Solid Earth, 2016, 121: 2 112-2 128
[23] Swenson S, Chambers D, Wahr J. Estimating Geocenter Variations from a Combination of GRACE and Ocean Model Output [J]. J Geophys Res, 2008, 113: B08410
[24] Cheng M, Tapley B D. Variations in the Earth’s Oblateness During the Past 28 Years [J]. J Geophys Res, 2004, 109: B09402
[25] Chen J L, Rodell M, Wilson C R, et al. Low Degree Spherical Harmonic Influences on Gravity Recovery and Climate Experiment (GRACE) Water Storage Estimates [J].Geophys Res Lett, 2005, 32: L14405
[26] Chambers P D, Wahr J, Nerem R S. Preliminary Observations of Global Ocean Mass Variations with GRACE [J]. Geophys Res Lett, 2004, 31: L13310
[27] Chambers D, Tamisiea M, Nerem R S, et al. Effects of Ice Melting on GRACE Observations of Ocean Mass Trends [J]. Geophys Res Lett, 2007, 34: L05610
[28] Sun Y, Riva R, Ditmar P. Optimizing Estimates of Annual Variations and Trends in Geocenter Motion and J2 from a Combination of GRACE Data and Geophysical Models [J]. J Geophys Res: Solid Earth, 2016, 121: 8 352-8 370
[29] Sun Y, Ditmar P, Riva R. Observed Changes in the Earth’s Dynamic Oblateness from GRACE Data and Geophysical Models [J]. J Geod, 2016, 90: 81-89
[30] Sun Y, Ditmar P, Riva R. Statistically Optimal Estimation of Degree-1 and C20 Coefficients Based on GRACE Data and an Ocean Bottom Pressure Model [J]. Geophys J Int, 2017, 210(3): 1 305-1 322
[31] Chanard K, Fleitout L, Calais E, et al. Toward a Global Horizontal and Vertical Elastic Load Deformation Model Derived from GRACE and GNSS Station Position Time Series [J]. J Geophys Res: Solid Earth, 2018, doi: 10.1002/2017JB015245
[32] Chao B F, Gross R S. Changes in the Earth’s Rotation and Low-Degree Gravitational Field Induced by Earthquakes [J]. Geophys J R Astron Sac, 1987, 91: 569-596
[33] Cretaux J F, Soudarin L, Davidson F J M, et al. Seasonal and Interannual Geocenter Motion from SLR and DORIS Measurements: Comparison with Surface Loading Data [J]. J Geophys Res, 2002, 107(B12): 2 374
[34] Wahr J, Molenaar M, Bryan F. Time Variability of the Earth’s Gravity Field: Hydrological and Oceanic Effects and Their Possible Detection Using GRACE [J]. J Geophys Res, 1998, 103(B12): 30 205-30 229
[35] Wang Hansheng, Xu Houze, Li Guoying. Improvement of Computations of Load Love Numbers of SNREI Earth Model [J]. Chinese J of Geophys, 1996, 39(suppl): 182-189(汪汉胜,许厚泽, 李国营. SNREI弹性地球模型表面负荷勒夫数数值计算的新进展 [J]. 地球物理学报, 1996,39 (suppl): 182-189)
[36] Wang H, Xiang L, Jia L, et al. Load Love Numbers and Green’s Functions for Elastic Earth Mo- dels PREM, Iasp91, Ak135, and Modified Models with Refined Crustal Structure from Crust 2.0 [J]. Computers and Geosciences, 2012, 49: 190-199
[37] Dziewonski A M, Anderson D L. Preliminary Re- ference Earth Model [J]. Physics of the Earth and Planetary Interiors, 1981, 25: 297-356
[38] Blewitt G. Self-consistency in Reference Frames, Geocenter Definition, and Surface Loading of the Solid Earth [J]. J Geophys Res, 2003, 108(B2): L2103
[39] Farrell W. Deformation of the Earth by Surface Loads [J]. Reviews of Geophysics and Space Physics, 1972, 10(3): 761-797
[2] Ning Jinsheng, Wang Zhengtao, Chao Nengfang. Research Status and Progress in International Next-Generation Satellite Gravity Measurement Missions [J]. Geomatics and Information Science of Wuhan University, 2016, 41(1):1-8 (宁津生,王正涛,超能芳.国际新一代卫星重力探测计划研究现状与进展[J]. 武汉大学学报·信息科学版, 2016, 41(1):1-8)
[3] Xu Caijun, Gong Zheng. Review of the Post-processing Methods on GRACE Time Varied Gravity Data [J]. Geomatics and Information Science of Wuhan University, 2016, 41(4): 503-510(许才军, 龚正. GRACE时变重力数据的后处理方法研究进展[J]. 武汉大学学报·信息科学版, 2016, 41(4): 503-510)
