Mean gravity field models
The links below give access to the models. For a description of how the models are built, go to the tabs "Release 01", "Release 02" or "Release 03". You can use the interactive tool to compute the meanvariable gravity field at a given date, or download the software kit that we provide from here.
Associated with Release 03:
 EIGENGRGS.RL03.MEANFIELD (based on 28 years of LAGEOS data, 10 years of GRACE data and 3 years of GOCE data)
 Reference field_for_RL03v1_grids: The geoid and EWH grids and images are computed by difference of the RL03v1 solutions to a static reference mean field, which is an arbitrary reference. In the case of the RL03v1 grids and images, we have used Reference field_for_RL03v1_grids. This static mean field is close to the actual value of the Earth's gravity field at the date 2008.0.
 EIGENGRGS.RL03v2.MEANFIELD (based on 28 years of LAGEOS data, 12 years of GRACE data and 3 years of GOCE data). This is the reference gravity field for the GDRE altimetric standards.
 EIGENGRGS.RL03v2.MEANFIELD.mean_slope_extrapolation (identical to EIGENGRGS.RL03v2.MEANFIELD, except that the null slope on extrapolation is replaced by the average slope of the signal over the period 2003.0  2014.0)
Nota bene: For the computation of the periodic coefficients, see the note at the bottom of the page.
Associated with Release 02:
 EIGENGRGS.RL02.MEANFIELD (based on 4.5 years of data)
 EIGENGRGS.RL02bis.MEANFIELD (update based on 8 years of data). This is the reference gravity field for the GDRD altimetric standards.
 EIGEN6S2 (proposal for ITRF2013 standards)
 EIGEN6S2.extended (this field is no longer available, there was an error in the TVG part for the years 20122013. It is replaced by EIGEN6S2.extended.v2)
 EIGEN6S2.extended.v2 (same as EIGEN6S2, except that the TVG part has been extended to end of 2013 for the needs of the ITRF2013 computation)
Associated with Release 01:
Introduction to static coefficients and timevariable terms
For many applications, particularly precise orbit computation, a static gravity field is not sufficient. The main features of the time variations of the gravity field are annual and semiannual signals, and secular drifts. This is why most of the recent models propose a series of periodic and secular gravity variations for the lowest degrees of the gravity field. Those variations include annual, semiannual and drift terms, based on the GRACE timevariable solutions.
Formats
The (old) GRGS format of the gravity field files is described here. The currently used extended GRACE format is given here.
Computation of the periodic coefficients
For the determination of the periodic coefficients of all Release 03 mean fields, the following equation has been used:
coef_perio(T) = GCOS1A * cos( 2 PI * (T  T0) / MYD ) + GSIN1A * sin( 2 PI * (T  T0) / MYD ) + etc.
With:
T  T0  Time of computation, in days, from the reference date T0; with T0 = 2005/01/01 at 0. h 
MYD  Mean year duration = 365.25 days 
GCOS1A  Amplitude of cosine term at the annual period 
GSIN1A  Amplitude of sine term at the annual period 
GCOS2A  Amplitude of cosine term at the semi annual period 
GSIN2A  Amplitude of sine term at the semi annual period 
In the software kit that we provide ( here), however, a slightly different equation is used, in order to take into account the remarks of some users who were not happy that on the first of January of each year a sine term, for instance, would not give exactly 0.
The equation in the software kit is therefore:
coef_perio(T) = GCOS1A * cos( 2 PI * (T  T0') / EYD ) + GSIN1A * sin( 2 PI * (T  T0') / EYD ) + etc.
With:
T  T0'  Time of computation, in days, from T0'; with T0' = the first of January of the current year, at 0. h 
EYD  Exact duration, in days, of the current year (= 365 or 366 days, depending on the year) 
GCOS1A  Amplitude of cosine term at the annual period 
GSIN1A  Amplitude of sine term at the annual period 
GCOS2A  Amplitude of cosine term at the semi annual period 
GSIN2A  Amplitude of sine term at the semi annual period 
EIGENGL04S
EIGENGL04S is a strictly static gravity field model, up to degree and order 150 from GRACE and LAGEOS data only. It is given in normalized spherical harmonic (SH) coefficients in ITRF2000, and uses exactly 2 years of GRACE + LAGEOS data (73 10day periods between 2003/02/24 and 2005/02/23). Its reference date is 2004.0. This field does not include timevariable terms (see EIGENGL04SANNUAL below).
Download EIGEN_GL04S (GINS format) / EIGEN_GL04S (GRACE format)
EIGENGL04C
EIGENGL04C is a strictly static gravity field model, up to degree and order 360, from GRACE and LAGEOS data,plus surface data (Earth altimetric and gravimetric data). Its reference date is 2004.0.
