GGM02 – An improved Earth gravity field model from GRACE

A new generation of Earth gravity field models called GGM02 are derived using approximately 14 months of data spanning from April 2002 to December 2003 from the Gravity Recovery And Climate Experiment (GRACE). Relative to the preceding generation, GGM01, there have been improvements to the data products, the gravity estimation methods and the background models. Based on the calibrated covariances, GGM02 (both the GRACE-only model GGM02S and the combination model GGM02C) represents an improvement greater than a factor of two over the previous GGM01 models. Error estimates indicate a cumulative error less than 1 cm geoid height to spherical harmonic degree 70, which can be said to have met the GRACE minimum mission goals. Electronic Supplementary Material Supplementary material is available in the online version of this article at     

S<Subscript>2</Subscript> tide aliasing in GRACE time-variable gravity solutions

Errors in high-frequency ocean tide models alias to low frequencies in time-variable gravity solutions from the Gravity Recovery and Climate Experiment (GRACE). We conduct an observational study of apparent gravity changes at a period of 161 days, the alias period of errors in the S₂ semidiurnal solar tide. We examine this S₂ alias in the release 4 (RL04) reprocessed GRACE monthly gravity solutions for the period April 2002 to February 2008, and compare with that in release 1 (RL01) GRACE solutions. One of the major differences between RL04 and RL01 is the ocean tide model. In RL01, the alias is evident at high latitudes, near the Filchner-Ronne and Ross ice shelves in Antarctica, and regions surrounding Greenland and Hudson Bay. RL04 shows significantly lower alias amplitudes in many of these locations, reflecting improvements in the ocean tide model. However, RL04 shows continued alias contamination between the Ronne and Larson ice shelves, somewhat larger than in RL01, indicating a need for further tide model improvement in that region. For unknown reasons, the degree-2 zonal spherical harmonics (C₂₀) of the RL04 solutions show significantly larger S₂ aliasing errors than those from RL01.     

GRACE时变重力数据后处理方法评价

针对GRACE Level2卫星时变重力数据后处理方法如何评价的问题,该文以中国数字地震观测网络获得的青藏高原地区地面重力变化图像为参考,基于平均结构相似性等图像相似度指标,研究了与该区域地面重力观测同期、不同后处理方法得到的GRACE卫星重力变化图像的可靠性。结果显示,GRACE卫星重力和地面重力观测结果具有一定的可比性,滑动窗口去相关滤波和高斯400 km滤波的组合方法可以获得最优的处理效果。本文的方法和结论对GRACE及GRACE Follow-On卫星重力数据应用中后处理方法和参数的选取有一定的借鉴意义。     

GRACE时变重力位系数误差的改进去相关算法

GRACE卫星时变重力场模型的高阶位系数存在较大误差,用它反演的重力场结果中表现为严重的条带噪声。Swenson提出的滑动窗多项式拟合去相关误差方法在赤道两侧区域取得了显著效果,但其在文献中并没有说明实现的具体步骤,因而许多学者在利用其思想进行滤波时并没有达到其文献中的滤波效果。针对滑动窗的特点,使用反向边界延拓技术,对滑动窗去相关误差数据处理方法作了改进。改进的滑动窗去相关误差方法应用于GRACE时变重力场模型时,在赤道两侧区域取得了显著的去条带误差效果,并利用全球地面资料同化系统GLDAS土壤湿度资料验证该方法的正确性。     

利用GRACE数据检测日本Mw9.0地震同震和震后重力变化

基于德国地学中心（GFZ）发布的GRACE RL05月重力场模型数据,考虑全球陆地同化系统陆地水储量的影响,采用300 km的扇形滤波,利用叠积法提取了日本Mw9.0地震的同震和震后重力时变信号,并利用最小二乘拟合的方法计算了两个同震重力变化极值点在地震前后85个月的重力年变率。结果表明：土壤水分和雪水引起的重力变化为-0.34~0.09 μgal;利用GRACE数据检测到的同震重力变化为-5.3~4.2 μgal,与基于PSGRN/PSCMP模型计算的结果在空间分布和量级上具有较好的一致性;震后5 a震中附近区域的重力整体上呈现增加趋势,断层上盘所在的日本海域与下盘所在的太平洋区域重力增加的最大值分别为2.6、4.5 μgal,下盘重力增加较大,可能与断层下盘所在地层的黏滞性相对较低有关。     