[4] Wang Xingxing, Li Fei, Hao Weifeng, et al. Comparison of Several Filters in the Rates of Antarctic Ice Sheet Mass Change Based on GRACE RL05 Data [J]. Geomatics and Information Science of Wuhan University, 2016, 41(11): 1 450-1 457(王星星, 李斐, 郝卫峰, 等. GRACE RL05反演南极冰盖质量变化方法比较[J]. 武汉大学学报·信息科学版, 2016, 41(11): 1 450-1 457)
[5] Han S C, Shum C K, Bevis M, et al. Crustal Dilatation Observed by GRACE After the 2004 Sumatra-Andaman Earthquake [J]. Science, 2006, 313: 658-662
[6] Wang Hansheng, Wu P, Xu Houze. A Review of Research in Glacial Isostatic Adjustment [J]. Progress in Geophysics, 2009, 24(6): 1 958-1 967(汪汉胜, Wu P, 许厚泽. 冰川均衡调整(GIA)的研究 [J]. 地球物理学进展,2009, 24(6): 1 958-1 967)
[7] Rodell M, Velicogna I, Famiglietti J S. Satellite-Based Estimates of Groundwater Depletion in India [J]. Nature, 2009, 460(7 258): 999-1 002
[8] Feng W, Zhong M, Lemoine J M, et al. Evaluation of Groundwater Depletion in North China Using the Gravity Recovery and Climate Experiment (GRACE) Data and Ground-Based Measurements [J]. Water Resour Res, 2013, 49: 2 110-2 118
[9] Wang H, Jia L, Steffen H, et al. Increased Water Storage in North America and Scandinavia from GRACE Gravity Data [J]. Nature Geoscience, 2013, 6: 38-42
[10] Li T, Wu P, Wang H, et al. Hydrology Signal from GRACE Gravity Data in the Nelson River Basin, Canada: A Comparison of Two Approaches [J]. Planets and Space, 2018, 70: 41-53
[11] Xiang L, Wang H, Steffen H, et al. Groundwater Storage Changes in the Tibetan Plateau and Adjacent Areas Revealed from GRACE Satellite Gravity Data [J]. Earth and Planetary Science Letters, 2016, 449: 228-239
[12] Wang Hansheng, Wang Zhiyong, Yuan Xudong, et al. Water Storage Changes in Three Gorges Water Systems Area Inferred from GRACE Time-Variable Gravity Data [J]. Chinese Journal of Geophysics, 2007, 50(3): 76-82(汪汉胜,王志勇,袁旭东,等. 基于GRACE时变重力场的三峡水库补给水系水储量变化[J]. 地球物理学报,2007,50(3): 76-82)
[13] Famiglietti J S, Lo M, Ho S L, et al. Satellites Measure Recent Rates of Groundwater Depletion in California’s Central Valley [J]. Geophys Res Lett, 2011, 38: L03403
[14] Scanlon B R, Zhang Z, Save H, et al. Global Mo-dels Underestimate Large Decadal Declining and Rising Water Storage Trends Relative to GRACE Satellite Data [J]. Proceedings of the National Academy of Sciences, 2018, 115(6): E1 080-E1 089
[15] Thomas A C, Reager J T, Famiglietti J S, et al. A GRACE-Based Water Storage Deficit Approach for Hydrological Drought Characterization[J]. Geophys Res Lett, 2014,41:1 537-1 545, doi: 10.1002/2014GL059323
[16] Chen J L, Wilson C R, Tapley B D. Antarctic Regional Ice Loss Rates from GRACE [J]. Earth and Planetary Science Letters, 2008, 266(1-2): 140-148
[17] Matsuo K, Heki K. Time-Variable Ice Loss in Asian High Mountains from Satellite Gravimetry [J]. Earth Planet Sci Lett, 2010, 290: 30-36
[18] Wang H, Wu P. Effects of Lateral Variations in Lithospheric Thickness and Mantle Viscosity on Glacially Induced Surface Motion on a Spherical, Self-Gravitating Maxwell Earth [J]. Earth and Planetary Science Letters, 2006, 244: 576-589
[19] Wang H, Wu P. Effects of Lateral Variations in Lithospheric Thickness and Mantle Viscosity on Glacially Induced Relative Sea Levels and Long Wavelength Gravity Field in a Spherical, Self-Gravitating Maxwell Earth [J]. Earth and Planetary Science Letters, 2006, 249: 368-383
[20] Wang H, Wu P, van der Wal W. Using Postglacial Sea Level, Crustal Velocities and Gravity-Rate-of-Change to Constrain the Influence of Thermal Effects on Mantle Lateral Heterogeneities [J]. J Geodyn, 2008, 46: 104-117
