Abstract
Global Positioning System technique has been widely used to estimate ocean tide loading displacements, but classical harmonic analysis with satellite modulation typically disregards the effects of hundreds of minor tides within the same tidal species of major tides. We present an improved harmonic analysis of eight major tidal constituents (M2, S2, N2, K2, K1, O1, P1 and Q1) that are adjusted by more adjacent minor tides in semidiurnal and diurnal species than the usual satellite modulation approach, through the tidal admittance interpolation. Our results show that this approach allows for a more reliable determination of GPS-observed N2, Q1, P1 and S2 constituents in the northwest European shelf than the classical method, as demonstrated by a comparison with FES2014b and TPXO9-Atlas ocean tide model predictions. The advantages of our method are more pronounced in the harmonic analysis of GPS time series of short duration (1–2 years) than long duration. These improvements mainly depend on some inferred minor tides with larger equilibrium amplitudes, which provide effective admittance constraints to major tidal estimation. Among the major tidal estimates, the most significant improvement is seen for the N2 constituent (with the maximum improvement of 9.9%, 9.0% and 9.7% for the up, east and north components in terms of agreement with FES2014b model predictions), particularly along the Wadden Sea coast where significant satellite modulation deviations occur.
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Data availability
The GPS data can be acquired from https://www.epncb.oma.be, and the GNSS precise products can be accessed at https://www.tugraz.at/institute/ifg/downloads/gnss-reprocessing-products/. Model predictions of OTL displacements are available at https://holt.oso.chalmers.se/loading/.
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Acknowledgements
This research is sponsored by the National Natural Science Foundation of China (42174028, 41931075, 42030109). We thank the EUREF Permanent Network for the GPS observations, the Graz University of Technology for the GNSS precise products, and the free ocean tide loading provider website for the model predictions of OTL displacements. The calculations for GPS PPP solutions have been done on the supercomputing system in the Supercomputing Center of Wuhan University. We also thank two anonymous reviewers and the editor Dr. Michael Schindelegger, for their constructive suggestions and comments.
Funding
National Natural Science Foundation of China, 42174028, Na Wei, 41931075, Min Li, 42030109, Qile Zhao.
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NW and ML devised and conceptualized the study. HW conducted data collection and experimental analysis and wrote the first draft of the manuscript. NW, ML, S-CH, RF and QZ revised the manuscript. All authors approved the final manuscript for publication.
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Appendix
Appendix
See Table 2; Figs. 11, 12, 13, 14, 15, and 16.
Similar to Fig. 3d–f but for the magnitude of vector differences between the FES2014b and TPXO9-Atlas model predictions
Results for the up component of the N2, Q1 and P1 constituents in Fig. 4. The left side of the blue dashed line shows the results for the 1–2 year time span and the right side shows the results for the 3–6 year time span
Stacked PSD of GPS residuals derived from IHA and CHA for all GPS stations for the east and north components. The IHA-derived residuals are shifted by 10 for clarity. Gray vertical lines represent the eight major tidal frequencies
Similar to Fig. 7 but for the east component
Similar to Fig. 7 but for the north component
Stacked power spectra of CHA-derived GPS residuals minus that of IHA-derived GPS residuals. The four major tides and six minor tides in the semidiurnal tidal species are the same as in Fig. 8
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Wang , H., Wei, N., Li, M. et al. Estimation of GPS-observed ocean tide loading displacements with an improved harmonic analysis in the northwest European shelf. J Geod 97, 108 (2023). https://doi.org/10.1007/s00190-023-01796-0
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DOI: https://doi.org/10.1007/s00190-023-01796-0