Geometry and accuracy of reflecting points in bistatic satellite altimetry

The analysis of the time and space distribution of specular (reflecting) points in bistatic altimetry between GPS and CHAMP satellites or SAC-C (taken as examples) is extended from Wagner and Klokočník (2003 J. Geod 77: 128–138). We demonstrate a significantly higher number and density of reflecting points in bistatic altimetry in comparison with traditional monostatic altimetry. After an outline of our older accuracy assessment for the vertical position of the reflecting point, we add a new independent derivation and compare both approaches. We account for orbit errors of both the transmitters (GPS) and receiver (CHAMP) satellites, and the measurement (delay) error. We found that the accuracy of the vertical position of the reflecting point decreases only slowly with increasing off-nadir angle and that the orbit errors must be accounted for if decimeter and better accuracy is required. In this paper, we do not study errors such as state of the ocean, technical parameters of the receiving system, and atmospheric corrections.     

Magnetic activity inside the auroral zones and field-aligned currents

Big perturbations of the magnetic field (amplitudes larger than 250 nT) are simply detected by subtracting the values of a model from the measurements of CHAMP satellite. Taking a full year of CHAMP data and organizing them in four subsets of three months length (spring, summer, autumn, winter), it is found that: (a) the two domains where such big perturbations mainly exist are limited, in both hemispheres, by a parallel of high latitude of the corrected geomagnetic coordinates system; (b) a conspicuous seasonal (annual) variation affects the density of the perturbations and is opposite in the two hemispheres. We hold that these perturbations are linked to the midday magnetic activity within the auroral zone, long ago described by one of us (Mayaud, 1956). The source of the perturbations observed at the satellite altitude would be field-aligned currents resulting from the penetration of the solar wind into the magnetospheric cusps. To cite this article: J.-L. Le Mouël et al., C. R. Geoscience 335 (2003).     

基于经验模式给定热层温度对热层大气密度反演影响的评估

利用加速度计数据反演热层大气密度算法一般需由经验模式给定热层大气温度,进而计算大气阻尼系数C_D.本文基于CHAMP卫星加速度计数据反演得到大气密度,以2008年为例,利用反演得到的热层大气密度循环迭代修正大气阻尼系数C_D,通过对比修正前后密度偏差,评估经验模式给定热层温度对热层大气密度反演造成的影响.结果表明,经验模式热层温度计算偏差对大气密度反演造成的影响小于5%,而且考虑大气成分的改变则进一步降低了这种影响.

     

改进的能量守恒方法及其在CHAMP重力场恢复中的应用

An efficient method for gravity field determination from CHAMP orbits and accelerometer data is referred to as the energy balance approach. A new CHAMP gravity field recovery strategy based on the improved energy balance approach IS developed in this paper. The method simultaneously solves the spherical harmonic coefficients, daily Integration constant, scale and bias parameters. Two 60 degree and order gravitational potential models, XISM-CHAMPO1S from the classical energy balance approach, and XISM-CHAMPO2S from the improved energy balance, are determined using about one year＇s worth of CHAMP kinematic orbits from TUM and accelerometer data from GFZ. Comparisons among XISM-CHAMPO1S, XISM-CHAMPO2S, EIGEN-CGO3C, EIGEN-CHAMPO3S, EIGEN2, ENIGNIS and EGM96 are made. The results show that the XISM-CHAMPO2S model is more accurate than EGM96, EIGENIS, EIGEN2 and XISM-CHAMPO1S at the same degree and order, and has almost the same accuracy as EIGEN-CHAMPO3S.     

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GRlM5-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400km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3cm,重力异常的精度改善了0．4mgal。     

A study on the reference frame consistency in recent Earth gravitational models

All gravity field functionals obtained from an Earth gravitational model (EGM) depend on the underlying terrestrial reference frame (TRF), with respect to which the EGM’s spherical harmonic coefficients refer to. In order to maintain a coherent framework for the comparison of current and future EGMs, it is thus important to investigate the consistency of their inherent TRFs, especially when their use is intended for high precision studies. Following the methodology described in an earlier paper by Kleusberg (1980), the similarity transformation parameters between the associated reference frames for several EGMs (including the most recent CHAMP/GRACE models at the time of writing this paper) are estimated in the present study. Specifically, the differences between the spherical harmonic coefficients for various pairs of EGMs are parameterized through a 3D-similarity spatial transformation model that relates their underlying TRFs. From the least-squares adjustment of such a parametric model, the origin, orientation and scale stability between the EGMs’ reference frames can be identified by estimating their corresponding translation, rotation and scale factor parameters. Various aspects of the estimation procedure and its results are highlighted in the paper, including data weighting schemes, the sensitivity of the results with respect to the selected harmonic spectral band, the correlation structure and precision level of the estimated transformation parameters, the effect of the estimated differences of the EGMs’ reference frames on their height anomaly signal, and the overall feasibility of Kleusberg’s formulae for the assessment of TRF inconsistencies among global geopotential models.     

