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1. Adam, D , 2002 :
   Gravity measurement: Amazing grace .
   NATURE 416 10 - 11
2. Aguirre-Martinez, M; Sneeuw, N , 2003 :
   Needs and tools for future gravity measuring missions .
   SPACE SCIENCE REVIEWS 108 409 - 416

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.

3. Balmino, G , 2003 :
   Gravity field recovery from GRACE: Unique aspects of the high precision inter-satellite data and analysis methods .
   SPACE SCIENCE REVIEWS 108 47 - 54

The very high accuracy of the Doppler and range measurements between the two low-flying and co-orbiting spacecraft of the GRACE mission, which will be at the mum/sec and similar to10 mum levels respectively, requires that special procedures be applied in the processing of these data. Parts of the existing orbit determination and gravity field parameters retrieval methods and software must be modified in order to fully benefit from the capabilities of this mission. This is being done in the following areas: (i) numerical integration of the equations of motion (summed form, accuracy of the predictor-corrector loop, Encke's formulation); (ii) special inter-satellite dynamical parameterization for very short arcs; (iii) accurate solution of large least-squares problems (normal equations vs. orthogonal decomposition of observation equations); (iv) handling the observation equations with high accuracy. Theoretical concepts and first tests of some of the newly implemented algorithms are presented.

4. Balmino, G , 2001 :
   New space missions for mapping the Earth's gravity field .
   COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE IV PHYSIQUE ASTROPHYSIQUE 2 1353 - 1359

The knowledge of the gravity field of the Earth and of an associated reference surface of altitudes (the geoid) is necessary for geodesy, for improving theories of the, physics of the planet interior and for modeling the ocean circulation in absolute. This knowledge comes from several observing techniques but, although it benefited: from the artificial satellite approach, it remains incomplete and erroneous in places. Within a reasonable future, a substantial improvement can only come from new space techniques. Thanks: to the intense lobbying by the concerned geoscientists, the coming decade will see the advent of three techniques already proposed in the seventies and to be implemented by different space agencies these are the CHAMP, GRACE and GOCE missions. (C) 2001 Academic des sciences/Editions scientifiques et medicales Elsevier SAS.

5. Bender, PL; Nerem, RS; Wahr, JM , 2003 :
   Possible future use of laser gravity gradiometers .
   SPACE SCIENCE REVIEWS 108 385 - 392

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 et 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.

6. Bond, P , 2003 :
   Gravity map from GRACE .
   ASTRONOMY & GEOPHYSICS 44 4 - 4
7. Bouman, J; Koop, R , 2003 :
   Geodetic methods for calibration of GRACE and GOCE .
   SPACE SCIENCE REVIEWS 108 293 - 303

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.

8. Boy, JP; Chao, BF , 2002 :
   Time-variable gravity signal during the water impoundment of China's Three-Gorges Reservoir .
   GEOPHYSICAL RESEARCH LETTERS 29 - 2200

[1] Beginning in 2003, China's Three-Gorges Reservoir will start water impoundment in phases. By 2009, it will be holding 40 km 3 of water, flooding a stretch of middle Yangtze River about 600 km in length. The water impoundment process represents a geophysical "controlled experiment'' offering a unique opportunity for detailed studies of a classical forward/inverse modeling problem of surface loading. While Wang [2000] studied the large loading effects on a local scale, we aim for longer spatial scales upwards from several hundred km, specially on the time-variable gravity signals that can be detected by the newly-launched GRACE satellite mission, whose 5-year lifetime (until 2007) will span the major impoundment period. Our results using the Green's function method adopting the PREM elastic Earth model indicate that the per-year geoid height increase is above the GRACE observational sensitivity out to harmonic degree 20, and to degree 50 (corresponding to a wavelength of 800 km) when integrated over the 5-year period.

9. Chen, JL; Wilson, CR , 2003 :
   Low degree gravitational changes from earth rotation and geophysical models .
   GEOPHYSICAL RESEARCH LETTERS 30 - 2257

Spherical harmonic degree 2 gravitational variations DeltaC(21), DeltaS(21), and DeltaC(20) are estimated from accurately measured Earth rotational changes and compared with predictions from atmospheric, oceanic, and hydrological models. Earth rotation-derived changes agree very well with model predictions over a broad frequency band, and particularly well at intraseasonal and seasonal time scales. The agreement is significantly better compared to previous studies, due mainly to improved oceanic and hydrological models. An independent determination of degree 2 changes serves as an important constraint for satellite-based estimates such as those of the Gravity Recovery and Climate Experiment (GRACE) mission.

10. Cheng, MK , 2002 :
    Gravitational perturbation theory for intersatellite tracking .
    JOURNAL OF GEODESY 76 169 - 185

An analytical gravitational perturbation theory for the intersatellite tracking range and range-rate measurement between two satellites is developed. The satellite-to-satellite tracking (SST) range data measure the difference between the position perturbations of two satellites along the direction of the intersatellite range. The SST range-rate data measure the difference between the velocity perturbations along the direction of the intersatellite range, and the difference of the position perturbation along the direction perpendicular to the intersatellite range (cross-range). The SST range and range rate depend on different orbital excitations for mapping the gravity field. For the Gravity Recovery and Climate Experiment (GRACE), approximately 97% of the geopotential coefficient pairs produce perturbations with a root-mean-square larger than I pm on the range and 0.1 mum/sec on the range rate based on the EGM96 gravity field truncated at degree and order 140. Results in this study showed that ocean tides produce significant perturbations in the range and range-rate measurements. An ocean tide field with a higher degree and order (>70) is required to model the ocean tide perturbations on the intersatellite range and range-rate measurement.

11. Damerow, H; Schwarz, J , 2003 :
    Satellite data reception system at multimission ground station .
    ACTA ASTRONAUTICA 52 753 - 756

The data reception of earth observation satellites and small satellites as well as the processing, archiving and distribution of the received data are the main activities of the National Ground Segment in Neustrelitz. There are two 7.3m antennas available for data reception at S- and X-band frequencies and additionally one 4m antenna for L- and S-Band. The ground station enables a daily and operational data reception of the missions ERS-2, LANDSAT-7, IRS-1C, IRS-1D, IRS-P3 and CHAMP. The data reception of the satellites ENVISAT, GRACE, BIRD and CORONAS-F will start in 2001. Therefore the station has been improved continuously under aspects of automatior, flexibility and redundancy. Quality information from all components is collected and stored during the satellite pass. The internal procedures are unified for all mission projects. A software system for station control and management was realized, which integrates the antennas and their RF components, all demodulators and bitsyncronizers and partly the data recording components in a unified system. (C) 2003 Published by Elsevier Science Ltd.

12. Foldvary, L; Fukuda, Y , 2001 :
    IB and NIB hypotheses and their possible discrimination by GRACE .
    GEOPHYSICAL RESEARCH LETTERS 28 663 - 666

The NASA, the GFZ and the DLR plan the GRACE satellite mission to obtain an accurate gravity field after every 2-4 weeks. Because of its extreme high precision, GRACE is expected to determine the temporal variations of the gravity fields due to time varying geophysical phenomena. Among them, the effects of the atmospheric surface pressure have the largest signals and we investigated its effects mainly from the viewpoint of degree amplitudes. Behaviour of atmospheric variations over oceanic areas is unknown. The response of the ocean is essentially important not only for the corrections of the atmospheric effects on gravity fields, but also for many other studies such as satellite altimetry, crustal deformation and the Earth rotations. We proposed and applied several ocean response models, i.e., IB, NIB, and intermediate ones, and evaluated the degree power differences between each one of them. The results show that almost all the differences are distinguishable by GRACE.

13. Ganachaud, A; Mercier, H , 2002 :
    Ocean response to meridional ekman transport in the Atlantic and implication for gravity missions .
    GEOPHYSICAL RESEARCH LETTERS 29 - 2145

[1] Wind friction at the ocean surface introduces energetic variations in the net mass transport across the oceanic basins. To conserve mass, the whole water column adjusts rapidly, introducing a depth-independent perturbation in the pressure field. This signal is analyzed in a high resolution numerical model of the Atlantic Ocean. While the pressure perturbation cannot be extracted from the energetic sea surface height signals, it represents up to 90% of the bottom pressure signal when integrated across the Atlantic Ocean in the daily and monthly frequencies. This signal will be an important part of the signal measured by the GRACE (Gravity Recovery And Climate Experiment) mission.

14. Hughes, CW; Stepanov, V , 2003 :
    Feasibility, and contribution to ocean circulation studies, of ocean bottom pressure determination .
    SPACE SCIENCE REVIEWS 108 217 - 224

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.

15. Ilk, KH; Kusche, J; Rudolph, S , 2002 :
    A contribution to data combination in ill-posed downward continuation problems .
    JOURNAL OF GEODYNAMICS 33 75 - 99

The spaceborne gravity field missions CHAMP, GRACE and GOCE, to be realized in the coming years, will improve our knowledge of the Earth's gravity field in the short, medium and long wavelength parts. Nevertheless, it is necessary to supplement this gravity field information with available terrestrial data. While the combination of data of different origin is comparably well-understood in well-posed problems there are some open questions in combining satellite derived and terrestrial data sets in the case of improperly posed problems, In this investigation, the future satellite missions are shortly characterized. The downward continuation process and its regularization based on Tikhonov's regularization method is reviewed, The test strategies to detect the contributions of satellite derived and terrestrial gravity field information applied in this investigation are summarized. A detailed simulation based on a GRACE-type SST mission scenario and additional terrestrial data with the task to derive parameters of a gravity field representation by local base functions is performed. The investigation tries to tackle a clarification of various questions related to the data combination by numerical tests. (C) 2002 Elsevier Science Ltd. All rights reserved.

