GRACE/GOCE扩展重力场模型确定我国1985高程基准重力位的精度分析

高精度高程基准重力位的确定往往依赖于高精度全球重力场模型,其对全球和区域高程基准的高精度统一非常关键,GRACE、GOCE卫星重力计划极大地提高了全球重力场模型中长波的精度.本文首先对GRACE/GOCE卫星重力场模型的内符合和外符合精度进行讨论分析,结果说明卫星重力模型的截断误差影响可达到分米级水平,在确定高程基准重力位时该影响不可忽略.利用EGM2008模型扩展GRACE/GOCE卫星重力场模型至2190阶,可有效减弱卫星重力模型的截断误差影响,但不同模型扩展时的最优拼接阶次不同,其中DIR-1、DIR-5模型对应的最优拼接阶次分别为180阶和220阶,以GPS水准数据检验,扩展模型在中国区域的精度均优于18cm.最后,基于最优拼接阶次获得的扩展重力场模型对我国1985高程基准重力位进行了估计,DIR-5和TIM-5模型对应数值分别为62636853.47m^2·s^-2和62636853.49m^2·s^-2,精度均为1.51m^2·s^-2;发现在中国区域模型大地水准面与GPS/水准数据的差值存在微弱的系统性倾斜,东西向倾斜约为9cm,南北向倾斜约为1.4cm,考虑倾斜改正后基于DIR-5和TIM-5模型估计我国1985高程基准重力位的精度提高了0.16m^2·s^-2.

利用GOCE和GRACE卫星观测数据确定静态重力场模型

高精度静态卫星重力场模型在全球海洋环流研究、全球/区域数字高程基准面确定等领域有重要应用,本文研究仅利用GOCE卫星和联合GRACE卫星观测数据确定高精度高阶次静态重力场模型.利用GOCE卫星全周期高精度引力梯度分量(V_(xx)、V_(yy)、V_(zz)和V_(xz))观测值基于直接最小二乘法构建300阶次的SGG(Satellite Gravity Gradiometry)法方程,并利用卫星跟踪卫星观测值基于点域加速度法构建130阶SST(Satellite-to-Satellite Tracking)法方程,然后利用方差分量估计联合SGG和SST法方程确定300阶次纯GOCE卫星重力场模型GOSG02S.利用全周期GRACE观测数据由动力学方法解算了180阶次的SWPU-GRACE2021S模型,并将其对应法方程与GOCE卫星法方程联合解算了GRACE和GOCE的联合模型WHU-SWPU-GOGR2022S.分别基于XGM2019模型和GPS水准数据对本文解算的三个模型GOSG02S、SWPU-GRACE2021S和WHU-SWPU-GOGR2022S在频域和空域进行了精度分析,结果表明,GOSG02S和WHU-SWPU-GOGR2022S模型与GO_CONS_GCF_2_DIR_R6、GO_CONS_GCF_2_TIM_R6、GO_CONS_GCF_2_SPW_R5、GOCO06s和Tongji-GMMG2021S等使用了GOCE卫星全周期数据的模型精度相当,精度差异基本都在毫米量级;SWPU-GRACE2021S模型在160阶次之前与国际主流GRACE卫星重力场模型ITSG-Grace2018s和Tongji-Grace02s精度相当.

联合GRACE/GOCE重力场模型和GPS/水准数据确定我国85高程基准重力位

GRACE、GOCE卫星重力计划的实施,对确定高精度重力场模型具有重要贡献。联合GRACE、GOCE卫星数据建立的重力场模型和我国均匀分布的649个GPS/水准数据可以确定我国高程基准重力位,但我国高程基准对应的参考面为似大地水准面,是非等位面,将似大地水准面转化为大地水准面后确定的大地水准面重力位为62 636 854.395 3m^2s^(-2),为提高高阶项对确定大地水准面的贡献,利用高分辨率重力场模型EGM2008扩展GRACE/GOCE模型至2190阶,同时将重力场模型和GPS/水准数据统一到同一参考框架和潮汐系统,最后利用扩展后的模型确定的我国大地水准面重力位为62 636 852.751 8m^2s^(-2)。其中组合模型TIM_R4+EGM2008确定的我国85高程基准重力位值62 636 852.704 5m^2s^(-2)精度最高。重力场模型截断误差对确定我国大地水准面的影响约16cm,潮汐系统影响约4~6cm。