In-flight performance analysis of the CHAMP BlackJack GPS Receiver

JPL's BlackJack receiver currently represents the most widely used geodetic grade GPS receiver for space applications. Using data from the CHAMP science mission, the in-flight performance of the BlackJack receiver has been assessed and the impact of various software updates performed during the 2.5 years since launch is described. Key aspects of the study comprise the channel allocation, anomalous data points, and the noise level of the code and carrier data. In addition, it has been demonstrated that the code measurements collected onboard the CHAMP satellite are notably affected by multipath errors in the aft-looking hemisphere, which can be attributed to cross-talk between the occultation antenna string and the primary precise orbit determination antenna. For carrier smoothed 10 s normal points, the code noise itself varies between a minimum of 5 cm at high elevations and 0.5 m (C/A) to 1.0 m (P₁, P₂) at 10° elevation. Carrier-phase data exhibit representative errors of 0.2 to 2.5 mm. The results of the CHAMP GPS data analysis contribute to a better understanding and possible improvement of the BlackJack receiver and support the design of optimal data editing and weighting strategies in precise orbit determination applications.     

上海天文台CHAMP掩星资料处理结果的统计分析

随着GPS全球定位系统的发展,已经有可能使用GPS掩星技术反演精确的大气温度,压强和湿度剖面．在概要地描述上海天文台(SHAO)开发的GPS掩星数据资料反演地球大气流程模块以后,分析了2002年8月1日至2002年8月17日期间2700多次CHAMP掩星数据资料的结果,并且与欧洲中尺度天气预报分析(ECMWF)资料进行比较和统计分析,讨论了CHAMP掩星数据的质量,并分析了CHAMP掩星数据的观测误差和ECMWF的分析模型误差．提出了一种优化的统计分析方法,它能更客观地反映GPS掩星技术的外部符合．统计分析结果表明GPS掩星数据将有可能成为数值天气预报和长期监测地球气候的非常有价值的数据资料．     

Evaluation of the accuracy of the EIGEN-1S and -2 CHAMP-derived gravity field models by satellite crossover altimetry

Since the advent of CHAMP, the first in a series of low-altitude satellites being almost continuously and precisely tracked by GPS, a new generation of long-wavelength gravitational geopotential models can be derived. The accuracy evaluation of these models depends to a large extent on the comparison with external data of comparable quality. Here, two CHAMP-derived models, EIGEN-1S and EIGEN-2, are tested with independent long-term-averaged single satellite crossover (SSC) sea heights from three altimetric satellites (ERS-1, ERS-2 and Geosat). The analyses show that long-term averages of crossover residuals still are powerful data to test CHAMP gravity field models. The new models are tested in the spatial domain with the aid of ERS-1/-2 and Geosat SSCs, and in the spectral domain with latitude-lumped coefficient (LLC) corrections derived from the SSCs. The LLC corrections allow a representation of the satellite-orbit-specific error spectra per order of the models spherical harmonic coefficients. These observed LLC corrections are compared to the LLC projections from the models variance–covariance matrix. The excessively large LLC errors at order 2 found in the case of EIGEN-2 with the ERS data are discussed. The degree-dependent scaling factors for the variance-covariance matrices of EIGEN-1S and –2, applied to obtain more realistic error estimates of the solved-for coefficients, are compatible with the results found here.     

A technique for modeling the Earth’s gravity field on the basis of satellite accelerations

A technique is proposed for Earths gravity field modeling on the basis of satellite accelerations that are derived from precise orbit data. The functional model rests on Newtons second law. The computational procedure is based on the pre-conditioned conjugate-gradient (PCCG) method. The data are treated as weighted average accelerations rather than as point-wise ones. As a result, a simple three-point numerical differentiation scheme can be used to derive them. Noise in the orbit-derived accelerations is strongly dependent on frequency. Therefore, the key element of the proposed technique is frequency-dependent data weighting. Fast convergence of the PCCG procedure is ensured by a block-diagonal pre-conditioner (approximation of the normal matrix), which is derived under the so-called Colombo assumptions. Both uninterrupted data sets and data with gaps can be handled. The developed technique is compared with other approaches: (1) the energy balance approach (based on the energy conservation law) and (2) the traditional approach (based on the integration of variational equations). Theoretical considerations, supported by a numerical study, show that the proposed technique is more accurate than the energy balance approach and leads to approximately the same results as the traditional one. The former finding is explained by the fact that the energy balance approach is only sensitive to the along-track force component. Information about the cross-track and the radial component of the gravitational potential gradient is lost because the corresponding force components do no work and do not contribute to the energy balance. Furthermore, it is shown that the proposed technique is much (possibly, orders of magnitude) faster than the traditional one because it does not require the computation of the normal matrix. Hints are given on how the proposed technique can be adapted to the explicit assembling of the normal matrix if the latter is needed for the computation of the model covariance matrix.Acknowledgments. Professor R. Klees is thanked for support of the project and for numerous fruitful discussions. The authors are also thankful to Dr. J. Kusche for useful remarks and to Dr. E. Schrama, his solid background in satellite geodesy proved to be very helpful. A large number of valuable comments were made by Dr. S.-C. Han, Dr. P. Schwintzer, and an anonymous reviewer; their contribution is greatly acknowledged. The satellite orbits used in the numerical study were kindly provided by Dr. P. Visser (Aerospace Department, Delft University of Technology). Access to the SGI Origin 3800 computer was provided by Stichting Nationale Computerfaciliteiten (NCF), grant SG-027.