J. M. L. Lemoine

A new global Earth's gravity field model from satellite orbit perturbations: GRIM5‐S1

A new model of the Earths gravity field, called GRIM5-S1, was prepared in a joint German-French effort. The solution is based on satellite orbit perturbation analysis and exploits tracking data from 21 satellites to solve simultaneously for the gravitational and ocean tide potential and tracking station positions. The satellite-only solution results in a homogeneous representation of the geoid with an approximation error of about 45 cm in terms of 5×5 degree block mean values, and performs globally better in satellite orbit restitution than any previous gravity field model. The GRIM5 normals, which were generated taking into account the latest computational standards, shall be the reference for use during the coming geopotential satellite mission CHAMP and should provide new standards in computing orbits of next altimetric missions like Jason and ENVISAT. The GRIM5-S1 normals also give the basis for the tracking/surface data combined solution GRIM5-C1.

Earth Gravity Field and Seasonal Variability from CHAMP

GPS-CHAMP satellite-to-satellite and accelerometry data covering 2.5 years of the CHAMP mission period were exploited to generate the global gravity field model EIGEN-3p revealing considerable improvements in both accuracy and resolution with respect to the previous model EIGEN-2. For the year 2001, CHAMP and satellite laser ranging data of four satellites were combined to recover largest scale monthly gravity field variations that are subsequently analyzed for the annually varying constituents. The temporal gravity field variations observed by CHAMP and the SLR satellites are compared in the spectral and spatial domain with geophysically (atmosphere, ocean, hydrology) predicted gravity variations that do not reflect the large observed scattering in the monthly solutions but are of comparable size and distribution on the annual time scale.

GRIM5‐C1: Combination solution of the global gravity field to degree and order 120

The new satellite Earth gravity field model GRIM5-S1 was recently prepared in a joint GFZ and GRGS effort. Based on this satellite solution and terrestrial and altimetric gravity anomalies from NMA, a combined model GRIM5-C1, with full variance-covariance matrix up to degree and order 120, was computed. Surface gravity and altimetric gravity data are corrected for several systematic effects, such as ellipsoidal corrections and aliasing. A weighting scheme for gravity anomalies, according to their given standard deviations was developed. From each data set full normal equations were set up and finally combined with the GRM5-S1 normals. To take into account good information from the satellite-only model a procedure was developed to identify such coefficients and appropriately weighed them in the final normal equation system. Internal error propagation and comparisons to external data sets show, that the GRJM5-C1 model represents the best state of long wavelength gravity field models.

ESA's satellite‐only gravity field model via the direct approach based on all GOCE data

Gravity field and steady state Ocean Circulation Explorer (GOCE) gravity gradient data of the entire science mission and data from LAGEOS 1/2 and Gravity Recovery and Climate Experiment (GRACE) were combined in the construction of a satellite-only gravity field model to maximum degree 300. When compared to Earth Gravitational Model 2008, it is more accurate at low to medium resolution, thanks to GOCE and GRACE data. When compared to earlier releases of European Space Agency GOCE models, it is more accurate at high degrees owing to the larger amount of data ingested, which was moreover taken at lower altitude. The impact of orbiting at lower altitude in the last year of the mission is large: a model based on data of the last 14 months is significantly more accurate than the release 4 model constructed with the first 28 months. The (calibrated) cumulated geoid error estimate at 100 km resolution is 1.7 cm. The optimal resolution of the GOCE model for oceanographic application is between 100 and 125 km.

Comparison of in situ bottom pressure data with GRACE gravimetry in the Crozet-Kerguelen region

Two time series of deep ocean bottom pressure records (BPRs) in between the Crozet Islands and Kerguelen are compared with GRACE (Gravity Recovery And Climate Experiment) equivalent water heights. An analysis of the correlation is performed for four time series: 1) monthly averages of the equivalent water height at the Crozet Islands, 2) the same near the Kerguelen Islands, 3) the mean of the two preceding series and 4) the difference between the two locations expressed in terms of geostrophic transport. We find that smoothed GRACE solutions are strongly correlated with the BPR data with correlation coefficients in the order of 0.7–0.8. Consequently GRACE measures real oceanic mass variations in this region.