联合GOCE和GRACE重力场模型位系数的谱组合法

针对GOCE和GRACE在地球重力场反演中的频谱互补性,研究联合GOCE和GRACE重力场模型位系数的谱组合法,给出了基于位系数误差阶方差定权、误差方差定权和块对角误差协方差定权的谱组合计算公式。以GRACE重力场模型ITG-GRACE2010s和GOCE重力场模型GO_CONS_GCF_2_DIR_R1为例进行谱组合法计算。结果表明,三种谱组合方法建立的联合重力场模型精度均优于GRACE或GOCE单独求解的模型的精度,并且它们的整体精度均优于由GOCE和GRACE联合求解的GOCO01S模型的精度;基于块对角误差协方差定权的谱组合法相对最优,它考虑了同次m位系数之间的相关性。

利用卫星测高、GRACE 和 GOCE 资料估计全球海洋表面地转流

重力恢复和气候试验 GRACE（gravity recovery and climate experiment）卫星极大地提高了地球重力场的精度和分辨率，特别是中长波分量，联合卫星测高数据可获得全球海洋表面大尺度洋流循环。另外，新一代地球重力和海洋环流探测卫星 GOCE（gravity field and steady-state ocean circulation explorer）于2009年3月成功发射，采用卫星重力梯度测量原理，对重力场的高频部分非常敏感，使其高分辨率监测全球海洋循环成为可能。本文利用1～7年 GRACE 观测数据确定的重力场模型和18个月 GOCE 观测数据确定的地球重力场模型 GO CONS GCF 2 TIM R3，联合卫星测高确定的平均海面高模型 MSS CNES CLS 11，分别估计全球海洋表面地转流，并且与实测浮标数据结果进行比较。分析表明 GOCE 重力卫星确定的重力场模型具有更高的空间分辨率，能够确定高精度和高空间分辨率的全球海洋地转流，如墨西哥湾暖流的细节和特征，并且与实测浮标结果基本一致。而基于1～4年 GRACE 观测资料的模型不能很好估计全球地转流特征，基于7年 GRACE 观测资料的重力场模型 ITG-Grace2010s 确定的全球地转流的精度仍低于18个月 GOCE 观测数据确定的地球重力场模型 GO CONS GCF 2 TIM R3的结果，估计的全球地转流仍含有较大的噪声，不能很好地反应中小尺度地转流细节特征。并计算 ITG Grace2010s 和 GOCE TIM3的稳态海面地形和全球平均地转流的内符合精度，结果显示，在全球范围内，GOCE TIM3的稳态海面地形和全球平均地转流的精度都比 ITG Grace2010s 结果的精度有着很大的改善，其中 ITG Grace2010s 的稳态海面地形的精度为21．6 cm，而 GOCE TIM3的结果则为7．45 cm，ITG Grace2010s 的全球平均地转流的精度为40．7 cm/s，而 GOCE TIM3的结果则为19．6 cm/s。

基于谱组合的GRACE／GOCE重力场模型融合处理

本文讨论了谱组合的基本原理，给出了多种类型重力测量数据融合处理的谱权及谱组合的通用表达式；根据位系数的误差阶方差，推导了由GRACE和GOCE数据构建地球重力场模型的谱组合公式及对应谱权的具体形式；采用谱组合法，由tongji—grace01和go—cons—gcf-2-tim—r5模型构建了谱组合模型grace＋goce，并与go—cons—gcf-2-dir—r5模型的精度进行比较。试验结果表明，GRACE数据可以显著改善GOCE数据模型在中长波部分的精度，从而提高谱组合模型的整体精度；与单一卫星数据解算的重力场模型相比，谱组合模型精度明显提升。

