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.     

Measuring the Distribution of Ocean Mass Using GRACE

The Gravity Recovery and Climate Experiment (GRACE), which was successfully launched March 17, 2002, has the potential to create a new paradigm in satellite oceanography with an impact perhaps as large as was observed with the arrival of precision satellite altimetry via TOPEX/Poseidon (T/P) in 1992. The simulations presented here suggest that GRACE will be able to monitor non-secular changes in ocean mass on a global basis with a spatial resolution of ≈500 km and an accuracy of ≈3 mm water equivalent. It should be possible to recover global mean ocean mass variations to an accuracy of ≈1 mm, possibly much better if the atmospheric pressure modeling errors can be reduced. We have not considered the possibly significant errors that may arise due to temporal aliasing and secular gravity variations. Secular signals from glacial isostatic adjustment and the melting of polar ice mass are expected to be quite large, and will complicate the recovery of secular ocean mass variations. Nevertheless, GRACE will provide unprecedented insight into the mass components of sea level change, especially when combined with coincident satellite altimeter measurements. Progress on these issues would provide new insight into the response of sea level to climate change. This revised version was published online in August 2006 with corrections to the Cover Date.     

Error Characteristics Estimated from Champ,GRACE and GOCE Derived Geoids and from Satellite Altimetry Derived Mean Dynamic Topography

This paper presents a review of geoid error characteristics of three satellite gravity missions in view of the general problem of separating scientifically interesting signals from various noise sources. The problem is reviewed from the point of view of two proposed applications of gravity missions, one is the observation of the mean oceanic circulation whereby an improved geoid model is used as a reference surface against the long term mean sea level observed by altimetry. In this case we consider the presence of mesoscale variability during assimilation of derived surface currents in inverse models. The other experiment deals with temporal changes in the gravity field observed by GRACE in which case a proposed experiment is to monitor changes in the geoid in order to detect geophysical interesting signals such as variations in the continental hydrology and non-steric ocean processes. For this experiment we will address the problem of geophysical signal contamination and the way it potentially affects monthly geoid solutions of GRACE. This revised version was published online in August 2006 with corrections to the Cover Date.     

Resolution Needed for an Adequate Determination of the Mean Ocean Circulation from Altimetry and an Improved Geoid

The sea surface topography observed by satellite altimetry is a combination of the geoid and of the ocean dynamic topography. Satellite altimetry has thus the potential to supply quasi-global maps of mean sea surface heights from which the mean geostrophic surface ocean currents can be derived, provided that the geoid is known with a sufficient absolute accuracy. At present, however, given the limited accuracy of the best available geoid, altimetric mean sea surface topographies have been derived only up to degree 15 or so, i.e. for wavelengths of approximately 2000 km and larger. CHAMP, GRACE, and the future GOCE missions are dedicated to the improvement of the Earth's gravity field from space. Several studies have recently investigated the impact of these improvements for oceanography, concluding to reductions of uncertainties on the oceanic flux estimates as large as a factor of 2 in the regions of intense an narrow currents. The aim of this paper is to focus on what are the typical horizontal scales of the mean dynamic topography of the ocean, and to compare their characteristics to the error estimates expected from altimetry and these future geoids. It gives also an illustration of the oceanic features that will be resolved by the combination of altimetry and the GRACE and GOCE geoids. It further reassesses the very demanding requirements in term of accuracy and resolution agreed in the design of these new gravity missions for ocean science applications. The present study relies on recent very high-resolution numerical Ocean General Circulation Model simulations. This revised version was published online in August 2006 with corrections to the Cover Date.     

