Groupe de Recherche de Géodésie Spatiale Centre national d’études spatiales

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 mean-variable gravity field at a given date, or download the software kit that we provide from here.

Associated with Release 03:

  • EIGEN-GRGS.RL03.MEAN-FIELD (based on 28 years of LAGEOS data, 10 years of GRACE data and 3 years of GOCE data)
  • Reference field_for_RL03-v1_grids: The geoid and EWH grids and images are computed by difference of the RL03-v1 solutions to a static reference mean field, which is an arbitrary reference. In the case of the RL03-v1 grids and images, we have used Reference field_for_RL03-v1_grids. This static mean field is close to the actual value of the Earth's gravity field at the date 2008.0.
  • EIGEN-GRGS.RL03-v2.MEAN-FIELD (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 GDR-E altimetric standards.
  • EIGEN-GRGS.RL03-v2.MEAN-FIELD.mean_slope_extrapolation (identical to EIGEN-GRGS.RL03-v2.MEAN-FIELD, 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:

  • EIGEN-GRGS.RL02.MEAN-FIELD (based on 4.5 years of data)
  • EIGEN-GRGS.RL02bis.MEAN-FIELD (update based on 8 years of data). This is the reference gravity field for the GDR-D altimetric standards.
  • EIGEN-6S2 (proposal for ITRF2013 standards)
  • EIGEN-6S2.extended (this field is no longer available, there was an error in the TVG part for the years 2012-2013. It is replaced by EIGEN-6S2.extended.v2)
  • EIGEN-6S2.extended.v2 (same as EIGEN-6S2, 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 time-variable 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 semi-annual 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, semi-annual and drift terms, based on the GRACE time-variable 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

EIGEN-GL04S

EIGEN-GL04S 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 10-day periods between 2003/02/24 and 2005/02/23). Its reference date is 2004.0. This field does not include time-variable terms (see EIGEN-GL04S-ANNUAL below).

Download EIGEN_GL04S (GINS format) / EIGEN_GL04S (GRACE format)

EIGEN-GL04C

EIGEN-GL04C 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)

EIGEN-GL04S-ANNUAL

EIGEN-GL04S-ANNUAL is based on EIGEN-GL04S, this field includes time-variable components: drift, annual and semi-annual 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)

EIGEN-GRGS.RL02.MEAN-FIELD

EIGEN-GRGS.RL02.MEAN-FIELD 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 time-variable 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",
    • semi-annual 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 EIGEN-GRGS.RL02.MEAN-FIELD is a "post-Sumatra" mean gravity field and that the Sumatra correction has only to be added if one works before the earthquake date of occurrence.
  • Download EIGEN-GRGS.RL02.MEAN-FIELD (GINS format) / EIGEN-GRGS.RL02.MEAN-FIELD (GRACE format)

EIGEN-GRGS.RL02.MEAN-FIELD.static_part.dg_050

We also provide the static-only part of EIGEN-GRGS.RL02.MEAN-FIELD, limited to maximum degree and order 50, under the name EIGEN-GRGS.RL02.MEAN-FIELD.static_part.dg_050. This is the same as the above-described model, but all time-dependant terms and all terms of spherical harmonic degree greater than 50 have been removed. To see the full temporal gravity variations, the 10-day solutions must be compared to this model (i.e. by subtracting this reference from the 10-day solutions).

Download EIGEN-GRGS.RL02.MEAN-FIELD.static_part.dg_050 in GINS format / GRACE format

EIGEN-GRGS.RL02.MEAN-FIELD.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 EIGEN-GRGS.RL02.MEAN-FIELD.static_part.dg_050 in Geoid Heights grid / Equivalent Water Heights grid

EIGEN-GRGS.RL02bis.MEAN-FIELD

EIGEN-GRGS.RL02bis.MEAN-FIELD is an extension of EIGEN-GRGS.RL02.MEAN-FIELD based on 8 years of GRACE and LAGEOS data. This is the reference gravity field for the GDR-D altimetric standards.