16. Iorio, L , 2003 :
    The impact of the static part of the Earth's gravity field on some tests of general relativity with satellite laser ranging .
    CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY 86 277 - 294

In this paper we calculate explicitly the classical secular precessions of the node Omega and the perigee omega of an Earth artificial satellite induced by the even zonal harmonics of the static part of the geopotential up to degree l = 20. Subsequently, their systematic errors induced by the mismodelling in the even zonal spherical harmonics coefficients J(l) are compared to the general relativistic secular gravitomagnetic and gravitoelectric precessions of the node and the perigee of the existing laser-ranged geodetic satellites and of the proposed LARES. The impact of the future terrestrial gravity models from CHAMP and GRACE missions is discussed as well. Preliminary estimates with the recently released EIGEN-1S gravity model including the first CHAMP data are presented.

17. Iorio, L , 2002 :
    A critical approach to the concept of a polar, low-altitude LARES satellite .
    CLASSICAL AND QUANTUM GRAVITY 19 L175 - L183

According to very recent developments of the LARES mission, which is devoted to the measurement of the general relativistic Lense-Thirring effect in the gravitational field of the Earth with satellite laser ranging, it seems that the LARES satellite might be finally launched in a polar, low-altitude orbit by means of a relatively low-cost rocket. The observable would be the node only. The Lense-Thirring effect on it would consist of a secular linear trend. The biasing classical secular nodal precessions due to the even zonal harmonics of the geopotential, which represent the major source of uncertainty, vanish if and only if the orbit is exactly polar. Due to the small altitude, even small possible deviations from the projected inclination, which might be induced by the orbital injection errors, should yield a rather large systematic error due to the mismodelled even zonal harmonics of geopotential in the measurement of the relativistic nodal shift. So, in this paper we show how such a configuration, in fact, to the present level of knowledge of the terrestrial gravitational field according to the EGM96 gravity model, should be of relatively little utility in increasing the obtainable accuracy in measuring the Lense-Thirring effect with respect not only to the originally proposed supplementary LARES-LAGEOS configuration, but also to the present LAGEOS-LAGEOS II experiment which has a total accuracy of the order of 20-30%. Maybe the situation will improve, at least to a certain extent, when the new, more accurate Earth gravity models from the CHAMP and GRACE missions become available.

18. Iorio, L , 2002 :
    Constraints on a Yukawa gravitational potential from laser data of LAGEOS satellites .
    PHYSICS LETTERS A 298 315 - 318

In this Letter we investigate the possibility of constraining the hypothesis of a fifth force at the length scale of two Earth's radii by investigating the effects of a Yukawa gravitational potential on the orbits of the laser-ranged LAGEOS and LAGEOS II satellites. The existing constraints on the Yukawa coupling a, obtained by fitting the LAGEOS orbit, are of the order of \alpha\ < 10(-5)-10(-8) for distances of the order of 10(9) cm. Here we show that with a suitable combination of LAGEOS and LAGEOS It data it should be possible to constrain alpha at a level of 4 x 10(-12) or less. Various sources of systematic errors are accounted for, as well. Their total impact amounts to 1 x 10(-11) during an observational time span of 5 years. In the near future, when the new data on the terrestrial gravitational field will be available from the CHAMP and GRACE missions, these limits will be further improved. The use of the proposed LARES laser-ranged satellite would yield an experimental accuracy in constraining a of the order of 1 x 10(-12). (C) 2002 Elsevier Science B.V. All rights reserved.

19. Iorio, L; Ciufolini, I; Pavlis, EC , 2002 :
    Measuring the relativistic perigee advance with satellite laser ranging .
    CLASSICAL AND QUANTUM GRAVITY 19 4301 - 4309

The pericentric advance of a test body by a central mass is one of the classical tests of general relativity. Today, this effect is measured with radar ranging by the perihelion shift of Mercury and other planets, in the gravitational field of Sun, with a relative accuracy of the order of 10(-2)-10(-3). In this paper, we explore the possibility of a measurement of the pericentric advance in the I gravitational field of Earth by analysing the laser-ranged data of some orbiting, or proposed, laser-ranged geodetic satellites. Such a measurement of the perigee advance would place limits on hypothetical, very weak, Yukawa-type components of the gravitational interaction, with a finite range of the order of 104 km. Thus, we show that, at the I present level of knowledge of the orbital perturbations, the relative accuracy, achievable with suitably combined orbital elements of LAGEOS and LAGEOS II, is of the order of 10(-3). With the corresponding measured value of (2 + 2gamma - beta)/3, by using eta = 4beta - gamma - 3 from lunar laser ranging, we could get an estimate of the PPN parameters gamma and beta with an accuracy of the order of 10(-2)-10(-3). Nevertheless, these accuracies would be substantially improved in the near future with the new Earth gravity field models by the CRAMP and GRACE missions. The use of the perigee of LARES (LAser RElativity Satellite), with a suitable combination of orbital residuals including also the node and the perigee of LAGEOS II, would also further improve the accuracy of the proposed measurement.

20. Iorio, L; Lucchesi, D , 2003 :
    LAGEOS-type satellites in critical supplementary orbit configuration and the Lense-Thirring effect detection .
    CLASSICAL AND QUANTUM GRAVITY 20 2477 - 2490

In this paper we analyse quantitatively the concept of LAGEOS-type satellites in critical supplementary orbit configuration (CSOC) which has proved capable of yielding various observables for many tests of general relativity in the terrestrial gravitational field, with particular emphasis on the measurement of the Lense-Thirring effect. By using an entirely new pair of LAGEOS-type satellites in identical, supplementary orbits with, e.g., semimajor axes a = 12 000 kin, eccentricity e = 0.05 and inclinations is, = 63.4degrees and i(S2) = 116.6degrees, it would be possible to cancel out the impact of the mismodelling of the static part of the gravitational field of the Earth to a very high level of accuracy. The departures from the ideal supplementary orbital configuration due to the orbital injection errors would yield systematic gravitational errors of the order of a few per cent, according to the covariance matrix of the EGM96 gravity model up to degree l = 20. However, the forthcoming, new gravity models from the CHAMP and GRACE missions should greatly improve the situation. So, it should be possible to measure the gravitomagnetic shifts of the sum of their nodes Sigma(Omega) over dot(LT) with an accuracy level perhaps less than 1%, of the difference of their perigees Delta(omega) over dot(LT) with an accuracy level of 5% and of (X) over dot(LT) = Sigma(Omega) over dot(LT) - Delta(omega) over dot(LT) with an accuracy level of 2.8%. Such results, which are due to the non-gravitational perturbations mismodelling, have been obtained for an observational time span of about 6 years and could be further improved by fitting and removing from the analysed time series the major time-varying perturbations which have known periodicities.

21. Iorio, L; Lucchesi, DM; Ciufolini, I , 2002 :
    The LARES mission revisited: an alternative scenario .
    CLASSICAL AND QUANTUM GRAVITY 19 4311 - 4325

In the original LARES mission, the general relativistic Lense-Thirring effect was to be detected using as an observable the sum of the residuals of the nodes of the existing passive geodetic laser-ranged LAGEOS satellite and of its proposed twin LARES. The proposed nominal orbital configuration of the latter would reduce the systematic error due to the mismodelling in the even zonal harmonics of the geopotential, which is the main source of error (to 0.3%) according to the most recent Earth gravity model EGM96. This observable turns out to be sensitive to possible departures of the LARES orbital parameters from their nominal values due to the orbital injection errors. By adopting a suitable combination of the orbital residuals of the nodes of LAGEOS, LAGEOS II and LARES and the perigees of LAGEOS II and LARES, it should be possible to reduce the error due to the geopotential by one order of magnitude, according to the EGM96 model. Moreover, the sensitivity to the orbital injection errors should be greatly reduced. According to a preliminary estimate of the error budget, the total error of the experiment should be reduced to less than 1%. In the near future, when the new data on, the terrestrial gravitational field from CHAMP and GRACE missions become available, a further increase in the accuracy should be obtained. The proposal to place LARES in a polar 2000 km altitude orbit and consider only its nodal rate would present the drawback that even small departures from the polar geometry would yield notable errors due to the mismodelled even zonal harmonics of the geopotential, according to the EGM96 model.

22. Jekeli, C , 1999 :
    The determination of gravitational potential differences from satellite-to-satellite tracking .
    CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY 75 85 - 101

A new, rigorous model is developed for the difference of gravitational potential between two close earth-orbiting satellites in terms of measured range-rates, velocities and velocity differences, and specific forces. It is particularly suited to regional geopotential determination from a satellite-to-satellite tracking mission. Based on energy considerations, the model specifically accounts for the time variability of the potential in inertial space, principally due to earth's rotation. Analysis shows the latter to be a significant (+/- 1 m(2)/s(2)) effect that overshadows by many orders of magnitude other time dependencies caused by solar and lunar tidal potentials. Also, variations in earth rotation with respect to terrestrial and celestial coordinate frames are inconsequential. Results of simulations contrast the new model to the simplified linear model (relating potential difference to range-rate) and delineate accuracy requirements in velocity vector measurements needed to supplement the range-rate measurements. The numerical analysis is oriented toward the scheduled Gravity Recovery and Climate Experiment (GRACE) mission and shows that an accuracy in the velocity difference vector of 2 x 10(-5) m/s would be commensurate within the model to the anticipated accuracy of 10(-6) m/s in range-rate.

