Pure and Applied Geophysics

, Volume 175, Issue 10, pp 3485–3509 | Cite as

Analysis of Seasonal Signal in GPS Short-Baseline Time Series

  • Kaihua Wang
  • Weiping JiangEmail author
  • Hua Chen
  • Xiangdong An
  • Xiaohui Zhou
  • Peng Yuan
  • Qusen Chen


Proper modeling of seasonal signals and their quantitative analysis are of interest in geoscience applications, which are based on position time series of permanent GPS stations. Seasonal signals in GPS short-baseline (< 2 km) time series, if they exist, are mainly related to site-specific effects, such as thermal expansion of the monument (TEM). However, only part of the seasonal signal can be explained by known factors due to the limited data span, the GPS processing strategy and/or the adoption of an imperfect TEM model. In this paper, to better understand the seasonal signal in GPS short-baseline time series, we adopted and processed six different short-baselines with data span that varies from 2 to 14 years and baseline length that varies from 6 to 1100 m. To avoid seasonal signals that are overwhelmed by noise, each of the station pairs is chosen with significant differences in their height (> 5 m) or type of the monument. For comparison, we also processed an approximately zero baseline with a distance of < 1 m and identical monuments. The daily solutions show that there are apparent annual signals with annual amplitude of ~ 1 mm (maximum amplitude of 1.86 ± 0.17 mm) on almost all of the components, which are consistent with the results from previous studies. Semi-annual signal with a maximum amplitude of 0.97 ± 0.25 mm is also present. The analysis of time-correlated noise indicates that instead of flicker (FL) or random walk (RW) noise, band-pass-filtered (BP) noise is valid for approximately 40% of the baseline components, and another 20% of the components can be best modeled by a combination of the first-order Gauss–Markov (FOGM) process plus white noise (WN). The TEM displacements are then modeled by considering the monument height of the building structure beneath the GPS antenna. The median contributions of TEM to the annual amplitude in the vertical direction are 84% and 46% with and without additional parts of the monument, respectively. Obvious annual signals with amplitude > 0.4 mm in the horizontal direction are observed in five short-baselines, and the amplitudes exceed 1 mm in four of them. These horizontal seasonal signals are likely related to the propagation of daily/sub-daily TEM displacement or other signals related to the site environment. Mismodeling of the tropospheric delay may also introduce spurious seasonal signals with annual amplitudes of ~ 5 and ~ 2 mm, respectively, for two short-baselines with elevation differences greater than 100 m. The results suggest that the monument height of the additional part of a typical GPS station should be considered when estimating the TEM displacement and that the tropospheric delay should be modeled cautiously, especially with station pairs with apparent elevation differences. The scheme adopted in this paper is expected to explicate more seasonal signals in GPS coordinate time series, particularly in the vertical direction.


Monument thermal expansion seasonal signal GPS short-baseline noise characteristic 



We thank the two anonymous for their helpful recommendations. We thank the SOPAC and NCEP/ECMWF for providing raw GPS observations and temperature dataset, respectively. We thank Dr. Williams for providing CATS software package. We also thank Juergen Neumeyer, Thomas Nylen, Gudmundur Valsson, and Ryan Ruddick for providing pictures and information about the IGS stations. This research is supported by the National Science Foundation for Distinguished Young Scholars of China (Grant no. 41525014) and the National Natural Science Foundation of China (Grant nos. 41374033 and 41210006), and the Program for Changjiang Scholars of the Ministry of Education of China. This research is also supported by the project of Wuhan University for overseas exchange graduate.

Supplementary material

24_2018_1871_MOESM1_ESM.jpg (110 kb)
Supplementary material 1 (JPEG 109 kb)
24_2018_1871_MOESM2_ESM.jpg (144 kb)
Supplementary material 2 (JPEG 144 kb)
24_2018_1871_MOESM3_ESM.jpg (223 kb)
Supplementary material 3 (JPEG 223 kb)
24_2018_1871_MOESM4_ESM.jpg (166 kb)
Supplementary material 4 (JPEG 166 kb)
24_2018_1871_MOESM5_ESM.jpg (391 kb)
Supplementary material 5 (JPEG 390 kb)
24_2018_1871_MOESM6_ESM.jpg (470 kb)
Supplementary material 6 (JPEG 469 kb)


