Challenges From Solid Earth Dynamics for Satellite Gravity Field Missions in the Post-Goce Era

Examples from four main categories of solid-earth deformation processes are discussed for which the GOCE and GRACE satellite gravity missions will not provide a high enough spatial or temporal resolution or a sufficient accuracy. Quasi-static and episodic solid-earth deformation would benefit from a new satellite gravity mission that would provide a higher combined spatial and temporal resolution. Seismic and core periodic motions would benefit from a new satellite mission that would be able to detect gravity variations with a higher temporal resolution combined with very high accuracies.     

Efficient Determination of Global Gravity Field from Satellite-to-satellite Tracking Mission

The gravity field dedicated satellite missions like CHAMP, GRACE, and GOCE are supposed to map the Earth's global gravity field with unprecedented accuracy and resolution. New models of the Earth's static and time-variable gravity fields will be available every month as one of the science products from GRACE. A method for the efficient gravity field recovery is presented using in situ satellite-to-satellite observations at altitude and results on static as well as temporal gravity field recovery are shown. Considering the energy relationship between the kinetic energy of the satellite and the gravitational potential, the disturbing potential observations can be computed from the orbital state vector, using high-low GPS tracking data, low–low satellite-to-satellite GRACE measurements, and data from 3-axis accelerometers. The solution method is based on the conjugate gradient iterative approach to efficiently recover the gravity field coefficients and approximate error covariance up to degree and order 120 every month. Based on the monthly GRACE noise-only simulation, the geoid was obtained with an accuracy of a few cm and with a resolution (half wavelength) of 160 km. However, the geoid accuracy can become worse by a factor of 6–7 because of spatial aliasing. The approximate error covariance was found to be a very good accuracy measure of the estimated coefficients, geoid, and gravity anomaly. The temporal gravity field, representing the monthly mean continental water mass redistribution, was recovered in the presence of measurement noise and high frequency temporal variation. The resulting recovered temporal gravity fields have about 0.3 mm errors in terms of geoid height with a resolution of 670 km.     

Future Gravity Missions and Quasi-steady Ocean Circulation

The quasi-permanent sea surface slope, i.e. the signature of oceanic currents that does not vanish when dynamic topography observations are averaged over a long period of time, will be resolved up to spatial scales of about 100 km by the GOCE space gravity mission. However, estimates of the quasi-permanent ocean dynamic topography, derived qualitatively either from models or from observations, indicate that some non-negligible residual signal remains below 100 km in areas of strong surface currents like the core of the Gulf Stream. One therefore expects that future missions can improve our knowledge of the ocean circulation in these areas. However, the potential improvements are small compared to the improvements expected from GOCE itself.     

Ice Mass Balance and Ice Dynamics from Satellite Gravity Missions

An overview of advances in ice research which can be expected from future satellite gravity missions is given. We compare present and expected future accuracies of the ice mass balance of Antarctica which might be constrained to 0.1–0.3 mm/year of sea level equivalent by satellite gravity data. A key issue for the understanding of ice mass balance is the separation of secular and interannual variations. For this aim, one would strongly benefit from longer uninterrupted time series of gravity field variations (10 years or more). An accuracy of 0.01 mm/year for geoid time variability with a spatial resolution of 100 km would improve the separability of ice mass balance from mass change due to glacial isostatic adjustment and enable the determination of regional variations in ice mass balance within the ice sheets. Thereby the determination of ice compaction is critical for the exploitation of such high accuracy data. A further benefit of improved gravity field models from future satellite missions would be the improvement of the height reference in the polar areas, which is important for the study of coastal ice processes. Sea ice thickness determination and modelling of ice bottom topography could be improved as well.     

Geoid and Gravity in Earth Sciences – An Overview

Precise global geoid and gravity anomaly information serves essentially three different kinds of applications in Earth sciences: gravity and geoid anomalies reflect density anomalies in oceanic and continental lithosphere and the mantle; dynamic ocean topography as derived from the combination of satellite altimetry and a global geoid model can be directly transformed into a global map of ocean surface circulation; any redistribution or exchange of mass in Earth system results in temporal gravity and geoid changes. After completion of the dedicated gravity satellite missions GRACE and GOCE a high standard of global gravity determination, both of the static and of the time varying field will be attained. Thus, it is the right time to investigate the future needs for improvements in the various fields of Earth sciences and to define the right strategy for future gravity field satellite missions.     