V: SEA LEVEL: Benefits of GRACE and GOCE to sea level studies

The recently published Third Assessment Reports of the Intergovernmental Panel on Climate Change have underlined the scientific interest in, and practical importance of past and potential future sea level changes. Space gravity missions will provide major benefits to the understanding of the past, and, thereby, in the prediction of future, sea level changes in many ways. The proposal for the GOCE mission described well the improvements to be expected from improved gravity field and geoid models in oceanography (for example, in the measurement of the time-averaged, or ‘steady state’, ocean surface circulation and better estimation of ocean transports), in geophysics (in the improvement of geodynamic models for vertical land movements), in geodesy (in positioning of tide gauge data into the same reference frame as altimeter data, and in improvement of altimeter satellite orbits), and possibly in glaciology (in improved knowledge of bedrock topography and ice sheet mass fluxes). GRACE will make many important steps towards these ‘steady state’ aims. However, its main purpose is the provision of oceanographic (and hydrological and meteorological) temporally-varying gravity information, and should in effect function as a global ‘bottom pressure recorder’, providing further insight into the 3-D temporal variation of the ocean circulation, and of the global water budget in general. This paper summaries several of these issues, pointing the way towards improved accuracy of prediction of future sea level change. This revised version was published online in August 2006 with corrections to the Cover Date.     

Feasibility,and Contribution to Ocean Circulation Studies,of Ocean Bottom Pressure Determination

An assessment is presented of the probable magnitude of ocean signals causing aliasing in ocean bottom pressure measurements from the GRACE satellite mission. Even after modelling as much of the high frequency signal as possible, variability between 1 mbar (in quiet ocean regions) and 10 mbar (on some shelves) is likely to remain. Interpretation of the resulting retrievals will therefore rely on the facts that the satellite sampling will average the aliasing signal to some extent, and that the spatial patterns of aliased signal and true signal will be different. To this end, a theoretical argument is given, and supported by model diagnostics, suggesting that observable bottom pressure signals will be strongly constrained by the shape of the ocean floor. The modelled magnitudes offer the prospect of significant detectable signals and, while the model accuracy can be called into question, there are hints from Earth rotation and satellite orbit measurements that significant mass redistributions occur in the ocean. It seems certain that we will learn something new about the oceans from GRACE. This revised version was published online in August 2006 with corrections to the Cover Date.     

What Might GRACE Contribute to Studies of Post Glacial Rebound?

The NASA/DLR satellite gravity mission GRACE, launched in March, 2002, will map the Earth's gravity field at scales of a few hundred km and greater, every 30 days for five years. These data can be used to solve for time-variations in the gravity field with unprecedented accuracy and resolution. One of the many scientific problems that can be addressed with these time-variable gravity estimates, is post glacial rebound (PGR): the viscous adjustment of the solid Earth in response to the deglaciation of the Earth's surface following the last ice age. In this paper we examine the expected sensitivity of the GRACE measurements to the PGR signal, and explore the accuracy with which the PGR signal can be separated from other secular gravity signals. We do this by constructing synthetic GRACE data that include contributions from a PGR model as well as from a number of other geophysical processes, and then looking to see how well the PGR model can be recovered from those synthetic data. We conclude that the availability of GRACE data should result in improved estimates of the Earth's viscosity profile. This revised version was published online in August 2006 with corrections to the Cover Date.     

Spacecraft orbit determination using GPS navigation solutions

The orbit determination using the GPS navigation solutions for the KOMPSAT-1 spacecraft has been studied. The Cowell method of special perturbation theories was employed to develop a precision orbit propagation, and the perturbations due to geopotential, the gravity of the Sun and the Moon, solid Earth tides, ocean tides, the Earth's dynamic polar motion, solar radiation pressure, and atmospheric drag were modeled. Specifically, the satellite box-wing macro model was applied to minimize the drag errors at low altitude. The estimation scheme consisted of an extended Kalman filter and Bayesian least square method. To investigate the applicability of the method to the KOMPSAT-1 spacecraft, the orbit determination was accomplished using the GPS navigation solutions for the TOPEX/POSEIDON and TAOS satellites. The orbit determination results were compared with NASA POE generated by global laser tracking. The position and velocity accuracy was estimated about 16∼7 m and 0.0157∼0.0074 m·s⁻¹ RMS, respectively, for the two satellites in the presence of SA. These results verify that an orbit determination scheme using GPS navigation solutions can provide the static orbit information and reduce conspicuously the position and velocity errors of navigation solutions. It can be suggested that the sequential and batch orbit determination using the GPS navigation solutions be the most appropriate method in the KOMPSAT-1 type mission.     