基于SLR的GRACE卫星定轨中重力场模型对轨道精度的影响

以GRACE卫星为例,分析比较利用SLR观测资料进行卫星定轨时,采用不同重力场模型对GRACE卫星定轨精度的影响;以及重力场截断阶引起的积分轨道差异;同时,将定轨结果与采用GPS确定的定轨结果进行比较,分析与GPS定轨结果的差异.实验证明.重力场模型选择GGM02C的定轨结果优于选择JGM-3的定轨结果,基于SLR的定...     

GRACE和GOCE卫星监测的青藏高原重力场特征

文章阐述了对青藏高原重力场进行研究的意义,并进一步利用重力卫星GRACE和GOCE的数据对该区域的重力场特征进行了描述.通过对该区域的重力异常、径向引力梯度的计算和分析,可以得出:在青藏高原的西部,有明显的3条重力异常区,这与当地的地形有关,也与断层的位置有关;引力梯度比重力异常具有更高的空间分辨率;重力变化剧烈的区域与梯度的异常区有一定的对应关系,同时也是地球动力活动变化剧烈的区域.     

GRACE卫星GPS数据系统误差分布及其对精密定轨的影响

分析了GRACE卫星在掩星天线关闭和开启状态下GPS观测数据中系统误差的分布情况。结果表明,在掩星天线开启时,观测数据中存在着由于“信号串扰”引起的系统误差,其在消电离层组合P3上的数值最大可达6 m,而对载波相位的影响相对较小。进一步采用降权方法分析了P3观测值对精密定轨的影响。当P3组合观测值标准差大于等于4.0 m时,定轨精度达到最优,在X、Y和Z轴的定轨精度分别为3.9 cm、4.0 cm和3.3 cm。     

Wavelet Modeling of Regional and Temporal Variations of the Earth’s Gravitational Potential Observed by GRACE

This work is dedicated to the wavelet modeling of regional and temporal variations of the Earth’s gravitational potential observed by the GRACE (gravity recovery and climate experiment) satellite mission. In the first part, all required mathematical tools and methods involving spherical wavelets are provided. Then, we apply our method to monthly GRACE gravity fields. A strong seasonal signal can be identified which is restricted to areas where large-scale redistributions of continental water mass are expected. This assumption is analyzed and verified by comparing the time-series of regionally obtained wavelet coefficients of the gravitational signal originating from hydrology models and the gravitational potential observed by GRACE. The results are in good agreement with previous studies and illustrate that wavelets are an appropriate tool to investigate regional effects in the Earth’s gravitational field. Electronic Supplementary Material Supplementary material is available for this article at     

An estimate of the errors in gravity ocean tide loading computations

The error contributions within the ocean tide loading (OTL) convolution integral computation were determined to be able to estimate the numerical accuracy of the gravity OTL values. First, the comparison of four OTL programs by different authors (CONMODB, GOTIC2, NLOADF and OLFG/OLMPP) at ten globally distributed gravity stations using exactly the same input values shows discrepancies between 2% and 5%. A new program, called CARGA, was written that is able to reproduce the results of these programs to a level of 0.1%. This has given us the ability to state with certainty the cause of the discrepancies among the four programs. It is shown that by choosing an appropriate interpolation of the Green’s function, refinement of the integration mesh and a high-resolution coastline, an accuracy level of better than 1% can be obtained for stations in Europe. Besides this numerical accuracy, there are errors in the ocean tide model such as a 1% uncertainty in the mean value of the sea-water density and the lack of conservation of tidal water mass, which can produce offsets of around 0.04 μgal.     