Download EIGEN_GL04C (GINS format) / EIGEN_GL04C (GRACE format)
EIGENGL04SANNUAL
EIGENGL04SANNUAL is based on EIGENGL04S, this field includes timevariable components: drift, annual and semiannual sine and cosine.Drift terms however should be taken with some care since they were determined over only two years.
Download EIGEN_GL04S_ANNUAL (GINS format)
EIGENGRGS.RL02.MEANFIELD
EIGENGRGS.RL02.MEANFIELD is a static gravity field model, up to degree and order 160, based on 4.5 years of GRACE and LAGEOS data (March 2003 to September 2007). It includes timevariable terms up to degree and order 50.
 Reference epoch is 2005.00;
 Tide convention is "tide free";
 The field is complete to degree and order 160;
 Up to degree and order 50, are present...
 drifts with the acronym "DOT",
 annual sine and cosine terms with the acronym "S1A" and "C1A",
 semiannual sine and cosine terms with the acronym "S2A" and "C2A",
 an offset, with the acronym "SUM", to take into account the permanent deformation of the gravity field associated with the December 2004 Sumatra earthquake. The principle of this correction is that if one works BEFORE December 24, 2004, one has to ADD this correction to the static gravity field; if one works AFTER this date, one has to IGNORE this correction. This means that EIGENGRGS.RL02.MEANFIELD is a "postSumatra" mean gravity field and that the Sumatra correction has only to be added if one works before the earthquake date of occurrence.
 Download EIGENGRGS.RL02.MEANFIELD (GINS format) / EIGENGRGS.RL02.MEANFIELD (GRACE format)
EIGENGRGS.RL02.MEANFIELD.static_part.dg_050
We also provide the staticonly part of EIGENGRGS.RL02.MEANFIELD, limited to maximum degree and order 50, under the name EIGENGRGS.RL02.MEANFIELD.static_part.dg_050. This is the same as the abovedescribed model, but all timedependant terms and all terms of spherical harmonic degree greater than 50 have been removed. To see the full temporal gravity variations, the 10day solutions must be compared to this model (i.e. by subtracting this reference from the 10day solutions).
Download EIGENGRGS.RL02.MEANFIELD.static_part.dg_050 in GINS format / GRACE format
EIGENGRGS.RL02.MEANFIELD.static_part.dg_050 grids
In addition, we provide grids in geoid heights and equivalent water heights, with the following characteristics:
 Tides: “tide free”
 Degrees included: 02 to 50
 Parameters of the ellipsoid:
 a= 0.63781364600000E+07
 1/f= 0.29825765000000E+03
 GM= 0.39860044150000E+15
Download EIGENGRGS.RL02.MEANFIELD.static_part.dg_050 in Geoid Heights grid / Equivalent Water Heights grid
EIGENGRGS.RL02bis.MEANFIELD
EIGENGRGS.RL02bis.MEANFIELD is an extension of EIGENGRGS.RL02.MEANFIELD based on 8 years of GRACE and LAGEOS data. This is the reference gravity field for the GDRD altimetric standards.
Download EIGENGRGS.RL02bis.MEANFIELD (GINS format)
EIGEN6S2
EIGEN6S2 is a result of the cooperation between GFZ (GeoForschungsZentrum, Potsdam) and CNES/GRGS on the "EIGEN" series of models. This model is proposed for the ITRF2013 standards.
Complete to degree and order 260, it is based on a GFZ internal GRACE+GOCE solution for the part between degree 51 and 260. The timevariable gravity (TVG) coefficients between degrees 2 and 50 are obtained from a regression on the GRGSRL02 10day time series (20032012). For degree 2 this TVG part is extended to 19852012 through the use of a GRGS SLRonly (Lageos+Lageos2) solution between 1985 and 2003.
Outside of the measurements period (19852012 for degree 2, 20032012 for degrees 3 to 50), the gravity field is extrapolated with a zeroslope assumption.
The new modeling of the TVG part includes:
 Two annual and two semiannual coefficients
 One bias and one drift for each year. (Note that the reference date of the bias is the beginning of the period of validity of the coefficient, i.e. the beginning of the year in most cases, see format). The bias and drift are in general coherent so that the result is a piece wise linear function, except in the case of earthquakes
The extended GRACE format is an extension of the official GRACE format for gravity fields. An explanation of the format is given here.
It is possible with our interactive tools to compute a static gravity field at any given date from this model.
