Abstract
Traditional conversion from gravity Stokes coefficients into the surface mass, e.g., in the GRACE(-FO) applications, presumes the Earth as a perfect sphere that is apparently against the reality. Recent studies manage to correct the conversion by considering the Earth’s oblateness, in another word, the Earth is treated as an ellipsoid. However, the Earth’s geometry is far more complicated due to the topography, so that neither a sphere nor an ellipsoid is exact. Evidences from recent studies and this one demonstrate that any geometrical approximation of the Earth shape like a presumed sphere will inevitably lead to a bias in the surface mass estimation from GRACE gravity fields, resulting in a possible misinterpretation of geophysical signals that may occur in polar regions or mountain areas. In this context, we propose an iterative scaling factor method to numerically realize a more accurate surface mass estimate, considering a more realistic geometry of the Earth including its oblateness, topography and geoid undulation. Verified with a series of simulations, the proposed method is found to be efficient (less than four iterations), reliable (after a broad range of tests) and universally accurate (reducing at least 80% of the bias). Relative to our method, the mean linear trend in 2002–2015 estimated from GRACE under an ideal spherical Earth is found to be underestimated by about 3.1% and 5.5% over Greenland and West Antarctica, respectively. Among the trend underestimation, the topography-related contribution takes up − 0.5% (0.79 Gt/yr, the negative sign denotes an overestimation) and − 0.4% (0.34 Gt/yr), respectively. Although the value is small, it is a systematic bias worth considering, for example, it is greater than the influence (0.3 Gt/yr on the trend estimation over West Antarctica) by switching atmospherical de-aliasing products from RL05 to RL06. Besides, the topography-induced bias rapidly increases to 2.7% (0.26 mm/yr) at mountain Himalayas, which is even larger than the ellipsoid-induced bias (0.19 mm/yr). Based on the results obtained so far, the topography-induced bias is found to be roughly one order of magnitude smaller than GRACE’s present measurement error; nevertheless, it will be relevant once the GRACE is improved toward its baseline accuracy. In particular, the topography correction should be considered for NGGM that expects to map the Earth gravity field in an unprecedented accuracy and spatial resolution.
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Data availability
The Level-2 GRACE gravity fields analyzed during the current study are available from GFZ data center (ftp://isdcftp.gfz-potsdam.de/grace/). The software (python code) generated during the study are available in https://doi.org/10.6084/m9.figshare.17072969.v2.
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Acknowledgements
We appreciate the constructive comments from the anonymous reviewers, which led to significant improvement of the manuscript. F.Y. acknowledges financial supports through the National Natural Science Foundation of China (Grant No. 42274112, No. 41804016, No. 41931074, No. 42061134007). J.K. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) -SFB1502/1-2022-Project Number 450058266.
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All authors read and approved the final manuscript. FY and JK designed research; FY performed research; FY, ZL and HZ analyzed data; FY and JK wrote the paper.
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Yang, F., Luo, Z., Zhou, H. et al. On study of the Earth topography correction for the GRACE surface mass estimation. J Geod 96, 95 (2022). https://doi.org/10.1007/s00190-022-01683-0
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DOI: https://doi.org/10.1007/s00190-022-01683-0