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

EIGEN-6S4 A time-variable satellite-only gravity field model to d/o 300 based on LAGEOS, GRACE and GOCE data from the collaboration of GFZ Potsdam and GRGS Toulouse
[version 2.0]
ISO19139(INSPIRE)
DIF
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Dataset

Förste, Christoph
• Bruinsma, Sean
• Abrikosov, Oleh
• Rudenko, Sergiy
• Lemoine, Jean-Michel
• (et. al.)

__Abstract:__EIGEN-6S4 (Version 2) is a satellite-only global gravity field model from the combination of LAGEOS, GRACE and GOCE data. All spherical harmonic coefficients up to degree/order 80 are time variable. Their time variable parameters consist of drifts as well as annual and semi-annual variations per year. The time series of the time variable spherical harmonic coefficients are based on the LAGEOS-1/2 solution (1985 to 2003) and the GRACE-LAGEOS monthly gravity fields RL03-v2 (August 2002 to July 2014) from GRGS/Toulouse (Bruinsma et al. 2009). The herein included GRACE/LAGEOS data were combined with all GOCE data which have been processed via the direct numerical approach (Pail et al. 2011). The polar gap instabilty has been overcome using the Sperical Cap Regularization (Metzler and Pail 2005). That means this model is a combination of LAGEOS/GACE with GO_CONS_GCF_2_DIR_R5 (Bruinsma et al. 2013). Version History: This data set is an updated version of Foerste et al. (2016, http://doi.org/10.5880/icgem.2016.004) Compared to the first version, EIGEN-6S4v2 contains an improved modelling of the time variable part, in particular for C20.

ITSG-Grace2018 - Monthly, Daily and Static Gravity Field Solutions from GRACE
ISO19139(INSPIRE)
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Dataset

Mayer-Gürr, Torsten
• Behzadpur, Saniya
• Ellmer, Matthias
• Kvas, Andreas
• Klinger, Beate
• (et. al.)

Monthly solutions:product_type gravity_fieldmodelname ITSG-Grace2018_nLL_YYYY-MMearth_gravity_constant 3.9860044150e+14radius 6.3781363000e+06max_degree LL errors formalnorm fully_normalizedtide_system zero_tide Daily solutions:product_type gravity_fieldmodelname ITSG-Grace2018_n40_YYYY-MM-DDearth_gravity_constant 3.9860044150e+14radius 6.3781363000e+06max_degree 40errors formalnorm fully_normalizedtide_system zero_tide Static Field:product_type gravity_fieldmodelname ITSG-Grace2018searth_gravity_constant 3.9860044150e+14radius 6.3781363000e+06max_degree 200errors formalnorm fully_normalizedtide_system zero_tide

__Abstract:__The ITSG-Grace2018 gravity field model is the latest GRACE-only gravity field model computed at Graz University of Technology, providing unconstrained monthly and regularized daily solutions as well as a long-term static field. For each month of the observation period, sets of spherical harmonic coefficients for different maximum degrees (60, 96, 120) were estimated without applying any regularization. In order to resolve high-frequency gravity field variations as detailed as possible, a set of spherical harmonic coefficients up to degree and order 40 was co-estimated. K-band range rates with a sampling of 5 seconds and kinematic orbits with a sampling of 5 minutes were used as observations. The kinematic orbits of the GRACE satellites (Zehentner and Mayer-Gürr 2013, 2014) were processed using the GPS orbits and clock solutions provided by CODE. Additionally, a full accelerometer scale factor matrix was estimated per day (Klinger and Mayer-Gürr, 2016). The accelerometer bias was modelled through cubic splines with a node interval of six hours and estimated for each axis and day. Detailed information about ITSG-Grace2018 is available at http://ifg.tugraz.at/ITSG-Grace2018. The monthly and daily data covers the period between April 2002 and August 2016.