Accuracy assessment of the monthly GRACE geoids based upon a simulation

The purpose of this paper is to demonstrate the effect of geophysical background model errors that affects temporal gravity solutions provided by the Gravity Recovery And Climate Experiment (GRACE). Initial performance estimates by Dickey et al. (1997) suggested a formal geoid RMS error better than 0.1 mm up to spherical harmonic degree 5. Now that the GRACE gravity models and data are available, it is evident that these original expectations were too optimistic. Our hypothesis is that this is partially explained by errors in geophysical background models that need to be applied in the GRACE data reduction, and that this effect was not considered by Dickey et al. (1997). We discuss the results of a closed-loop simulation, where satellite trajectory prediction software is used for the generation of GRACE range-rate data and GRACE orbit solutions with the help of the Global Positioning System (GPS). During the recovery step in our closed-loop simulation, we show that simulated nuisance signals (based on tide and air pressure model differences) map to a 0.7 mm geoid effect for periods longer than 3 months and to less than 0.4 mm for periods shorter than 3 months. The long-period geoid hydrology signal is at a level of 4.5 mm, while the short-period hydrology is at 0.25 mm. The long-period ocean bottom pressure (OBP) signal maps at 0.8 mm and for short periods it is 0.4 mm. We conclude that short-period effects are difficult to observe by GRACE and that long-period effects, like hydrology, are easier to recover than OBP variations.     

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。     

Localized spectral analysis of global satellite gravity fields for recovering time-variable mass redistributions

A spatiospectral localization method is discussed for processing the global geopotential coefficients from satellite mission data to investigate time-variable gravity. The time-variable mass variation signal usually appears associated with a particular geographical area yielding inherently regional structure, while the dependence of the satellite gravity errors on a geographical region is not so evident. The proposed localization amplifies the signal-to-noise ratio of the (non-stationary) time-variable signals in the geopotential coefficient estimates by localizing the global coefficients to the area where the signal is expected to be largest. The results based on localization of the global satellite gravity coefficients such as Gravity Recovery And Climate Experiment (GRACE) and Gravity and Ocean Circulation Explorer (GOCE) indicate that the coseismic deformation caused by great earthquakes such as the 2004 Sumatra–Andaman earthquake can be detected by the low-low tracking and the gradiometer data within the bandwidths of spherical degrees 15–30 and 25–100, respectively. However, the detection of terrestrial water storage variation by GOCE gradiometer is equivocal even after localization.     

A parametric study on the impact of satellite attitude errors on GOCE gravity field recovery

In the recent design of the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite mission, the gravity gradients are defined in the gradiometer reference frame (GRF), which deviates from the actual flight direction (local orbit reference frame, LORF) by up to 3–4°. The main objective of this paper is to investigate the effect of uncertainties in the knowledge of the gradiometer orientation due to attitude reconstitution errors on the gravity field solution. In the framework of several numerical simulations, which are based on a realistic mission configuration, different scenarios are investigated, to provide the accuracy requirements of the orientation information. It turns out that orientation errors have to be seriously considered, because they may represent a significant error component of the gravity field solution. While in a realistic mission scenario (colored gradiometer noise) the gravity field solutions are quite insensitive to small orientation biases, random noise applied to the attitude information can have a considerable impact on the accuracy of the resolved gravity field models.     

Variations in the accuracy of gravity recovery due to ground track variability: GRACE,CHAMP, and GOCE

Following an earlier recognition of degraded monthly geopotential recovery from GRACE (Gravity Recovery And Climate Experiment) due to prolonged passage through a short repeat (low order resonant) orbit, we extend these insights also to CHAMP (CHAllenging Minisatellite Payload) and GOCE (Gravity field and steady state Ocean Circulation Explorer). We show wide track-density variations over time for these orbits in both latitude and longitude, and estimate that geopotential recovery will be as widely affected as well within all these regimes, with lesser track density leading to poorer recoveries. We then use recent models of atmospheric density to estimate the future orbit of GRACE and warn of degraded performance as other low order resonances are encountered in GRACE’s free fall. Finally implications for the GOCE orbit are discussed.     

