1. Representative Research Achievements of Tongji UniversitySatelliteGravity Team

1.1 Tongji-Grace01 Satellite Gravity Static Gravity Field Model

Based on theModifiedshort arc method developed by the satellite gravity team of Tongji University (Shen Y, 2013; Chen Q et al., 2015), the 160 degree and order static gravity field model Tongji GRACE01 was solved using the reduced-dynamic orbit, inter-satellite range rate nonconservative force acceleration, and attitude data published by JPL from 2003 to 2007. Some reference force models information required during data processing is as follows:

Static gravity field: ITG-GRACE2010S

N-Body perturbations: IERS 2010

Solid Earth (pole) tides: IERS2010

Ocean tides: EOT11a model

Ocean pole tides: Desai model

Atmospheric andOceanic Dealiasing: AOD1B RL05 up to degree and order 100

Relativistic effects: IERS 2010

Nonconservative force acceleration: GRACE onboard accelerometer linear acceleration

Reference:

[1] Shen Y, Chen Q, Hsu H, Lou L. 2013. A modified short arc approach for recovering gravity field model. GRACE Science team Meeting.

[2] Chen Q, Shen Y, Zhang X, Chen W, Hsu H. 2015. Tongji-GRACE01: A GRACE-only static gravity field model recovered from GRACE Level-1B data using modified short arc approach. Advances in Space Research, 56(5): 941-951.Click

[3] Chen Q, Shen Y, Zhang X, Hsu H, ChenW.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.Click

Tongji-GRACE01 model download link:

https://workdrive.zohopublic.com.cn/external/8676f7592df3093840e10bddef42c985f0ee828f794152e4c905db21f28b2326

1.2 Tongji-Grace02s/k Satellite Gravity Static Gravity Field Model

In order to avoid over parameterization of accelerometer calibration, the scale and deviation of the accelerometer were calibrated monthly and daily,comprehensive considering the observation errors of orbit, inter-satellite range rate, attitude and accelerometer data to modify short arc method. Based on the modified short arc method, the 180 degree and order Tongji-Grace02s unconstrained static gravity field model is obtained by solving the GRACE satellite data (including accelerometer data, attitude data and inter-satellite range rate data) and geometric orbit data from January 2003 to July 2016, and further regularization constraint processing is performed on the high degree and order coefficients to obtain Tongji-Grace02k model.

The inter-satellite range rate, nonconservative force acceleration and satellite attitude parameters used for calculating gravity field model are derived from JPL, and the kinematic orbits are derived from Graz University of Technology. Some background force models required in the data processing process are as follows:

Static gravity field: EGM96

N-Body perturbations: DE421

Solid Earth (pole) tides: IERS 2010

Ocean tides: EOT11a model

Ocean pole tides: Desai model

Atmospheric andOceanic Dealiasing: AOD1B RL05 up to degree and order 100

Relativistic effects: IERS 2010

Nonconservative force acceleration: GRACE onboard accelerometer linear acceleration

Reference:

[1] Chen Q, Shen Y, Francis O, Chen W, Zhang X, Hsu H. 2018. Tongji‐Grace02s and Tongji‐Grace02k: high‐precision static GRACE‐only global Earth's gravity field models derived by refined data processing strategies. Journal of Geophysical Research: Solid Earth, 123(7): 6111-6137.Click

Tongji-Grace02s model download link：

https://workdrive.zohopublic.com.cn/external/1fdcb08e58115c4755a10de21d17b42836eda1282bce0a113b0e11a5037b734b.

Tongji-Grace02k model download link:

https://workdrive.zohopublic.com.cn/external/b54e08a9a994d95adf57e12c97cfc1804b3eb003cb7d52acec8594ffa42b824a.

1.3 Tongji-GMMG2021SSatelliteGravity Static Gravity Field Model

By integrating the Level 1b gravity gradient data and corresponding orbital products of the GOCE satellite's complete mission cycle, as well as GRACE satellite gravity observation data from January 2003 to July 2016, we calculate Tongji-GMMG2021S static gravity field modelupto 300 degree and order. The low-frequency error of gravity gradient data is processed through IIR filter, and the relevant background models used for correcting time-varying gravity field changes is as follows:

N-Body perturbations: DE430

Solid Earth (pole) tides: IERS 2010

Ocean tides: EOT11a model

Ocean pole tides: Desai model

Atmospheric andOceanic Dealiasing: AOD1B RL06

Reference:

[1] Chen J, Zhang X, Chen Q, Shen Y, NieY.2022. Static Gravity Field Recovery and Accuracy Analysis Based on Reprocessed GOCE Level 1b Gravity Gradient Observations EGU General Assembly 2022, Vienna, Austria, 23–27 May, EGU22-6771.

