Abstract
Recently, \(C_{30}\) coefficients of time-variable gravity field models from GRACE and GRACE-Follow On (GRACE/GRACE-FO) are reported to contain larger uncertainties when only one of the two onboard accelerometers is fully functional, which mainly concerns the GRACE-FO period and the final stage of the GRACE period. Using these problematic coefficients leads to incorrect mass change (rate) estimates, especially over Antarctic Ice-Sheet (AIS), and a replacement with those from satellite laser ranging (SLR) is currently recommended. In this study, we aim to discuss the possibility of improving the \(C_{30}\) coefficients by extending the GRACE-OBP approach that has previously been applied to the estimation of geocenter motion and variations in the Earth’s dynamic oblateness. Such an approach mainly relies on GRACE/GRACE-FO level 2 products and an ocean bottom pressure model, and it produces compatible coefficients with the GRACE/GRACE-FO product labeled as GSM. With a numerical experiment, we demonstrate the effectiveness of the proposed approach and identify the optimal implementation parameter setup. The resulting \(C_{30}\) coefficient time series is generally consistent with those based on SLR and the original solutions from the GRACE dual-accelerometer period, but with differences in the annual amplitude estimates. Then, we obtain \(C_{30}\) coefficients based on real data and check the AIS mass change time series with and without replacing the original ones with our solution. Our \(C_{30}\) solution ensures consistent linear trend estimates for the dual- and single-accelerometer periods.
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Data availability
GRACE/GRACE-FO level 2 data are publicly available from the ICGEM website (http://icgem.gfz-potsdam.de/home). The GSFC SLR \(C_{30}\) coefficients (TN-14) are taken from https://podaac-tools.jpl.nasa.gov/drive/files/GeodeticsGravity/gracefo/docs/TN-14_C30_C20_GSFC_SLR.txt. The CSR SLR \(C_{30}\) coefficients are extracted from http://download.csr.utexas.edu/pub/slr/degree_5/CSR_Monthly_5x5_Gravity_Harmonics.txt. The IGG SLR solution is available at http://icgem.gfz-potsdam.de/series/04_SLR/IGG_SLR_HYBRID. The updated ESM can be accessed at https://isdc.gfz-potsdam.de/esmdata/esaesm/. The A12 GIA model is provided by Geruo A through personal communications. The Caron17 GIA model can be downloaded from https://vesl.jpl.nasa.gov/solid-earth/gia/ and the Peltier18 GIA model can be taken from https://www.atmosp.physics.utoronto.ca/~peltier/data.php. The resulting \(C_{30}\) coefficients of this study for CSR, GFZ and JPL GRACE/GRACE-FO level 2 data are available in the supplementary materials. \(C_{30}\) time series based on the GRACE-OBP approach using other data center’s TVG models are available upon requests.
References
A G, Wahr J, Zhong S (2012) Computations of the viscoelastic response of a 3-D compressible Earth to surface loading: an application to Glacial Isostatic Adjustment in Antarctica and Canada. Geophys J Int 192(2):557–572. https://doi.org/10.1093/gji/ggs030
Bandikova T, McCullough C, Kruizinga GL et al (2019) GRACE accelerometer data transplant. Adv Space Res 64(3):623–644. https://doi.org/10.1016/j.asr.2019.05.021
Caron L, Métivier L, Greff-Lefftz M et al (2017) Inverting glacial isostatic adjustment signal using bayesian framework and two linearly relaxing rheologies. Geophys J Int 209(2):1126–1147. https://doi.org/10.1093/gji/ggx083
Chen JL, Wilson CR, Li J et al (2015) Reducing leakage error in GRACE-observed long-term ice mass change: a case study in West Antarctica. J Geodesy 89(9):925–940. https://doi.org/10.1007/s00190-015-0824-2
Cheng M, Ries J (2017) The unexpected signal in GRACE estimates of \(C_{20}\). J Geodesy 91(8):897–914. https://doi.org/10.1007/s00190-016-0995-5