23. Johnson, TJ; Wilson, CR; Chao, BF , 2001 :
    Nontidal oceanic contributions to gravitational field changes: Predictions of the Parallel Ocean Climate Model .
    JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH 106 11315 - 11334

This study examines the nontidal contributions of the oceans to the Earth's gravitational field variations as predicted by a global ocean general circulation model: the Parallel Ocean Climate Model. Such variations in the gravitational field Stokes coefficient are determined up to spherical harmonic degree and order 20 and compared with satellite laser ranging (SLR) data from LAGEOS I and LAGEOS II. For most Stokes coefficients except the lowest-degree ones, this investigation indicates that the application of sea level adjustment to reduce the effects of the model's lack of mass conservation due to the Boussinesq approximation has a negligible effect on timescales less than a few years. Predicted gravitational changes show strong seasonal variability and account for a portion of the variations estimated from SLR. We conclude that, in addition to the atmosphere, the oceans are an important contributor to the temporal variations in the Earth's gravitational field. The Stokes coefficients are useful in examining oceanic mass transport between hemispheres and ocean basins. The estimated oceanic power spectrum has a spectral shape similar to the atmosphere and is well above the noise level of planned satellite missions like the Gravity Recovery and Climate Experiment (GRACE).

24. Kang, Z; Nagel, P; Pastor, R , 2003 :
    Precise orbit determination for GRACE .
    INTEGRATED SPACE GEODETIC SYSTEMS AND SATELLITE DYNAMICS ADVANCES IN SPACE RESEARCH 31 1875 - 1881

The twin, co-orbiting GRACE (Gravity Recovery and Climate Experiment) satellites were launched in March 2002. The primary objective of the GRACE mission is to determine the Earth's gravity field and its temporal variations with unprecedented accuracy. To satisfy this objective as well as other applications (e.g. atmospheric profiling by radio occultation), accurate orbits for GRACE are required. This paper describes several results related to the use of the data collected by the GRACE GPS receiver, high precision accelerometer observations and precise attitude data from star trackers in the application of the GRACE Precise Orbit Determination (POD). The orbit accuracy is assessed using a number of tests, which include analysis of GPS tracking observation residuals, Satellite Laser Ranging (SLR) residuals, K-Band Ranging (KBR) residuals and external orbit comparisons. The results show that an accuracy of better than 5 cm in each direction for GRACE orbits can be obtained. The relative accuracy of the two GRACE satellites is about 1 cm in position and 10 micrometers per second in velocity. (C) 2003 COSPAR. Published by Elsevier Science Ltd. All rights reserved.

25. Kaufmann, G , 2000 :
    Ice-ocean mass balance during the Late Pleistocene glacial cycles in view of CHAMP and GRACE satellite missions .
    GEOPHYSICAL JOURNAL INTERNATIONAL 143 142 - 156

During the last glacial cycles, global sea level dropped several times by about 120 m and large ice sheets covered North America, northern Europe and Antarctica during the glacial stages. The changes in the ice-ocean mass balance have displaced mantle material mainly via viscous flow, and the perturbation of the equilibrium figure of the Earth by glacial isostatic adjustment is still observable today in time-dependent changes of gravitational and rotational observations. Contemporary ice-ocean mass balance from volume changes of polar ice caps also contributes to secular variations of the Earth's gravitational field. In the near future, several satellite gravity missions will significantly improve the accuracy of the observed time-dependent gravitational field. In view of the expected improvements in the observations, we predict glacially induced perturbations of the gravitational field, induced by Late Pleistocene and contemporary ice volume changes, for a variety of radial mantle viscosity profiles. We assess the degree of uncertainty for the glacially induced contributions to gravitational and rotational parameters, both in the spectral and the spatial domain. Predictions of power spectra for the glacially induced free-air gravity and geoid anomalies are about one order of magnitude lower than the observed values, and uncertainties arising from different plausible viscosity profiles are around 0.15-0.4 mGal and 0.2-1.5 m, respectively. Uncertainties from different ice models are of secondary importance for the predicted power spectra. Predicted secular changes in geoid anomalies in formerly glaciated areas are mainly controlled by the viscosity profile and contemporary ice volume changes. We also show that the simple three-layer viscosity profiles currently employed for the majority of postglacial rebound studies represent a limited subset for model predictions of the time-dependent gravitational field.

26. Kern, M; Schwarz, KP; Sneeuw, N , 2003 :
    A study on the combination of satellite, airborne, and terrestrial gravity data .
    JOURNAL OF GEODESY 77 217 - 225

Satellite gravity missions, such as CHAMP, GRACE and GOCE, and airborne gravity campaigns in areas without ground gravity will enhance the present knowledge of the Earth's gravity field. Combining the new gravity information with the existing marine and ground gravity anomalies is a major task for which the mathematical tools have to be developed. In one way or another they will be based on the spectral information available for gravity data and noise. The integration of the additional gravity information from satellite and airborne campaigns with existing data has not been studied in sufficient detail and a number of open questions remain. A strategy for the combination of satellite, airborne and ground measurements is presented. It is based on ideas independently introduced by Sjoberg and Wenzel in the early 1980s and has been modified by using a quasi-deterministic approach for the determination of the weighting functions. In addition, the original approach of Sjoberg and Wenzel is extended to more than two measurement types, combining the Meissl scheme with the least-squares spectral combination. Satellite (or geopotential) harmonics, ground gravity anomalies and airborne gravity disturbances are used as measurement types, but other combinations are possible. Different error characteristics and measurement-type combinations and their impact on the final solution are studied. Using simulated data, the results show a geoid accuracy in the centimeter range for a local test area.

27. Knudsen, P , 2003 :
    Ocean tides in GRACE monthly averaged gravity fields .
    SPACE SCIENCE REVIEWS 108 261 - 270

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 S-2 and the K-2 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.

28. Knudsen, P; Andersen, O , 2002 :
    Correcting GRACE gravity fields for ocean tide effects .
    GEOPHYSICAL RESEARCH LETTERS 29 - 1178

[1] The GRACE mission will be launch in early 2002 and 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. The difference between two existing ocean tide models can be used as an estimate of current tidal model error for the M-2,S-2,K-1, and O-1 constituents. When compared with the expected accuracy of the GRACE system, both expressed as spherical harmonic degree variances, we find that the current ocean tide models are not accurate enough to correct GRACE data at harmonic degrees lower that 35. The accumulated tidal errors may affect the GRACE data up to harmonic degree 56. Furthermore, the atmospheric (radiation) tides may cause significant errors in the ocean tide model if altimetry corrected for inverted barometer effects was used in its derivation. To study the temporal characteristics of the ocean tidal constituents when sampled by GRACE, approximate alias frequencies were derived assuming a sampling of half a sidereal day. Those results show that the ocean tide errors will not cancel in the GRACE monthly averaged temporal gravity fields. The S-2 and the K-2 terms have alias frequencies much longer than 30 days, so they remain almost unreduced in the monthly averages.

29. Koch, KR; Kusche, J , 2002 :
    Regularization of geopotential determination from satellite data by variance components .
    JOURNAL OF GEODESY 76 259 - 268

Different types of present or future satellite data have to be combined by applying appropriate weighting for the determination of the gravity field of the Earth, for instance GPS observations for CHAMP with satellite to satellite tracking for the coming mission GRACE as well as gradiometer measurements for GOCE. In addition, the estimate of the geopotential has to be smoothed or regularized because of the inversion problem. It is proposed to solve these two tasks by Bayesian inference on variance components. The estimates of the variance components are computed by a stochastic estimator of the traces of matrices connected with the inverse of the matrix of normal equations, thus leading to a new method for determining variance components for large linear systems. The posterior density function for the variance components, weighting factors and regularization parameters are given in order to compute the confidence intervals for these quantities. Test computations with simulated a,,radiometer observations for GOCE and satellite to satellite tracking for GRACE show the validity of the approach.

30. Konig, R; Reigber, C; Neumayer, KH; Schmidt, R; Zhu, S; Baustert, G; Flechtner, F; Meixner, H , 2003 :
    Satellite dynamics of the CHAMP and GRACE LEOs as revealed from space- and ground-based tracking .
    INTEGRATED SPACE GEODETIC SYSTEMS AND SATELLITE DYNAMICS ADVANCES IN SPACE RESEARCH 31 1869 - 1874

The Low Earth Orbiters (LEOs) CHAMP and GRACE are precisely and continuously tracked by means of space-borne GPS. In case of the GRACE mission the distance between the twin satellites is also measured by a micrometer-precision ranging system. Thus the satellite dynamics are densely recorded and show up in the tracking residuals of the various data types in a dynamic Precise Orbit Determination (POD) solution. The signatures in the residuals time series axe mainly caused by mis-modeling of the gravity field because the non-conservative forces such as atmospheric drag are taken care of by the on-board accelerometers. In addition all satellites carry laser retro-reflectors for centimeter accuracy range measurements from the ground. Examples of gravity signals in the residuals are displayed and discussed in view of the gravity field recovery and the POD tasks. (C) 2003 COSPAR. Published by Elsevier Science Ltd. All rights reserved.