Tongji-GMMG2021Smodel download link:

https://workdrive.zohopublic.com.cn/external/ea6bc05d7362a76cb5401e662029953ed574cb5c654e90a3934ca99bcf2de669

1.4 Refined Time Series of GRACE Monthly Solutions Tongji‐Grace2018.

Considering that long-arc techniques is more likely to suppress the influence of atmospheric and oceanic mixing noise and observation errors, and amplifying the effect of small signals on low orbit satellites, we further optimize the short arc method based on the modified short arc method. By introducing position parameters into the boundary orbit of the integral arc segment and separating the GRACE orbit from the inter-satellite distance observation equation, the direct inversion of large-scale matrices is avoided, effectively reducing the condition number of the normal equation matrix, and successfully extending the arc length to 6 hours. The optimized short arc method effectively reduces the high-frequency noise of the time-variable gravity field model. Based on the optimized short arc method, we process GRACE Level1b RL03 observation data from April 2002 to December 2016, and solve 90 degree and order Tongji Grace 2018 time-variable gravity field model.

Inter-satellite distance range rate, nonconservative force acceleration, and satellite attitude parameters used for gravity field model calculation are derived from JPL, and the kinematic orbits are derived from Graz University of Technology. Some background force models required in the data processing process are as follows:

Static gravity field: Tongji Race02s

N-Body perturbations: DE430

Solid Earth (pole) tides: IERS 2010

Ocean tides: FES2014b model

Ocean pole tides: Desai model

Atmospheric andOceanic non tidal changes: AOD1B RL06

Relativistic effects: IERS 2010

Nonconservative force acceleration: GRACE onboard accelerometer linear acceleration

Reference:

[1] Chen Q, Shen Y, Chen W, Francis O, Zhang X, Chen Q, Li W, Chen T.2019. An optimized short‐arc approach: Methodology and application to develop refined time series of Tongji‐Grace2018 GRACE monthly solutions. Journal of Geophysical Research: Solid Earth, 124(6): 6010-6038.Click

Tongji-Grace2018 model download link:

https://workdrive.zohopublic.com.cn/external/ec51983596e71232983774fb217bdf08de13c02675688774d3fa870b35c4dda8.

1.5 Tongji-LEO2021:Low Earth Orbit Satellites Time Variable Gravity Field Model

In this work, a new time series of monthly gravity field models Tongji-LEO2021 complete to degree and order (d/o) 40 over the period January 1993 to December 2004 determined from the observations of LEO satellites consisting of SPOT2, SPOT3, SPOT4, ERS1, ERS2 and TOPEX/Poseidon.The model fills the gap in the time-variable gravity field model before the launch of gravity satellites. At the same time, the reliability of the Tongji LEO2021 model was verified by comparing the IGG-SLR-HYBRID and CSR RL06 models. The global mean ocean mass level change estimated by the Tongji LEO2021 time-variable gravity field model is consistent with the estimation results of altimetry, temperature and salinity. For the period from 1993 to 2004, the mass changes over oceans contribute∼36% of the observed global mean total sea level change rate (2.36 ± 0.30 mm/year).

Reference:

[1]Chen Q, Wang F, Shen Y, Zhang X, Nie Y, Chen J. 2022. Monthly Gravity Field Solutions from Early LEO Satellites’ Observations Contribute to Global Ocean Mass Change Estimates over 1993∼2004. Geophysical Research Letters, e2022GL099917.Click

Tongji-LEO2021model download link:

https://workdrive.zohopublic.com.cn/external/db8ff6e6b1153f577c44c1b197c33c97b4dafa1af635fae5a02ea981bfcf761f.

1.6 Full Scale Simulation of Next Generation Gravity Satellites

Considering the limitation of insufficient sampling of GRACE/GRACE-FO single polar satellites, the next generation satellite gravity mission plans to use two pairs of GRACE/GRACE-FO low-low SST modes to form a satellite constellation. The current mainstream constellation pattern is Bender type, which consists of a pair of polar gravity satellites and a pair of inclined satellites. In addition, it is also possible to use polar orbit gravity satellites launched by different institutions for collaborative observation, such as GRACE-FO currently in orbit and future polar orbit gravity satellite combinations. By comparing different polar orbit satellite inclination combination schemes, we proposed a bipolar orbit constellation model based on 89° and 91° orbital inclination (89+91). Compared to the constellation composed of two pairs of 89° inclined satellites (89+89), this mode increases the isotropic characteristics of the combined observation system, thus effectively reducing the inversion error of the combined gravity model.

Currently, different institutions use different strategies to suppress the effects of observation noise and background field model errors when solving time-variable gravity field models based on GRACE/GRACE-FO data. The mainstream strategies include estimating acceleration empirical parameters, estimating KBR empirical parameters, using a non-diagonal variance-covariance matrix and digital filtering based on time series models. Our team systematically elucidated the differences and connections between the four strategies mentioned above in theory, using a unified framework of the least squares configuration model to classify each strategy into two categories: parameterized absorption and random model compensation. In addition, we comprehensively analyze the effectiveness of various methods in error suppression through numerical simulation.

Reference:

[1] Nie Y, Shen Y, Chen Q. 2019. Combination analysis of future polar-type gravity mission and GRACE Follow-On. Remote sensing, 2019, 11(2): 200.

[2] Nie Y, Shen Y, Pail R, Chen Q, XiaoY.2022. Revisiting Force Model ErrorModeling in GRACE Gravity Field Recovery. Surveys in Geophysics, 2022: 1-31.