EIGEN-6C: A High-Resolution Global Gravity Combination Model Including GOCE Data

GOCE satellite gradiometry data were combined with data from the satellite missions GRACE and LAGEOS and with surface gravity data. The resulting high-resolution model, EIGEN-6C, reproduces mean seasonal variations and drifts to spherical harmonic degree and order (d/o) 50 whereas the mean spherical harmonic coefficients are estimated to d/o 1420. The model is based on satellite data up to d/o 240, and determined with surface data only above degree 160. The new GOCE data allowed the combination with surface data at a much higher degree (160) than was formerly done (70 or less), thereby avoiding the propagation of errors in the surface data over South America and the Himalayas in particular into the model.

Global Gravity Field Recovery Using Solely GPS Tracking and Accelerometer Data from Champ

A new long-wavelength global gravity field model, called EIGEN-1. has been derived in a joint German-French effort from orbit perturbations of the CHAMP satellite, exploiting CHAMPGPS satellite-to-satellite tracking and on-board accelerometer data over a three months time span. For the first time it becomes possible to recover the gravity field from one satellite only. Thanks to CHAMP’s tailored orbit characteristics and dedicated instrumentation, providing continuous tracking and on-orbit measurements of non-gravitational satellite accelerations. the three months CHAMP-only solution provides the geoid and gravity with an accuracy of 20 cm and 1 mgal, respectively, at a half wavelength resolution of 550 km, which is already an improvement by a factor of two compared to any pre-CHAMP satellite-only gravity field model.

On Board Evaluation of the STAR Accelerometer

The main results of the on-board evaluation of the STAR accelerometer are presented after 18 months of mission. The instrument demonstrates high performances in terms of resolution and reliability and its contribution to dynamic orbit determination is clear. However, unexplained signal jumps have been detected and analysed. In addition, an anomalous behaviour of the X3 electrode of the accelerometer, affects the Radial, Roll and Pitch accelerations. Nevertheless, corrected observations can be recovered from a new combination of the electrode voltages. The in-orbit calibration will also benefit from the new EIGEN gravity field model that includes CHAMP data.

Assimilation of satellite altimetry referenced to the new GRACE geoid estimate

[1] Currently, two satellite gravimetric missions (CHAMP, GRACE) are dedicated to the improvement of our knowledge of the geoid, and one (GOCE) is planned in the near future. This will allow the absolute altimeter ocean height measurements to be exploited, instead of only sea level variations. In this paper, we evaluate the impact of the GRACE mission on ocean data assimilation. The new approach is to directly assimilate the full altimetric signal relative to the first release of a GRACE geoid. The response of an eddy-permitting ocean model of the North Atlantic to the assimilation of this altimetric signal is analysed. The results are compared to that obtained using the usual approach, i.e., the assimilation of the dynamic topography derived from the addition of altimetric sea level anomalies and a mean dynamic topography estimate. Even if the GRACE mission resolution (333 km) is not yet compatible with oceanographic studies at mid latitude, we show that the geoid estimate can already be used with success in basin scale altimetric data assimilation problems.

On regularized time varying gravity field models based on grace data and their comparison with hydrological models

Determination of spherical harmonic coefficients of the Earth’s gravity field is often an ill-posed problem and leads to solving an ill-conditioned system of equations. Inversion of such a system is critical, as small errors of data will yield large variations in the result. Regularization is a method to solve such an unstable system of equations. In this study, direct methods of Tikhonov, truncated and damped singular value decomposition and iterative methods of ν, algebraic reconstruction technique, range restricted generalized minimum residual and conjugate gradient are used to solve the normal equations constructed based on range rate data of the gravity field and climate experiment (GRACE) for specific periods. Numerical studies show that the Tikhonov regularization and damped singular value decomposition methods for which the regularization parameter is estimated using quasioptimal criterion deliver the smoothest solutions. Each regularized solution is compared to the global land data assimilation system (GLDAS) hydrological model. The Tikhonov regularization with L-curve delivers a solution with high correlation with this model and a relatively small standard deviation over oceans. Among iterative methods, conjugate gradient is the most suited one for the same reasons and it has the shortest computation time.