31. Kusche, J , 2002 :
    On fast multigrid iteration techniques for the solution of normal equations in satellite gravity recovery .
    JOURNAL OF GEODYNAMICS 33 173 - 186

Dedicated satellite-to-satellite tracking (SST) or gradiometry missions like GRACE and GOCE will provide gravity field information with unprecedented resolution and precision. It has been recognized that better gravity field models and estimates of the geoid are useful for a wide range of research and application, including ocean circulation and climate change studies, physics of the Earth's interior and height datum connection and unification. The computation of these models will require the solution of large and non-sparse normal equation systems. especially if "brute force" approaches are applied. Evidently, there is a need for fast solvers. The multigrid approach is not only art extremely fast iterative solution technique. it yields, en passant, a well-defined sequence of coarser approximations as a byproduct to the final gravity field solution. We investigate the implementation of multigrid methods to satellite data analysis using space-domain representations of the anomalous gravity field. Multigrid algorithms are considered as stand-alone solvers as well as for the construction of preconditioners in the conjugate gradient technique. Out' numerical results, concerning two regional gravity inversions from simulated GRACE and GOCE data, show that multigrid solvers run much faster than conjugate gradient solvers with conventional preconditioners. (C) 2002 Elsevier Science Ltd. All rights reserved.

32. Kusche, J , 2001 :
    Implementation of multigrid solvers for satellite gravity anomaly recovery .
    JOURNAL OF GEODESY 74 773 - 782

Dedicated SST - or gradiometry missions like GRACE and GOCE will provide gravity field information of unprecedented resolution and precision. It has been recognized that better gravity field models and estimates of the geoid are useful for a wide range of research and application, including ocean circulation and climate change studies, physics of the earth's interior and height datum connection and unification. The computation of these models will require the solution of large and non-sparse normal equation systems, especially if "brute force" approaches are applied. Evidently there is a need for fast solvers. The multigrid approach is not only an extremely fast iterative solution technique, it yields en passant a well-defined sequence of coarser approximations as a byproduct to the final gravity field solution. We investigate the implementation of multigrid methods to satellite data analysis using space-domain representations of the anomalous gravity field. Theoretical and numerical aspects are covered. Multigrid algorithms are applied as stand-alone solvers as well as for the construction of preconditioners in the conjugate gradient technique. Our numerical results, concerning a regional gravity inversion from simulated GRACE data, show that multigrid solvers run much faster than conjugate gradient solvers with conventional preconditioners.

33. Le Meur, E; Huybrechts, P , 2001 :
    A model computation of the temporal changes of surface gravity and geoidal signal induced by the evolving Greenland ice sheet .
    GEOPHYSICAL JOURNAL INTERNATIONAL 145 835 - 849

This paper deals with present-day gravity changes in response to the evolving Greenland ice sheet. We present a detailed computation from a 3-D thermomechanical ice sheet model that is interactively coupled with a self-gravitating spherical viscoelastic bedrock model. The coupled model is run over the last two glacial cycles to yield the loading evolution over time. Based on both the ice sheet's long-term history and its modern evolution averaged over the last 200 years, results are presented of the absolute gravity trend that would arise from a ground survey and of the corresponding geoid rate of change a satellite would see from space. The main results yield ground absolute gravity trends of the order of +/-1 mu gal yr(-1) over the ice-free areas and total geoid changes in the range between - 0.1 and + 0.3 mm yr(-1). These estimates could help to design future measurement campaigns by revealing areas of strong signal and/or specific patterns, although there are uncertainties associated with the parameters adopted for the Earth's rheology and aspects of the ice sheet model, Given the instrumental accuracy of a particular surveying method, these theoretical trends could also be useful to assess the required duration of a measurement campaign. According to our results, the present-day gravitational signal is dominated by the response to past loading changes rather than current mass changes of the Greenland ice sheet. We finally discuss the potential of inferring the present-day evolution of the Greenland ice sheet from the geoid rate of change measured by the future geodetic GRACE mission. We find that despite the anticipated high-quality data from satellites, such a method is compromised by the uncertainties in the earth model, the dominance of isostatic recovery on the current bedrock signal, and other inaccuracies inherent to the method itself.

34. Le Provost, C; Bremond, M , 2003 :
    Resolution needed for an adequate determination of the mean ocean circulation from altimetry and an improved geoid .
    SPACE SCIENCE REVIEWS 108 163 - 178

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.

35. LeGrand, P , 2001 :
    Impact of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission on ocean circulation estimates. Volume fluxes in a climatological inverse model of the Atlantic .
    JOURNAL OF GEOPHYSICAL RESEARCH-OCEANS 106 19597 - 19610

The Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission, by providing a precise estimate of the marine geoid height, will allow the determination of absolute geostrophic velocities at the surface of the ocean with unprecedented accuracy. The resulting impact on oceanic flux estimates is quantified within a climatological inverse model of the Atlantic in terms of reduction of uncertainties in volume transports. These uncertainty reductions are obtained by replacing the error spectrum of present-day geoid models by the error spectrum expected for the GOCE mission. The impact is large in the Circumpolar Current, with relative uncertainty reductions reaching 50% in the upper layers of the ocean, and 40% in the whole water column. It is also large in regions of sharp oceanic fronts like the Gulf Stream or the Brazil Current, with uncertainty reductions reaching 60% in the upper layers of the ocean. The reduction in transport uncertainties is large enough in absolute terms to have a significant impact on estimates of important climate processes like the rate of overturning in the Atlantic or the exchange of water between the Circumpolar Current and the South Atlantic. The impact of the Gravity Recovery and Climate Experiment (GRACE) mission, estimated within the same inverse model, is on average less than half the impact of GOCE because of the lower precision of this mission at small spatial scales. The fact that uncertainties in the baroclinic component of the velocity field limit the impact of GOCE at depths points to the need for precise in situ observations to complement gravity and altimetric observations.

36. Leuliette, EW; Nerem, RS; Russell, GL , 2002 :
    Detecting time variations in gravity associated with climate change .
    JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH 107 - 2112

[1] General circulation models offer a way to estimate the impact of mass redistributions on the Earth's time-varying gravity field. In this way, the prospects for detecting climate signals in the gravity field by dedicated satellite gravity missions, such as Gravity Recovery and Climate Experiment (GRACE), can be assessed. Using monthly averaged fluid mass diagnostics from a coupled atmosphere-ocean model developed at the Goddard Institute for Space Studies (GISS), we have estimated geoid variations from the fundamental model mass components. From these estimates the seasonal geoid signals from sea level, snow, soil moisture, water vapor, and atmospheric mass can be compared to the estimated errors for GRACE. All of these seasonal mass flows from the GISS model are well above the preliminary GRACE measurement errors. In addition, mass flows with significant secular trends attributable to the model's simulated increase of greenhouse gases would, in principle, be detectable by GRACE. However, the interannual variability of mass flows may require longer time series of gravity data, pattern analysis, or modeling improvements in order to detect trends.

37. Levi, BG , 2003 :
    GRACE satellites start to map Earth's gravity field .
    PHYSICS TODAY 56 18 - 18
38. Losch, M; Redler, R; Schroter, J , 2002 :
    Estimating a mean ocean state from hydrography and sea-surface height data with a nonlinear inverse section model: Twin experiments with a synthetic dataset .
    JOURNAL OF PHYSICAL OCEANOGRAPHY 32 2096 - 2112

The recovery of the oceanic flow field from in situ data is one of the oldest problems of modern oceanography. In this study, a stationary, nonlinear inverse model is used to estimate a mean geostrophic flow field from hydrographic data along a hydrographic section. The model is augmented to improve these estimates with measurements of the absolute sea-surface height by satellite altimetry. Measurements of the absolute sea-surface height include estimates of an equipotential surface, the geoid. Compared to oceanographic measurements, the geoid is known only to low accuracy and spatial resolution, which restricts the use of sea-surface height data to applications of large-scale phenomena of the circulation. Dedicated satellite missions that are designed for high precision, high-resolution geoid models are planned and/or in preparation. This study, which relies on twin experiments, assesses the important contribution of improved geoid models to estimating the mean flow field along a hydrographic section. When the sea-surface height data are weighted according to the error estimates of the future highly accurate geoid models GRACE (Gravity Recovery And Climate Experiment) and GOCE (Gravity Field and Steady-State Ocean Circulation Explorer), integrated fluxes of mass and temperature can be determined with an accuracy that is improved over the case with no sea-surface height data by up to 55%. With the error estimates of the currently best geoid model EGM96, the reduction of the estimated flux errors does not exceed 18%.

39. Nerem, RS; Eanes, RJ; Thompson, PF; Chen, JL , 2000 :
    Observations of annual variations of the Earth's gravitational field using satellite laser ranging and geophysical models .
    GEOPHYSICAL RESEARCH LETTERS 27 1783 - 1786

We have analyzed 6 years of satellite laser ranging (SLR) data to the Lageos 1 & 2 satellites to determine the annual variation of a set of spherical harmonic coefficients of the Earth's gravity field complete to degree and order 4 (half-wavelength resolution of similar to 5000 km). We have compared these results to a suite of geophysical models describing annual variations of the gravity field due to changes in the distribution of mass in the atmosphere, in the ocean, and continental hydrology (soil moisture and snow). We find that spherical harmonic coefficients derived from the satellite-observations and the aggregate of these geophysical models agree to about 1 mm RMS in geoid height, and have degree correlations that generally exceed the 90% confidence limit. We found that the SLR data could distinguish between two different hydrologic models, but were unable to distinguish between competing models of atmosphere and ocean mass variation, probably due to the small magnitude of the differences in these models (and the small total magnitude of the ocean signal) at the long wavelengths that can be observed by the satellite data. The satellite results should improve considerably in 2001 with the launch of the Gravity Recovery and Climate Experiment (GRACE), which will allow the determination of the time variations of the Earth's gravity field with a spatial resolution of about 300 km.

