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ITU_GRACE16 The global gravity field model including GRACE data up to degree and order 180 of ITU and other collaborating institutions

ITU_GRACE16 is a static global gravity field model up to degree order 180 computed from GRACE SST data of 50 months collected between April 2009 to October 2013 by collaboration of various national institutions (YTU, KOU, NEU, SU) lead by ITU and OSU as the international collaborator with the support of research grant no 113Y155 from the Scientific and Technological Research council of Turkey (TUBITAK). The model coefficients are obtained following a two-step approach. (1) the in-situ geopotential differences (GPDs) between GRACE satellite are estimated using SST and precise orbit using improved energy integral method given in Guo et al. 2015 and Shang et al. 2015. (2) The estimated GPDs were then used as the observables of the SH expansion for the inversion.ITU_GRACE16 is not regularized or constrained in any way, the errors increase with degree. We do not recommend to use ITU_GRACE16 beyond the degree 130 without smoothing. No rate terms were modeled, and no corrections for earthquakes have been applied. For additional details on the background modeling,see the GFZ RL05 processing standards document available at:

A GOCE only gravity model GOSG02S based on the SGG and SST observations

GOSG02S is a static gravity field model complete to spherical harmonic degree and order of 300 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 and Vxz) in GRF (9/10/2009-20/10/2013) -- GOCE SST data: SST_PKI_2, SST_PCV_2, SST_PRD_2 (9/10/2009-20/10/2013) -- 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, ... -- GOSG02S 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 - Direct LS method - Max degree: up to 300 - Data: GGT, PRD, IAQ, PRM - Band-pass filter: used to deal with colored-noise of GGT observations (pass band 0.005-0.100Hz ) - 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 300 - The VCE technique is used to estimate the relative weights for Vxx, Vyy, Vzz and Vxz - Tikhonov Regularization Technique (TRT) is only applied to near (zonal) terms (m<20, n<=200) and high degree terms (n>200) - Strictly inverse the normal matrix based on OpenMP

WHU-SWPU-GOGR2022S: A combined gravity model of GOCE and GRACE

WHU-SWPU-GOGR2022S is a static gravity field model complete to spherical harmonic degree and order of 300 by combining GOCE and GRACE normal equations. Details of the processing procedures are as follows: (1) Details of the GOCE processing procedures: (1a) Input data: -- GOCE SGG data: EGG_NOM_2 (GGT: Vxx, Vyy, Vzz and Vxz) in GRF (9/10/2009-20/10/2013) -- GOCE SST data: SST_PKI_2, SST_PCV_2, SST_PRD_2 (9/10/2009-20/10/2013) -- 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, ... (1b) 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 - Direct LS method - Max degree: up to 300 - Data: GGT, PRD, IAQ, PRM - Band-pass filter: used to deal with colored-noise of GGT observations (pass band 0.005-0.100Hz ) - 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 300 - The VCE technique is used to estimate the relative weights for Vxx, Vyy, Vzz and Vxz - Tikhonov Regularization Technique (TRT) is only applied to near (zonal) terms (m<20, n<=200) and high degree terms (n>200) - Strictly inverse the normal matrix based on OpenMP (2) Details of the GRACE processing procedures: (2a) Input data: -- GRACE L1B (JPL) data products: GNV1B RL02, ACC1B RL02, SCA1B RL03 and KBR1B RL03 -- AOD1B RL06 (GFZ) de-aliasing product -- Data period: 04/2002-05/2017 (2b) Data preprocessing: -- Splitting data of SCA1B into subsections for gaps > 120s and interpolation with polynomial for gaps <= 120s -- Splitting data of ACC1B into subsections for gaps > 5s and interpolation with polynomial for gaps <= 5s -- Gross outlier elimination ACC1B with a moving window of length 10 min, and interpolation with polynomial -- Pre-calibration of ACC1B with a-priori bias and scale Parameters provided by GRACE TN-02 (2c) Calculation method: - dynamic approach - numerical integrator: 8th-order Gauss-Jackson integrator - integrator step: 5 seconds - arc length: 24 hours (2d) Combination - GNV1B and KBR1B are combined with their a-priori precision, i.e. 2cm of GNV1B and 2um/s of KBR1B - The normal equations of different months are combined with variance components estimation (2e) Force models: - Earth's static gravity field: GGM05s up to d/o 180 - Solid earth tides: IERS 2010 - Ocean tides: FES2014b up to d/o 180 - Solid Earth pole tide: IERS 2010 - Ocean pole tide: Desai 2002 up to d/o 180 - N-body Perturbation: the Sun and Moon with JPL DE421 - atmospheric tides: Bode and Biancale model - AOD1B product: AOD1B RL06 model up to d/o 180 - General Relativistic effects: Schwarzschild terms of IERS 2010

