Decorrelated GRACE time-variable gravity solutions by GFZ,and their validation using a hydrological model

We have analyzed recent gravity recovery and climate experiment (GRACE) RL04 monthly gravity solutions, using a new decorrelating post-processing approach. We find very good agreement with mass anomalies derived from a global hydrological model. The post-processed GRACE solutions exhibit only little amplitude damping and an almost negligible phase shift and period distortion for relevant hydrological basins. Furthermore, these post-processed GRACE solutions have been inspected in terms of data fit with respect to the original inter-satellite ranging and to SLR and GPS observations. This kind of comparison is new. We find variations of the data fit due to solution post-processing only within very narrow limits. This confirms our suspicion that GRACE data do not firmly ‘pinpoint’ the standard unconstrained solutions. Regarding the original Kusche (J Geod 81:733–749, 2007) decorrelation and smoothing method, a simplified (order-convolution) approach has been developed. This simplified approach allows to realize a higher resolution—as necessary, e.g., for generating computed GRACE observations—and needs far less coefficients to be stored.     

Degradation of Geopotential Recovery from Short Repeat-Cycle Orbits: Application to GRACE Monthly Fields

Throughout 2004 the GRACE (Gravity Recovery And Climate Experiment) orbit contracted slowly to yield a sparse repeat track of 61 revolutions every 4 days on 19 September 2004. As a result, we show from linear perturbation theory that geopotential information previously available to fully resolve a gravity field every month of 120× 120 (degree by order) in spherical harmonics was compressed then into about one-fourth of the necessary observation space. We estimate from this theory that the ideal gravity field resolution in September 2004 was only about 30 × 30. More generally, we show that any repeat-cycle mission for geopotential recovery with full resolution L × L requires the number of orbit-revolutions-to-repeat to be greater than 2L.     

Detection of small hydrological variations in gravity by repeated observations with relative gravimeters

Recently, a new application of time-dependent gravity observations is emerging: the study of natural hydrological mass changes and their underlying processes. Complementary to GRACE data and continuous recordings with superconducting gravimeters, repeated observations with relative instruments on a local network may contribute to gain additional information on spatial changes in hydrology. The questions that need to be addressed are whether the results of these repeated measurements will be of sufficiently high resolution and accuracy, as well as how unique the information obtained will be. To examine this, a local gravity network with maximum point distances of 65 m was established in a hilly area around the Geodynamic Observatory Moxa, Germany. Using three to five LaCoste & Romberg relative gravimeters repeated measurements were carried out in a seasonal rhythm as well as at particular events like snowmelt or dryness in 17 campaigns between November 2004 and April 2007. The standard deviations obtained by least squares adjustment range from ±9 to ±14 nm/s² for a gravity difference of one campaign, thus for gravity changes between two campaigns from ±13 to ±20 nm/s². Between the points of the network, spatial gravity changes of up to 171 nm/s² (139 nm/s² between two successive campaigns) could be proven significantly. They correlate with changes in the local hydrological situation. Particularly, a steep slope next to the observatory is identified as a gravimetrically significant hydrological compartment. The results obtained contribute to an improved reduction of the local hydrological signal in continuous gravity recordings and provide constraints to hydrological 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。     

Seasonal global mean sea level change from satellite altimeter, GRACE, and geophysical models

We estimate seasonal global mean sea level changes using different data resources, including sea level anomalies from satellite radar altimetry, ocean temperature and salinity from the World Ocean Atlas 2001, time-variable gravity observations from the Gravity Recovery and Climate Experiment (GRACE) mission, and terrestrial water storage and atmospheric water vapor changes from the NASA global land data assimilation system and National Centers for Environmental Prediction reanalysis atmospheric model. The results from all estimates are consistent in amplitude and phase at the annual period, in some cases with remarkably good agreement. The results provide a good measure of average annual variation of water stored within atmospheric, land, and ocean reservoirs. We examine how varied treatments of degree-2 and degree-1 spherical harmonics from GRACE, laser ranging, and Earth rotation variations affect GRACE mean sea level change estimates. We also show that correcting the standard equilibrium ocean pole tide correction for mass conservation is needed when using satellite altimeter data in global mean sea level studies. These encouraging results indicate that is reasonable to consider estimating longer-term time series of water storage in these reservoirs, as a way of tracking climate change.     