40. Nerem, RS; Wahr, JM; Leuliette, EW , 2003 :
    Measuring the distribution of ocean mass using GRACE .
    SPACE SCIENCE REVIEWS 108 331 - 344

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 TOPER/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 similar to500 km and an accuracy of similar to3 mm water equivalent. It should be possible to recover global mean ocean mass variations to an accuracy of similar to 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.

41. Oberndorfer, H; Muller, J; Rummel, R; Sneeuw, N , 2002 :
    A simulation tool for the new gravity field satellite missions .
    NEW TRENDS IN SPACE GEODESY ADVANCES IN SPACE RESEARCH 30 227 - 232

In the new decade three important gravity missions will measure the Earth's gravity field: CHAMP, GRACE and GOCE. As main sensor of these three missions accelerometers are used for measuring the non-gravitational disturbance acceleration of the satellites. Moreover, in case of GOCE, the observables are acceleration differences between six accelerometers. The accelerometer is modeled by a simulation tool in which orbit dynamics, satellite control systems, accelerometer characteristics and errors are taken into account. This tool allows to verify the projected accelerometer and gradiometer accuracies. The results of the simulator are time series of 'measured' accelerations and their corresponding error power spectral densities. (C) 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved.

42. Peltier, WR , 2002 :
    Global glacial isostatic adjustment: palaeogeodetic and space-geodetic tests of the ICE-4G (VM2) model .
    JOURNAL OF QUATERNARY SCIENCE 17 491 - 510

Analyses of the global process of glacial isostatic adjustment and post-glacial relative sea-level change continue to deliver important insights into Earth system form and process. One successful model of the related phenomenology is based upon a spherically symmetric internal viscoelastic structure for the solid Earth, which has been denoted VM2, and a model of the most recent deglaciation event of the current ice-age, denoted ICE-4G. The primary purpose of this paper is to describe several new a posteriori tests that have recently been performed to further investigate the quality of this global 'solution' to the inverse problem for both mantle viscosity and deglaciation history that is posed by the observables associated with this large-scale geodynamic phenomenon. I focus especially upon the 'misfits' of observations to the theoretical predictions of this model, which I am currently using to further refine its properties, and upon predictions made using it of geophysical signals that should soon become visible in the context of the Gravity Recovery and Climate Experiment (GRACE) satellite mission. Among the required refinements to ICE-4G, one that is necessary to eliminate a recently revealed misfit to space geodetic constraints on the present-day rate of radial motion at the Yellowknife location well to the west of Hudson Bay, and a similar misfit to absolute gravity measurements to the southwest of the Bay, is the insertion of a 'Keewatin Dome' of thick ice centred over Yellowknife with a ridge of ice extending to the south east. In the geomorphological literature, the existence of such a Keewatin Dome previously has been hypothesised but chronological control was lacking on the surface features that suggested its former existence. An important additional constraint that requires the late glacial existence of this important feature consists of new inferences of the Last Glacial Maximum lowstand of the sea from sites in the far field of the main concentrations of land ice. Copyright (C) 2002 John Wiley Sons, Ltd.

43. Peltier, WR , 1999 :
    Global sea level rise and glacial isostatic adjustment .
    GLOBAL AND PLANETARY CHANGE 20 93 - 123

The fact that the ongoing global process of glacial isostatic adjustment (GIA) contributes significantly to present-day observed rates of secular sea level change that are recorded on tide gauges is now rather well established. There is a continuing discussion, however, of the magnitude of the globally averaged rate of relative sea level rise that is residual to this GIA related 'contamination'. Accurate estimation of this residual is clearly important to the understanding of ongoing global change in the earth system. In the analyses presented herein, following a review of the global theory of the GIA process that focuses on the issue of rotational feedback, I begin by revisiting the issue of estimating this residual on the basis of secular sea level change measurements derived from long time series of annually averaged tide gauge recordings. These observations, all from the US east coast, are then decontaminated by subtracting estimates of the GIA effect determined on the basis of analysis of C-14 dated relative sea level histories to infer a (climate related?) residual signal. Also discussed herein, from a global modelling perspective, is the issue of the extent to which a globally averaged rate of sea level rise based upon TOPEX/POSEIDON type altimetric data (or secular gravity field data from the future GRACE mission) is expected to be contaminated by the GIA process. This issue has not been addressed previously and our analyses show that this contamination of the satellite altimeter estimated rate of global sea level rise will also be significantly influenced, locally, by ongoing glacial isostatic adjustment. However, when this signal is averaged over the surface track of TOPEX/POSEIDON we find that the extent to which this instrument's measure of the globally averaged rate of sea level rise is contaminated by the GIA process is small. (C) 1999 Elsevier Science B.V. All rights reserved.

44. Ponte, RM; Ray, RD , 2002 :
    Atmospheric pressure corrections in geodesy and oceanography: A strategy for handling air tides .
    GEOPHYSICAL RESEARCH LETTERS 29 - 2153

Global pressure data are often needed for processing or interpreting modern geodetic and oceanographic measurements. The most common source of these data is the analysis or reanalysis products of various meteorological centers. Tidal signals in these products can be problematic for several reasons, including potentially aliased sampling of the semidiurnal solar tide as well as the presence of various modeling or timing errors. Building on the work of Van den Dool and colleagues, we lay out a strategy for handling atmospheric tides in (re) analysis data. The procedure also offers a method to account for ocean loading corrections in satellite altimeter data that are consistent with standard ocean-tide corrections. The proposed strategy has immediate application to the ongoing Jason-1 and GRACE satellite missions.

45. Ray, RD; Eanes, RJ; Egbert, GD; Pavlis, NK , 2001 :
    Error spectrum for the global M-2 ocean tide .
    GEOPHYSICAL RESEARCH LETTERS 28 21 - 24

The most accurate determinations of the global ocean tides are currently based on altimeter measurements made by the Topex/Poseidon satellite. The error spectrum corresponding to the Mt tidal solution is here estimated, primarily by inverse methods and secondarily by simple differencing of several of the best tidal models. The tidal error spectrum is flatter than the tidal signal spectrum, and it exceeds 10% of the signal at spherical harmonic degree 15 and above. The tide errors also exceed the anticipated sensitivity of the upcoming GRACE satellite gravity mission for all degrees below 40, and possibly below 50.

46. Ray, RD; Rowlands, DD; Egbert, GD , 2003 :
    Tidal models in a new era of satellite gravimetry .
    SPACE SCIENCE REVIEWS 108 271 - 282

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.

47. Rodell, M; Famiglietti, JS , 2002 :
    The potential for satellite-based monitoring of groundwater storage changes using GRACE: the High Plains aquifer, Central US .
    JOURNAL OF HYDROLOGY 263 245 - 256

Groundwater storage in the High Plains aquifer has been steadily decreasing for 50 or more years due to withdrawals for irrigation. This trend has been documented in annually published United States Geological Survey reports of water level changes in the High Plains aquifer. but assessments of groundwater storage changes in other parts of the world are incomplete. NASA's gravity recovery and climate experiment (GRACE) soon may provide an alternative means for monitoring groundwater changes, via satellite remote sensing. That terrestrial water storage changes are likely to be detectable by GRACE satellites has been demonstrated by prior studies, This investigation builds on those studies by evaluating the potential for isolating changes in the groundwater component of terrestrial water storage. In the High Plains, the magnitude of annual groundwater storage changes averaged 19.8 mm between 1987 and 1998. Uncertainty in deriving estimates of High Plains aquifer storage changes from GRACE observations will arise mainly from the removal, via land surface modeling, of the effects of soil moisture changes from the gravity signal. Total uncertainty is predicted to be about 8.7 mm. (C) 2002 Elsevier Science B.V. All rights reserved.

48. Rodell, M; Famiglietti, JS , 2001 :
    An analysis of terrestrial water storage variations in Illinois with implications for the Gravity Recovery and Climate Experiment (GRACE) .
    WATER RESOURCES RESEARCH 37 1327 - 1339

Variations in terrestrial water storage affect weather, climate, geophysical phenomena, and life on land, yet observation and understanding of terrestrial water storage are deficient. However, estimates of terrestrial water storage changes soon may be derived from observations of Earth's time-dependent gravity field made by NASA's Gravity Recovery and Climate Experiment (GRACE). Previous studies have evaluated that concept using modeled soil moisture and snow data. This investigation builds upon their results by relying on observations rather than modeled results, by analyzing groundwater and surface water variations as well as snow and soil water variations, and by using a longer time series. Expected uncertainty in GRACE-derived water storage changes are compared to monthly, seasonal, and annual terrestrial water storage changes estimated from observations in Illinois (145,800 km(2)). Assuming those changes are representative of larger regions, detectability is possible given a 200,000 km(2) or larger area. Changes in soil moisture are typically the largest component of terrestrial water storage variations, followed by changes in groundwater plus intermediate zone storage.

