Space-Wise,Time-Wise,Torus and Rosborough Representations in Gravity Field Modelling

The decade of the geopotentials started July 2000 with the launch of the German high-low SST mission CHAMP. Together with the joint NASA-DLR low-low SST mission GRACE and the ESA gradiometry mission GOCE an unprecedented wealth of geopotential data becomes available over the next few years. Due to the sheer number of unknown gravity field parameters (up to 100 000) and of observations (millions), especially the latter two missions are highly demanding in terms of computational requirements. In this paper several modelling strategies are presented that are based on a semi-analytical approach. In this approach the set of normal equations becomes block-diagonal with maximum block-sizes smaller than the spherical harmonic degree of resolution. The block-diagonality leads to a rapid and powerful gravity field analysis tool. Beyond the more-or-less conventional space-wise and time-wise formulations, the torus approach and Rosborough's representation are discussed. A trade-off between pros and cons of each of the modelling strategies will be given. This revised version was published online in August 2006 with corrections to the Cover Date.     

GRACE gravity field modeling with an investigation on correlation between nuisance parameters and gravity field coefficients

The GRACE (Gravity Recovery And Climate Experiment) monthly gravity models have been independently produced and published by several research institutions, such as Center for Space Research (CSR), GeoForschungsZentrum (GFZ), Jet Propulsion Laboratory (JPL), Centre National d’Etudes Spatiales (CNES) and Delft Institute of Earth Observation and Space Systems (DEOS). According to their processing standards, above institutions use the traditional variational approach except that the DEOS exploits the acceleration approach. The background force models employed are rather similar. The produced gravity field models generally agree with one another in the spatial pattern. However, there are some discrepancies in the gravity signal amplitude between solutions produced by different institutions. In particular, 10%–30% signal amplitude differences in some river basins can be observed. In this paper, we implemented a variant of the traditional variational approach and computed two sets of monthly gravity field solutions using the data from January 2005 to December 2006. The input data are K-band range-rates (KBRR) and kinematic orbits of GRACE satellites. The main difference in the production of our two types of models is how to deal with nuisance parameters. This type of parameters is necessary to absorb low-frequency errors in the data, which are mainly the aliasing and instrument errors. One way is to remove the nuisance parameters before estimating the geopotential coefficients, called NPARB approach in the paper. The other way is to estimate the nuisance parameters and geopotential coefficients simultaneously, called NPESS approach. These two types of solutions mainly differ in geopotential coefficients from degree 2 to 5. This can be explained by the fact that the nuisance parameters and the gravity field coefficients are highly correlated, particularly at low degrees. We compare these solutions with the official and published ones by means of spectral analysis. It is found that our solutions are, in general, consistent with others in the spatial pattern. The water storage variations of the Amazon, Chari and Ganges river basins have also been computed. The variations computed with the NPARB approach are closer to those produced by JPL and DEOS solutions, while the variations produced with the NPESS approach are in good agreement with those produced by the CSR and GFZ solutions. A simulation study is implemented with considering realistic noise and low-frequency error. The two approaches are used to recover the true model. The NPESS solution appears closer to the true one. Therefore we are inclined to estimate the nuisance parameters simultaneously with the geopential coefficients.     

星载GPS的毫米级编队卫星相对定位

在比较分析编队卫星相对定位与陆地相对定位技术的基础上,结合陆地相对定位技术和 卫星精密定轨技术提出了基于GPS进行编队卫星相对定位的方法及原理。文章采用2004年4月 1日到10日的GRACE卫星实测数据进行了相对定位计算,并采用KBR观测数据对本文相对定位 结果和JPL单独定轨结果进行了外部检核,检核结果表明：1. 与直接采用单独定轨结果相 比,该方法可以明显提高卫星的相对位置精度。2. 利用本文方法计算的两颗GRACE卫星相 对位置精度约为4.5 mm。
     

Spaceborne GPS receiver antenna phase center offset and variation estimation for the Shiyan 3 satellite