GOCE卫星重力计划及其应用

基于CHAMP和GRACE卫星，GOCE(Gravity Field and Stead—state Ocean Circulation Explore)是欧空局(ESA)的一颗重力场和静态洋流探测卫星。利用它可得到空间分辨率为200—80km的全球重力场模型和1cm精度的大地水准面．简要介绍了目前重力卫星的发展现状与其局限性，详细叙述了GOCE卫星的组成、科学目标、测量原理、在地球物理等学科中的重要应用，并提出GOCE等重力卫星资料在我国的应用设想。     

Impact of Limitations in Geophysical Background Models on Follow-on Gravity Missions

Purpose of this article is to demonstrate the effect of background geophysical corrections on a follow-on gravity mission. We investigate the quality of two effects, tides and atmospheric pressure variations, which both act as a surface load on the lithosphere. In both cases direct gravitational attraction of the mass variations and the secondary potential caused by the deformation of the lithosphere are sensed by a gravity mission. In order to assess the current situation we have simulated GRACE range-rate errors which are caused by differences in present day tide and atmospheric pressure correction models. Both geophysical correction models are capable of generating range-rate errors up to 10 μm/s and affect the quality of the recovered temporal and static gravity fields. Unlike missions such as TOPEX/Poseidon where tides can be estimated with the altimeter, current gravity missions are only to some degree capable of resolving these (geo)physical limitations. One of the reasons is the use of high inclination low earth orbits without a repeating ground track strategy. The consequence is that we will face a contamination of the gravity solution, both in the static and the time variable part. In the conclusions of this paper we provide suggestions for improving this situation, in particular in view of follow-on gravity missions after GRACE and GOCE, which claim an improved capability of estimating temporal variations in the Earth’s gravity field.     

卫星跟踪卫星模式中轨道参数需求分析

首次基于半解析法利用GRACE(Gravity Recovery and Climate Experiment)双星K波段星间速度误差、GPS接收机轨道误差和加速度计非保守力误差影响累计大地水准面精度的联合模型开展了卫星跟踪卫星模式中轨道参数的需求分析.建议我国将来首颗重力卫星的平均轨道高度设计为400 km和平均星间距离设计为220 km较优.此研究不仅为我国将来卫星重力测量计划中轨道参数的优化选取以及全球重力场精度的有效和快速估计提供了理论基础和计算保证,同时对将来国际GRACE Follow-On地球重力测量计划和GRAIL(Gravity Recovery and Interior Laboratory)月球重力探测计划的发展方向具有一定的指导意义.     

Science Requirements on Future Missions and Simulated Mission Scenarios

The science requirements on future gravity satellite missions, following from the previous contributions of this issue, are summarized and visualized in terms of spatial scales, temporal behaviour and accuracy. This summary serves the identification of four classes of future satellite mission of potential interest: high-altitude monitoring, satellite-to-satellite tracking, gradiometry, and formation flights. Within each class several variants are defined. The gravity recovery performance of each of these ideal missions is simulated. Despite some simplifying assumptions, these error simulations result in guidelines as to which type of mission fulfils which requirements best.     

Future Benefits of Time-Varying Gravity Missions to Ocean Circulation Studies

A summary is offered of the potential benefits of future measurements of temporal variations in gravity for the understanding of ocean dynamics. Two types of process, and corresponding amplitudes are discussed: ocean basin scale pressure changes, with a corresponding amplitude of order 1 cm of water, or 1 mm of geoid height, and changes in along-slope pressure gradient, at cross-slope length scales corresponding to topographic slopes, with a corresponding amplitude of order 1 mm of water, or a maximum of about 0.01 mm of geoid. The former is feasible with current technology and would provide unprecedented information about abyssal ocean dynamics associated with heat transport and climate. The latter would be a considerable challenge to any foreseeable technology, but would provide an exceptionally clear, quantitative window on the dynamics of abyssal ocean currents, and strong constraints on ocean models. Both options would be limited by the aliassing effect of rapid mass movements in the earth system, and it is recommended that any future mission take this error source explicitly into account at the design stage. For basin-scale oceanography this might involve a higher orbit than GRACE or GOCE, and the advantages of exact-repeat orbits and multiple missions should be considered.     

