Abstract
The background noise in Global Navigation Satellite Systems (GNSS) station position time series is known to be both temporally and spatially correlated. Its temporal correlations are well modeled and routinely taken into account when deriving parameters of interest like station velocities. On the other hand, a general model of the spatial correlations in GNSS time series is lacking, and they are usually ignored, although their consideration could benefit several purposes such as offset detection, velocity estimation or spatial filtering. In order to improve the realism of current spatio-temporal correlation models, we investigate in this study how the spatial correlations of GNSS time series vary with the temporal frequency. A frequency-dependent measure of the spatial correlations is therefore introduced and applied to station position time series from the latest reprocessing campaign of the International GNSS Service (IGS), as well as to Precise Point Positioning time series provided by the Nevada Geodetic Laboratory (NGL). Different spatial correlation regimes are thus evidenced at different temporal frequencies. The different levels of spatial correlations between IGS and NGL datasets furthermore suggest that some part of the spatially correlated background noise in GNSS time series consists of GNSS errors rather than aperiodic Earth surface deformation signal.
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Data availability
The IGS repro3 combined solutions analyzed during current study are available from online archives of the Crustal Dynamics Data Information System (CDDIS) (Noll 2010) at https://cddis.nasa.gov/archive/gnss/products/. The station position time series provided by NGL (Blewitt et al. 2018) can be downloaded from http://geodesy.unr.edu/gps_timeseries/tenv3/IGS14/.
References
Altamimi Z, Rebischung P, Collilieux X et al (2022) ITRF2020: main results and key performance indicators. In: EGU general assembly 2022, Vienna, Austria, 23–27 May 2022. https://doi.org/10.5194/egusphere-egu22-3958
Rebischung P (2021) Terrestrial frame solutions from the IGS third reprocessing. EGU General Assembly 2021, Vienna, Austria, 19–30 Apr 2021. https://doi.org/10.5194/EGUSPHERE-EGU21-2144
Abraha KE, Teferle FN, Hunegnaw A, Dach R (2018) Effects of unmodelled tidal displacements in GPS and GLONASS coordinate time-series. Geophys J Int 214:2195–2206. https://doi.org/10.1093/GJI/GGY254
Amiri-Simkooei AR (2009) Noise in multivariate GPS position time-series. J Geod 83:175–187. https://doi.org/10.1007/s00190-008-0251-8
Amiri-Simkooei AR (2013) On the nature of GPS draconitic year periodic pattern in multivariate position time series. J Geophys Res Solid Earth 118:2500–2511. https://doi.org/10.1002/JGRB.50199
Amiri-Simkooei AR, Mohammadloo TH, Argus DF (2017) Multivariate analysis of GPS position time series of JPL second reprocessing campaign. J Geod 91(6):85–704. https://doi.org/10.1007/S00190-016-0991-9
Benoist C, Collilieux X, Rebischung P et al (2020) Accounting for spatiotemporal correlations of GNSS coordinate time series to estimate station velocities. J Geodyn 135:101693. https://doi.org/10.1016/J.JOG.2020.101693
Blewitt G, Lavallée D (2002) Effect of annual signals on geodetic velocity. J Geophys Res Solid Earth 107(7):9ETG9-1-1ETG9-11
Blewitt G, Hammond WC, Kreemer C (2018) Harnessing the GPS data explosion for interdisciplinary science. Eos. https://doi.org/10.1029/2018EO104623
Bock Y, Melgar D (2016) Physical applications of GPS geodesy: a review. Rep Prog Phys 79:106801. https://doi.org/10.1088/0034-4885/79/10/106801
Carrère L, Lyard F (2003) Modeling the barotropic response of the global ocean to atmospheric wind and pressure forcing—comparisons with observations. Geophys Res Lett 30:1275. https://doi.org/10.1029/2002GL016473
Collilieux X, Lebarbier E, Robin S (2019) A factor model approach for the joint segmentation with between-series correlation. Scand J Stat 46:686–705. https://doi.org/10.1111/SJOS.12368
Dong D, Fang P, Bock Y et al (2002) Anatomy of apparent seasonal variations from GPS-derived site position time series. J Geophys Res Solid Earth 107:2075. https://doi.org/10.1029/2001jb000573
Dziewonski AM, Anderson DL (1981) Preliminary reference earth model. Phys Earth Planet Int 25:297–356. https://doi.org/10.1016/0031-9201(81)90046-7
Gazeaux J, Lebarbier E, Collilieux X, Métivier L (2015) Joint segmentation of multiple GPS coordinate series. Journal De La Société Française De Statistique 156(4):163–179
Gobron K (2021) Statistical analysis of vertical land motions and sea level measurements at the coast. Dissertation, Université de La Rochelle. https://tel.archives-ouvertes.fr/tel-03566564
Gobron K, Rebischung P, Van Camp M et al (2021) Influence of aperiodic non-tidal atmospheric and oceanic loading deformations on the stochastic properties of global GNSS vertical land motion time series. J Geophys Res Solid Earth 126:e2021JB022370. https://doi.org/10.1029/2021JB022370
Gobron K, Rebischung P, de Viron O et al (2022) Impact of offsets on assessing the low-frequency stochastic properties of geodetic time series. J Geod 96:46. https://doi.org/10.1007/s00190-022-01634-9
