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publicationYear 2017
datacentre DOIDB.ICGEM - ICGEM International Centre for Global Earth Models

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The gravity field model based on the second invariant of the GOCE gravitational gradient tensor: IGGT_R1
ISO19139(INSPIRE)
DIF
DataCite
Model

Lu, Biao
• Luo, Zhicai
• Zhong, Bo
• Zhou, Hao
• Förste, Christoph
• (et. al.)

__Abstract:__IGGT_R1 is a static gravity field model based on the second invariant of the GOCE gravitational gradient tensor, up to degree and order 240. Based on tensor theory, three invariants of the gravitational gradient tensor (IGGT) are independent of the gradiometer reference frame (GRF). Compared to traditional methods for calculation of gravity field models based on GOCE data, which are affected by errors in the attitude indicator, using IGGT and least squares method avoids the problem of inaccurate rotation matrices. IGGT_R1 is the first experiment to use this method to build a real gravity field model by using GOCE gravitational gradients. This new model has been developed by Wuhan University (WHU), GFZ German Research Centre for Geosciences (GFZ), Technical University of Berlin (TUB), Huazhong University of Science and Technology (HUST) and Zhengzhou Information Engineering University (IEU). More details about the gravity field model IGGT_R1 is given in our paper “The gravity field model IGGT_R1 based on the second invariant of the GOCE gravitational gradient tensor” (Lu et al., 2017, http://doi.org/10.1007/s00190-017-1089-8). This work is supported by the Chinese Scholarship Council (No. 201506270158), the Natural Science Foundation of China (Nos. 41104014, 41131067, 41374023, 41474019 and 41504013) and the Key Laboratory of Geospace Environment and Geodesy, Ministry Education, Wuhan University (No. 16-02-07).

Wu, Hu
• Müller, Jürgen
• Brieden, Phillip

Processing procedures: Gravity from orbits (SST): * Acceleration approach was applied to the kinematic orbit data; * PKI data was at 1 s sampling rate; * Model was derived up to d/o (degree/order) 150; * VCM (Variance-Covariance Matrix) was derived arc-wisely from the post-fit residuals. Gravity from gradients (SGG): * Gradients Vxx, Vyy and Vzz in the GRF (Gradiometer Reference Frame) were used; * Gradients were down-sampled to 2 s; * Model was derived up to d/o 250; * VCM was estimated arc-wisely from the post-fit residuals. Regularization: * A strong Kaula-regularization was applied to constrain the (near-)zonal coefficients that are degraded by the polar gap problem; * A slight Kaula-regularization was applied to improve the signal-to-noise ratio of the coefficients between d/o 201 and 250; * The regularization parameters were empirically determined. Combined solution: * The normal equations for SST and SGG were summed wih proper weighting factors; * Weighting factors for SST and SGG were determined from variance component estimation; * A direct inversion was applied on the final normal equation.

__Abstract:__IfE_GOCE05s is a GOCE-only global gravity field model, which was developed at the Institut für Erdmessung (IfE), Leibniz Universität Hannover, Germany. The observations with a time span from 1 November 2009 to 20 October 2013 are used for the model recovery. The GOCE precise kinematic orbit with 1-s sampling rate is processed for the gravity field up to degree/order 150, while the three main diagonal gravity gradients are down-sampled to 2 s and used to recover the model up to degree/order 250. With two additional Kaula’s regularizations, the combined model “IfE_GOCE05s” is derived, with a maximum degree of 250. To develop IfE_GOCE05s, the following GOCE data (01.11.2009 - 20.10.2013) was used: * Orbits: SST_PKI_2, SST_IAQ_2; * Gradients: EGG_GGT_2, EGG_IAQ_2. None any priori gravity field information was used.

Processing procedures: Gravity from orbits (SST): * Acceleration approach was applied to the kinematic orbit data; * PKI data was at 1 s sampling rate; * Model was derived up to d/o (degree/order) 150; * VCM (Variance-Covariance Matrix) was derived arc-wisely from the post-fit residuals. Gravity from gradients (SGG): * Gradients Vxx, Vyy and Vzz in the GRF (Gradiometer Reference Frame) were used; * Gradients were down-sampled to 2 s; * Model was derived up to d/o 250; * VCM was estimated arc-wisely from the post-fit residuals. Regularization: * A strong Kaula-regularization was applied to constrain the (near-)zonal coefficients that are degraded by the polar gap problem; * A slight Kaula-regularization was applied to improve the signal-to-noise ratio of the coefficients between d/o 201 and 250; * The regularization parameters were empirically determined. Combined solution: * The normal equations for SST and SGG were summed wih proper weighting factors; * Weighting factors for SST and SGG were determined from variance component estimation; * A direct inversion was applied on the final normal equation.