49. Rodell, M; Famiglietti, JS , 1999 :
    Detectability of variations in continental water storage from satellite observations of the time dependent gravity field .
    WATER RESOURCES RESEARCH 35 2705 - 2723

Continental water storage is a key variable in the Earth system that has never been adequately monitored globally. Since variations in water storage on land affect the time dependent component of Earth's gravity field, the NASA Gravity Recovery and Climate Experiment (GRACE) satellite mission, which will accurately map the gravity field at 2-4 week intervals, may soon provide global data on temporal changes in continental water storage. This study characterizes water storage changes in 20 drainage basins ranging in size from 130,000 to 5,782,000 km(2) and uses estimates of uncertainty in the GRACE technique to determine in which basins water storage changes may be detectable by GRACE and how this detectability may vary in space and time. Results indicate that GRACE will likely detect changes in water storage in most of the basins on monthly or longer time steps and that instrument errors, atmospheric modeling errors, and the magnitude of the variations themselves will be the primary controls on the relative accuracy of the GRACE-derived estimates.

50. Rodrigues, M; Foulon, B; Liorzou, F; Touboul, P , 2003 :
    Flight experience on CHAMP and GRACE with ultra-sensitive accelerometers and return for LISA .
    CLASSICAL AND QUANTUM GRAVITY 20 S291 - S300

The challenging drag-free sensor of the Laser Interferometer Space Antenna (LISA) mission is derived from electrostatic accelerometers developed for a long time in ONERA. The LISA sensor includes a gold platinum alloy inertial mass free-floating in space and used as reflectors for the laser interferometer. This test mass should not undergo more than 3 x 10(-15) m s(-2) Hz(-1/2) acceleration at 0.1 mHz. This tremendous performance is not close to what has been reached so far, but should be approached within one order of magnitude with the projected SMART-2 ESA mission by 2006. Meanwhile, ONERA has participated in several space missions with the flight of increasingly sensitive accelerometers. The German CHAMP mission aims at mapping the Earth's magnetic and gravity fields. More than two years data have been accumulated showing a resolution better than 3 x 10(-9) In s(-2) Hz(-1/2) for the accelerometer. With the JPL/NASA GRACE mission launched in March 2002, even more sensitive measurements have been obtained. From these two flight experiments with electrostatic sensors very similar in concept to that of LISA, the accelerometric environment on board a satellite is discussed at nanogravity levels. It is also shown that these first analyses are compatible with the expected LISA performance when the results are extrapolated to the LISA environment, needing femto-gravity levels.

51. Rowlands, DD; Ray, RD; Chinn, DS; Lemoine, FG , 2002 :
    Short-arc analysis of intersatellite tracking data in a gravity mapping mission .
    JOURNAL OF GEODESY 76 307 - 316

A technique for the analysis of low-low intersatellite range-rate data in a gravity mapping mission is explored. The technique is based on standard tracking data analysis for orbit determination but uses a spherical coordinate representation of the 12 epoch state parameters describing the baseline between the two satellites. This representation of the state parameters is exploited to allow the intersatellite range-rate analysis to benefit from information provided by other tracking data types without large simultaneous multiple-datatype solutions. The technique appears especially valuable for estimating gravity from short arcs (e.g. less than 15 minutes) of data. Gravity recovery simulations which use short arcs are compared with those using arcs a day in length. For a high-inclination orbit, the short-arc analysis recovers low-order gravity coefficients remarkably well, although higher-order terms, especially sectorial terms, are less accurate. Simulations suggest that either long or short arcs of the Gravity Recovery and Climate Experiment (GRACE) data are likely to improve parts of the geopotential spectrum by orders of magnitude.

52. Rummel, R , 2003 :
    How to climb the gravity wall .
    SPACE SCIENCE REVIEWS 108 1 - 14

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 attenuation by differential measurement and measurement precision. The latter depends on the performance of the complete sensor system and involves items such as required dynamic range, baseline length, sensor type (ambient temperature or cryogenic), number of test masses, etc. Before any mission profile is to be studied the science issues to be addressed by GRACE and GOCE follow-on missions need to be clarified. Whether further improvement of the quasi-stationary part of the gravity fields is needed depends on the needs in solid earth physics, oceanography and geodesy and on the availability and quality of complementary data. Complementary data are also the key to the adequate use of measurements of temporal variations of gravity, apart from issues such as spatial and temporal data coverage.

53. Rummel, R; Balmino, G; Johannessen, J; Visser, P; Woodworth, P , 2002 :
    Dedicated gravity field missions - principles and aims .
    JOURNAL OF GEODYNAMICS 33 3 - 20

Current knowledge of the Earth's gravity field and its geoid, as derived from various observing techniques and sources, is incomplete. Within a reasonable time, substantial improvement can only come by exploiting new approaches based on satellite gravity observation methods. For this purpose three satellite missions will be realised, starting with CHAMP in 2000, followed by GRACE in 2002 and GOCE in 2004. Typical for all three missions is their extremely low and (almost) polar orbit, continuous and three-dimensional tracking by GPS and their ability to separate non-gravitational from gravitational signal parts. A further amplification of the gravity signal is achieved by inter-satellite tracking between two low orbiters in the case of GRACE and by gravity gradiometry in the case of GOCE. The rationale of GOCE will be discussed in more detail. The missions have a wide range of applications in solid Earth physics.. oceanography, ice research, climatology, geodesy and sea level research. (C) 2002 Elsevier Science Ltd. All rights reserved.

54. Schrama, EJO , 2003 :
    Error characteristics estimated from CHAMP, GRACE and GOCE derived geoids and from satellite altimetry derived mean dynamic topography .
    SPACE SCIENCE REVIEWS 108 179 - 193

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.

55. Schroter, J; Losch, M; Sloyan, B , 2002 :
    Impact of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission on ocean circulation estimates 2. Volume and heat fluxes across hydrographic sections of unequally spaced stations .
    JOURNAL OF GEOPHYSICAL RESEARCH-OCEANS 107 - 3012

[1] Accurate geoids are expected to improve our knowledge of the dynamic sea surface height (SSH) as a mirror of the dynamic state of the oceans. The dedicated Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission will lead to a highly accurate geoid model with a resolution of degree and order 200. We examine the impact of this mission on the assessment of large-scale oceanic mass and heat transports via its expected error characteristics. We do so applying a linear box inverse model and a nonlinear section inverse model to hydrographic data and to (synthetic) SSH data. The results are compared to those obtained when substituting the error estimates of the Gravity Recovery and Climate Experiment (GRACE) mission and the present day Earth Gravitational Model 1996. For the box inverse model we find an average reduction in transport uncertainties of about 9% for GRACE geoid error covariances and about 17% for GOCE over the "hydrography-only'' solution. In both GRACE and GOCE these average percentage improvements are significantly increased when model error is excluded. Summarizing our results and those of the companion parts of this study, we conclude that the GRACE mission reduces the marine geoid uncertainties such that altimetry may become useful for the study of the steady state ocean circulation. The GOCE mission will improve the accuracy of the circulation estimates significantly on the large scales and introduce higher accuracy on shorter wavelengths as well. Furthermore, it will enable us to study individual ocean currents.

56. Sneeuw, N , 2003 :
    Space-wise, time-wise, torus and Rosborough representations in gravity field modelling .
    SPACE SCIENCE REVIEWS 108 37 - 46

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.

57. Swenson, S; Wahr, J , 2003 :
    Monitoring changes in continental water storage with GRACE .
    SPACE SCIENCE REVIEWS 108 345 - 354

The Gravity Recovery and Climate Experiment, GRACE, will enable the recovery of monthly estimates of changes in water storage, on land and in the ocean, averaged over arbitrary regions having length scales of a few hundred km and larger. These data will allow the examination of changes in the distribution of water in the ocean, in snow and ice on polar ice sheets, and in continental water and snow storage. Extracting changes in water storage from the GRACE dataset requires the use of averaging kernels which can isolate a particular region. To estimate the accuracy to which continental water storage changes in a few representative regions may be recovered, we construct a synthetic GRACE dataset from global, gridded models of surface-mass variability. We find that regional changes in water storage can be recovered with rms error less than 1 cm of equivalent water thickness, for regions having areas of 4 x 10(5) km(2) and larger. Signals in smaller regions may also be recovered; however, interpretations of such results require a careful consideration of model resolution, as well as the nature of the averaging kernel.

58. Swenson, S; Wahr, J , 2002 :
    Methods for inferring regional surface-mass anomalies from Gravity Recovery and Climate Experiment (GRACE) measurements of time-variable gravity .
    JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH 107 - 2193

The Gravity Recovery and Climate Experiment, GRACE, will deliver monthly averages of the spherical harmonic coefficients describing the Earth's gravity field, from which we expect to infer time-variable changes in mass, averaged over arbitrary regions having length scales of a few hundred kilometers and larger, to accuracies of better than 1 cm of equivalent water thickness. These data will be useful for examining changes in the distribution of water in the ocean, in snow and ice on polar ice sheets, and in continental water and snow storage. We describe methods of extracting regional mass anomalies from GRACE gravity coefficients. Spatial averaging kernels were created to isolate the gravity signal of individual regions while simultaneously minimizing the effects of GRACE observational errors and contamination from surrounding glacial, hydrological, and oceanic gravity signals. We then estimated the probable accuracy of averaging kernels for regions of arbitrary shape and size.

