GOCE Gravity Field Model

Direct Solution - Third generation

Model Characteristics
GOCE Input Data:
- Gradients: EGG_NOM_2
- Orbits:    SST_PKI (kinematic orbits)
- Attitude:  EGG_IAQ_2C
- Data period: 20091101T000000-20110419T235959
The full list of input data to this direct-approach model is provided in the IHD file.

A-priori Information used:
A-priori gravity field for the processing of the GOCE gravity radients:
The GOCE-model 2nd realease from the direct approach GO_CONS_GCF_2_DIR_R2
up to degree/order 240

Processing Procedures:
The GOCE gravity gradients are processed without applying the calibration factors.
The observation equations are filtered with a 10-125 mHz bandpass filter, and
subsequently "SGG" normal equations to d/o 240 are computed individually for the
gradient components Txx, Tyy and Tzz.
The Txx, Tyy and Tzz SGG normal equations are accumulated with the relative weight 1.0
To overcome the numerical instability of the GOCE-SGG normal equations due to the
polar gaps and to compensate for the poor sensitivity of the GOCE measurements in
the low degrees the following stabilizations were applied:
1) The GOCE-SGG normal equation was fully combined with a GRACE normal equation.
Details about this GRACE contribution are given below.
2) A spherical cap regularization in accordance to Metzler and Pail (2005) was
iteratively computed to d/o 240 using the GRACE data mentioned below to d/o 130.
3) Additionally a Kaula regularization was applied to all coefficients beyond degree 200

Details of the GRACE contribution:
GRACE normal equations to d/o 160 for the period 24 February 2003 through 30 June 2009,
based on the improved data editing and solution regularization procedure of the
GRGS release 2 gravity field models (Bruinsma et al., 2009), are used in this model.
Thanks to tailored regularization of each individual Stokes coefficient applied in
the solution procedure, and secondly a time-variable reference model containing
mean annual, semiannual and secular variations for degrees 2 through 50, the
release 2 procedure significantly reduces the noise over deserts and oceans in
the form of North-South striping (NB: the present model is a static model without
temporal coefficients).
The harmonics of very-low degree, in particular degrees 2 and 3, cannot be estimated
accurately with GRACE and GOCE data. Therefore, LAGEOS-1 and -2 normal equations over
the same time period as GRACE were used in the combination in order to improve the
gravity field solution.
The solution was obtained by Cholesky decomposition of the accumulated normal equations.
This included the estimation of the time variable parameters from the GRACE contribution.
These time variable parameters were afterwards extrapolated to the mid of the GOCE
measurement period (1st June 2010)

Specific features of resulting gravity field:
The model is a satellite-only model based on a full combination of GOCE-SGG with
GRACE and LAGEOS, leading to both excellent orbit fits as well as GPS/leveling results
Processing details are presented in Bruinsma et al. 2010 and Pail et al. 2011.

Bruinsma S.L., Marty J.C., Balmino G., Biancale R., Foerste C.,
Abrikosov O. and Neumayer H, 2010, GOCE Gravity Field Recovery by Means
of the Direct Numerical Method, presented at the ESA Living Planet
Symposium, 27th June - 2nd July 2010, Bergen, Norway; See also: earth.esa.int/GOCE
Bruinsma, S.L., J.M. Lemoine, R. Biancale, N. Vales (2009) CNES/GRGS 10-day
gravity field models (release 2) and their evaluation, Adv. Space Res.,
Metzler B. and Pail R., 2005, GOCE Data Processing: The Sperical Cap Regularization
Approach, Stud. Geophys. Geod. 49 (2005), 441-462
Pail R., Bruinsma S., Migliaccio F., Foerste C., Goiginger H., Schuh W.-D, Hoeck E,
Reguzzoni M., Brockmann J.M, Abrikosov O., Veicherts M., Fecher T., Mayrhofer R.,
Krasbutter I., Sanso F. & Tscherning C.C., 2011, First GOCE gravity field models
derived by three different approaches. Journal of Geodesy, 85, 11, 819-843