GOCE gravity field model by means of the space-wise approach (release R5)
ISO19139(INSPIRE)
DIF
DataCite
Dataset

Gatti, Andrea
• Reguzzoni, Mirko

__Abstract:__GOCE input data:- Gradients: EGG_GGT_2C, EGG_NOM_2- Orbits: SST_PRD_2I (reduced dynamic orbits for geo-locating gravity gradients); SST_PKI_2I (kinematic orbits for long-wavelength gravity field recovery); SST_PCV_2I (variance information of kinematic orbit positions); SST_PRM_2I (rotation between inertial and Earth-fixed reference frames)- Attitude: EGG_IAQ_2C- Non-conservative accelerations: EGG_CCD_2C- Data period: 01/11/2009 - 20/10/2013 A-priori information used:- No corrections to any prior gravity field model are computed (GOCE-only model).- EIGEN-6C4 and GOCO05C are used for signal covariance modelling.- FES2004 is used for ocean tide modelling. Processing procedure:- The space-wise approach is a multi-step collocation procedure, developed in the framework of the GOCE HPF data processing for the estimation of gravity gradient grids at satellite altitude. By analysing these grids, spherical harmonic coefficients of the Earth gravitational field and their error covariance matrix can be computed.- SST model: gravitational potential estimation by energy conservation approach applied to kinematic orbits; grid interpolation of gravitational potential at mean satellite altitude by least-squares adjustment with local collocation refinement; spherical harmonic analysis of the estimated grids by numerical integration.- SST+SGG model: orbital filtering of the data reduced by SST model (Wiener filter followed by whitening filter); grid interpolation of gravitational gradients at mean satellite altitude by local collocation; spherical harmonic analysis of the estimated grids by numerical integration.- The full error covariance matrices of the estimated grids and spherical harmonic coefficients are derived by Monte Carlo simulations. Remarks:- The maximum spherical harmonic degree is 330 because this is the maximum degree used for the modelling of the signal covariance functions in the local collocation gridding.- The spherical harmonic coefficients with the highest degrees have globally a small signal power, but they could contribute to better model local areas with a high signal-to-noise ratio.- Any truncation of the spherical harmonic expansion to a maximum degree lower than 330 could introduce errors due to the correlation of the estimated spherical harmonic coefficients.- The variance-covariance error information of the estimated spherical harmonic coefficients is computed by Monte Carlo simulations, also including the signal omission error up to degree and order 330.- An error covariance propagation to functionals of the gravitational potential by only using coefficient error variances could be strongly approximated because coefficient error correlations are significant. The use of the full error variance-covariance matrix is therefore recommended.

A new time-series of GRACE monthly gravity field solutions obtained by accounting for the colored noise in the K-Band range-rate measurements
DataCite
Dataset

Guo, X.
• Zhao, Q.
• Ditmar, P.
• Liu, J.

__Abstract:__The WHU_RL01 GRACE monthly gravity field solutions are produced with the classical dynamic approach at the GNSS Research Center of Wuhan University. Three sets of monthly solutions complete to d/o 60, 90 and 120 are produced without any regularization for the time period from 2002-04 to 2016-07. K-Band range rates with a sampling of 5 seconds and reduced-dynamic orbits with a sampling of 5 minutes are used as observations. To account for the colored noise in the K-Band range-rate measurements, the frequency-dependent data weighting scheme proposed by Ditmar et al. (2007) is adopted. Additionally, a unified weight for the reduced-dynamic orbits is applied based on its a priori precision of 2 cm for each component. The strategy adopted for producing the WHU_RL01 GRACE monthly gravity field models is summarized in Table 1 (please find it in the attached explanatory file). It should be noted that relatively short arcs (6 hours per arc) are used to reduce the resonance effects caused by inaccuracies in initial state vectors and background force models (Colombo, 1984). The reduced-dynamic orbits are also used as observations in our data processing. Although a reduced-dynamic orbit contain certain a priori gravity field information, the resulting bias in the gravity field solutions have been proved to be limited when inverted together with the K-band measurements (Chen et al., 2014; Liu et al., 2010).

Pail, Roland
• Fecher, Thomas
• Barnes, Daniel
• Factor, John
• Holmes, Simon
• (et. al.)

