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 For the period 20120801 to 20120831 Txx has been replaced by linear combination of Tyy and Tzz. Tyy has been replaced by linear combinaytion of Txx and Tzz for the time span 20130530 to 20130731.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: grgs.obs-mip.fr/grace/variable-models-grace-lageos/grace-solutions-release-03 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. References: --------------------------------------------------------------------------- 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. doi.org/10.1002/grl.50716 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