TIM_R6e is an extended version of the satellity-only global gravity field model TIM_R6 (Brockmann et al., 2019) which includes additional terrestrial gravity field observations over GOCE's polar gap areas. The included terrestrial information consists of the PolarGap campaign data (Forsberg et al., 2017) augumented by the AntGG gravity data compilation (Scheinert et al., 2016) over the southern polar gap (>83°S) and the ArcGP data (Forsberg et al. 2007) over the northern polar gap (>83°N). The combination is performed on normal equation level, encompassing the terrestrial data as spectrally limited geographic 0.5°x0.5° grids over the polar gaps.
"ESA’s Release 6 GOCE gravity field model by means of the direct approach based on improved filtering of the reprocessed gradients of the entire mission (GO_CONS_GCF_2_DIR_R6)" is a static gravitational model available via ICGEM (Ince et al., 2019)Model Characteristics----------------------GOCE Input Data:- Gradients: EGG_NOM_2 (re-calibrated release 2018, Siemes et al. 2019)- Orbits: SST_PRD_2 (reduced dynamic orbits)- Attitude: EGG_IAQ_2C- Data period: 20091009T000000-20131020T235959A-priori Information used:----------------------------The a-priori gravity field for the processing of the GOCE gravity gradients was the GOCE-model 5th release from the direct approach GO_CONS_GCF_2_DIR_R5 up to its maximum degree/order 300 (Bruinsma et al. 2014).Processing Procedures:----------------------The GOCE gravity gradients were processed without applying the external calibration corrections.The observation equations were filtered with a 0 - 125.0 mHz lowpass filter. Subsequently "SGG" normal equations to degree/order 300 have been computed separately for 46 continous time segments of approximately 1270 days totally (identified after the preprocessing of the data) and for each of the gradient components Txx, Tyy, Tzz and Txz.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 GRACE and SLR normal equations. Details about the latter contributions 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/SLR data mentioned below to degree/order 130.3) Additionally a Kaula regularization was applied to all coefficients beyond degree 180The solution was obtained by Cholesky decomposition of the accumulated normal equations.Details of the GRACE contribution:----------------------------------The GRACE part consists of 85 monthly normal equations to degree/order 200 out of the time span January 2007 till November 2014 from GFZ's GRACE Release 06 processing based on GNSS-SST and K-Band-Range-Rate data. For details of this GRACE release see Dahle et al. 2018.The following individual months are not covered by GRACE: 2001101, 201106, 201205, 201210, 201303, 201304, 201308, 201402 and 201407The harmonics of very-low degree, in particular degrees 2 and 3, cannot be estimated accurately with GRACE and GOCE data only. Therefore, normal equations from the following SLR missions were used in the combination in order to improve the gravity field solution:- LAGEOS-1/2, AJISAI, STARLETTE and STELLA from Jan. 2002 till Oct. 2018- LARES from Feb. 2012 till Oct. 2018The SLR tracking data were processed according to the GRACE Release 6 standards During the combination with GOCE, the GRACE contribution was taken only up to degree/order 130 and the SLR contribution only up to degree/oder 5As GRACE is sensitive for temporal variations in the Earth gravity field, the date 20100901 should be taken as reference epoch of this model. This date is mean of the included GRACE measurement time span by considering the mentioned missed months. This reference epoch is close to the mean of the measurement time span of the included SLR tracking data (20100701)Specific features of resulting gravity field--------------------------------------------The model is a satellite-only model based on a full combination of GOCE-SGG with GRACE and SLR tracking data, leading to both excellent orbit fits as well as GPS/leveling resultsProcessing details are presented in Pail et al. 2011.