Evaluation and validation of mascon recovery using GRACE KBRR data with independent mass flux estimates in the Mississippi Basin

The direct recovery of surface mass anomalies using GRACE KBRR data processed in regional solutions provides mass variation estimates with 10-day temporal resolution. The approach undertaken herein uses a tailored orbit estimation strategy based solely on the KBRR data and directly estimates mass anomalies from the GRACE data. We introduce a set of temporal and spatial correlation constraints to enable high resolution mass flux estimates. The Mississippi Basin, with its well understood surface hydrological modelling available from the Global Land Data Assimilation System (GLDAS), which uses advanced land surface modeling and data assimilation techniques, and a wealth of groundwater data, provides an opportunity to quantitatively compare GRACE estimates of the mass flux in the entire hydrological column with those available from independent and reliable sources. Evaluating GRACE’s performance is dependent on the accuracy ascribed to the hydrological information, which in and of itself is a complex challenge (Rodell in Hydrogeol J, doi:, 2007). Nevertheless, the Mississippi Basin is one of the few regions having a large hydrological signal that can support a meaningful GRACE comparison on the spatial scale resolved by GRACE. The isolation of the hydrological signal is dependent on the adequacy of the forward mass flux modeling for tides and atmospheric pressure variations. While these models have non-uniform global performance they are excellent in the Mississippi Basin. Through comparisons with the independent hydrology, we evaluate the effect on the solution of changing correlation times and distances in the constraints, altering the parameter recovery for areas external to the Mississippi Basin, and changing the relative strength of the constraints with respect to the KBRR data. The accuracy and stability of the mascon solutions are thereby assessed, especially with regard to the constraints used to stabilize the solution. We show that the mass anomalies, as represented by surface layer of water within regional cells have accuracy estimates of ±2–3 cm on par with the best hydrological estimates and consistent with our accuracy estimates for GRACE mass anomaly estimates. These solutions are shown to be very stable, especially for the recovery of semi-annual and longer period trends, where for example, the phase agreement for the dominant annual signal agrees at the 10-day level of resolution provided by GRACE. This validation confirms that mascons provide critical environmental data records for a wide range of applications including monitoring ground water mass changes.     

Extraction and validation of cartosat-1 DEM

CARTOSAT-1 satellite, launched in May, 2005 is a dedicated along track stereo mission providing high quality data for topographic and cartographic applications. The present paper describes the evaluation of the Cartosat-1 stereo data, mainly through the generation and validation of DEM for moderately undulating and hilly areas. Photogrammetric techniques have been used for generation of DEM and Orthoimage for two cases i.e. 1) using RPCs (Rational Polynomial Coefficients) and 2) using RPCs along with ground control points. Root Mean Square Error (RMSE) in elevation values for the moderately undulating (Dehradun) and hilly area (Shimla), are found to be 4.38 and 3.69m respectively.     

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.     

Space-borne BDS receiver for LING QIAO satellite: design,implementation and preliminary in-orbit experiment results

GPS Solutions - Known as China’s first low earth orbit (LEO) mobile communication experimental satellite, the LING QIAO satellite was launched on September 4, 2014. In addition to the two...     

高分一号多光谱影像正射精度验证与分析

为了验证和分析高分一号卫星影像的正射精度,填补相关研究的空白,该文采用有理函数模型对高分一号卫星PMS传感器多光谱影像进行正射校正,采集检查点检验多光谱影像的几何正射精度。实验结果表明,高分一号卫星PMS相机多光谱影像正射精度能够满足1:25 000比例尺地形图的更新要求,为相关研究提供参考。     

Efficient propagation of error covariance matrices of gravitational models: application to GRACE and GOCE

We have applied efficient methods for computing variances and covariances of functions of a global gravity field model expanded in spherical harmonics, using the full variance–covariance matrix of the coefficients. Examples are given with recent models derived from GRACE (up to degree and order 150), and with simulated GOCE derived solutions (up to degree and order 200).     

