GRGS > Research > Subjects > Earth's Gravitational Field

Bureau des longitudes Centre national d’études spatiales Institut national de l'information géographique et forestière - Laboratoire LAREG Observatoire de Paris Institut national des sciences de l'Univers Observatoire de la Côte d'Azur Service Hydrographique et Océanographique de la Marine Observatoire Midi-Pyrénées Université de la Polynésie Française Ecole Supérieure des Géomètres et Topographes - Conservatoire national des arts et métiers Ecole et Observatoire des Sciences de la Terre

GRGS has long been involved in the modeling of the Earth’s gravitational field. The first global models of the Earth’s gravitational field, called GRIM and represented by the coefficients (Clm, Slm) of/with/ spherical harmonics functions, date from the 1970s. These models (from GRIM-1 to GRIM-5) were made in a joint cooperation project between GRGS and a German institute (first named TUM, then DGFI and finally GFZ). Since 2000 and the launch of the satellite mission CHAMP (DLR / GFZ), the models produced have been given the name EIGEN.

These models are available on the website of "The International Centre for Global Earth Models (ICGEM):

Champ de gravité de la Terre

After the launch of the twin satellites GRACE (NASA / DLR) in 2002, the team of Space Geodesy CNES / GRGS became involved in the estimation of decadal temporal variations (other than tides) in the gravity field through the analysis of derived, inter-satellite KBR measurements. Previously, the observation of variations in the Earth’s gravitational field was limited to the dynamic flattening of the Earth (coefficient C20) through the analysis of orbital perturbations of the LAGEOS satellites based on laser tracking data.

The variable GRACE models are described and delivered in the form of spherical harmonic coefficients, as maps of geoid height, or converted into equivalent water heights, on this site as well as that of BGI (

Variation de l'aplatissement dynamique de la Terre (coefficient C20)

Variation de l'aplatissement dynamique de la Terre (coefficient C20)

Cartes saisonnières (boréales) de transfert de masses représenté sous forme de hauteur d'eau équivalente (m)

Cartes saisonnières (boréales) de transfert de masses représenté sous forme de hauteur d'eau équivalente (m)

Regional variations in surface water bodies by inversion of GRACE inter-satellite measurements

In order to study the redistribution of water bodies on the Earth’s surface, a new approach has been proposed in order to estimate time series of regional maps of mass area density by the inversion of anomalies of potential difference along the short-arc orbits of GRACE satellites. These anomalies are deduced from precise K-Band Range (KBR) measurements of velocity differences between the two GRACE vehicles, following the energy integral method. After correcting for known gravitational variations (i.e., solid Earth, variable fields created by planets, atmosphere, oceans, tides, and also the movements of the pole), during orbit adjustments performed by the software GINS (developed by GRGS), the residuals of potential, non-modelled physical phenomena corresponded mainly to hydrological changes on the continents. Instead of applying a method of matrix regularization, spatial constraints (i.e., linear correlations based on the angular distance between the surface elements) are introduced to stabilize the system of normal equations to be solved in order to estimate the distributions of equivalent water heights, and to effectively mitigate the noise in the KBR measurements. The first series of regional solutions 2 ° x2 ° at 10 days at the continental scale are in the process of being calculated and validated at GRGS Toulouse.

variations régionales des masses d'eau superficielles


G. Ramillien, CNRS, GRGS, OMP, Toulouse (, R. Biancale, CNES, GRGS, OMP, Toulouse (, L. Seoane, Post-doc. RTRA, GRGS, OMP, Toulouse (


G. Ramillien, R. Biancale, S. Gratton, X. Vasseur and S. Bourgogne, GRACE-derived surface mass anomalies by energy integral approach. Application to continental hydrology, J. of Geodesy, forthcoming, October 2010.

GRACE ICA-filtered solutions Release 4

An approach based on Independent Component Analysis (ICA) has been applied on a combination of monthly GRACE satellite solutions computed from official providers (CSR, JPL and GFZ), to separate useful geophysical signals from important striping undulations. We pre-filtered the raw GRACE Level-2 solutions using Gaussian filters of 400 and 500-km of radius to verify the non-gaussianity condition which is necessary to apply the ICA. This linear inverse approach ensures to separate components of the observed gravity field which are statistically independent. As the most energetic component found by ICA corresponds mainly to the contribution of continental water mass change. Series of ICA-estimated global maps of continental water storage have been produced over 08/2002-12/2010.

solution grace


The ICA grids are 1° x 1° global grids of equivalent water heights differences (in mm) between time-variable solutions and static field (at reference date if the static field includes time-variable terms). They have the following format:

lon (°) lat (°) EWH CSR (mm) EWH GFZ (mm) EWH JPL (mm)


Frappart F., Ramillien G., Maisongrande P., Bonnet M-P. (2010). Denoising satellite gravity signals by Independent Component Analysis, IEEE Geoscience and Remote Sensing Letters, 7(3), 421-425, doi:10.1109/LGRS.2009.2037837.
Frappart F., Ramillien G., Leblanc M., Tweed S.O., Bonnet M-P., Maisongrande P. (2011). An independent Component Analysis approach for filtering continental hydrology in the GRACE gravity data, Remote Sensing of Environment, 115(1), 187-204, doi: 10.1016/j.rse.2010.08.017.

The GOCE (Gravity field and Ocean Circulation Explorer) satellite from ESA, launched March 17, 2009, aims to map the Earth’s gravitational field from an altitude of 250 km using six accelerometers on board. Within the consortium EGGc (European GOCE Gravity Consortium), the CNES Space Geodesy team participates in the analysis of gradiometric measurements. The expected accuracy is 1 mGal at 100 km resolution (level 200), or 1 cm on the geoid.

High-resolution regional models of the gravity field

The team LAREG / GRGS develops high-resolution regional models of the gravity field by combining different types of gravimetric measurements and therefore increasing the density of information obtained for a given location using spatial gravimetry. To do this, a multi-scale modeling approach has been developed using wavelets defined in spherical geometry. This type of approach has proven useful for combining data with varied spatial and spectral characteristics. Moreover, taking into account mobile gravimetric measurements is of great interest, because it enables the coverage of areas that are difficult to access.