59. Swenson, S; Wahr, J , 2002 :
    Estimated effects of the vertical structure of atmospheric mass on the time-variable geoid .
    JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH 107 - 2194

The GRACE satellite mission is designed to map the Earth's gravity field at a resolution of a few hundred kilometers every 30 days beginning in 2002. At these timescales, much of the change in the gravity field may be attributed to processes involving the redistribution of water on the surface of the Earth. Contributions from continental water storage, the oceans, and the atmosphere will all be present in the time-varying gravity solutions. Isolating the hydrological and oceanographic signals will first require the removal of the atmospheric component of the gravity field estimates provided by GRACE. The vertical distribution of mass in the atmosphere is typically neglected when calculating the atmospheric gravity signal. We examine the accuracy of this approximation, as well as the accuracies of models which determine idealized atmospheric vertical structure from surface values of temperature and pressure. Using isobaric geopotential height data from a global forecast center to characterize the true atmospheric density distribution, we compute an exact atmospheric gravity signal with which to compare the gravity signal of each of these models. In addition, we examine the effects of including the aspherical component of the Earth's shape when calculating the atmospheric component of the gravity field. Because gravity estimates from GRACE will have limited spatial resolution, we average our results over regions of 200 to 500 km. At these length scales, our results show that using models based solely on surface data can introduce errors in the time variable surface mass signal inferred from GRACE as large as a few millimeters equivalent water thickness, with a global RMS of about 1 mm.

60. Swenson, S; Wahr, J; Milly, PCD , 2003 :
    Estimated accuracies of regional water storage variations inferred from the Gravity Recovery and Climate Experiment (GRACE) .
    WATER RESOURCES RESEARCH 39 - 1223

[1] The satellite Gravity Recovery and Climate Experiment ( GRACE) provides data describing monthly changes in the geoid, which are closely related to changes in vertically integrated terrestrial water storage. Unlike conventional point or gridded hydrologic measurements, such as those from rain gauges, stream gauges, rain radars, and radiometric satellite images, GRACE data are sets of Stokes coefficients in a truncated spherical harmonic expansion of the geoid. Swenson and Wahr [2002] describe techniques for constructing spatial averaging kernels, with which the average change in vertically integrated water storage within a given region can be extracted from a set of Stokes coefficients. This study extends that work by applying averaging kernels to a realistic synthetic GRACE gravity signal derived in part from a large-scale hydrologic model. By comparing the water storage estimates inferred from the synthetic GRACE data with the water storage estimates predicted by the same hydrologic model, we are able to assess the accuracy of the GRACE estimates and to compare the performance of different averaging kernels. We focus specifically on recovering monthly water storage variations within North American river basins. We conclude that GRACE will be capable of estimating monthly changes in water storage to accuracies of better than 1 cm of water thickness for regions having areas of 4.0 . 10(5) km(2) or larger. Accuracies are better for larger regions. The water storage signal of the Mississippi river basin (area = 3.9 . 10(6) km(2)), for example, can be obtained to better than 5 mm. For regional- to global-scale water balance analyses, this result indicates that GRACE will provide a useful, direct measure of seasonal water storage for river-basin water balance analyses; such data are without precedent in hydrologic analysis.

61. Tamisiea, ME; Mitrovica, JX; Milne, GA; Davis, JL , 2001 :
    Global geoid and sea level changes due to present-day ice mass fluctuations .
    JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH 106 30849 - 30863

We predict gravitationally self-consistent global geoid and relative sea level (RSL) perturbations due to present-day melting of ice complexes, including the Antarctic and Greenland ice sheets and a suite of mountain glaciers and ice sheets. Classic analyses of sea level change indicate that these perturbations will depart significantly from eustatic (i.e., geographically uniform) trends [e.g., Woodward, 1888; Farrell and Clark, 1976], although this result has not always been appreciated in modern analyses. Mass flux of individual ice reservoirs will produce unique geometries of sea level change, and this distinctiveness admits the possibility of using global geoid, sea surface, and RSL signatures of recent climate change to infer the ongoing mass balance of each reservoir rather than simply the net mass flux. As an example, we show that perturbations to the geoid arising from noneustatic water loads associated with each ice reservoir are sufficiently large (at low degrees) to be theoretically measurable within 5 years by the GRACE satellite mission. We complete the study by reanalyzing tide gauge data at 23 sites selected by Douglas [1997] in a recent analysis of global RSL rise. Traditionally, estimates of global sea level rise are generated by taking the mean of a set of secular tide gauge trends that have been corrected for the influence of ongoing glacial isostatic adjustment (GIA) related to the late Pleistocene glacial cycles. The common assumption in such studies is that the geographic scatter in the residual, GIA-corrected trends is due to errors in the GIA model or unmodeled processes (e.g., tectonics). We consider a large suite of GIA model predictions and apply a least squares approach to the GIA-corrected tide gauge trends to estimate the weighting of various present-day sea level signatures. We find that the fit to the residual RSL trends is significantly improved and that the procedure is able to resolve a long-standing observation of anomalously low sea level rates in Europe. This preliminary analysis, which is relatively insensitive to changes in the assumed geometry of the present-day mass balance, assumes that ocean thermal expansion is globally uniform. However, the procedure can be easily extended to incorporate a realistic steric contribution once the geometry of the process is sufficiently well constrained.

62. Tapley, BD; Chambers, DP; Bettadpur, S; Ries, JC , 2003 :
    Large scale ocean circulation from the GRACE GGM01 Geoid .
    GEOPHYSICAL RESEARCH LETTERS 30 - 2163

[ 1] The GRACE Gravity Model 01 ( GGM01), computed from 111 days of GRACE K- band ranging ( KBR) data, is differenced from a global mean sea surface ( MSS) computed from a decade of satellite altimetry to determine a mean dynamic ocean topography ( DOT). As a test of the GGM01 gravity model, large- scale zonal and meridional surface geostrophic currents are computed from the topography and are compared with those derived from a mean hydrographic surface. Reduction in residual RMS between the two by 30 - 60% ( and increased correlation) indicates that the GGM01 geoid represents a dramatic improvement over older geoid models, which were developed from multiple satellite tracking data, altimetry, and surface gravity measurements. For the first time, all major current systems are clearly observed in the DOT from space- based measurements.

63. Velicogna, I; Wahr, J , 2002 :
    Postglacial rebound and Earth's viscosity structure from GRACE .
    JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH 107 - 2376

The Gravity Recovery and Climate Experiment (GRACE) satellite mission was launched in March 2002 and has an expected 5-year lifetime. One potential application of GRACE measurements of time-variable gravity will be to isolate the postglacial rebound signal, which can then be used to estimate the Earth's viscosity structure. In this paper we present a sensitivity analysis of simulated GRACE data, designed to assess the accuracy with which those data can be used to recover a simple model of Earth viscosity. We find that without combining with any other data type, but ignoring complications caused by uncertainties in the global ice loading history, GRACE data alone would allow us to determine the viscosity of a uniform lower mantle layer and an upper mantle/transition zone layer to within +/-30-40% and to estimate lithospheric thickness to within +/-15-20%. GRACE will have a harder time differentiating between the separate viscosities of the transition zone and upper mantle, but accuracies of within a factor of 2 might still be achievable for those parameters. Errors in the ice loading history could significantly degrade these viscosity estimates, particularly for the transition zone and upper mantle. The accuracy of recovery of the true Earth viscosity will depend in part on how well the model parameterization used for the grid search can represent the true Earth structure. However, combining GRACE data with data from other more traditional measurements of postglacial rebound has the potential of dramatically improving viscosity estimates throughout the Earth, particularly in the lower mantle.

64. Velicogna, I; Wahr, J , 2002 :
    A method for separating antarctic postglacial rebound and ice mass balance using future ICESat Geoscience Laser Altimeter System, Gravity Recovery and Climate Experiment, and GPS satellite data .
    JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH 107 - 2263

[1] Measurements of ice elevation from the Geoscience Laser Altimeter System (GLAS) aboard the Ice, Cloud, and Land Elevation Satellite can be combined with time-variable geoid measurements from the Gravity Recovery and Climate Experiment (GRACE) satellite mission to learn about ongoing changes in polar ice mass and viscoelastic rebound of the lithosphere under the ice sheet. We estimate the accuracy in recovering the spatially varying ice mass trend and postglacial rebound signals for Antarctica, from combining 5 years of simulated GRACE and GLAS data. We obtain root-mean square accuracies of 5.3 and 19.9 mm yr(-1) for postglacial rebound and ice mass trend, respectively, when smoothed over 250 km scales. The largest source of error in the combined signals is the effect of the unknown time-variable accumulation on the density of the ice column. To estimate this contribution and so obtain better estimates of ice mass trend and postglacial rebound, we add Global Positioning System (GPS) measurements of vertical velocities as additional constraints. Using an empirical relation between the errors in postglacial rebound and ice mass trend that result from the unknown density variation within the ice column, we are able to solve for all three unknowns in the problem: ice mass trend, postglacial rebound, and the snow compaction trend. The addition of a plausible distribution of GPS measurements reduces the errors in estimates of postglacial rebound and ice mass trend to 3.4 and 15.9 mm yr(-1), respectively.