  1. Altamimi, Z., Rebischung, P., Métivier, L., & Collilieux, X. (2016). ITRF2014: A new release of the international terrestrial reference frame modeling nonlinear station motions. Journal of Geophysical Research: Solid Earth, 121, 6109–6131.Google Scholar
  2. Blewitt, G., Lavallee, D., Clarke, P., & Nurutdinov, K. (2001). A new global mode of Earth deformation: Seasonal cycle detected. Science, 294(5550), 2342–2345.CrossRefGoogle Scholar
  3. Boehm, J., Niell, A., Tregoning, P., & Schuh, H. (2006). Global mapping function (GMF): A new empirical mapping function based on numerical weather model data. Geophysical Research Letters, 33(7).Google Scholar
  4. Chen, Q., Jiang, W., Meng, X., Jiang, P., Wang, K., Xie, Y., et al. (2018). Vertical deformation monitoring of the suspension bridge tower using GNSS: A case study of the forth road bridge in the UK. Remote Sensing, 10(3), 364.CrossRefGoogle Scholar
  5. Collilieux, X., Altamimi, Z., Coulot, D., van Dam, T., & Ray, J. (2010). Impact of loading effects on determination of the International Terrestrial Reference Frame. Advances in Space Research, 45(1), 144–154.CrossRefGoogle Scholar
  6. Davis, J. L., Wernicke, B. P., & Tamisiea, M. E. (2012). On seasonal signals in geodetic time series. Journal of Geophysical Research: Solid Earth, 117(B1).CrossRefGoogle Scholar
  7. Deng, L., Jiang, W., Li, Z., Chen, H., Wang, K., & Ma, Y. (2016). Assessment of second- and third-order ionospheric effects on regional networks: case study in China with longer CMONOC GPS coordinate time series. Journal of Geodesy, 91(2), 207–227.CrossRefGoogle Scholar
  8. Dong, D., Fang, P., Bock, Y., Cheng, M. K., & Miyazaki, S. (2002). Anatomy of apparent seasonal variations from GPS-derived site position time series. Journal of Geophysical Research Atmospheres, 107(B4), ETG 9-1–ETG 9-16.CrossRefGoogle Scholar
  9. Fang, M., Dong, D., & Hager, B. H. (2014). Displacements due to surface temperature variation on a uniform elastic sphere with its centre of mass stationary. Geophysical Journal International, 196, 194–203.CrossRefGoogle Scholar
  10. Haas, R., Bergstrand, S., & Lehner, W. (2013). Evaluation of GNSS monument stability. In Reference frames for applications in geosciences (pp. 45–50). Berlin: Springer.Google Scholar
  11. Herring, T. A. (2009). Example of the usage of TRACK, Massachusetts’s Institute Mass., Inst. of Technol., Cambridge.
  12. Herring, T. A., King, R. W., & McClusky, S. C. (2010). GAMIT reference manual, release 10.4: Cambridge, Massachusetts Institute of Technology Department of Earth, Atmospheric, and Planetary Sciences, 171 pp.Google Scholar
  13. Hill, E. M., Davis, J. L., Elósegui, P., Wernicke, B. P., Malikowski, & Niemi, E. N. A (2009). Characterization of site-specific GPS errors using a short-baseline network of braced monuments at Yucca Mountain, Southern Nevada. Journal of Geophysical Research, 114(B11).Google Scholar
  14. Jiang, W., Liu, H., & Zhou, X. (2012). Analysis of long-term deformation of reservoir using continuous GPS observations. Acta Geodaetica Et Cartographica Sinica, 41(5), 682–689.Google Scholar
  15. Johnson, C. W., Fu, Y., & Bürgmann, R. (2017). Stress models of the annual hydrospheric, atmospheric, thermal, and tidal loading cycles on California faults: Perturbation of background stress and changes in seismicity. Journal of Geophysical Research: Solid Earth, 122, 10605–10625.Google Scholar
  16. King, M. A., & Watson, C. S. (2010). Long GPS coordinate time series: Multipath and geometry effects. Journal of Geophysical Research Solid Earth, 115(B4), 2500–2522.Google Scholar
  17. King, M. A., Watson, C. S., Penna, N. T., & Clarke, P. J. (2008). Sub-daily signals in GPS observations and their effect at semi-annual and annual periods. Geophysical Research Letters, 35(3), 247–255.CrossRefGoogle Scholar
  18. King, M. A., & Williams, S. D. P. (2009). Apparent stability of GPS monumentation from short-baseline time series. Journal of Geophysical Research, 114(B10).Google Scholar
  19. Langbein, J. (2004). Noise in two-color electronic distance meter measurements revisited. Journal of Geophysical Research: Solid Earth, 109(B4).Google Scholar
  20. Langbein, J. (2008). Noise in GPS displacement measurements from Southern California and Southern Nevada. Journal of Geophysical Research, 113(B5).Google Scholar
  21. Langbein, J. (2012). Estimating rate uncertainty with maximum likelihood: differences between power-law and flicker–random-walk models. Journal of Geodesy, 86(9), 775–783.CrossRefGoogle Scholar
  22. Leh ner, W. M. (2011). Evaluation of environmental stresses on GNSS-monuments. Master of Science Thesis, Chalmers University of Technology.Google Scholar
  23. Ma, F., Xi, R., & Xu, N. (2016). Analysis of railway subgrade frost heave deformation based on GPS. Geodesy and Geodynamics, 7(2), 143–147.CrossRefGoogle Scholar
