Contents

## Mean gravity field models

Based on the GRACE/GRACE-FO time series of solutions (plus SLR data and more recently DORIS data), **mean gravity field model** are computed. They include time variable coefficients in the form of yearly biases + slope + annual and semi-annual periodic terms up the the maximum degree of the series, plus static terms above. These models are mainly useful for Precise Orbit Determination.

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« , « Release 03« , « Release 04 » or « Release 05« . 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 05:**

**CNES_GRGS.RL05MF_COMBINED_GRACE_SLR_DORIS**(based on 25 years of SLR data, 10 years of DORIS data, 21 years of GRACE/GRACE-FO data and 3 years of GOCE data).- In GRACE format: CNES_GRGS.RL05MF_COMBINED_GRACE_SLR_DORIS.shc
- In ICGEM .gfc format: CNES_GRGS.RL05MF_COMBINED_GRACE_SLR_DORIS.gfc

**Reference field for RL05 grids**: The geoid, gravity anomalies and EWH grids and images are computed by difference of the RL05 solutions to a static reference mean field, which is an arbitrary reference. In the case of the RL05 grids and images, we have used the same static reference field as for RL04-v1. This static mean field is close to the actual value of the Earth’s gravity field at mid-2009.- In GRACE format: reference_field_for_RL05_grids.shc
- In ICGEM .gfc format: reference_field_for_RL05_grids.gfc

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

**Associated with Release 04:**

**EIGEN-GRGS.RL04.MEAN-FIELD**(based on 25 years of SLR data, 15 years of GRACE data and 3 years of GOCE data).**This is the reference gravity field for the GDR-F altimetric standards.**-
**Reference field_for_RL04_grids**: The geoid and EWH grids and images are computed by difference of the RL04 solutions to a static reference mean field, which is an arbitrary reference. In the case of the RL04 grids and images, we have used Reference field_for_RL04-v1_grids. This static mean field is close to the actual value of the Earth’s gravity field at mid-2009.- In GRACE format: reference_field_for_RL04-v1_grids.shc
- In ICGEM .gfc format: reference_field_for_RL04-v1_grids.gfc

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

**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 currently used extended GRACE format is given here.

The (old) GRGS format of the gravity field files is described here.

## Computation of the periodic coefficients

For the determination of the periodic coefficients mean fields, the following equation has been used:

**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 |

We provide a software kit (here), that allows the computation of a static field from a mean field at any given date.