融合GOCE和GRACE卫星数据的无约束重力场模型Tongji-GOGR2019S

本文在法方程层面融合GOCE卫星的V xx、V yy、V zz和V xz重力梯度分量观测数据和GRACE卫星观测数据,采用直接法解算了220阶次的重力场模型Tongji-GOGR2019S.首先利用IIR带通滤波器在5~41 mHz的重力梯度带宽范围内对约24个月的GOCE重力梯度观测方程进行无相移滤波处理,并组成解算220阶次重力场模型的法方程,各梯度分量根据相对于参考模型统计精度进行定权;然后与13.5 a GRACE数据建立的180阶次Tongji-Grace02s重力场模型的法方程进行叠加,解算了220阶次的无约束纯卫星重力场模型Tongji-GOGR2019S.利用EIGEN-6C4重力场模型、GNSS/水准数据、DTU15重力异常数据以及欧洲区域似大地水准面模型EGG2015等数据对Tongji-GOGR2019S模型精度进行全面的检核评定,结果表明:引入GOCE卫星梯度数据后,高于72阶的位系数精度优于Tongji-Grace02s模型,Tongji-GOGR2019S模型的整体精度接近同阶次的DIR-R6等GOCE卫星第6代模型.

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.

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.

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.

Regional Evaluation of GOCE-Based GGMs with Ground-Based Gravity and GPS/Levelling Data over Egypt

The gravity field and steady-state ocean circulation explorer (GOCE) satellite mission has provided numerous Global Geopotential Models (GGMs) with different processing methodologies and model accuracies. In the current contribution, the latest releases of GOCE-based GGMs are evaluated on the regional scale using the available terrestrial GPS/Levelling and gravity data collected over Egypt. To overcome the spectral inconsistency between the GOCE-based GGMs and the ground-based data, the spectral enhancement method (SEM) is applied. Five of GOCE-based GGMs have been used, namely GOSG01S, IGGT_R1, IfE_GOCE05s_ GO_CONS_GCF_2_SPW_R5 (SPW_R5 in the following) and NULP-02. The evaluation process of GOCE-based GGMs with the available ground data over Egypt considering the SEM method shows remarkable improvements obtained from the SPW_R5 model. The model provides lower differences of the standard deviations with respect to the EGM2008 and the other applied geopotential gravity models as well as the applied ground-based gravity and GPS/Levelling data. The findings regarding the ground-based data show obvious reductions of about 15.16% and 32.22% achieved by the GOCE-based model in term of standard deviations differences of gravity anomalies and geoid heights, respectively. Therefore, the SPW_R5 model is recommended to be applied as a reference model for compensating the long-to-short wavelength (up to spherical harmonics degree/order 280) components when modelling the gravimetric geoid over Egypt.

基于GOCE卫星数据的重力场模型比较研究

从重力场模型的大地水准面起伏误差阶方差以及位系数差阶方差角度,对近几年已经公布的基于GOCE卫星数据建立的重力场模型的精度进行分析。结果显示：1）GO_CONS_GCF_2_TIM_R3、GO_CONS_GCF_2_DIR_R2、GO_CONS_GCF_2_SPW_R2等GOCE-only模型在150~180阶之间每阶的精度较ITG-GRACE2010S等GRACE-only模型提高了一个数量级;2）基于直接法解算的重力场模型精度最高,时域法次之,空域法最低;3）目前,GOCE卫星恢复地球重力场模型的最大能力为250阶次,在250阶处的累计大地水准面精度约为14.7 cm。

利用GOCE卫星数据计算日本地震区域重力异常

依据卫星重力探测技术在地球动力学应用研究中的优越性,利用GOCE卫星重力梯度测量计算重力场信息的原理,针对2011年Ms9.0级日本大地震期间GOCE重力场数据实验计算了日本及邻近区域重力异常情况,对比分析了GRACE卫星数据结果的异同,说明两种不同探测技术的特点,初步探讨了GOCE卫星重力资料在地震中重要的参考价值。

On the Accuracy Assessment of the Latest Releases of GOCE Satellite-Based Geopotential Models with EGM2008 and Terrestrial GPS/Levelling and Gravity Data over Egypt

The Global Geopotential Models (GGMs) of GOCE (Gravity Recovery and steady- state Ocean Circulation Explorer) differ globally as well as regionally in their accuracy and resolution based on the maximum degree and order (d/o) of the fully normalized spherical harmonic (SH) coefficients, which express each GGM. The main idea of this study is to compare the free-air gravity anomalies and quasi geoid heights determined from several recent GOCE-based GGMs with the corresponding ones from the Earth Gravitational Model 2008 (EGM2008) over Egypt on the one hand and with ground-based measurements on the other hand. The results regarding to the comparison of GOCE-based GGMs with terrestrial gravity and GPS/levelling data provide better improvement with respect to EGM2008. The 4th release GOCE-based GGM developed with the use of space-wise solution strategy (SPW_R4) approximates the gravity field well over the Egyptian region. The SPW_R4 model is accordingly suggested as a reference model for recovering the long wavelength (up to SH d/o 200) components of quasi geoid heights when modelling the gravimetric quasi-geoid over the Egypt. Finally, three types of transformation models: Four-, Five- and Seven-parameter transformations have been applied to reduce the data biases and to provide a better fitting of quasi geoid heights obtained from the studied GOCE-based GGMs to those from GPS/levelling data. These models reveal that the standard deviation of vertical datum over Egypt is at the level of about 32 cm.

