GOCE Gravity Field Model

Direct Solution - Fourth generation

Model Characteristics
GOCE Input Data:
- Gradients:   EGG_NOM_2
- Orbits:      SST_PKI (kinematic orbits)
- Attitude:    EGG_IAQ_2C
- Data period: 20091101T000000-20120801T060000
The full list of input data to this direct-approach model is provided in the IHD file.

A-priori Information used:
The a-priori gravity field for the processing of the GOCE gravity gradients was the
GOCE-model 3rd release from the direct approach GO_CONS_GCF_2_DIR_R3 up to its
maximum degree/order 240.

Processing Procedures:
The GOCE gravity gradients were processed without applying the external calibration 
The observation equations were filtered with a 8.3 - 125.0 mHz bandpass filter.
Subsequently "SGG" normal equations to degree/order 260 have been computed
separately for 30 continuos time segments (identified after the preprocessing
of the data) and for each of the gradient components Txx, Tyy, Tzz and Txz.
The Txx, Tyy, Tzz and Txz SGG normal equations were accumulated with the relative
weight 1.0. But within the SGG components, all observation equations have been 
weighted individually according to its standard deviation estimated w.r.t. the
a-priori gravity field.
To overcome the numerical instability of the GOCE-SGG normal equation 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 260 using the GRACE/LAGEOS data mentioned below to
degree/order 130.
3) Additionally a Kaula regularization was applied to all coefficients beyond
degree 200.
The solution was obtained by Cholesky decomposition of the accumulated normal 

Details of the GRACE contribution:
The GRACE part is a GRACE normal equation to degree/order 180 for the time period
2003 through 2012. This normal equation system consists of two different
- The normal equation entries for the spherical harmonic degree range to degree
54 came from the GRGS/CNES release 2 GRACE processing (Bruinsma et al., 2009).
- The remaining part from degree 55 till degree 180 was taken from the new
GFZ GRACE release 05 (Dahle et al. 2012).
Such a blended composition has been chosen since the GRGS/CNES release 2 has
a better performance w.r.t. the GFZ release 5 regarding the longe wavelengths
below degree 55. This has been proved in satellite orbit computation tests.
Otherwise, the GFZ release 5 has a significant better performance in the shorter
wavelengths beyond degree 54 since this new GRACE release shows a significant
noise reduction over deserts and oceans w.r.t. the GRGS release 2 concerning
the North-South striping.
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 time period  1985 through 2010 were used in the combination in order 
to improve the gravity field solution.

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.,
Dahle C., Flechtner F., Gruber C., Koenig D., Koenig R., Michalak G. and
Neumayer K.-H. (2012): GFZ GRACE Level-2 Processing Standards Document for Level-2
Product Release 0005, (Scientific Technical Report - Data , 12/02), Potsdam, 20 p.
DOI: 10.2312/GFZ.b103-1202-25
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