Abstract
The thermal expansion effects of GNSS stations are influenced by not only temperature variations, but also bedrock depths and types. Unfortunately, the current studies treat the subsurface GNSS monument and their nearby bedrock as a whole, without taking into account the inconsistencies among bedrock depths and types, while the existing full-spectrum finite element method (FEM) cannot be easily extended to consider the bedrock information. To solve this problem, we propose a refined full-spectrum temperature-induced subsurface thermal expansion model (FSHBDT) that considers both seasonal and non-seasonal temperature variations as well as bedrock information based on the half-space harmonic model. Results show that the full-spectrum half-space harmonic model (FSH), which considers only seasonal and non-seasonal temperature variations, can obtain comparable results to the FEM and even outperform the FEM for inland stations. In addition, the depth and type of bedrock have significant effects on the annual amplitude and phase of thermal expansion-induced vertical displacement. In particular, we find that the station displacement increases by more than 1 mm and the annual phase delays by up to 10° for high-latitude and deeper bedrock stations when bedrock depths are taken into account. The FSHBDT improves the correlation coefficient between GNSS height and mass load displacements by up to 42.3% compared to the FEM and explains up to 8.2% of the nonlinear variation in the GNSS height time series. Our work confirms the advantage of rigorous subsurface thermal expansion modeling to correct the nonlinear variations of global GNSS stations, which might provide a potential opportunity to improve the terrestrial reference frame toward the goal of 1 mm accuracy.
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Data availability
The NCEP/NCAR reanalysis data set is available at https://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis.html, the GNSS time series are available at http://garner.ucsd.edu/pub/measuresESESES_products/Timeseries/—username: anonymous; password: your email address, the ESMGFZ mass loads products for NTAL, NTOL, and HYDL datasets in CF reference frame are available at http://rz-vm115.gfz-potsdam.de:8080/repository, and the bedrock information are available at http://sopac-csrc.ucsd.edu/index.php/sitelogs/.
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Acknowledgements
We thank the teams from NOAA, NASA, and GFZ for making their data sets publicly available. This work is sponsored by the National Natural Science Foundation of China (No. 42174030, 42004017), the Basic Science Center Project of the National Natural Science Foundation of China (No. 42388102), the Special Fund of Hubei Luojia Laboratory (No. 220100020, 220100048), and the Hubei Provincial Science and Technology Innovation Talents (No. 2022EJD010). We are very grateful to the editor and the three reviewers, in particular Jim Ray, for their constructive comments and suggestions.
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Z.L. and R.L. proposed the initial idea, designed the experiments, developed the software, and wrote the manuscript. W.J. supervised the study and modified the manuscript. D.D. worked out technical details and revised the manuscript. J.L. provided the FEM program. Y.L. helped the visualization. X.D., K.Y., H.C., and Q.C. gave some advices and revised the manuscript. All authors approved of the manuscript.
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Li, Z., Lu, R., Jiang, W. et al. A refined full-spectrum temperature-induced subsurface thermal expansion model and its contribution to the vertical displacement of global GNSS reference stations. J Geod 98, 25 (2024). https://doi.org/10.1007/s00190-024-01834-5
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DOI: https://doi.org/10.1007/s00190-024-01834-5