2. Reference

[1] Shen Y．2000.Study on refining the Earth's gravity field model by using Champ Ephemeris [ doctoral dissertation ] . Wuhan: Institute of Chinese Academy of Sciences and geophysics.

[2] Zhang X,Shen Y,Hu L.2007.Earth gravity field model based on CHAMP short-arc dynamic orbit. The geophysics, (01): 106-110.

[3] Zhang X,Shen Y.2007.The CHAMP accelerometer data were calibrated by dynamic method. Journal of Wuhan University Sciences (information science edition), (02): 176-179.

[4]Zhang X.2007.Inversion of the Earth's gravity field model using LEO satellite tracking data [ doctoral thesis ] . Shanghai: Tongji University.

[5] Shen Y, Chen Q, Xu H. 2015. Monthly gravity field solution from GRACE range measurements using modified short arc approach. 2015. Geodesy and Geodynamics, 2015, 6(4): 261-266.

[6] Chen Q, Shen Y, Zhang X, Chen W, Hsu H. 2015. Tongji-GRACE01: A GRACE- only static gravity field model recovered from GRACE Level-1B data using modified short arc approach. Advances in Space Research, 56(5): 941-951.

[7] Chen Q, Shen Y, Zhang X, Hsu H, ChenW.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.

[8] Chen Q, Shen Y,Chen W, Zhang X, Hsu H, Ju X. 2015. A modified acceleration- based monthly gravity field solution from GRACE data. Geophysical Journal International, 2015, 202(2): 1190-1206.

[9] Chen Q, Shen Y, Chen W, Zhang X, Hsu H. 2016. An improved GRACE monthly gravity field solution by modeling the non-conservative acceleration and attitude observation errors. Journal ofGeodesy,90(6): 503-523.

[10] Chen Q,2016.Grace gravity inversion theory, Method and application based on improved short-arc integral method [ phd thesis ] . Shanghai: Tongji University.

[11] Shen Y.2017.Characteristics and improvement of satellite gravity inversion algorithm based on dynamic method. Journal of surveying and mapping,46(10): 1308-1315.

[12] Chen Q, Shen Y, Francis O, Chen W, Zhang X, Hsu H. 2018. Tongji‐Grace02s and Tongji‐Grace02k: high‐precision static GRACE‐only global Earth's gravity field models derived by refined data processing strategies. Journal of Geophysical Research: Solid Earth, 123(7): 6111-6137.

[13] Chen Q, Shen Y, Chen W, Francis O, Zhang X, Chen Q, Li W, Chen T. 2019. An optimized short‐arc approach: Methodology and application to develop refined time series of Tongji‐Grace2018 GRACE monthly solutions. Journal of Geophysical Research: Solid Earth, 124(6): 6010-6038.

[14] Nie Y, Shen Y, Chen Q. 2019. Combination analysis of future polar-type gravity mission and GRACE Follow-On. Remote sensing, 2019, 11(2): 200.

[15] Nie Y, Shen Y, Chen Q, XiaoY.2020. Hybrid-precision arithmetic for numerical orbit integration towards future satellite gravimetry missions. Advances in Space Research, 2020, 66(3): 671-688.

[16]Chen J,Zhang X,Chen Q,Liang J,Shen Y.2020.The unconstrained gravity field model tongji-gogr2019s. The Geophysics, 63(09): 3251-3262.

[17] Chen Q, Shen Y, Kusche J, Chen W, Chen T, Zhang X. 2021. High‐Resolution GRACE Monthly Spherical Harmonic Solutions. Journal of Geophysical Research: Solid Earth, 126(1): e2019JB018892.

[18] Nie Y, Shen Y, Pail R, Chen Q, XiaoY.2022. Revisiting Force Model Error Modeling in GRACE Gravity Field Recovery. Surveys in Geophysics, 2022: 1-31.

[19] Nie Y, Shen Y, Pail R, Chen Q. 2022. Efficient variance component estimation for large-scale least-squares problems in satellite geodesy. Journal ofGeodesy,96(2): 1-15.

[20] Chen Q, Wang F, Shen Y, Zhang X, Nie Y, Chen J. 2022. Monthly Gravity Field Solutions from Early LEO Satellites’ Observations Contribute to Global Ocean Mass Change Estimates over 1993∼2004. Geophysical Research Letters, e2022GL099917.

[21]Chen J,Zhang X,Shen Y,Chen Q,Li W.2021. GOCE Correction and influence analysis of time-varying gravity field variation of satellite gravity gradient observations. Journal of surveying and mapping, 2021, 50(03): 324-332.

[22] Chen J, Zhang X, Chen Q, Shen Y, Nie Y.2022. Static Gravity Field Recovery and Accuracy Analysis Based on Reprocessed GOCE Level 1b Gravity Gradient Observations EGU General Assembly 2022, Vienna, Austria, 23–27May,EGU22- 6771.

[23]Qiu L,Chen Q,Zhang X,Shen Y,Chen J.2022.Effect of ionospheric delay on KBR data from GRACE-FO satellite. Journal of Huazhong University of Science and Technology Science, 50(09): 134-140.