A timewise kinematic method for satellite gradiometry: GOCE simulations

We have defined new algorithms for the data processing of a satellite geodesy mission with gradiometer (such as the next European mission GOCE) to extract the information on the gravity field coefficients with a realistic estimate of their accuracy. The large scale data processing can be managed by a multistage decomposition. First the spacecraft position is determined, i.e., a kinematic method is normally used. Second we use a new method to perform the necessary digital calibration of the gradiometer. Third we use a multiarc approach to separately solve for the global gravity field parameters. Fourth we use an approximate resonant decomposition, that is we partition in a new way the harmonic coefficients of the gravity field. Thus the normal system is reduced to blocks of manageable size without neglecting significant correlations. Still the normal system is badly conditioned because of the polar gaps in the spatial distribution of the data. We have shown that the principal components of the uncertainty correspond to harmonic anomalies with very small signal in the region where GOCE is flying; these uncertainties cannot be removed by any data processing method. This allows a complete simulation of the GOCE mission with affordable computer resources. We show that it is possible to solve for the harmonic coefficients up to degree 200–220 with signal to error ratio ≥1, taking into account systematic measurement errors. Errors in the spacecraft orbit, as expected from state of the art satellite navigation, do not degrade the solution. Gradiometer calibration is the main problem. By including a systematic error model, we have shown that the results are sensitive to spurious gradiometer signals at frequencies close to the lower limit of the measurement band. If these spurious effects grow as the inverse of the frequency, then the actual error is larger than the formal error only by a factor ≃2, that is the results are not compromised.     

GRACE重力计划在揭示地球系统质量重新分布中的应用

2002年3月成功发射的美德合作卫星重力计划GRACE(Gravity Recovery And ClimateExperiment),即将提供空间分辨率约为200 km而时间分辨率为1个月的时变地球重力场模型序列。GRACE计划的星座由两颗相距约220 km,高度保持为300-500 km、倾角保持约90°的近极轨卫星组成。由于采用星载GPS和非保守力加速度计等高精度定轨技术,以及高精度的星一星跟踪数据反演地球重力场,在几百公里和更大空间尺度上, GRACE重力场的精度大大超过此前的卫星重力计划。根据GRACE时变重力场反演的地球系统质量重新分布,将对固体地球物理、海洋物理、气候学以及大地测量等应用有重要的意义。虽然其设计寿命只有5 yr,但研究表明GRACE的结果可用于研究北极冰长期时间尺度的变化,并进而研究极冰融化对全球气候变化,特别是对海平面长期变化的影响。在季节性时间尺度上,利用GRACE重力场反演的质量重新分布足以揭示平均小于1 cm的地表水变化,或小于1 mbar。的海底压强变化。除了巨大的社会效益和经济效益外,这些变化对了解地球系统的物质循环(主要是水循环)和能量循环有非常重要的意义。介绍GRACE重力场揭示的地球系统质量重新分布,为理解其地球物理应用提供必需的准备;同时针对我国大陆和沿海地区的地球物理应用提出初步的设想。     

GRACE observations of changes in continental water storage

Signatures between monthly global Earth gravity field solutions obtained from GRACE satellite mission data are analyzed with respect to continental water storage variability. GRACE gravity field models are derived in terms of Stokes' coefficients of a spherical harmonic expansion of the gravitational potential from the analysis of gravitational orbit perturbations of the two GRACE satellites using GPS high–low and K-band low–low intersatellite tracking and on-board accelerometry. Comparing the GRACE observations, i.e., the mass variability extracted from temporal gravity variations, with the water mass redistribution predicted by hydrological models, it is found that, when filtering with an averaging radius of 750 km, the hydrological signals generated by the world's major river basins are clearly recovered by GRACE. The analyses are based on differences in gravity and continental water mass distribution over 3- and 6-month intervals during the period April 2002 to May 2003. A background model uncertainty of some 35 mm in equivalent water column height from one month to another is estimated to be inherent in the present GRACE solutions at the selected filter length. The differences over 3 and 6 months between the GRACE monthly solutions reveal a signal of some 75 mm scattering with peak values of 400 mm in equivalent water column height changes over the continents, which is far above the uncertainty level and about 50% larger than predicted by global hydrological models. The inversion method, combining GRACE results with the signal and stochastic properties of a hydrological model as ‘a priori’ in a statistical least squares adjustment, significantly reduces the overall power in the obtained water mass estimates due to error reduction, but also reflects the current limitations in the hydrological models to represent total continental water storage change in particular for the major river basins.     

