A.4.1 to A.4.3 - Mean Field
(Convener: )

ESA's GOCE mission: latest (direct approach) models
(S. Bruinsma, C. Foerste)

Spectral Combination Method for Combining GOCE and GRACE Gravity Field Models
(B. Zhong, L. Biao, L. Zhicai)

EIGEN-6C3 - The newest high resolution global combined gravity field model based the GOCE Direct Approach
(S. Bruinsma, C. Foerste, O. Abrikosov, F. Flechtner, C.Dahle, K.H. Neumayer, F. Barthelmes, R. Koenig, J.-C. Marty, J-M. Lemoine, R. Biancale )

Title: ESA's GOCE mission: latest (direct approach) models
Presenter: Bruinsma, Sean
Co-Authors: S. Bruinsma; C. Foerste

Abstract: The three-axes gradiometer (approximately radial, along-track, normal to the orbit plane) of GOCE provides gravity gradients that are measured with a high accuracy only within its measurement bandwidth of approximately 0.005 to 0.1 Hz. Due to this instrumental behavior, the gravity gradient observation equations must be filtered. Within the direct numerical method this has been done using a band pass filter of 8 - 120 seconds. The GOCE GPS-SST data are only used to geolocate the gradients. The low-to-medium degree spherical harmonic coefficients of the gravity field are determined using GRACE GPS-SST and KBR data, as well as LAGEOS SLR data. All data are combined at normal equation level, which are solved using Cholesky decomposition. We apply the spherical cap regularization to stabilize the low-order spherical harmonic coefficients for the polar gaps in the GOCE data. Furthermore, Kaula regularization is used at the high degrees. The fourth release of the direct model will be presented, as well as an evaluation of the four-stage orbit lowering on the gravity field model accuracy and resolution.

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Title: Spectral Combination Method for Combining GOCE and GRACE Gravity Field Models
Presenter: Zhong, Bo
Co-Authors: L. Biao; L. Zhicai

Abstract: GOCE and GRACE are complementary in the spectral domain for recovering the earth's gravity field, and combining these two types of data can obtain high precision and high resolution satellite-only gravity field model. A commonly used method called combined adjustment was done by superposition of normal equations from each type of data and applying optimized relative weighting strategies, such as the GOCO series combined models. But this is a challenging task from the numerical point of view due to the sophisticated treatment of the data and simultaneous determination of the large number of unknowns. In order to provide a fast and effective method to determining GOCE and GRACE combined model, the spectral combination methods for combining GOCE and GRACE gravity field models are studied. The spectral combination formulas are established by the weighting of geopotential coefficients based on their error degree variances, error variances and block-diagonal error covariances, respectively. As a test, the GRACE gravity field model ITG-GRACE2010s and GOCE gravity field model GO_CONS_GCF_2_DIR_R1 are used for calculating and checking the spectral combination method. The results show that the accuracies of the combined gravity field models computed by these three kinds of spectral combination formulas are higher than those of GRACE or GOCE models, and their total accuracies are better than that of the GOCO01S model, which was solved from GOCE and GRACE data based on the combined adjustment method. In addition, the spectral combination formula weighted by the block-diagonal error covariances is better than the other two kinds of weighting schemes, because it considers the correlation among the coefficients of the same order.

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Title: EIGEN-6C3 - The newest high resolution global combined gravity field model based the GOCE Direct Approach
Presenter: Bruinsma, Sean
Co-Authors: C. Foerste; O. Abrikosov; F. Flechtner; C.Dahle; K.H. Neumayer; F. Barthelmes; R. Koenig; J.-C. Marty; J-M. Lemoine; R. Biancale

Abstract: GFZ Potsdam and GRGS Toulouse have a long-time close cooperation in the field of global gravity field determination, which presently focuses on (1) GOCE gravity field determination, and (2) computation of high-resolution combined gravity field models. Such data products play a fundamental role in geodesy and Earth sciences, ranging from practical purposes, like precise orbit determination, to scientific applications, like investigations of the density structure of the Earth's interior. Here we present our latest combined gravity field model EIGEN-6C3, which is an update of EIGEN-6C2 (EIGEN = European Improved Gravity model of the Earth by New techniques). The initial release of EIGEN-6, published in 2011, was the first global combined gravity field model containing GOCE data. It had been computed from a combination of LAGEOS, GRACE and GOCE data, augmented with the DTU10 surface gravity data and is complete to degree and order 1440 (corresponding to 14 km spatial resolution). The combination of the different data types has been done on the basis of full normal equations up to maximum degree/order 370. The spherical harmonic coefficients of the shorter wavelengths were obtained from a block diagonal normal equation from the terrestrial data only. As EIGEN-6C2 (published in 2012), the new EIGEN-6C3 will be complete to degree and order 1949 (corresponding to approx. 10 km spatial resolution). EIGEN-6C3 notably will contain the data of the 4th release of the GOCE Direct Approach model and additionally GOCE data from the lowered altitude phase after August 2012. The combination of GRACE and GOCE data is done on the basis of normal equations and allowed the construction of an accurate satellite-only contribution to the final combined model up to degree and order 260, in which the GOCE gradiometer data contribute only for degrees upwards of 45. This is achieved through filtering of the GOCE observation equations, which is necessary because of the degraded gradiometer performance outside the measurement bandwidth. The surface data normal equations are combined with satellite normal equations at a higher degree than formerly applied in pre-GOCE combined models (for instance at degree 70 in EIGEN-5C).

The quality evaluation (orbit computation, GPS leveling) of this latest EIGEN model with GOCE-only models, EGM2008, GGM03 and ITG10S demonstrates the gain in accuracy at high degrees, while its performance is identical to a GRACE-only model for the low degrees. Compared to the first release of EIGEN-6 this new release shows a general improvement. EIGEN-6C3 will available at the ICGEM data base at GFZ Potsdam (http://icgem.gfz-potsdam.de) by end of this year.

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