Download EIGEN-GRGS.RL02bis.MEAN-FIELD (GINS format)

EIGEN-6S2

EIGEN-6S2 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 time-variable gravity (TVG) coefficients between degrees 2 and 50 are obtained from a regression on the GRGS-RL02 10-day time series (2003-2012). For degree 2 this TVG part is extended to 1985-2012 through the use of a GRGS SLR-only (Lageos+Lageos-2) solution between 1985 and 2003.

Outside of the measurements period (1985-2012 for degree 2, 2003-2012 for degrees 3 to 50), the gravity field is extrapolated with a zero-slope assumption.

The new modeling of the TVG part includes:

  • Two annual and two semi-annual 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 ICGEM-V2 (and vice versa) format converter: here
  • a kit to compute the gravity field at any given date from the new extended GRACE format: here
  • warning
    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 EIGEN-6S2 in extended GRACE format / ICGEM-V2 format

IMPORTANT NOTICE:

For the needs of the ITRF2013 computation, the TVG part of EIGEN-6S2 has been extended beyond 2012.0, until 2014.0, using for the slopes of 2012-2013 the mean slopes of 2009-2010-2011. This extended field is named EIGEN-6S2.extended.v2. It replaces a previous field named EIGEN-6S2.extended which contained an error in the slopes for 2012-2013.

Download EIGEN-6S2.extended.v2 in extended GRACE format / ICGEM-V2 format

Nota bene: For the computation of the periodic coefficients, see the note at the bottom of the " Introduction tab" page.

EIGEN-GRGS.RL03.MEAN-FIELD

EIGEN-GRGS.RL03.MEAN-FIELD is complete to degree and order 260. It is based on EIGEN-6S2 for the part between degree 81 and 260. The time-variable gravity (TVG) coefficients between degrees 1 and 80 are obtained from a regression on the GRGS-RL03-v1 monthly time series (2003-2012). For degree 2 this TVG part is extended to 1985-2012 through the use of a GRGS SLR-only (Lageos+Lageos-2) solution between 1985 and 2003.

Outside of the measurements period (1985-2012 for degree 2, 2003-2012 for degrees 3 to 80), the gravity field is extrapolated with a zero-slope assumption.

The modeling of the TVG part includes, as was the case for EIGEN-6S2:

  • Two annual and two semi-annual 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 EIGEN-GRGS.RL03.MEAN-FIELD in extended GRACE format / ICGEM-V2 format

Reference field_for_RL03-v1_grids

The geoid and EWH grids and images are computed by difference of the RL03-v1 solutions to a static reference mean field, which is an arbitrary reference. In the case of the RL03-v1 grids and images, we have used the following reference mean-field :  Reference field_for_RL03-v1_grids. This static mean field is close to the actual value of the Earth's gravity field at the date 2008.0.

EIGEN-GRGS.RL03-v2.MEAN-FIELD

EIGEN-GRGS.RL03-v2.MEAN-FIELD is complete to degree and order 260. It is based on GOCE-DIR5 for the part between degree 81 and 260. The time-variable gravity (TVG) coefficients between degrees 1 and 80 are obtained from a regression on the GRGS-RL03-v2 monthly time series (2002.5-2014.5). For degree 2 this TVG part is extended to 1985-2014.5 through the use of a GRGS SLR-only (Lageos+Lageos-2) solution between 1985 and 2003.

Outside of the measurements period (1985-2014.5 for degree 2, 2003-2014.5 for degrees 3 to 80), the gravity field is extrapolated with a zero-slope assumption.

The modeling of the TVG part includes for the first time two annual and two semi-annual 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 semi-annual coefficients for each year.

This gravity field model has been adopted as the geopotential model of the GDR-E altimetric standards.

Download EIGEN-GRGS.RL03-v2.MEAN-FIELD in extended GRACE format / ICGEM-V2 format

EIGEN-GRGS.RL03-v2.MEAN-FIELD.mean_slope_extrapolation

Identical to EIGEN-GRGS.RL03-v2.MEAN-FIELD, except that the null slope on extrapolation is replaced by the average slope of the signal over the period 2003.0 - 2014.0.

Download EIGEN-GRGS.RL03-v2.MEAN-FIELD.mean_slope_extrapolation in extended GRACE format / ICGEM-V2 format

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