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.     

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.     

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.     

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.     

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...     

Impact of Geoid Improvement on Ocean Mass and Heat Transport Estimates

One long-standing difficulty in estimating the large-scale ocean circulation is the inability to observe absolute current velocities. Both conventional hydrographic measurements and altimetric measurements provide observations of currents relative to an unknown velocity at a reference depth in the case of hydrographic data, and relative to mean currents calculated over some averaging period in the case of altimetric data. Space gravity missions together with altimetric observations have the potential to overcome this difficulty by providing absolute estimates of the velocity of surface oceanic currents. The absolute surface velocity estimates will in turn provide the reference level velocities that are necessary to compute absolute velocities at any depth level from hydrographic data. Several studies have been carried out to quantify the improvements expected from ongoing and future space gravity missions. The results of these studies in terms of volume flux estimates (transport of water masses) and heat flux estimates (transport of heat by the ocean) are reviewed in this paper. The studies are based on ocean inverse modeling techniques that derive impact estimates solely from the geoid error budgets of forthcoming space gravity missions. Despite some differences in the assumptions made, the inverse modeling calculations all point to significant improvements in estimates of oceanic fluxes. These improvements, measured in terms of reductions of uncertainties, are expected to be as large as a factor of 2. New developments in autonomous ocean observing systems will complement the developments expected from space gravity missions. The synergies of in situ and satellite observing systems are considered in the conclusion of this paper. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

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.     

Aiming at a 1-cm Orbit for Low Earth Orbiters: Reduced-Dynamic and Kinematic Precise Orbit Determination

The computation of high-accuracy orbits is a prerequisite for the success of Low Earth Orbiter (LEO) missions such as CHAMP, GRACE and GOCE. The mission objectives of these satellites cannot be reached without computing orbits with an accuracy at the few cm level. Such a level of accuracy might be achieved with the techniques of reduced-dynamic and kinematic precise orbit determination (POD) assuming continuous Satellite-to-Satellite Tracking (SST) by the Global Positioning System (GPS). Both techniques have reached a high level of maturity and have been successfully applied to missions in the past, for example to TOPEX/POSEIDON (T/P), leading to (sub-)decimeter orbit accuracy. New LEO gravity missions are (to be) equipped with advanced GPS receivers promising to provide very high quality SST observations thereby opening the possibility for computing cm-level accuracy orbits. The computation of orbits at this accuracy level does not only require high-quality GPS receivers, but also advanced and demanding observation preprocessing and correction algorithms. Moreover, sophisticated parameter estimation schemes need to be adapted and extended to allow the computation of such orbits. Finally, reliable methods need to be employed for assessing the orbit quality and providing feedback to the different processing steps in the orbit computation process. This revised version was published online in August 2006 with corrections to the Cover Date.     

Tidal Models in a New Era of Satellite Gravimetry

The high precision gravity measurements to be made by recently launched (and recently approved) satellites place new demands on models of Earth, atmospheric, and oceanic tides. The latter is the most problematic. The ocean tides induce variations in the Earth's geoid by amounts that far exceed the new satellite sensitivities, and tidal models must be used to correct for this. Two methods are used here to determine the standard errors in current ocean tide models. At long wavelengths these errors exceed the sensitivity of the GRACE mission. Tidal errors will not prevent the new satellite missions from improving our knowledge of the geopotential by orders of magnitude, but the errors may well contaminate GRACE estimates of temporal variations in gravity. Solar tides are especially problematic because of their long alias periods. The satellite data may be used to improve tidal models once a sufficiently long time series is obtained. Improvements in the long-wavelength components of lunar tides are especially promising. 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.     

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.     

VII: CLOSING SESSION: GOCE: ESA's First Earth Explorer Core Mission

This paper introduces the first ESA Core Earth Explorer mission, GOCE, in the context of ESA's Living Planet programme. GOCE will measure highly accurate, high spatial resolution differential accelerations in three dimensions along a well characterised orbit: the mission is planned for launch in early 2006. The mission objectives are to obtain gravity gradient data such that new global and regional models of the static Earth's gravity field and of the geoid can be deduced at length scales down to 100 km. These products will have broad application in the fields of geodesy, oceanography, solid-earth physics and glaciology. This revised version was published online in August 2006 with corrections to the Cover Date.     

导航系统高动态校准火箭橇试验平台研制

火箭橇试验是在地面实现导航系统高动态校准的最佳方法。针对国内导航系统校准火箭橇试验尚处在起步阶段且缺乏通用试验设施的现状,提出了构建校准火箭橇试验平台的设想,以提高试验安全性和数据有效性。完成了最高速度2Ma、最大航向过载30g的校准平台研制,详细介绍了结构设计和仿真分析过程,开展了最高速度306m/s、最大过载11g的火箭橇验证试验。试验结果表明：校准平台运行安全、回收可靠、数据全面,能够满足导航系统高动态校准的指标要求。后续将在此平台上开展更高速度的多套、多类型导航系统校准火箭橇试验研究。     

Microscope Instrument Development,Lessons for GOCE

Two space missions are presently under development with payload based on ultra-sensitive electrostatic accelerometers. The GOCE mission takes advantage of a three axis gradiometer accommodated in a very stable thermal case on board a drag-free satellite orbiting at a very low altitude of 250 km. This ESA mission will perform the very highly accurate mapping of the Earth gravity field with a geographical resolution of 100 km. The MICROSCOPE mission is devoted to the test of the “Universality of free fall” in view of the verification of the Einstein Equivalence Principle (EP) and of the search of a new interaction. The MICROSCOPE instrument is composed of two pairs of differential electrostatic accelerometers and the accelerometer proof-masses are the bodies of the EP test. The satellite is also a drag-free satellite exhibiting a fine attitude control and in a certain way, each differential accelerometer is a one axis gradiometer with an arm of quite null length. The development of this instrument much interests the definition and the evaluation of the sensor cores of the gradiometer. The in flight calibration process of both instruments is also very similar. Lessons form these parallel developments are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Autonomous orbit determination using epoch-differenced gravity gradients and starlight refraction

Autonomous orbit determination via integration of epoch-differenced gravity gradients and starlight refraction is proposed in this paper for low-Earth-orbiting satellites operating in GPS-denied environments.Starlight refraction compensates for the significant along-track position error that occurs from only using gravity gradients and benefits from integration in terms of improved accuracy in radial and cross-track position estimates.The between-epoch differencing of gravity gradients is employed to eliminate slowly varying measurement biases and noise near the orbit revolution frequency.The refraction angle measurements are directly used and its Jacobian matrix derived from an implicit observation equation.An information fusion filter based on a sequential extended Kalman filter is developed for the orbit determination.Truth-model simulations are used to test the performance of the algorithm,and the effects of differencing intervals and orbital heights are analyzed.A semi-simulation study using actual gravity gradient data from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) combined with simulated starlight refraction measurements is further conducted,and a three-dimensional position accuracy of better than 100 m is achieved.     

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.     

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.     

Airborne platform capability assessment

It is expected that the multimode weapons systems of the future will be highly fault tolerant, possessing the ability to perform tactical missions with both full or degraded functional capabilities. The fault-tolerant system characteristics will allow systems with less than the fully specified functional capabilities to be engaging in combat. This design feature will present the operators of these weapons system with the operational challenge of selecting and/or assigning weapons platforms with degraded capabilities to carry out tactical missions. An in-system assessment process is proposed to evaluate the operability for these weapons platforms on the basis of current functional status, the reliability of the hardware resources within the system's avionics, and the resources required by the various application modes to accomplish mission tasks