The static gravitational model GO_CONS_GCF_2_TIM_R6 Is the 6th release of the GOCE gravity field model by means of the time-wise approach.GOCE Input Data:- Gradients: EGG_NOM_2 (re-calibration, released 2018, version 0202)- Orbits:-- SST_PKI (kinematic orbits); SST_PCV (variance information of kinematic orbit positions),-- SST_RNX (original RINEX orbit data)- Attitude: EGG_IAQ_2C- Non-conservative accelerations: EGG_CCD_2C- Data period: 09/10/2009 - 20/10/2013No static a-priori gravity field information applied (neither as reference model, nor for constraining the solution)Processing procedures:- Gravity from orbits (SST):- short-arc integral method applied to kinematic orbits, up to degree/order 150- orbit variance information included as part of the stochastic model, it is refined by empirical covariance functions- Gravity from gradients (SGG):- parameterization up to degree/order 300- observations used: Vxx, Vyy, Vzz and Vxz in the Gradiometer Reference Frame (GRF)- realistic stochastic modelling by applying digital decorrelation filters to the observation equations; estimated separately for individual data segments applying a robust procedure- Combined solution:- addition of normal equations (SST D/O 150, SGG D/O 300)- Constraints:* Kaula-regularization applied to coefficients of degrees/orders 201 - 300 (constrained towards zero)* observation equations for zero gravity anomaly observations in polar regions (>83°) to constrain polar gaps towards zero (degree 11 to 300)- Optimum weighting (SST, SGG, constraints) based on variance component estimationSpecific features of resulting gravity field:- Gravity field solution is independent of any other gravity field information- Constraint towards zero starting from degree/order 201 to improve signal-to-noise ratio- Related variance-covariance information represents very well the true errors of the coefficients- Solution can be used for independent comparison and combination on normal equation level with other satellite-only models (e.g. GRACE), terrestrial gravity data, and altimetry- Since in the low degrees the solution is based solely on GOCE orbits, it is not competitive with a GRACE model in this spectral region is available via this data publication and via ICGEM (Ince et al., 2019). Link to ICGEM Website: http://icgem.gfz-potsdam.de- The reference epoch is 2010-01-01 (MJD 55197)Further processing details can be found in Brockmann (2014), Brockmann et al. (2014) Mayer-Gürr et al. (2005) and Pail et al. (2014).
GOCO06s is a satellite-only, global gravity field model up to degree and order 300, with secular and annual variations up to degree and order 120. It was produced by the GOCO Team (Technical University of Munich, University of Bonn, Graz University of Technology, Austrian Academy of Sciences, University of Bern) and is based on 1,160,000,000 observations from 19 satellites. The contributing satellite mission are: GOCE (TIM6 gradiometer observations), GRACE (ITSG-Grace2018s), kinematic orbits from Swarm A+B+C, TerraSAR-X, TanDEM-X, CHAMP, GRACE and GOCE, and SLR observations to LAGEOS, LAGEOS 2, Starlette, Stella, AJISAI, LARES, LARETS, Etalon 1/2 and BLITS. The combination of the individual data sources is performed on the basis of the full systems of normal equations, where the relative weighting between each constituent is determined by variance component estimation. In order to account for the polar gap of GOCE, the solution is Kaula-regularized after degree and order 150.The model is available via the ICGEM Service (Ince et al., 2019)
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.
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 - 20/10/2013A-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.
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.
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).
EIGEN-6S4 is satelite-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 GRACE-LAGEOS monthly gravity fields RL03-v1 (2003.0-2013.0) from GRGS/Toulouse (Bruinsma et al. 2009).The herein included GRACE 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/GRACE with GO_CONS_GCF_2_DIR_R5 (Bruinsma et al. 2013). We recommmend to use the updated version of this dataset (Förste et al. 2016, http://doi.org/10.5880/icgem.2016.008). that contains an improved modelling of the time variable part, in particular for C20.
GOCO05c is a static global combined gravity field model up to d/o 720. It has been elaborated by the GOCO Group (TU Munich, Bonn University, TU Graz, Austrian Academy of Sciences, University Bern). GOCO05c is a combination model based on the satellite-only gravity field model GOCO05s and several gravity anomaly datasets, constituting a global 15'x15' data grid. The combination is carried out in term of full normal equation systems.Contributing Institutions are: (1) TU Muenchen, DE, Institute of Astronomical and Physical Geodesy; (2) University of Bonn, DE, Institute of Geodesy and Geoinformation; (3) TU Graz, AU, Institute of Theoretical and Satellite Geodesy; (4) Austrian Academy of Sciences, Space Research Institute, and (5) University of Bern, CH, Astronomical Institute
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