In determining the orbits of low Earth orbit (LEO) satellites using spaceborne GPS, the errors caused by receiver antenna phase center offset (PCO) and phase center variations (PCVs) are gradually becoming a major limiting factor for continued improvements to accuracy. Shiyan 3, a small satellite mission for space technology experimentation and climate exploration, was developed by China and launched on November 5, 2008. The dual-frequency GPS receiver payload delivers 1 Hz data and provides the basis for precise orbit determination within the range of a few centime-ters. The antenna PCO and PCV error characteristics and the principles influencing orbit determi-nation are analyzed. The feasibility of PCO and PCV estimation and compensation in different directions is demonstrated through simulation and in-flight tests. The values of receiver antenna PCO and PCVs for Gravity Recovery and Climate Experiment (GRACE) and Shiyan 3 satellites are estimated from one month of data. A large and stable antenna PCO error, reaching up to 10.34 cm in the z-direction, is found with the Shiyan 3 satellite. The PCVs on the Shiyan 3 satellite are estimated and reach up to 3.0 cm, which is slightly larger than that of GRACE satellites. Orbit validation clearly improved with independent k-band ranging (KBR) and satellite laser ranging (SLR) measurements. For GRACE satellites, the average root mean square (RMS) of KBR resid-uals improved from 1.01 cm to 0.88 cm. For the Shiyan 3 satellite, the average RMS of SLR resid-uals improved from 4.95 cm to 4.06 cm.     

Coastal sea level changes in Europe from GPS,tide gauge,satellite altimetry and GRACE, 1993–2011

Sea level changes are threatening the human living environments, particularly along the European Coasts with highly dense population. In this paper, coastal sea level changes in western and southern Europe are investigated for the period 1993–2011 using Global Positioning System (GPS), Tide Gauge (TG), Satellite Altimetry (SA), Gravity Recovery and Climate Experiment (GRACE) and geophysical models. The mean secular trend is 2.26 ± 0.52 mm/y from satellite altimetry, 2.43 ± 0.61 mm/y from TG+GPS and 1.99 ± 0.67 mm/y from GRACE mass plus steric components, which have a remarkably good agreement. For the seasonal variations, annual amplitudes of satellite altimetry and TG+GPS results are almost similar, while GRACE Mass+Steric results are a little smaller. The annual phases agree remarkably well for three independent techniques. The annual cycle is mainly driven by the steric contributions, while the annual phases of non-steric (mass component) sea level changes are almost a half year later than the steric sea level changes.     

GRACE重力卫星揭示的水储量季节性变化

利用覆盖时间段为2004年1月至2009年10月共70个月的美国NASA和德国DLR联合研制的“重力场恢复与气候实验”卫星（GRACE）时变重力场数据,估计了非洲、中国以及亚马逊流域水储量的季节性变化。结果表明：非洲北部、南部、中国南部、亚马逊流域水储量变化的季节性幅度分别为10．5cm±2．1cm、16．2cm±2．9cm、8．3cm±1．5cm、30．5cm±5．6cm。研究证实了GRACE重力卫星在监测水质量变化,乃至于一个相对较小的区域的水质量变化方面的潜能。文章的结果有助于水资源管理以及预防和缓解灾害性事件等工作的决策;此外,改进的以监测地表质量变化、全球性气候改变、灾害性事件等为目标的GRACE类型的探测计划,将促进对水文学、海洋动力学以及地球物理学等的理解。     

GRACE products and land surface models for estimating the changes in key water storage components in the Nile River Basin