The lunar gravity mission MAGIA: preliminary design and performances

The importance of an accurate model of the Moon gravity field has been assessed for future navigation missions orbiting and/or landing on the Moon, in order to use our natural satellite as an intermediate base for next solar system observations and exploration as well as for lunar resources mapping and exploitation. One of the main scientific goals of MAGIA mission, whose Phase A study has been recently funded by the Italian Space Agency (ASI), is the mapping of lunar gravitational anomalies, and in particular those on the hidden side of the Moon, with an accuracy of 1 mGal RMS at lunar surface in the global solution of the gravitational field up to degree and order 80. MAGIA gravimetric experiment is performed into two phases: the first one, along which the main satellite shall perform remote sensing of the Moon surface, foresees the use of Precise Orbit Determination (POD) data available from ground tracking of the main satellite for the determination of the long wavelength components of gravitational field. Improvement in the accuracy of POD results are expected by the use of ISA, the Italian accelerometer on board the main satellite. Additional gravitational data from recent missions, like Kaguya/Selene, could be used in order to enhance the accuracy of such results. In the second phase the medium/short wavelength components of gravitational field shall be obtained through a low-to-low (GRACE-like) Satellite-to-Satellite Tracking (SST) experiment. POD data shall be acquired during the whole mission duration, while the SST data shall be available after the remote sensing phase, when the sub-satellite shall be released from the main one and both satellites shall be left in a free-fall dynamics in the gravity field of the Moon. SST range-rate data between the two satellites shall be measured through an inter-satellite link with accuracy compliant with current state of art space qualified technology. SST processing and gravitational anomalies retrieval shall benefit from a second ISA accelerometer on the sub-satellite in order to decouple lunar gravitational signal from other accelerations. Experiment performance analysis shows that the stated scientific requirements can be achieved with a low mass and low cost sub-satellite, with a SST gravimetric mission of just few months.     

The dynamical environment of Dawn at Vesta

Dawn is the first NASA mission to operate in the vicinity of the two most massive asteroids in the main belt, Ceres and Vesta. This double-rendezvous mission is enabled by the use of low-thrust solar electric propulsion. Dawn will arrive at Vesta in 2011 and will operate in its vicinity for approximately one year. Vesta's mass and non-spherical shape, coupled with its rotational period, presents very interesting challenges to a spacecraft that depends principally upon low-thrust propulsion for trajectory-changing maneuvers. The details of Vesta's high-order gravitational terms will not be determined until after Dawn's arrival at Vesta, but it is clear that their effect on Dawn operations creates the most complex operational environment for a NASA mission to date. Gravitational perturbations give rise to oscillations in Dawn's orbital radius, and it is found that trapping of the spacecraft is possible near the 1:1 resonance between Dawn's orbital period and Vesta's rotational period, located approximately between 520 and 580 km orbital radius. This resonant trapping can be escaped by thrusting at the appropriate orbital phase. Having passed through the 1:1 resonance, gravitational perturbations ultimately limit the minimum radius for low-altitude operations to about 400 km, in order to safely prevent surface impact. The lowest practical orbit is desirable in order to maximize signal-to-noise and spatial resolution of the Gamma-Ray and Neutron Detector and to provide the highest spatial resolution observations by Dawn's Framing Camera and Visible InfraRed mapping spectrometer. Dawn dynamical behavior is modeled in the context of a wide range of Vesta gravity models. Many of these models are distinguishable during Dawn's High Altitude Mapping Orbit and the remainder are resolved during Dawn's Low Altitude Mapping Orbit, providing insight into Vesta's interior structure. Ultimately, the dynamics of Dawn at Vesta identifies issues to be explored in the planning of future EP missions operating in close proximity to larger asteroids.     