In addition, you will find two software packages in Fortran90:
 a GRACE to ICGEMV2 (and vice versa) format converter: here
 a kit to compute the gravity field at any given date from the new extended GRACE format: here

On 2015/02/06 a new version of the two softwares has been uploaded. A bug had been uncovered in the subroutine "interpolate_gravity_model_at_date_t" in the file "read_write_interpolate.mod.f90" of the kits. This bug will not affect any calculation done with the present mean gravity field models which have only one set of periodic terms per coefficient, but will affect the future mean gravity field models in which there will be one set of periodic terms per coefficient and per year. We strongly recommend to download the new versions of the softwares and install them in replacement of the old ones.
Download EIGEN6S2 in extended GRACE format / ICGEMV2 format
IMPORTANT NOTICE:
For the needs of the ITRF2013 computation, the TVG part of EIGEN6S2 has been extended beyond 2012.0, until 2014.0, using for the slopes of 20122013 the mean slopes of 200920102011. This extended field is named EIGEN6S2.extended.v2. It replaces a previous field named EIGEN6S2.extended which contained an error in the slopes for 20122013.
Download EIGEN6S2.extended.v2 in extended GRACE format / ICGEMV2 format
Nota bene: For the computation of the periodic coefficients, see the note at the bottom of the " Introduction tab" page.
EIGENGRGS.RL03.MEANFIELD
EIGENGRGS.RL03.MEANFIELD is complete to degree and order 260. It is based on EIGEN6S2 for the part between degree 81 and 260. The timevariable gravity (TVG) coefficients between degrees 1 and 80 are obtained from a regression on the GRGSRL03v1 monthly time series (20032012). For degree 2 this TVG part is extended to 19852012 through the use of a GRGS SLRonly (Lageos+Lageos2) solution between 1985 and 2003.
Outside of the measurements period (19852012 for degree 2, 20032012 for degrees 3 to 80), the gravity field is extrapolated with a zeroslope assumption.
The modeling of the TVG part includes, as was the case for EIGEN6S2:
 Two annual and two semiannual coefficients
 One bias and one drift for each year. (Note that the reference date of the bias is the beginning of the period of validity of the coefficient, i.e. the beginning of the year in most cases, see format). The bias and drift are in general coherent so that the result is a piece wise linear function, except in the case of earthquakes. Three major earthquakes have been introduced in the modelling: Sumatra on 2004/12/26, Concepcion on 2010/02/27 and Sendai on 2011/03/11.
Download EIGENGRGS.RL03.MEANFIELD in extended GRACE format / ICGEMV2 format
Reference field_for_RL03v1_grids
The geoid and EWH grids and images are computed by difference of the RL03v1 solutions to a static reference mean field, which is an arbitrary reference. In the case of the RL03v1 grids and images, we have used the following reference meanfield : Reference field_for_RL03v1_grids. This static mean field is close to the actual value of the Earth's gravity field at the date 2008.0.
EIGENGRGS.RL03v2.MEANFIELD
EIGENGRGS.RL03v2.MEANFIELD is complete to degree and order 260. It is based on GOCEDIR5 for the part between degree 81 and 260. The timevariable gravity (TVG) coefficients between degrees 1 and 80 are obtained from a regression on the GRGSRL03v2 monthly time series (2002.52014.5). For degree 2 this TVG part is extended to 19852014.5 through the use of a GRGS SLRonly (Lageos+Lageos2) solution between 1985 and 2003.
Outside of the measurements period (19852014.5 for degree 2, 20032014.5 for degrees 3 to 80), the gravity field is extrapolated with a zeroslope assumption.
The modeling of the TVG part includes for the first time two annual and two semiannual coefficients for each year, in addition to one bias and one drift for each year:
 One bias and one drift for each year. (Note that the reference date of the bias is the beginning of the period of validity of the coefficient, i.e. the beginning of the year in most cases, see format). The bias and drift are in general coherent so that the result is a piece wise linear function, except in the case of earthquakes. Three major earthquakes have been introduced in the modelling: Sumatra on 2004/12/26, Concepcion on 2010/02/27 and Sendai on 2011/03/11.
 Two annual and two semiannual coefficients for each year.
This gravity field model has been adopted as the geopotential model of the GDRE altimetric standards.
Download EIGENGRGS.RL03v2.MEANFIELD in extended GRACE format / ICGEMV2 format
EIGENGRGS.RL03v2.MEANFIELD.mean_slope_extrapolation
Identical to EIGENGRGS.RL03v2.MEANFIELD, except that the null slope on extrapolation is replaced by the average slope of the signal over the period 2003.0  2014.0.
Download EIGENGRGS.RL03v2.MEANFIELD.mean_slope_extrapolation in extended GRACE format / ICGEMV2 format