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.     

Argos海洋浮标多普勒定位原理与方法

通过对海洋浮标进行定位,Argos系统在海洋科学方面得到较为广泛的应用。但Argos系统卫星过顶弧段甚短,加之信号发射周期较长,测量资料甚为稀疏,给海洋浮标的定位造成很不利的影响,容易出现矩阵奇异情况,造成定位失败。文章给出了有效的基于多普勒测量的用于数据收集发射平台的定位算法,并利用参考椭球面约束定位目标,从而改进定位算法,计算结果显示如果能有效的使用约束条件,可以使：①原先定位失败的情形成功解算;②原先定位成功的情形定位精度得到改进。文章还给出了针对海洋目标信标运动以及卫星星历误差等因素对定位结果造成的误差影响的统计分析。     

Mercury’s Interior Structure, Rotation, and Tides

This review addresses the deep interior structure of Mercury. Mercury is thought to consist of similar chemical reservoirs (core, mantle, crust) as the other terrestrial planets, but with a relatively much larger core. Constraints on Mercury’s composition and internal structure are reviewed, and possible interior models are described. Large advances in our knowledge of Mercury’s interior are not only expected from imaging of characteristic surface features but particularly from geodetic observations of the gravity field, the rotation, and the tides of Mercury. The low-degree gravity field of Mercury gives information on the differences of the principal moments of inertia, which are a measure of the mass concentration toward the center of the planet. Mercury’s unique rotation presents several clues to the deep interior. From observations of the mean obliquity of Mercury and the low-degree gravity data, the moments of inertia can be obtained, and deviations from the mean rotation speed (librations) offer an exciting possibility to determine the moment of inertia of the mantle. Due to its proximity to the Sun, Mercury has the largest tides of the Solar System planets. Since tides are sensitive to the existence and location of liquid layers, tidal observations are ideally suited to study the physical state and size of the core of Mercury.     

How to Climb the Gravity Wall

Space Science Reviews - What type of gravity satellite mission is required for the time after GRACE and GOCE? Essentially, the variables at our disposal are experiment altitude, compensation of...     

Modelling the Torques Affecting the Hipparcos Satellite

Reconstructed attitude data for the Hipparcos mission as obtained in the final stages of the data analysis for the published catalogue is used to derive detailed information on the dynamics of the satellite. Most elements of the inertia tensor of the satellite could be calibrated from the observed acceleration data, which are also used to reconstruct torques due to solar radiation and gravity gradient, and the magnetic moment of the satellite and it's interaction with the magnetic field surounding the Earth. The effects of the oblateness of the Earth on the gravity gradient are evaluated and shown to be negligable. The magnetic field model includes both the `main' and the `disturbance' fields. The remaining systematic effects in residual torques are most likely attributed to variations in the magnetic field that are local and are beyond the models used to describe it. The angular momentum vector for one of the gyros was reconstructed from the torque it asserted on the satellite while it was running in redundant mode. This revised version was published online in August 2006 with corrections to the Cover Date.     

Possible Future Use of Laser Gravity Gradiometers

With the GRACE mission under way and the GOCE mission well along in the design process, detailed questions concerning the type of future mission that may follow them have arisen. It is generally agreed that determining the time variations in the Earth's gravity field with as high spatial and temporal resolution as is feasible will be the main driver for such a mission. The possible use of laser heterodyne measurements between separate satellites in such a mission has been discussed by a number of people. The first suggestion of emphasizing time variation measurements in a laser mission was the TIDES concept presented in 1992 by Colombo and Chao. Then, in 2000, a GRACE Follow-On mission using laser measurements between two drag-free satellites was discussed by Watkins el al. (2000). More recently, the possibility of utilizing laser measurements between more than two satellites in order to determine two or more components of the gravity gradient tensor simultaneously has been proposed by Balmino. This approach may be desirable in order to reduce the aliasing of time variations between geopotential terms of different degree and order, as well as to improve the resolution in longitude, despite the cost of the additional satellites. In this paper, we discuss specific possible mission geometries for measuring the two diagonal in-plane components of the gravity gradient tensor simultaneously. This could be done, for example, by laser heterodyne measurements between two pairs of satellites in coplanar and nearly polar orbits. This revised version was published online in August 2006 with corrections to the Cover Date.     