Monthly solutions:product_type gravity_fieldmodelname ITSG-Grace2018_nLL_YYYY-MMearth_gravity_constant 3.9860044150e+14radius 6.3781363000e+06max_degree LL errors formalnorm fully_normalizedtide_system zero_tide Daily solutions:product_type gravity_fieldmodelname ITSG-Grace2018_n40_YYYY-MM-DDearth_gravity_constant 3.9860044150e+14radius 6.3781363000e+06max_degree 40errors formalnorm fully_normalizedtide_system zero_tide Static Field:product_type gravity_fieldmodelname ITSG-Grace2018searth_gravity_constant 3.9860044150e+14radius 6.3781363000e+06max_degree 200errors formalnorm fully_normalizedtide_system zero_tide

ITSG-Grace2016 - Monthly and Daily Gravity Field Solutions from GRACE
ISO19139(INSPIRE)
DIF
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Dataset

Mayer-Gürr, Torsten
• Behzadpour, Saniya
• Ellmer, Matthias
• Kvas, Andreas
• Klinger, Beate
• (et. al.)

__Abstract:__The ITSG-Grace2016 gravity field model is the latest GRACE only gravity field model computed at Graz University of Technology, providing unconstrained monthly and Kalman smoothed daily solutions. It covers the whole GRACE time span from 2002-04 and will be continually updated. For each month of the observation period, sets of spherical harmonic coefficients for different maximum degrees (60, 90, 120) were estimated without applying any regularization. In order to resolve daily gravity field variations as detailed as possible, a set of spherical harmonic coefficients up to degree and order 40 was estimated using the Kalman smoother estimation procedure introduced by Kurtenbach et al. 2012.K-band range rates with a sampling of 5 seconds and kinematic orbits with a sampling of 5 minutes were used as observations. The kinematic orbits of the GRACE satellites (Zehentner and Mayer-Gürr 2013, 2014) were processed using the GPS orbits and clock solutions provided by IGS. An improved attitude product derived from a combination of star camera data and angular accelerations (Klinger and Mayer-Gürr 2014) was used to estimate K-band antenna center variations (one set per month). Additionally, accelerometer scale factors were estimated per axis and day. The accelerometer bias was modelled through cubic splines with a node interval of six hours and estimated for each axis and day. Detailed information about ITSG-Grace2016 is available at http://ifg.tugraz.at/ITSG-Grace2016.

Ries, J.
• Bettadpur, S.
• Eanes, R.
• Kang, Z.
• Ko, U.
• (et. al.)

__Abstract:__GGM05C is an unconstrained global gravity model complete to degree and order 360 determined from 1) GRACE K-band intersatellite range-rate data, GPS tracking and GRACE accelerometer data, 2) GOCE gradiometer data (ZZ+YY+XX+XZ) spanning the entire mission using a band pass filter of 10-50 mHz and polar gap filled with synthetic gradients from GGM05S to degree/order 150 evaluated at 200-km altitude, and 3) terrestrial gravity anomalies from DTU13 (Andersen et al., 2014). The value for C20 has been replaced with a value derived from satellite laser ranging. No rate terms were modeled. For additional details on the background modeling, see the CSR RL05 processing standards document available at ftp://podaac.jpl.nasa.gov/allData/grace/docs/L2-CSR0005_ProcStd_v4.0.pdf (Bettadpur 2012). Detailed information about GGM05C is available at ftp://ftp.csr.utexas.edu/pub/grace/GGM05/README_GGM05C.pdf (Ries et al., 2016).

SGG-UGM-1: the high resolution gravity field model based on the EGM2008 derived gravity anomalies and the SGG and SST data of GOCE satellite
ISO19139(INSPIRE)
DIF
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Dataset

Liang, Wei

SGG-UGM-1 is a global gravity field model computed by the combination of EGM2008 gravity anomalies and GOCE SGG,SST data Input data:-- EGM2008 derived gravity anomalies (5' x 5' resolution)-- GOCE SGG data: EGG_NOM_2 (GGT: Vxx, Vyy, Vzz) in GRF-- GOCE SST data: SST_PKI_2, SST_PCV_2, SST_PRD_2 Processing procedure:-- Block-diagonal normal equation system up to degree and order 2159 are formed with EGM2008 gravity anomaly data using block-diagonal least squares method. -- Fully occupied normal equation system up to degree and order 220 are formed by GOCE SGG data and the SST observations along the GOCE orbit based on least-squares analysis. The diagonal components (Vxx, Vyy, Vzz) of the gravitational gradient tensor are used to form the system of observation equations with the band-pass ARMA filter. The point-wise acceleration observations (ax, ay, az) along the orbit are used to form the system of observation equations up to the maximum spherical harmonic degree/ order 130.-- SGG-UGM-1 is resolved by combining the two normal equation systems using the least-squares method.

