GOCE Gravity Field Model

Direct Solution - Fifth generation

Model Characteristics
GOCE Input Data:
- Gradients:   EGG_NOM_2
- Orbits:      SST_PKI (kinematic orbits)
- Attitude:    EGG_IAQ_2C
- Data period: 20091101T000000-20131020T235959
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 4th release from the direct approach GO_CONS_GCF_2_DIR_R4
up to its maximum degree/order 260 (Bruinsma et al. 2013).
Processing Procedures:
The GOCE gravity gradients were processed without applying the external
calibration corrections.
The observation equations were filtered with a 8.3 - 125.0 mHz bandpass
filter. Subsequently "SGG" normal equations to degree/order 300 have been
computed separately for 42 continuos time segments of 1259 days totally
(identified after the preprocessing of the data) and for each of the
gradient components Txx, Tyy, Tzz and Txz. For the period 20120801 to
20120831 Txx has been replaced by linear combination of Tyy and Tzz.
Tyy has been replaced by linear combinaytion of Txx and Tzz for the time
span 20130530 to 20130731.
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 orders 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 300 using the GRACE/LAGEOS data mentioned
   below to degree/order 130.
3) Additionally a Kaula regularization was applied to all coefficients
   beyond degree 180
The solution was obtained by Cholesky decomposition of the accumulated
normal equations.
Details of the GRACE contribution:
The GRACE part is a GRACE normal equation to degree/order 175 for the ten
years time period 2003 through 2012 from the GRGS/CNES release 3 GRACE
processing. For details of this GRACE release see:
During the combination with GOCE, the GRACE contribution was taken only up
to degree/order 130.
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., Foerste, C., Abrikosov, O., Marty, J.-C., Rio, M.-H.,
Mulet, S., Bonvalot, S. (2013): The new ESA satellite-only gravity field
model via the direct approach, Geophysical Research Letters, 40, 14, p. 3607-3612.
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