[21] Cazenave A, Dominh K, Guinehut S, et al. Sea Level Budget over 2003-2008: A Reevaluation from GRACE Space Gravimetry, Satellite Altimetry and Argo [J]. Global Planet Change, 2009, 65: 83-88
[22] Chen J, Wilson C, Ries J. Broad-Band Assessment of Degree-2 Gravitational Changes from GRACE and Other Estimates, 2002-2015 [J]. J Geophys Res: Solid Earth, 2016, 121: 2 112-2 128
[23] Swenson S, Chambers D, Wahr J. Estimating Geocenter Variations from a Combination of GRACE and Ocean Model Output [J]. J Geophys Res, 2008, 113: B08410
[24] Cheng M, Tapley B D. Variations in the Earth’s Oblateness During the Past 28 Years [J]. J Geophys Res, 2004, 109: B09402
[25] Chen J L, Rodell M, Wilson C R, et al. Low Degree Spherical Harmonic Influences on Gravity Recovery and Climate Experiment (GRACE) Water Storage Estimates [J].Geophys Res Lett, 2005, 32: L14405
[26] Chambers P D, Wahr J, Nerem R S. Preliminary Observations of Global Ocean Mass Variations with GRACE [J]. Geophys Res Lett, 2004, 31: L13310
[27] Chambers D, Tamisiea M, Nerem R S, et al. Effects of Ice Melting on GRACE Observations of Ocean Mass Trends [J]. Geophys Res Lett, 2007, 34: L05610
[28] Sun Y, Riva R, Ditmar P. Optimizing Estimates of Annual Variations and Trends in Geocenter Motion and J2 from a Combination of GRACE Data and Geophysical Models [J]. J Geophys Res: Solid Earth, 2016, 121: 8 352-8 370
[29] Sun Y, Ditmar P, Riva R. Observed Changes in the Earth’s Dynamic Oblateness from GRACE Data and Geophysical Models [J]. J Geod, 2016, 90: 81-89
[30] Sun Y, Ditmar P, Riva R. Statistically Optimal Estimation of Degree-1 and C20 Coefficients Based on GRACE Data and an Ocean Bottom Pressure Model [J]. Geophys J Int, 2017, 210(3): 1 305-1 322
[31] Chanard K, Fleitout L, Calais E, et al. Toward a Global Horizontal and Vertical Elastic Load Deformation Model Derived from GRACE and GNSS Station Position Time Series [J]. J Geophys Res: Solid Earth, 2018, doi: 10.1002/2017JB015245
[32] Chao B F, Gross R S. Changes in the Earth’s Rotation and Low-Degree Gravitational Field Induced by Earthquakes [J]. Geophys J R Astron Sac, 1987, 91: 569-596
[33] Cretaux J F, Soudarin L, Davidson F J M, et al. Seasonal and Interannual Geocenter Motion from SLR and DORIS Measurements: Comparison with Surface Loading Data [J]. J Geophys Res, 2002, 107(B12): 2 374
[34] Wahr J, Molenaar M, Bryan F. Time Variability of the Earth’s Gravity Field: Hydrological and Oceanic Effects and Their Possible Detection Using GRACE [J]. J Geophys Res, 1998, 103(B12): 30 205-30 229
[35] Wang Hansheng, Xu Houze, Li Guoying. Improvement of Computations of Load Love Numbers of SNREI Earth Model [J]. Chinese J of Geophys, 1996, 39(suppl): 182-189(汪汉胜,许厚泽, 李国营. SNREI弹性地球模型表面负荷勒夫数数值计算的新进展 [J]. 地球物理学报, 1996,39 (suppl): 182-189)
[36] Wang H, Xiang L, Jia L, et al. Load Love Numbers and Green’s Functions for Elastic Earth Mo- dels PREM, Iasp91, Ak135, and Modified Models with Refined Crustal Structure from Crust 2.0 [J]. Computers and Geosciences, 2012, 49: 190-199
[37] Dziewonski A M, Anderson D L. Preliminary Re- ference Earth Model [J]. Physics of the Earth and Planetary Interiors, 1981, 25: 297-356
[38] Blewitt G. Self-consistency in Reference Frames, Geocenter Definition, and Surface Loading of the Solid Earth [J]. J Geophys Res, 2003, 108(B2): L2103
[39] Farrell W. Deformation of the Earth by Surface Loads [J]. Reviews of Geophysics and Space Physics, 1972, 10(3): 761-797