65. Velicogna, I; Wahr, J; Van den Dool, H , 2001 :
    Can surface pressure be used to remove atmospheric contributions from GRACE data with sufficient accuracy to recover hydrological signals? .
    JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH 106 16415 - 16434

The Gravity Recovery and Climate Experiment (GRACE) satellite mission will resolve temporal variations in gravity orders of magnitude more accurately and with considerably higher resolution than any existing satellite. Effects of atmospheric mass over land will be removed prior to estimating the gravitational field, using surface pressure fields generated by global weather forecast centers. To recover the continental hydrological signal with ail accuracy of 1 cin of equivalent water thickness down to scales of a few hundred kilometers, atmospheric pressure must be known to an accuracy of I mbar or better. We estimate errors in analyzed pressure fields and the impact of those errors on GRACE surface mass estimates by comparing analyzed fields with barometric surface pressure measurements in the United States and North Africa/Arabian peninsula. We consider (1) the error in 30-day averages of the pressure field, significant because the final GRACE product will average measurements collected over 30-day intervals, and (2) the short-period error in the pressure fields which would be aliased by GRACE orbital passes. Because the GRACE results will average surface mass over scales of several hundred kilometers, we assess the pressure field accuracy averaged over those same spatial scales. The atmospheric error over the 30-day averaging period, which will map directly into GRACE data, is generally <0.5 mbar. Consequently, analyzed pressure fields will be adequate to remove the atmospheric contribution from GRACE hydrological estimates to subcentimeter levels. However, the short-period error in the pressure field, which would alias into GRACE data, could potentially contribute errors equivalent to 1 cm of water thickness. We also show that given sufficiently dense barometric coverage, an adequate surface pressure field can be constructed from surface pressure measurements alone.

66. Visser, PNAM , 1999 :
    Gravity field determination with GOCE and GRACE .
    SATELLITE DYNAMICS, ORBIT ANALYSIS AND COMBINATION OF SPACE TECHNIQUES ADVANCES IN SPACE RESEARCH 23 771 - 776

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) and Gravity Recovery And Climate Experiment (GRACE) are two gravity missions defined by the European Space Agency (ESA) and the National Aeronautics & Space Administration (NASA), respectively. The primary mission objective of GOCE is a high-accuracy, high-resolution determination of the constant part of the gravity field of the Earth, down to wavelengths of less than 200 km, whereas the GRACE mission aims at wavelengths down to 400 km and also focuses on monitoring changes in the Earth's gravity field. The foreseen mission duration is equal to 9 months for GOCE and 5 years for GRACE, respectively. With these mission durations, rigorous covariance analyses indicate that the gravity signal to noise ratio reaches I at about degree 250 for GOCE and 130 for GRACE, i.e. wavelengths of about 160 and 310 km, respectively. The covariance analyses indicate that GRACE and GOCE perform best in the long-to-medium wavelength (800 - 40,000 km) and medium-to-short wavelength (1500 - 160 km) domains, respectively. The GRACE and GOCE missions can be considered to be both supplementary and complementary. This offers the possibility to verify and calibrate gravity field recovery results, especially in the medium-wavelength domain. Moreover, a combined GOCE/GRACE gravity field solution might be formed, with optimal performance over all wavelengths down to 180 km. (C) 1999 COSPAR. Published by Elsevier Science Ltd.

67. Visser, PNAM; Sneeuw, N; Gerlach, C , 2003 :
    Energy integral method for gravity field determination from satellite orbit coordinates .
    JOURNAL OF GEODESY 77 207 - 216

A fast iterative method for gravity field determination from low Earth satellite orbit coordinates has been developed and implemented successfully. The method is based on energy conservation and avoids problems related to orbit dynamics and initial state. In addition, the particular geometry of a repeat orbit is exploited by using a very efficient iterative estimation scheme, in which a set of normal equations is approximated by a sparse block-diagonal equivalent. Recovery experiments for spherical harmonic gravity field models up to degree and order 80 and 120 were conducted based on a 29-day simulated data set of orbit coordinates. The method was found to be very flexible and could be easily adapted to include observations of non-conservative accelerations, such as (to be) provided by satellites like CHAMP, GRACE, and GOCE. A serious drawback of the method is its large sensitivity to satellite velocity errors. Existing orbit determination strategies need to be altered or augmented to include algorithms that focus on optimizing the accuracy of estimated velocities.

68. Visser, PNAM; Van den Ijssel, J , 2003 :
    Aiming at a 1-cm orbit for low earth orbiters: Reduced-dynamic and kinematic precise orbit determination .
    SPACE SCIENCE REVIEWS 108 27 - 36

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 em-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.

69. von Frese, RRB; Roman, DR; Kim, JH; Kim, JW; Anderson, AJ , 1999 :
    Satellite mapping of the Antarctic gravity field .
    ANNALI DI GEOFISICA 42 293 - 307

The production and analysis of the Antarctic digital magnetic anomaly map will be greatly aided by complementary gravity data. They help to constrain thickness variations of the crust and related magnetic effects that may be used for correcting long-wavelength errors in near-surface magnetic survey compilations. They also limit ambiguities in geological interpretations of magnetic anomalies. Antarctic free-air gravity anomalies are available from the 1 degrees Earth Gravity Model 1996 (EGM96). These coefficients satisfy gravity estimates from satellite radar altimetry, as well as surface or near-surface measurements in roughly 75% of the 30 are-minute blocks south of 60 degrees S. For the remaining blocks, the EGM96 predictions are limited in resolution to degree 70 based on satellite orbital analyses. Anomaly predictions over the unsurveyed regions of the Antarctic will be greatly improved by additional orbital measurements from the pending low-altitude (i.e., 150-500 km) CHAMP and GRACE satellite missions of ESA and NASA, respectively. Shorter wavelength anomalies are available from Geosat and ERS-1 & 2 radar altimetry data for marine regions away from the shoreline that compare very well with modern, good-quality shipborne data. Over the Gunnerus Ridge region, for example, satellite altimetry-derived free-air gravity predictions at a 3-5 km grid interval have an accuracy of about 3 mgals or less.

70. Wahr, J; Molenaar, M; Bryan, F , 1998 :
    Time variability of the Earth's gravity field: Hydrological and oceanic effects and their possible detection using GRACE .
    JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH 103 30205 - 30229

The GRACE satellite mission, scheduled for launch in 2001, is designed to map out the Earth's gravity field to high accuracy every 2-4 weeks over a nominal lifetime of 5 years. Changes in the gravity field are caused by the redistribution of mass within the Earth and on or above its surface. GRACE will thus be able to constrain processes that involve mass redistribution. In this paper we use output from hydrological, oceanographic, and atmospheric models to estimate the variability in the gravity field (i.e., in the geoid) due to those sources. We develop a method for constructing surface mass estimates from the GRACE gravity coefficients. We show the results of simulations, where we use synthetic GRACE gravity data, constructed by combining estimated geophysical signals and simulated GRACE measurement errors, to attempt to recover hydrological and oceanographic signals. We show that GRACE may be able to recover changes in continental water storage and in seafloor pressure, at scales of a few hundred kilometers and larger and at timescales of a few weeks and longer, with accuracies approaching 2 mm in water thickness over land, and 0.1 mbar or better in seafloor pressure.

71. Wahr, J; Velicogna, I , 2003 :
    What might GRACE contribute to studies of post glacial rebound? .
    SPACE SCIENCE REVIEWS 108 319 - 330

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.

72. Wahr, J; Wingham, D; Bentley, C , 2000 :
    A method of combining ICESat and GRACE satellite data to constrain Antarctic mass balance .
    JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH 105 16279 - 16294

Measurements from the Geoscience Laser Altimeter System (GLAS) aboard NASA's ICESat satellite (2001 launch) will be used to estimate the secular change in Antarctic ice mass. We have simulated 5 years of GLAS data to infer the likely accuracy of these GLAS mass balance estimates. We conclude that ICESat will be able to determine the linear rate of change in Antarctic ice mass occurring during those 5 years to an accuracy of similar to 7 mm/yr equivalent water thickness when averaged over the entire ice sheet. By further including the difference between the typical 5-year trend and the long-term (i.e., century-scale) trend, we estimate that GLAS should be able to provide the long-term trend in mass to an accuracy of about +/-9 mm/yr of equivalent water thickness, corresponding to an accuracy for the Antarctic contribution to the century-scale global sea level rise of about +/-0.3 mm/yr. For both cases the principal error sources are inadequate knowledge of postglacial rebound and of complications caused by interannual and decadal variations in the accumulation rate. We also simulate 5 years of gravity measurements from the NASA and Deutsches Zentrum fur Luft-und Raumfahrt (DLR) satellite mission Gravity Recovery and Climate Experiment (GRACE)(2001 launch). We find that by combining GLAS and GRACE measurements, it should be possible to slightly reduce the postglacial rebound error in the GLAS mass balance estimates. The improvement obtained by adding the gravity data would be substantially greater for multiple, successive altimeter and gravity missions.

73. Wahr, JM; Jayne, SR; Bryan, FO , 2002 :
    A method of inferring changes in deep ocean currents from satellite measurements of time-variable gravity .
    JOURNAL OF GEOPHYSICAL RESEARCH-OCEANS 107 - 3218

The NASA/Deutsches Zentrum fur Luft-und Raumfahrt (DLR) satellite gravity mission Gravity Recovery and Climate Experiment (GRACE), launched in March 2002, will map the Earth's gravity field at scales of a few hundred kilometers and greater every 30 days. We describe a method of using those gravity measurements to estimate temporal variations in deep ocean currents. We examine the probable accuracy of the current estimates by constructing synthetic GRACE data, based in part on output from an ocean general circulation model. We ignore the possible contamination caused by short-period gravity signals aliasing into the 30-day solutions. We conclude that in the absence of aliasing, GRACE should be able to recover the 30-day variability of midlatitude currents at a depth of 2 km with an error of about 6-15% in variance when smoothed with 500-700 km averaging radii.

74. Woodworth, PL; Gregory, JM , 2003 :
    Benefits of GRACE and GOCE to sea level studies .
    SPACE SCIENCE REVIEWS 108 307 - 317

The recently published Third A