Simulation of the Chang’E-5 mission contribution in lunar long wavelength gravity field improvement

The precision of lunar gravity field estimation has improved by means of three to five orders of magnitude since the successful GRAIL lunar mission. There are still discrepancies however, in the low degree coefficients and long wavelength components of the solutions developed by two space research centers (JPL and GSFC). These discrepancies hint at the possibilities for improving the accuracy in the long wavelength part of the lunar gravity field. In the near future, China will launch the Chang’E-5 lunar mission. In this sample-return mission, there will be a chance to do KBRR measurements between an ascending module and an orbiting module. These two modules will fly around lunar at an inclination of ～49 degrees, with an orbital height of 100 km and an inter-satellite distance of 200 km. In our research, we simulated the contribution of the KBRR tracking mode for different GRAIL orbital geometries. This analysis indicated possible deficiencies in the low degree coefficient solutions for the polar satellite-to-satellite tracking mode at various orbital heights. We also investigated the potential contributions of the KBRR to the Chang’E-5 mission goal of lunar gravity field recovery, especially in the long wavelength component. Potential improvements were assessed using various power spectrums of the lunar gravity field models. In addition, we also investigated possible improvements in solving lunar tidal Love number K2. These results may assist the implementation of the Chang’E-5 mission.     

GOCE: The Earth Gravity Field by Space Gradiometry

An artificial satellite, flying in a purely gravitational field is a natural probe, such that, by a very accurate orbit determination, would allow a perfect estimation of the field. A true satellite experiences a number of perturbational, non-gravitational forces acting on the shell of the spacecraft; these can be revealed and accurately measured by a spaceborne accelerometer. If more accelerometers are flown in the same satellite, they naturally eliminate (to some extent) the common perturbational accelerations and their differences are affected by the second derivatives of the gravity fields only (gradiometry). The mission GOCE is based on this principle. Its peculiar dynamical observation equations are reviewed. The possibility of estimating the gravity field up to some harmonic degree (200) is illustrated.     

Analysis of Land Water Storage in Southwest China Based on GRACE Data

The inversion of the variation in the land water storage in Southwest China is carried out by taking advantage of the data obtained by the earth gravity satellite GRACE (Gravity Recovery and Climate Experiment) for 64 months from January 2005 to April 2010. The result shows that by selecting an appropriate Gauss radius (R = 600 km) and taking the average gravitational field of the adopted data as the back-ground gravitational field, the land water storage in Southwest China inverted on the basis of the GRACE data reflects the drought in Southwest China at the beginning of 2010 very well.     

Ground-Based Observational Support for Spacecraft Exploration of the Outer Planets

This report presents both a retrospective of ground-based support for spacecraft missions to the outer solar system and a perspective of support for future missions. Past support is reviewed in a series of case studies involving the author. The most basic support is essential, providing the mission with information without which the planned science would not have been accomplished. Another is critical, without which science would have been returned, but missing a key element in its understanding. Some observations are enabling by accomplishing one aspect of an experiment which would otherwise not have been possible. Other observations provide a perspective of the planet as a whole which is not available to instruments with narrow fields of view and limited spatial coverage, sometimes motivating a re-prioritizing of experiment objectives. Ground-based support is also capable of providing spectral coverage not present in the complement of spacecraft instruments. Earth-based observations also have the capability of filling in gaps of spacecraft coverage of atmospheric phenomena, as well as providing surveillance of longer-term behavior than the coverage available to the mission. Future missions benefiting from ground-based support would include the Juno mission to Jupiter in the next decade, a flagship-class mission to the Jupiter or to the Saturn systems currently under consideration, and possible intermediate-class missions which might be proposed in NASA’s New Frontiers category. One of the principal benefits of future 30 m-class giant telescopes would be to improve the spatial resolution of maps of temperature and composition which are derived from observations of thermal emission at mid-infrared and longer wavelengths. In many situations, this spatial resolution is competitive with those of the relevant instruments on the spacecraft themselves.     

基于GRACE数据的西南陆地水储量分析

利用地球重力卫星GRACE(Gravity Recovey and Climate Experiment)2005年1月～2010年4月期间64个月的数据,对我国西南地区陆地水储量变化进行了反演.结果表明,选取适当的高斯半径(R=600 km)和所采用数据的平均引力场作为背景引力场,则基于GRACE数据反演的西南陆地水...