卫星测高与卫星重力对洋流的研究

卫星测高与卫星重力的发展为进一步研究洋流提供了前所未有的机遇。本文从EGM 96 ,GGM0

重力卫星和测高卫星五年来的进展

对近年升空的重力卫星CHAMP和GRACE及将于近期升空的GOCE卫星,以及测高卫星ENVISAT,Jason1,GFO,ICESat和CryoSat的技术特点进行了介绍和评估。

重力卫星五年运行对求定地球重力场模型的进展和展望

对近年升空的CHAMP和GRACE和将于2007年升空的GOCE卫星在测定地球重力场方面的技术特点和初步成果进行了回顾、比较和评估。并对它们今后在静态和动态的地球重力场构模方面可能的进展作一展望。现在只用一颗重力卫星的轨道摄动数据,就可以以前所未有的可靠性和精确性来求定地球重力场的长波和部分中波。如CHAMP重力卫星的33个月数据所求定的地球重力场模型,相对于曾利用多颗卫星资料所推算的GR1M5-S1重力场模型,在长波方面的精度和可靠性都有很大改善。而GRACE重力卫星的110天数据所导出成果的空间分辨率,又优于CHAMP的33个月的数据成果。GRACE卫星还有一个重要任务,就是测定重力场非潮汐的短期性或准实时的变化。还介绍了新发表的一个联合地球重力场模型EIGEN-CG03C,360完全阶次,分辨率约30′。CG03C同CHAMP/GRACE以前的重力场模型比较,在400 km波长的精度方面改善了一个量级,大地水准面的精度改善了3 cm,重力异常的精度改善了0.4 mgal。

卫星重力研究:21世纪大地测量研究的新热点

卫星重力发射将大大改善人们对地球重力场的了解 ,最近一些年已经和将要发射的 CHAMP、GRACE及GOCE卫星将把现有静态中长波长部分重力场的精度提高 1- 2个量级 ,并提供长波部分重力场随时间变化的信息。

大地重力学的新进展

介绍了当前利用卫星探测地球重力场的技术及其实践,也就是目前采用的高轨卫星追踪低轨卫星技术(hl-SST)、低轨卫星追踪低轨卫星技术(ll-SST)、卫星重力梯度测定技术(SSG),及其相应的正在运行的CHAMP、GRACE、GOCE卫星和考虑发射的GRACEFollow-On卫星。运行的三颗卫星所提供的地球重力场信息不论在精度和分辨率方面都是大地重力学的一个重大进展。介绍了地形数据在构建地球重力场模型中的作用和美国SRTM对全球地形数据的测量。最后介绍了EGM2008与我国已有大陆重力值的比较,平均差值约为11mgal,与我国大陆现有的高程异常值的比较,平均差值为27cm左右。

深空卫星重力测量计划研究综述

地球卫星重力测量计划CHAMP(CHAllenging Minisatellite Payload)、GRACE(Gravity Recovery and Climate Experiment)、GOCE(Gravity field and steady-state Ocean Circulation Explorer)和月球卫星重力测量计划(Gravity Recovery and Interior Laboratory,GRAIL)的成功实施,以及下一代地球重力卫星(GRACE Follow-On)的即将发射昭示着我们将迎来一个前所未有的高精度和高空间分辨的深空卫星重力探测时代。围绕深空卫星重力测量的研究背景、必要性、可行性、卫星重力反演软件平台构建、轨道摄动和未来研究方向开展了研究论证。研究表明:深空卫星重力测量作为新世纪重力探测技术,在精化量体重力场、提高惯性导航精度、天体动力学、天体物理学和军事技术的研究,以及促进国民经济发展和提高社会效益等方面具有广泛的应用前景。