Combined Use of Altimetry and In Situ Gravity Data for Coastal Dynamics Studies

Accurate local geoids derived from in situ gravity data will be valuable in the validation of GOCE results. In addition it will be a challenge to use GOCE data in an optimal way, in combination with in situ gravity, to produce better local geoid solutions. This paper discusses the derivation of a new geoid over the NW European shelf, and its comparison with both tide gauge and altimetric sea level data, and with data from ocean models. It is hoped that over the next few years local geoid methods such as these can be extended to cover larger areas and to incorporate both in situ and satellite measured gravity data. This revised version was published online in August 2006 with corrections to the Cover Date.     

星载双频GPS相位历元差缩减动力学定轨(英文)

研究了星载双频GPS相位历元差缩减动力学定轨方法,该方法既克服了相位历元差运动学方法在观测几何较差或数据不足情况下无法应用的缺点,又避免了相位非差动力学方法易受周跳和模糊度影响的缺点。历元差方法对相位周跳的影响不敏感,因此能够降低相位数据预处理中周跳探测的难度。在模型求解过程中,解决了高维矩阵的计算问题,将长弧段观测数据分成若干短弧段,相邻两个短弧段的连接处不做差分,仅在每个短弧段内部进行历元间差分处理。通过对GRACE卫星进行试算,并与GFZ事后科学轨道进行比较,结果表明相位历元差缩减动力学定轨精度在径向、沿迹方向和轨道法向分别可达1.92cm、3.83cm和3.80cm,三维位置精度可达5.76cm,该方法与相位非差缩减动力学定轨精度相当。     

Phase Residual Estimations for PCVs of Spaceborne GPS Receiver Antenna and Their Impacts on Precise Orbit Determination of GRACE Satellites

In-flight phase center systematic errors of global positioning system(GPS) receiver antenna are the main restriction for improving the precision of precise orbit determination using dual-frequency GPS.Residual approach is one of the valid methods for in-flight calibration of GPS receiver antenna phase center variations(PCVs) from ground calibration.In this paper,followed by the correction model of spaceborne GPS receiver antenna phase center,ionosphere-free PCVs can be directly estimated by ionosphere-free carrier phase post-fit residuals of reduced dynamic orbit determination.By the data processing of gravity recovery and climate experiment(GRACE) satellites,the following conclusions are drawn.Firstly,the distributions of ionosphere-free carrier phase post-fit residuals from different periods have the similar systematic characteristics.Secondly,simulations show that the influence of phase residual estimations for ionosphere-free PCVs on orbit determination can reach the centimeter level.Finally,it is shown by in-flight data processing that phase residual estimations of current period could not only be used for the calibration for GPS receiver antenna phase center of foretime and current period,but also be used for the forecast of ionosphere-free PCVs in future period,and the accuracy of orbit determination can be well improved.     