Cheng M, Ries JC, Tapley BD (2011) Variations of the Earth’s figure axis from satellite laser ranging and GRACE. J Geophys Res Solid Earth 116(B1):B01409. https://doi.org/10.1029/2010JB000850
Consortium E, Fukumori I, Wang O, et al (2020) Synopsis of the ECCO Central Production Global Ocean and Sea-Ice State Estimate, Version 4 Release 4. Tech. rep., Zenodo, https://doi.org/10.5281/zenodo.3765929
Dee DP, Uppala SM, Simmons AJ et al (2011) The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Q J R Meteorol Soc 137(656):553–597. https://doi.org/10.1002/qj.828
Devoti R, Luceri V, Sciarretta C et al (2001) The SLR secular gravity variations and their impact on the inference of mantle rheology and lithospheric thickness. Geophys Res Lett 28(5):855–858. https://doi.org/10.1029/2000GL011566
Ditmar P, Tangdamrongsub N, Ran J et al (2018) Estimation and reduction of random noise in mass anomaly time-series from satellite gravity data by minimization of month-to-month year-to-year double differences. J Geodyn 119:9–22. https://doi.org/10.1016/j.jog.2018.05.003
Dobslaw H, Bergmann-Wolf I, Dill R et al (2015) The updated ESA earth system model for future gravity mission simulation studies. J Geodesy 89(5):505–513. https://doi.org/10.1007/s00190-014-0787-8
Duan XJ, Guo JY, Shum CK et al (2009) On the postprocessing removal of correlated errors in GRACE temporal gravity field solutions. J Geodesy 83(11):1095–1106. https://doi.org/10.1007/s00190-009-0327-0
Feng W (2019) GRAMAT: a comprehensive Matlab toolbox for estimating global mass variations from GRACE satellite data. Earth Sci Inf 12(3):389–404. https://doi.org/10.1007/s12145-018-0368-0
Gruber T, Bamber JL, Bierkens MFP et al (2011) Simulation of the time-variable gravity field by means of coupled geophysical models. Earth Syst Sci Data 3(1):19–35. https://doi.org/10.5194/essd-3-19-2011
Jeon T, Seo KW, Youm K et al (2018) Global sea level change signatures observed by GRACE satellite gravimetry. Sci Rep 8(1):1–10. https://doi.org/10.1038/s41598-018-31972-8
Jungclaus JH, Fischer N, Haak H et al (2013) Characteristics of the ocean simulations in the max planck institute ocean model (MPIOM) the ocean component of the MPI-earth system model. J Adv Model Earth Syst 5(2):422–446. https://doi.org/10.1002/jame.20023
Kusche J, Schmidt R, Petrovic S et al (2009) Decorrelated GRACE time-variable gravity solutions by GFZ, and their validation using a hydrological model. J Geodesy 83(10):903–913. https://doi.org/10.1007/s00190-009-0308-3
Landerer FW, Flechtner FM, Save H et al (2020) Extending the global mass change data record: grace follow-on instrument and science data performance. Geophys Res Lett 47(12):e2020GL088306. https://doi.org/10.1029/2020GL088306
Loomis BD, Rachlin KE, Wiese DN et al (2020) Replacing GRACE/GRACE-FO \(C_{30}\) with satellite laser ranging: impacts on antarctic ice sheet mass change. Geophys Res Lett 47(3):e2019GL085488. https://doi.org/10.1029/2019GL085488
Löcher A, Kusche J (2020) A hybrid approach for recovering high-resolution temporal gravity fields from satellite laser ranging. J Geodesy 95(1):6. https://doi.org/10.1007/s00190-020-01460-x
Marshall J, Adcroft A, Hill C et al (1997) A finite-volume, incompressible navier stokes model for studies of the ocean on parallel computers. J Geophys Res Ocean 102(C3):5753–5766. https://doi.org/10.1029/96JC02775
Peltier WR, Argus DF, Drummond R (2018) Comment on “An Assessment of the ICE-6G_C (VM5a) Glacial Isostatic Adjustment Model’’ by Purcell. J Geophys Res Solid Earth 123(2):2019–2028. https://doi.org/10.1002/2016JB013844
Seo KW, Kim JS, Youm K et al (2021) Secular polar motion observed by GRACE. J Geodesy 95(4):40. https://doi.org/10.1007/s00190-021-01476-x
Sośnica K, Jäggi A, Meyer U et al (2015) Time variable Earth’s gravity field from SLR satellites. J Geodesy 89(10):945–960. https://doi.org/10.1007/s00190-015-0825-1