利用GRACE卫星Level-1B数据反演陆地水储量变化的方法研究

卫星重力探测技术为监测陆地水储量变化提供了新的技术手段。对利用GRACE卫星Level-1B数据反演地球陆地水储量变化的重力位差法和Mascon方法的数学模型作了详细推导分析,总结两种方法的特点和解算处理步骤。推导过程表明:重力位差法和Mascon方法在反演时只采用卫星飞临研究区域上空时的观测数据,能够提高反演结果的空间分辨率,比传统的球谐系数法更具优势;Mascon方法在解算时还引入了时空约束方程,进一步提高了反演结果的时空分辨率。     

利用GRACE/GRACE-FO时变重力场数据量化长江流域干旱事件特征

针对区域干旱事件特征精确量化的问题,本文首先提出了一种基于GRACE/GRACE-FO时变重力场数据的干旱事件评估方法,然后对基于GRACE/GRACE-FO数据的干旱指数进行了验证,最后利用上述评估方法探测了2002年4月—2020年12月长江流域发生的干旱事件,并对上述干旱事件特征进行量化分析。结果表明:在长江流域内,本文构建的干旱指数与传统干旱指数具有很好的一致性。在研究时间段内长江流域发生了8次较大的干旱事件,其中最严重的发生在2002年9月至2004年7月,共计持续了23个月,干旱严重程度为-14.07,平均40%的流域面积受到了干旱灾害的影响。     

A study on the combination of satellite, airborne, and terrestrial gravity data

Satellite gravity missions, such as CHAMP, GRACE and GOCE, and airborne gravity campaigns in areas without ground gravity will enhance the present knowledge of the Earths gravity field. Combining the new gravity information with the existing marine and ground gravity anomalies is a major task for which the mathematical tools have to be developed. In one way or another they will be based on the spectral information available for gravity data and noise. The integration of the additional gravity information from satellite and airborne campaigns with existing data has not been studied in sufficient detail and a number of open questions remain. A strategy for the combination of satellite, airborne and ground measurements is presented. It is based on ideas independently introduced by Sjöberg and Wenzel in the early 1980s and has been modified by using a quasi-deterministic approach for the determination of the weighting functions. In addition, the original approach of Sjöberg and Wenzel is extended to more than two measurement types, combining the Meissl scheme with the least-squares spectral combination. Satellite (or geopotential) harmonics, ground gravity anomalies and airborne gravity disturbances are used as measurement types, but other combinations are possible. Different error characteristics and measurement-type combinations and their impact on the final solution are studied. Using simulated data, the results show a geoid accuracy in the centimeter range for a local test area.     

Regional gravity modeling in terms of spherical base functions

This article provides a survey on modern methods of regional gravity field modeling on the sphere. Starting with the classical theory of spherical harmonics, we outline the transition towards space-localizing methods such as spherical splines and wavelets. Special emphasis is given to the relations among these methods, which all involve radial base functions. Moreover, we provide extensive applications of these methods and numerical results from real space-borne data of recent satellite gravity missions, namely the Challenging Minisatellite Payload (CHAMP) and the Gravity Recovery and Climate Experiment (GRACE). We also derive high-resolution gravity field models by effectively combining space-borne and surface measurements using a new weighted level-combination concept. In addition, we outline and apply a strategy for constructing spatio-temporal fields from regional data sets spanning different observation periods.     

Sumatra-Adaman大地震同震和震后形变的GRACE卫星检测

利用CSR公布的RL-04版GRACE卫星月重力场模型计算了9.1级Sumatra-Adaman大地震的同震和震后形变效应。数值结果表明,GRACE能够监测到的同震和震后形变量为-20～10cm的等效水高,为大地震同震和震后形变监测提供了一种独特、有效的方法。