He X, Montillet JP, Fernandes R et al (2017) Review of current GPS methodologies for producing accurate time series and their error sources. J Geodyn 106:12–29. https://doi.org/10.1016/J.JOG.2017.01.004
Heflin M, Donnellan A, Parker J et al (2020) Automated estimation and tools to extract positions, velocities, breaks, and seasonal terms from daily GNSS measurements: illuminating nonlinear salton trough deformation. Earth Sp Sci 7:e2019EA000644. https://doi.org/10.1029/2019EA000644
Hersbach H et al (2020) The ERA5 global reanalysis. Q J R Meteorol Soc 146:1999–2049. https://doi.org/10.1002/qj.3803
Jiang W, Deng L, Li Z et al (2014) Effects on noise properties of GPS time series caused by higher-order ionospheric corrections. Adv Sp Res 53:1035–1046. https://doi.org/10.1016/J.ASR.2013.12.037
Johnston G, Riddell A, Hausler G (2017) The international GNSS service. In: Teunissen PJG, Montenbruck O (eds) Springer handbooks of global navigation satellite systems. Springer, Cham, pp 967–982. https://doi.org/10.1007/978-3-319-42928-1
Mao A, Harrison CGA, Dixon TH (1999) Noise in GPS coordinate time series. J Geophys Res Solid Earth 104:2797–2816. https://doi.org/10.1029/1998JB900033
Munekane H, Boehm J (2010) Numerical simulation of troposphere-induced errors in GPS-derived geodetic time series over Japan. J Geod 84:405–417. https://doi.org/10.1007/S00190-010-0376-4
Noll C (2010) The crustal dynamics data information system: a resource to support scientific analysis using space geodesy. Adv Sp Res 45(12):1421–1440. https://doi.org/10.1016/j.asr.2010.01.018
Penna NT, Stewart MP (2003) Aliased tidal signatures in continuous GPS height time series. Geophys Res Lett. https://doi.org/10.1029/2003GL018828
Press WH, Rybicki GB (1989) Fast algorithm for spectral analysis of unevenly sampled data. Astrophys J 338:277–280
Ray J, Altamimi Z, Collilieux X, Van Dam T (2008) Anomalous harmonics in the spectra of GPS position estimates. GPS Solut 12:55–64. https://doi.org/10.1007/s10291-007-0067-7
Rebischung P, Chanard K, Métivier L, Altamimi Z (2017) Flicker noise in GNSS station position time series: how much is due to crustal loading deformations?AGU fall meeting 2017, New Orleans, USA, 11–15 Dec 2017. https://ui.adsabs.harvard.edu/abs/2017AGUFM.G13A..04R/abstract
Rebischung P, Collilieux X, Métivier L et al (2021) Analysis of IGS repro3 station position time series. AGU fall meeting 2021, New Orleans, USA, 13–17 Dec 2021
Robitaille TP, Tollerud EJ, Greenfield P et al (2013) Astropy: a community python package for astronomy. Astron Astrophys 558:A33. https://doi.org/10.1051/0004-6361/201322068
Santamaría-Gómez A, Ray J (2021) Chameleonic noise in GPS position time series. J Geophys Res Solid Earth 126:e2020JB019541. https://doi.org/10.1029/2020JB019541
Santamaría-Gómez A, Bouin MN, Collilieux X, Wöppelmann G (2011) Correlated errors in GPS position time series: implications for velocity estimates. J Geophys Res Solid Earth 116:1405. https://doi.org/10.1029/2010JB007701
Santamaría-Gómez A, Rebischung P, Ray J (2016) Separating station-dependent from regionally-coherent GPS draconitics in station positions. AGU fall meeting 2016, San Francisco, California, 12–16 Dec 2016.
Scargle JD (1982) Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data. Astrophys J 263:835–853
Scargle JD (1989) Studies in astronomical time series analysis. III. Fourier transforms, autocorrelation functions, and cross-correlation functions of unevenly spaced data. Astrophys J 8743:874–887
Shen Y, Li W, Xu G, Li B (2014) Spatiotemporal filtering of regional GNSS network’s position time series with missing data using principle component analysis. J Geod 88:1–12. https://doi.org/10.1007/S00190-013-0663-Y
Wdowinski S, Bock Y, Zhang J et al (1997) Southern California permanent GPS geodetic array: spatial filtering of daily positions for estimating coseismic and postseismic displacements induced by the 1992 Landers earthquake. J Geophys Res Solid Earth 102:18057–18070. https://doi.org/10.1029/97JB01378
Williams SDP, Bock Y, Fang P et al (2004) Error analysis of continuous GPS position time series. J Geophys Res Solid Earth. https://doi.org/10.1029/2003JB002741
Zhang J, Bock Y, Johnson H et al (1997) Southern California permanent GPS geodetic array: error analysis of daily position estimates and site velocities. J Geophys Res Solid Earth 102:18035–18055. https://doi.org/10.1029/97JB01380
Acknowledgments
Thanks to IGS for providing the repro3 solutions and NGL for providing the PPP time series on which this study is based.
Funding
This study was funded by the National Natural Science Foundation of China (41931075, 42174028). Yujiao Niu appreciated the financial support from China Scholarship Council (CSC) by State Scholarship Fund (No.202006270190).
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PR conceptualized and designed the study; YJN and PR performed the formal analysis and investigation; YJN wrote the first draft of the manuscript; PR and ZA revised the manuscript; ML, NW and CS commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Niu, Y., Rebischung, P., Li, M. et al. Temporal spectrum of spatial correlations between GNSS station position time series. J Geod 97, 12 (2023). https://doi.org/10.1007/s00190-023-01703-7
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DOI: https://doi.org/10.1007/s00190-023-01703-7