The Nile River Basin (NRB) is facing extreme demand for its water resources due to an alarming increase in population and the changing climate. The NRB is not compatible with ground-based in-situ observations owing to its large basin area size and limited hydrological data access from basin countries. Thus, it lends itself to remotely sensed approaches with high spatial resolution and extended temporal coverage. The Gravity Recovery and Climate Experiment (GRACE) avails a unique opportunity to investigate the changes in key components of terrestrial water storage (TWS). GRACE TWS solutions have specific tuning parameters and processing strategies that result in regionally specific variations and error patterns. We explored the TWS time series spatiotemporal changes, trends, uncertainties, and signal-to-noise ratio among different GRACE TWS data. We had also investigated the key terrestrial water storage components such as surface water, soil moisture, and groundwater storage changes. The results show that GRACE spherical harmonic solutions' uncertainty is higher than the mass concentration (mascon) over the NRB, and the Center for Space Research-mascons had the best performance. The evapotranspiration correlation (R² = 0.85) has the highest correlation with GRACE’s TWS, whereas the normalized difference vegetation index (R² = 0.82) has the second highest correlation. Notably, significant long-term (2003–2017) negative groundwater and soil moisture trends demonstrate a potential depletion of the NRB. Despite an increase in precipitation and the TWS time series, the rate of decline increased rapidly after 2008, thereby indicating the possibility of human-induced change (e.g. for irrigation purposes). Therefore, the results of this study provide a guide for future studies related to hydro-climatic change over the NRB and similar basins.     

Study of seasonal and long-term vertical deformation in Nepal based on GPS and GRACE observations

Lithospheric deformation signal can be detected by combining data from continuous global positioning system (CGPS) and satellite observations from the Gravity Recovery and Climate Experiment (GRACE). In this paper, we use 2.5- to 19-year-long time series from 35 CGPS stations to estimate vertical deformation rates in Nepal, which is located in the southern side of the Himalaya. GPS results were compared with GRACE observations. Principal component analysis was conducted to decompose the time series into three-dimensional principal components (PCs) and spatial eigenvectors. The top three high-order PCs were calculated to correct common mode errors. Both GPS and GRACE observations showed significant seasonal variations. The observed seasonal GPS vertical variations are in good agreement with those from the GRACE-derived results, particularly for changes in surface pressure, non-tidal oceanic mass loading, and hydrologic loading. The GPS-observed rates of vertical deformation obtained for the region suggest both tectonic impact and mass decrease. The rates of vertical crustal deformation were estimated by removing the GRACE-derived hydrological vertical rates from the GPS measurements. Most of the sites located in the southern part of the Main Himalayan Thrust subsided, whereas the northern part mostly showed an uplift. These results may contribute to the understanding of secular vertical crustal deformation in Nepal.     

Needs and Tools for Future Gravity Measuring Missions

This paper compares the requirements that can be expected of gravity measuring missions with respect to the status of the instrumentation and satellite technologies. The error sources of gravity gradiometry and satellite-to-satellite tracking are analysed and the elements limiting the accuracy are identified. Proposed and approved future missions that will fly technologies of interest for gravity sensing are recalled. Areas of technical development of interest are reviewed. The article finishes with two possible conceptual missions presented as examples and with a chapter of conclusions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Ocean Tides in GRACE Monthly Averaged Gravity Fields

The GRACE mission will map the Earth's gravity fields and its variations with unprecedented accuracy during its 5-year lifetime. Unless ocean tide signals and their load upon the solid earth are removed from the GRACE data, their long period aliases obscure more subtle climate signals which GRACE aims at. In this analysis the results of Knudsen and Andersen (2002) have been verified using actual post-launch orbit parameter of the GRACE mission. The current ocean tide models are not accurate enough to correct GRACE data at harmonic degrees lower than 47. The accumulated tidal errors may affect the GRACE data up to harmonic degree 60. A study of the revised alias frequencies confirm that the ocean tide errors will not cancel in the GRACE monthly averaged temporal gravity fields. The S₂ and the K₂ terms have alias frequencies much longer than 30 days, so they remain almost unreduced in the monthly averages. Those results have been verified using a simulated 30 days GRACE orbit. The results show that the magnitudes of the monthly averaged values are slightly higher than the previous values. This may be caused by insufficient sampling to fully resolve and reduce the tidal signals at short wavelengths and close to the poles. This revised version was published online in August 2006 with corrections to the Cover Date.