  24. Munekane, H. (2012). Coseismic and early postseismic slips associated with the 2011 off the Pacific coast of Tohoku Earthquake sequence: EOF analysis of GPS kinematic time series(J). Earth, Planets and Space, 64(12), 1077–1091.CrossRefGoogle Scholar
  25. Munekane, H. (2013). Sub-daily noise in horizontal GPS kinematic time series due to thermal tilt of GPS monuments. Journal of Geodesy, 87(4), 393–401.CrossRefGoogle Scholar
  26. Munekane, H., & Boehm, J. (2010). Numerical simulation of troposphere-induced errors in GPS-derived geodetic time series over Japan. Journal of Geodesy, 84(7), 405–417.CrossRefGoogle Scholar
  27. Penna, N. T., King, M. A., & Stewart, M. P. (2007). GPS height time series: Short-period origins of spurious long-period signals, Journal of Geophysical Research, 112(B2).Google Scholar
  28. Penna, N. T., & Stewart, M. P. (2003). Aliased tidal signatures in continuous GPS height time series. Geophysical Research Letters, 30(23), 69–73.CrossRefGoogle Scholar
  29. Prawirodirdjo, L., Ben-Zion, Y., & Bock, Y. (2006). Observation and modeling of thermoelastic strain in southern California integrated GPS network daily position time series. Journal of Geophysical Research, 111, B02408.CrossRefGoogle Scholar
  30. Ray, J., Altamimi, Z., Collilieux, X., & van Dam, T. (2007). Anomalous harmonics in the spectra of GPS position estimates. GPS Solutions, 12(1), 55–64.CrossRefGoogle Scholar
  31. Santamaría-Gómez, A. (2013). Very short baseline interferometry: assessment of the relative stability of the GPS stations at the Yebes Observatory (Spain). Studia Geophysica et Geodaetica, 57(2), 233–252.CrossRefGoogle Scholar
  32. Santamaría-Gómez, A., Bouin, M.-N., Collilieux, X., Wöppelmann, G. (2011). Correlated errors in GPS position time series: Implications for velocity estimates. Journal of Geophysical Research, 116(B1).Google Scholar
  33. Schenewerk, M. S., Vandam, T. M., & Nerem, R. S. (1999). Seasonal motion in the Annapolis. Maryland GPS monument. GPS Solutions, 2(3), 41–49.CrossRefGoogle Scholar
  34. Schön, S. (2006). Affine distortion of small GPS networks with large height differences. GPS Solutions, 11(2), 107–117.CrossRefGoogle Scholar
  35. Stewart, M. P., Penna, N. T., & Lichti, D. D. (2005). Investigating the propagation mechanism of unmodelled systematic errors on coordinate time series estimated using least squares. Journal of Geodesy, 79(8), 479–489.CrossRefGoogle Scholar
  36. Tregoning, P., & van Dam, T. (2005). Atmospheric pressure loading corrections applied to GPS data at the observation level. Geophysical Research Letters, 32(22).CrossRefGoogle Scholar
  37. Wang, K., Chen, H., Jiang, W., Li, Z., Ma, Y., & Deng, L. (2018). Improved vertical displacements induced by a refined thermal expansion model and its quantitative analysis in GPS height time series. Journal of Geophysics and Engineering, 15(2), 554–567.CrossRefGoogle Scholar
  38. Wilkinson, M., Appleby, G., Sherwood, R., & Smith, V. (2013). Monitoring Site Stability at the Space Geodesy Facility. Herstmonceux, UK, 138, 95–102.Google Scholar
  39. Williams, S. D. P. (2003). The effect of colored noise on the uncertainties of rates estimated from geodetic time series. Journal of Geodesy, 76(9–10), 483–494.CrossRefGoogle Scholar
  40. Williams, S. D. P. (2008). CATS: GPS coordinate time series analysis software. GPS Solutions, 147–153.CrossRefGoogle Scholar
  41. Williams, S. D. P., Bock, Y., Fang, P., Jamason, P., Nikolaidis, R. M., Prawirodirdjo, L., Miller, M., & Johnson, D. J. (2004). Error analysis of continuous GPS position time series. Journal of Geophysical Research, 109, B03412.Google Scholar
  42. Wu, J. (2012). Propagation delay induced by antenna snow cover using PPP technology. Geomatics & Information Science of Wuhan University, 37(5), 617–620.Google Scholar
  43. Xu, X., Dong, D., Fang, M., Zhou, Y., Wei, N., & Zhou, F. (2017). Contributions of thermoelastic deformation to seasonal variations in gps station position. GPS Solutions, 21(3), 1265–1274.CrossRefGoogle Scholar
  44. Yan, H., Chen, W., Zhu Y., Zhang, W., & Zhong, M. (2009). Contributions of thermal expansion of monuments and nearby bedrock to observed GPS height changes. Geophysical Research Letters, 36(13).Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.GNSS CenterWuhan UniversityWuhanPeople’s Republic of China
  2. 2.Collaborative Innovation Center of Geospatial TechnologyWuhan UniversityWuhanPeople’s Republic of China
  3. 3.School of Geodesy and GeomaticsWuhan UniversityWuhanPeople’s Republic of China
  4. 4.Key Laboratory of Geospace Environment and Geodesy, Ministry of EducationWuhan UniversityWuhanPeople’s Republic of China

Personalised recommendations