XGM2016 is a combination model based on the satellite-only gravity field model GOCO05s and a global 15'x15' data grid provided from NGA's data base.

__Abstract:__The experimental gravity field model XGM2016 is an outcome of TUM's assessment of a 15'x15' data grid excerpt provided from NGA's updated and revised gravity data base. The assessment shall support NGA's efforts on the way on the way to the Earth Gravity Model EGM2020.

XGM2016 is a combination model based on the satellite-only gravity field model GOCO05s and a global 15'x15' data grid provided from NGA's data base.

Tongji-Grace02s, a static unconstrained GRACE-only gravity field model
ISO19139(INSPIRE)
DIF
DataCite
Dataset

Chen, Qiujie
• Shen, Yunzhong
• Chen, Wu
• Zhang, Xingfu

Input Data:- GRACE RL02 L1B (JPL) data products: Jan. 2003 – Jul. 2016- AOD1B RL05 (GFZ) de-aliasing product Calculation method:- modified short-arc approach- arc length: 2 hours Force models: - can be found in Chen et al. 2015 (Chen, Q., Shen, Y., Zhang, X., Hsu, H., Chen, W., Ju, X., Lou, L., 2015. Monthly gravity field models derived from GRACE Level 1B data using a modified short-arc approach. Journal of Geophysical Research: Solid Earth, 120(3), 1804-1819. http://doi.org/10.1002/2014JB011470).

__Abstract:__Tongji-Grace02s, a static unconstrained GRACE-only gravity field model up to degree and order 180 was developed by Tongji University under the sponsorship of National Natural Science Foundation of China (41474017). To derive Tongji-Grace02s, the modified short-arc approach which estimates errors of non-conservative acceleration and attitude observations was adopted, and the GRACE-only data (including orbits, range-rates, non-conservative accelerations and attitudes) over the period Jan. 2003 to Jul. 2016 were used. The quality of Tongji-Grace02s is remarkably better than Tongji-GRACE01. In computing Tongji-Grace02s, neither constraint nor regularization was applied.

Input Data:- GRACE RL02 L1B (JPL) data products: Jan. 2003 – Jul. 2016- AOD1B RL05 (GFZ) de-aliasing product Calculation method:- modified short-arc approach- arc length: 2 hours Force models: - can be found in Chen et al. 2015 (Chen, Q., Shen, Y., Zhang, X., Hsu, H., Chen, W., Ju, X., Lou, L., 2015. Monthly gravity field models derived from GRACE Level 1B data using a modified short-arc approach. Journal of Geophysical Research: Solid Earth, 120(3), 1804-1819. http://doi.org/10.1002/2014JB011470).

The gravity field NULP-02s to d/o 250 based on radial derivatives EGG_TRF_2 of satellite mission GOCE
ISO19139(INSPIRE)
DIF
DataCite
Dataset

Marchenko, Alexander N.
• Marchenko, Dmitriy A.
• Lopyshansky, Alexander N.

Input Data:- GOCE EGG_TRF_2 gradients from November 2009 to October 2013. - radial derivatives of the EGM2008 model to d/o 360 for both polar gaps as additional information at the Gaussian grid nodesto avoid these polar gaps instability. Calculation method:- Kalman filtration of the radial derivatives with additional smoothing by Gauss filtering - Formation of Gaussian grid of radial gradients using modified local non-smooth splines - Estimation of harmonic coefficients via Gauss quadrature formula

__Abstract:__NULP-02S gravity field model up to degree/order 250 was developed based on EGG_TRF_2 GOCE radial gradients and Gauss quadrature formula in the frame of space-wise approach by National University “Lviv Polytechnic” (Institute of Geodesy, Laboratory for Theoretical Geodesy and Data Processing). All details of data pre-processing and applied method for model developing are presented in the paper “Gravity field models derived from the second degree radial derivatives of the GOCE mission: a case study” (ANNALS OF GEOPHYSICS, 59, 6, 2016, S0649; doi:10.4401/ag-7049).

Input Data:- GOCE EGG_TRF_2 gradients from November 2009 to October 2013. - radial derivatives of the EGM2008 model to d/o 360 for both polar gaps as additional information at the Gaussian grid nodesto avoid these polar gaps instability. Calculation method:- Kalman filtration of the radial derivatives with additional smoothing by Gauss filtering - Formation of Gaussian grid of radial gradients using modified local non-smooth splines - Estimation of harmonic coefficients via Gauss quadrature formula

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