A geopause satellite system concept

The forthcoming 10 cm range tracking accuracy capability holds much promise in connection with a number of Earth and ocean dynamics investigations. These include a set of earthquake-related studies of fault motions and the Earth's tidal, polar and rotational motions, as well as studies of the gravity field and the sea surface topography which should furnish basic information about mass and heat flow in the oceans. The state of the orbit analysis art is presently at about the 10 m level, or about two orders of magnitude away from the 10 cm range accuracy capability expected in the next couple of years or so. The realization of a 10 cm orbit analysis capability awaits the solution of four kinds of problems, namely, those involving orbit determination and the lack of sufficient knowledge of tracking system biases, the gravity field, and tracking station locations. The Geopause satellite system concept offers promising approaches in connection with all of these areas. A typical Geopause satellite orbit has a 14 hour period, a mean height of about 4.6 Earth radii, and is nearly circular, polar, and normal to the ecliptic. At this height only a relatively few gravity terms have uncertainties corresponding to orbital perturbations above the decimeter level. The orbit s, in this sense, at the geopotential boundary, i.e., the geopause. The few remaining environmental quantities which may be significant can be determined by means of orbit analyses and accelerometers. The Geopause satellite system also provides the tracking geometery and coverage needed for determining the orbit, the tracking system biases and the station locations. Studies indicate that the Geopause satellite, tracked with a 2 cm ranging system from nine NASA affiliated sites, can yield decimeter station location accuracies. Five or more fundamental stations well distributed in longitude can view Geopause over the North Pole. This means not only that redundant data are available for determining tracking system biases, but also that both components of the polar motion can be observed frequently. When tracking Geopause, the NASA sites become a two-hemisphere configuration which is ideal for a number of Earth physics applications such as the observation of the polar motion with a time resolution of a fraction of a day. Geopause also provides the basic capability for satellite-to-satellite tracking of drag-free satellites for mapping the gravity field and altimeter satellites for surveying the sea surface topography. Geopause tracking a coplanar, drag-free satellite for two months to 0.03 mm per second accuracy can yield the geoid over the entire Earth to decimeter accuracy with 2.5° spatial resolution. Two Geopause satellites tracking a coplanar altimeter satellite can then yield ocean surface heights above the geoid with 7° spatial resolution every two weeks. These data will furnish basic boundary condition information about mass and heat flows in the oceans which are important in shaping weather and climate.     

Geodetic Methods for Calibration of GRACE and GOCE

It is beyond doubt that calibration and validation are essential tools in the process of reaching the goals of gravity missions like GRACE and GOCE and to obtain results of the highest possible quality. Both tools, although general and obvious instruments for any mission, have specific features for gravity missions. Therefore, it is necessary to define exactly what is expected (and what cannot be expected) from calibration and what from validation and how these tools should work in our case. The general calibration and validation schemes for GRACE and GOCE are outlined. Calibration will be linked directly to the instrument and the measurements whereas validation will be linked to data derived from the original measurements. Calibration includes on-ground, internal, and external calibration as well as error assessment. The calibration phase results in corrected measurements along with an a posteriori error model. Validation of e.g. calibrated measurements or geoid heights means checking against independent data to assess whether there are no systematic errors left and/or whether the error model describes the true error reasonably well. Geodetic methods for calibration typically refer to external calibration and error assessment, and will be illustrated with an example. This revised version was published online in August 2006 with corrections to the Cover Date.     

A Review of the Effects of Non-migrating Atmospheric Tides on the Earth’s Low-Latitude Ionosphere

Solar thermal tides are planetary-scale waves in the neutral atmosphere with periods that are harmonics of 24?hours. In the thermosphere, they can achieve significant amplitude and can be the dominant source of variation in the atmosphere. Through their modification of the neutral atmosphere, they can also significantly modify the ionosphere, especially at low-latitudes where the dynamics of the Earth’s ionosphere is determined to a large extent by the neutral atmosphere. Much recent work has focused on characterizing and understanding the impact of one sub-group of tides, known as non-migrating tides, on the ionosphere. Whereas migrating tides are responsible for creating strong day-night variations in the ionosphere, non-migrating tides create longitudinal variations in the ionosphere, the signature of which can only be detected with distributed networks of ground-based observations or spacecraft. The present work reviews the recent observations and modeling efforts that have helped to characterize and explain this longitudinal variability. Emphasis is placed on the characteristics of tides throughout the thermosphere, their impacts on the chemical composition of the thermosphere, and impacts on the ionosphere.