# 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 |