联合GPS和GRACE研究青藏高原南部地区垂直形变的季节性波动

利用青藏高原南部地区GPS站点近10 a（2004年至2014年）的观测资料,结合重力场恢复与气候实验卫星（Gravity Recovery and Climate Experiment,GRACE）同时期观测数据反演得到的该区域水文负荷变化引起的垂向位移,发现该地区利用GPS和GRACE获取的垂向位移时间序列存在一定相关性,多数站点的相关系数在0.7左右,特别是沿喜马拉雅造山带区域内的站点相关性更高;此外,大部分站点（例如CHLM、KKN4）拟合的周期项振幅和相位也较为一致。计算GRACE估算垂直信号改正GPS结果前后的加权均方根误差（weighted root mean square,WRMS）,并定义R_WRMS来表征GRACE改正GPS垂向季节性波动的有效性,其数值越接近1表明GPS和GRACE数据具有越大的一致性。研究发现GPS站点的R_WRMS有明显差异:最大和最小值分别是0.96（TPLJ）和0.24（XZGE）,平均值为0.64,这与青藏高原南部地区垂直运动的复杂性有关,存在多种因素（构造运动、冰川均衡调整、大气和非潮汐海洋负荷,水文负荷、GPS交点年误差等）的共同作用。     

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     

GRACE反演南极冰盖质量变化的高斯与Wiener滤波比较

本文利用UTCSR 2003年1月到2008年8月间的GRACE Level-2 RL04重力场模型估计了南极冰盖质量变化.计算过程中分别采用高斯和Wiener滤波两种平滑方法,分别采用22、43和65个月重力场模型计算Wiener滤波信号与噪声函数,得出以下结论:在实际的计算过程中需要具体计算Wiener滤波平滑因子值,65个月GRACE重力场模型计算得到的Wiener滤波权值非常接近于平滑半径为540km高斯滤波权值;采用两种不同的滤波方法在相同区域质量变化率基本相同.     

Assessing antenna field of view and receiver clocks of COSMIC and GRACE satellites: lessons for COSMIC-2

We provide suggestions for the approved COSMIC-2 satellite mission regarding the field of view (FOV) and the clock stability of its future GNSS receiver based on numerical analyses using COSMIC GPS data. While the GRACE GPS receiver is mounted on the zenith direction, the precise orbit determination (POD) antennas of COSMIC are not. The COSMIC antenna design results in a narrow FOV and a reduction in the number of GPS observations. To strengthen the GPS geometry, GPS data from two POD antennas of COSMIC are used to estimate its orbits. The phase residuals of COSMIC are at the centimeter level, compared to the millimeter level of GRACE. The receiver clock corrections of COSMIC and GRACE are at the microsecond and nanosecond levels, respectively. The clock spectra of COSMIC at the frequencies of 0–0.005 Hz contain significant powers, indicating potential systematic errors in its clock corrections. The clock stability, expressed by the Allan deviation, of COSMIC ranges from 10^?9 to 10^?11 over 1 to 10⁴ s, compared to 10^?12 to 10^?14 for GRACE. Compared to USO-based clock of GRACE, the clock of COSMIC is degraded in its stability and is linked to the reduction of GPS data quality. Lessons for improvement of COSMIC-2 over COSMIC in FOV and receiver clock stability are given.     

World geodetic datum WD 1 and WD 2 from satellite and terrestrial observations

By minimizing the global distance between the (quasi-) geoid and an ellipsoid of revolution, the best parameters of an ellipsoid and its location parameters are estimated. Input data are the absolute value of the geopotential at (quasi-) geoid level, a set of harmonic coefficients from satellite, terrestrial or combined observations, the mean rotational speed of the earth, and approximate values of the seminajor axis and the eccentricity of the ellipsoid. The output ranges from 6378137,63 m and 6378141,62 m for the best semimajor axis and from 298.259758 and 298.259651 for the reciprocal value of the best ellipsoidal flattening within WD 1 and WD 2. The best translational parameters are 6.4 cm (Greenwich-direction), 0.8 cm (orthogonal to Greenwich-direction), and 1.9 cm (parallel to rotational axis of the earth); the best rotational parameters are −0.2” (around Greenwich-direction) and 1.1” (around orthogonal to Greenwich-direction). The dependence of the datum of the (quasi-) geoid geopotential is studied in detail.