IGG-Swarm: Temporal Gravity Models from Swarm

Monthly gravity fields from Swarm A, B, and C, using the integral equation approach with short arcs. Software: GROOPS; Approach: Short-arc approach (Mayer-Gürr, 2006); Kinematic orbit product: IfG Graz: https://ftp.tugraz.at/outgoing/ITSG/satelliteOrbitProducts/operational/Swarm-1/kinematicOrbit/; Arc length: 45 minutes; Reference GFM: GOCO06s (Kvas et. al, 2021), monthly mean has been added back to the solution; Drag model: NRLMSIS2; SRP and EARP and EIRP models: Vielberg & Kusche (2020); Empirical parameters: + for non-gravitational accelerations (sum of Drag+SRP+EIRP+EARP): Bias per arc and direction; + for Drag: Scale per arc and direction; + for radiation pressure (sum of SRP+EIRP+EARP): Scale per day and direction; Non-tidal model: Atmosphere and Ocean De-aliasing Level 1B RL06 (Dobslaw et al., 2017); Ocean tidal model: 2014 finite element solution FES2014b (Carrere et al., 2015); Atmospheric tidal model: AOD1B RL06 atmospheric tides ; Solid Earth tidal model: IERS2010; Pole tidal model: IERS2010; Ocean pole tidal model: IERS2010 (Desai 2002); Third-body perturbations: Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn, following the JPL DE421 Planetary and Lunar Ephemerides (Folkner et al., 2014).

ITU_GGC16 The combined global gravity field model including GRACE & GOCE data up to degree and order 280

ITU_GGC16 is a static global gravity field model up to degree order 280 computed from the combination of ITU_GRACE16 (up to d/o 180) and GO_CONS_GCF_2_TIM_R5 (up to d/o 280) by collaboration of various national institutions (YTU, KOU, NEU, SU) lead by ITU and OSU as the international collaborator with the support of research grant no 113Y155 from the Scientific and Technological Research council of Turkey (TUBITAK). The combination is performed at the normal equation level with variance component estimation. No rate terms were modeled, and no corrections for earthquakes have been applied.For additional details on the background modeling, see the GFZ RL05 processing standards document by Dahle et al. (2012).

EIGEN-6C4 The latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse

EIGEN-6C4 is a static global combined gravity field model up to degree and order 2190. It has been elaborated jointly by GFZ Potsdam and GRGS Toulouse. The combination of the different satellite and surface data sets has been done by a band-limited combination of normale equations (to max degree 370), which are gererated from observation equations for the spherical harmonic coefficients. A brief description of the applied techniques for the generation of such a combined gravity field model is given in Shako et al. 2014. The resulted solution to degree/order 370 has been extended to degree/order 2190 by a block diagonal solution using the DTU10 global gravity anomaly data grid.

The experimental gravity field model XGM2019e

XGM2019e is a combined global gravity field model represented through spheroidal harmonics up to d/o 5399, corresponding to a spatial resolution of 2’ (~4 km). As data sources it includes the satellite model GOCO06s in the longer wavelength area combined with terrestrial measurements for the shorter wavelengths. The terrestrial data itself consists over land and ocean of gravity anomalies provided by courtesy of NGA (identical to XGM2016, having a resolution of 15’) augmented with topographically derived gravity over land (EARTH2014). Over the oceans, gravity anomalies derived from satellite altimetry are used (DTU13, in consistency with the NGA dataset).The combination of the satellite data with the terrestrial observations is performed by using full normal equations up to d/o 719 (15’). Beyond d/o 719, a block-diagonal least-squares solution is calculated for the high-resolution terrestrial data (from topography and altimetry). All calculations are performed in the spheroidal harmonic domain.In the spectral band up to d/o 719 the new model shows over land a slightly improved behavior over preceding models such as XGM2016, EIGEN6c4 or EGM2008 when comparing it to independent GPS leveling data. Over land and in the spectral range above d/o 719 the accuracy of XGM2019e suffers from the sole use of topographic forward modelling; Hence, errors are increased in well-surveyed areas compared to models containing real gravity data, e.g. EIGEN6c4 or EGM2008. However, the performance of XGM2019e can be considered as globally more homogeneous and independent from existing high resolution global models. Over the oceans the model exhibits an improved performance throughout the complete spectrum (equal or better than preceding models).

SWPU-GRACE2021: a new temporal gravity model from GRAC

The new unconstrained GRACE monthly solution SWPU-GRACE2021 is recently developed with the dynamic approach. The reprocessed GRACE L1B RL03 data and de-aliasing product AOD1B RL06 are applied to compute SWPU-GRACE2021. The arc length is variable according to the L1B data quality, but the maximum is no more than 24 hours. The bias vector and scale matrix of the GRACE Accelerometer observation ACC1B product are estimable parameters. The data covers the period from April 2002 to Mai 2017. Due to data quality problems, there are some data gaps between September 2016 and April 2017.

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