__Abstract:__SGG-UGM-1 is a static gravity field model based on EGM2008 derived gravity anomalies and GOCE Satellite Gravity Gradiometry (SGG) data and the Satellite-to-Satellite Tracking (SST) observations up to degree and order 2159. Block-diagonal normal equation system up to degree and order 2159 are formed with EGM2008 gravity anomaly data using block-diagonal least squares method. Fully occupied normal equation system up to degree and order 220 are formed by GOCE SGG data and the SST observations along the GOCE orbit based on least-squares analysis. The diagonal components (Vxx, Vyy, Vzz) of the gravitational gradient tensor are used to form the system of observation equations with the band-pass ARMA filter. The point-wise acceleration observations (ax, ay, az) along the orbit are used to form the system of observation equations up to the maximum spherical harmonic degree/order 130. SGG-UGM-1 is resolved by combination of the two normal equation systems using least squares method. It is the first generation of high-resolution gravity model in ICGEM developed by School of Geodesy and Geomatics (SGG), Wuhan University (WHU). More details about the determination of the model are given in our paper “The determination of an ultra high gravity field model SGG-UGM-1 by combining EGM2008 gravity anomaly and GOCE observation data” (Liang W, Xu X, Li J, et al. Acta Geodaeticaet Cartographica Sinica. 2018, 47(4): 425-434. DOI:10.11947/j. AGCS.2018.20170269) and “A GOCE only gravity model GOSG01S and the validation of GOCE related satellite gravity models ” (Xu X, Zhao Y, Reubelt T, et al. Geodesy and Geodynamics. 2017, 8(4): 260-272. http://dx.doi.org/10.1016/j.geog.2017.03.013). The work is supported by the Natural Science Foundation of China (Nos. 41774020, 41210006 and 41404020

SGG-UGM-1 is a global gravity field model computed by the combination of EGM2008 gravity anomalies and GOCE SGG,SST data Input data:-- EGM2008 derived gravity anomalies (5' x 5' resolution)-- GOCE SGG data: EGG_NOM_2 (GGT: Vxx, Vyy, Vzz) in GRF-- GOCE SST data: SST_PKI_2, SST_PCV_2, SST_PRD_2 Processing procedure:-- Block-diagonal normal equation system up to degree and order 2159 are formed with EGM2008 gravity anomaly data using block-diagonal least squares method. -- Fully occupied normal equation system up to degree and order 220 are formed by GOCE SGG data and the SST observations along the GOCE orbit based on least-squares analysis. The diagonal components (Vxx, Vyy, Vzz) of the gravitational gradient tensor are used to form the system of observation equations with the band-pass ARMA filter. The point-wise acceleration observations (ax, ay, az) along the orbit are used to form the system of observation equations up to the maximum spherical harmonic degree/ order 130.-- SGG-UGM-1 is resolved by combining the two normal equation systems using the least-squares method.

A GOCE only gravity model GOSG01S based on the SGG and SST observations
ISO19139(INSPIRE)
DIF
DataCite
Dataset

Xu, Xinyu

GOSG01S is a static gravity field model complete to spherical harmonic degree of 220 derived by using the Satellite Gravity Gradiometry (SGG) data and the Satellite-to-Satellite Tracking (SST) observations along the GOCE orbit based on least-squares analysis. Input data:-- GOCE SGG data: EGG_NOM_2 (GGT: Vxx, Vyy, Vzz) in GRF (1/11/2009-31/5/2012)-- GOCE SST data: SST_PKI_2, SST_PCV_2, SST_PRD_2 (1/11/2009-5/7/2010)-- Attitude: EGG_NOM_2 (IAQ), SST_PRM_2 (PRM)-- Non-conservative force: Common mode ACC (GG_CCD_1i)-- Background model: tidal model (solid etc.), third-body acceleration, relativistic corrections, ...-- GOSG01S is a GOCE only satellite gravity model, since no priori gravity information was used in modelling procedure. Data progress strategies: Data preprocessing: - Gross outlier elimination and interpolation (only for the data gaps less than 40s). - Splitting data into subsections for gaps > 40s The normal equation from SST data: - Point-wise acceleration approach (PAA) - Extended Differentiation Filter (low-pass) - Max degree: up to 130 - Data: PKI, PCV, CCD The normal equation from SGG data: - Space-Wise LS method - Max degree: up to 220 - Data: GGT, PRD, IAQ, PRM - Band-pass filter: used to deal with colored-noise of GGT observations (pass band 0.005-0.041Hz ) - Forming the normal equations according to subsections - Spherical harmonic base function transformation instead of transforming GGT from GRF to LNRF Combination of SGG and SST: - Max degree: up to 220 - The VCE technique is used to estimate the relative weights for Vxx, Vyy, Vzz - Tikhonov Regularization Technique (TRT) is only applied to near (zonal) terms (m<20) - Strictly inverse the normal matrix based on MPI