Sun Y, Ditmar P, Riva R (2016) Observed changes in the Earth’s dynamic oblateness from GRACE data and geophysical models. J Geodesy 90(1):81–89. https://doi.org/10.1007/s00190-015-0852-y
Sun Y, Riva R, Ditmar P (2016) Optimizing estimates of annual variations and trends in geocenter motion and \(J_{2}\) from a combination of GRACE data and geophysical models. J Geophys Res Solid Earth 121(11):8352–8370. https://doi.org/10.1002/2016JB013073
Sun Y, Ditmar P, Riva R (2017) Statistically optimal estimation of degree-1 and \(C_{20}\) coefficients based on GRACE data and an ocean bottom pressure model. Geophys J Int 210(3):1305–1322. https://doi.org/10.1093/gji/ggx241
Sun Y, Riva R, Ditmar P et al (2019) Using GRACE to explain variations in the earth’s oblateness. Geophys Res Lett 46(1):158–168. https://doi.org/10.1029/2018GL080607
Swenson S, Wahr J (2006) Post-processing removal of correlated errors in GRACE data. Geophys Res Lett 33(8):L08402. https://doi.org/10.1029/2005GL025285
Swenson S, Chambers D, Wahr J (2008) Estimating geocenter variations from a combination of GRACE and ocean model output. J Geophys Res Solid Earth 113(B8):B08410. https://doi.org/10.1029/2007JB005338
Tapley BD, Bettadpur S, Watkins M et al (2004) The gravity recovery and climate experiment: mission overview and early results. Geophys Res Lett 31(9):L09607. https://doi.org/10.1029/2004GL019920
Tapley BD, Watkins MM, Flechtner F et al (2019) Contributions of GRACE to understanding climate change. Nat Clim Chang 9(5):358. https://doi.org/10.1038/s41558-019-0456-2
Wahr J, Molenaar M, Bryan F (1998) Time variability of the Earth’s gravity field: hydrological and oceanic effects and their possible detection using GRACE. J Geophys Res Solid Earth 103(B12):30205–30229. https://doi.org/10.1029/98JB02844
Wessel P, Luis JF, Uieda L et al (2019) The generic mapping tools version 6. Geochem Geophys Geosyst 20(11):5556–5564. https://doi.org/10.1029/2019GC008515
Wiese DN, Nerem RS, Han SC (2011) Expected improvements in determining continental hydrology ice mass variations ocean bottom pressure signals and earthquakes using two pairs of dedicated satellites for temporal gravity recovery. J Geophys Res Solid Earth. https://doi.org/10.1029/2011JB008375
Wu X, Ray J, van Dam T (2012) Geocenter motion and its geodetic and geophysical implications. J Geodyn 58:44–61. https://doi.org/10.1016/j.jog.2012.01.007
Acknowledgements
We thank our editors and three anonymous reviewers for their insightful comments which greatly improved the quality of the manuscript. We thank Riccardo Riva from Delft University of Technology for carefully revising the manuscript as well as constructive suggestions and insightful comments. This study is supported by the National Natural Science Foundation of China (grant 42171426 and 41904009) and open project from Key Lab of Spatial Data Mining and Information Sharing, Ministry of Education (grant 2022LSDMIS06). We estimate AIS mass change time series using a dedicated tool package provided by Wei Feng (Feng 2019). All the figures are prepared by the Generic Mapping Tools (Wessel et al. 2019).
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YS and XG conceived the idea and designed all the experiments; YS, YL, and XG performed the research and analyzed the data; YS and XG wrote the paper; JG revised the paper; all authors reviewed and commented on the paper.
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Sun, Y., Li, Y., Guo, X. et al. Estimating \(C_{30}\) coefficients for GRACE/GRACE-FO time-variable gravity field models using the GRACE-OBP approach. J Geod 97, 20 (2023). https://doi.org/10.1007/s00190-023-01707-3
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DOI: https://doi.org/10.1007/s00190-023-01707-3