__Abstract:__We compile the GOCE-only satellite model GOSG01S complete to spherical harmonic degree of 220 using Satellite Gravity Gradiometry (SGG) data and the Satellite-to-Satellite Tracking (SST) observations along the GOCE orbit based on applying a least-squares analysis. The diagonal components (Vxx, Vyy, Vzz) of the gravitational gradient tensor are used to form the system of observation equations with the band-pass ARMA filter. The point-wise acceleration observations (ax, ay, az) along the orbit are used to form the system of observation equations up to the maximum spherical harmonic degree/order 130. The GOCE related satellite gravity models GOSG01S, GOTIM05S, GODIR05S, GOTIM04S, GODIR04S, GOSPW04S, JYY_GOCE02S, EIGEN-6C2 and EGM2008 are also validated by using GPS-leveling data in China and USA. According to the truncation at degree 200, the statistic results show that all GGMs have very similar differences at GPS-leveling points in USA, and all GOCE related gravity models have better performance than EGM2008 in China. This new model was developed by School of Geodesy and Geomatics (SGG) of Wuhan University (WHU) and Institute of Geodesy of University of Stuttgart. More details about the gravity field model GOSG01S is given in our paper “A GOCE only gravity model GOSG01S and the validation of GOCE related satellite gravity models ” (Xu X, Zhao Y, Reubelt T, et al. Geodesy and Geodynamics. 2017, 8(4): 260-272. http://dx.doi.org/10.1016/j.geog.2017.03.013). This work is supported by the National Key Basic Research Program of China (973 program, grant no.: 2013CB733301), the Major International (Regional) Joint Research Project (grant no.: 41210006).

GOSG01S is a static gravity field model complete to spherical harmonic degree of 220 derived by using the Satellite Gravity Gradiometry (SGG) data and the Satellite-to-Satellite Tracking (SST) observations along the GOCE orbit based on least-squares analysis. Input data:-- GOCE SGG data: EGG_NOM_2 (GGT: Vxx, Vyy, Vzz) in GRF (1/11/2009-31/5/2012)-- GOCE SST data: SST_PKI_2, SST_PCV_2, SST_PRD_2 (1/11/2009-5/7/2010)-- Attitude: EGG_NOM_2 (IAQ), SST_PRM_2 (PRM)-- Non-conservative force: Common mode ACC (GG_CCD_1i)-- Background model: tidal model (solid etc.), third-body acceleration, relativistic corrections, ...-- GOSG01S is a GOCE only satellite gravity model, since no priori gravity information was used in modelling procedure. Data progress strategies: Data preprocessing: - Gross outlier elimination and interpolation (only for the data gaps less than 40s). - Splitting data into subsections for gaps > 40s The normal equation from SST data: - Point-wise acceleration approach (PAA) - Extended Differentiation Filter (low-pass) - Max degree: up to 130 - Data: PKI, PCV, CCD The normal equation from SGG data: - Space-Wise LS method - Max degree: up to 220 - Data: GGT, PRD, IAQ, PRM - Band-pass filter: used to deal with colored-noise of GGT observations (pass band 0.005-0.041Hz ) - Forming the normal equations according to subsections - Spherical harmonic base function transformation instead of transforming GGT from GRF to LNRF Combination of SGG and SST: - Max degree: up to 220 - The VCE technique is used to estimate the relative weights for Vxx, Vyy, Vzz - Tikhonov Regularization Technique (TRT) is only applied to near (zonal) terms (m<20) - Strictly inverse the normal matrix based on MPI

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.

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.

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