Abstract
A data homogenization method based on singular spectrum analysis (SSA) was developed and tested on real and simulated datasets. The method identifies abrupt changes in the atmospheric time series derived from Global Navigation Satellite System (GNSS) observations. For simulation and verification purposes, we used the ERA-Interim reanalysis data. Our method of change detection is independently applied to the precipitable water vapor (PWV) time series from GNSS, ERA-Interim and their difference. Then the detected offsets in the difference time series can be related to inconsistencies in the datasets or to abrupt changes due to climatic effects. The issue of missing data is also discussed and addressed using SSA. We appraised the performance of our method using a Monte Carlo simulation, which suggests a promising success rate of 81.1% for detecting mean shifts with values between 0.5 and 3 mm in PWV time series. A GNSS-derived PWV dataset, consisting of 214 stations in Germany, was investigated for possible inhomogeneities and systematic changes. We homogenized the dataset by identifying and correcting 96 inhomogeneous time series containing 134 detected and verified mean shifts from which 45 changes, accounting for approximately 34% of the offsets, were undocumented. The linear trends from the GNSS and ERA-Interim PWV datasets were estimated and compared, indicating a significant improvement after homogenization. The correlation between the trends was increased by 39% after correcting the mean shifts in the GNSS data. The method can be used to detect possible changes induced by climatic or meteorological effects.
Similar content being viewed by others
References
Alexandrov T (2008) A method of trend extraction using singular spectrum analysis. p 7. arXiv preprint arXiv:0804.3367
Alshawaf F, Balidakis K, Dick G, Heise S, Wickert J (2017) Estimating trends in atmospheric water vapor and temperature time series over Germany. Atmos Meas Tech 10:3117–3132. https://doi.org/10.5194/amt-10-3117-2017
Alshawaf F, Zus F, Balidakis K, Deng Z, Hoseini M, Dick G, Wickert J (2018) On the statistical significance of climatic trends estimated from GPS tropospheric time series. J Geophys Res Atmos. https://doi.org/10.1029/2018JD028703
Askne J, Nordius H (1987) Estimation of tropospheric delay for microwaves from surface weather data. Radio Sci 22(3):379–386. https://doi.org/10.1029/RS022i003p00379
Balidakis K, Nilsson T, Zus F, Glaser S, Heinkelmann R, Deng Z, Schuh H (2018) Estimating integrated water vapor trends from VLBI, GPS, and numerical weather models: sensitivity to tropospheric parameterization. J Geophys Res Atmos. https://doi.org/10.1029/2017JD028049
Bevis M, Businger S, Chiswell S, Herring TA, Anthes RA, Rocken C, Ware RH (1994) GPS meteorology: mapping zenith wet delays onto precipitable water. J Appl Meteorol 33(3):379–386. https://doi.org/10.1175/1520-0450(1994)033%3c0379:GMMZWD%3e2.0.CO;2
Dee DP, Uppala SM, Simmons A, Berrisford P, Poli P, Kobayashi S, Andrae U, Balmaseda M, Balsamo G, Bauer DP (2011) The ERA-interim reanalysis: configuration and performance of the data assimilation system. Q J R Meteorol Soc 137(656):553–597. https://doi.org/10.1002/qj.828
Escott-Price V, Zhigljavsky A (2003) An algorithm based on singular spectrum analysis for change-point detection. Commun Stat Simul Comput 32:319–352. https://doi.org/10.1081/SAC-120017494
Ghil M, Allen MR, Dettinger M, Ide K, Kondrashov D, Mann M, Saunders A, Tian Y, Varadi F (2001) Advanced spectral methods for climatic time series. Rev Geophys. https://doi.org/10.1029/2000RG000092
Golyandina N, Zhigljavsky A (2013) Singular spectrum analysis for time series. Springer, Berlin
Golyandina N, Viktorovich Nekrutkin V, Zhigljavsky A (2001) Analysis of time series structure: SSA and related techniques. Monogr Stat Appl Probab. https://doi.org/10.1201/9781420035841
Gradinarsky LP, Johansson J, Bouma HR, Scherneck H-G, Elgered G (2002) Climate monitoring using GPS. Phys Chem Earth 27:335–340. https://doi.org/10.1016/S1474-7065(02)00009-8
Hassani H, Thomakos D (2010) A review on singular spectrum analysis for economic and financial time series. Stat Interface 3:377–397
Jarušková D (1996) Change-point detection in meteorological measurement. Mon Weather Rev 124(7):1535–1543. https://doi.org/10.1175/1520-0493(1996)124%3c1535:CPDIMM%3e2.0.CO;2
Klos A, Van Malderen R, Pottiaux E, Bock O, Bogusz J, Chimani B, Elias M, Gruszczynska M, Guijarro J, Zengin Kazanci S, Ning T (2017) Study on homogenization of synthetic GNSS-retrieved IWV time series and its impact on trend estimates with autoregressive noise. European Geosciences Union General Assembly 2017, Vienna, Austria
Klos A, Hunegnaw A, Teferle FN, Abraha KE, Ahmed F, Bogusz J (2018) Statistical significance of trends in Zenith wet delay from re-processed GPS solutions. GPS Solut 22(2):51. https://doi.org/10.1007/s10291-018-0717-y
Kondrashov D, Ghil M (2006) Spatio-temporal filling of missing points in geophysical data sets. Nonlinear Process Geophys 13(2):151–159. https://doi.org/10.5194/npg-13-151-2006
Li X, Dick G, Ge M, Heise S, Wickert J, Bender M (2014) Real-time GPS sensing of atmospheric water vapor: precise point positioning with orbit, clock, and phase delay corrections. Geophys Res Lett 41(10):3615–3621. https://doi.org/10.1002/2013GL058721
Modiri S, Belda S, Heinkelmann R, Hoseini M, Ferrándiz J, Schuh H (2018) Polar motion prediction using the combination of SSA and Copula-based analysis. Earth Planets Space 70:115. https://doi.org/10.1186/s40623-018-0888-3
Nilsson T, Elgered G (2008) Long-term trends in the atmospheric water vapor content estimated from ground-based GPS data. J Geophys Res Atmos. https://doi.org/10.1029/2008JD010110
Ning T, Wickert J, Deng Z, Heise S, Dick G, Vey S, Schöne T (2016) Homogenized time series of the atmospheric water vapor content obtained from the GNSS reprocessed data. J Clim 29:2443–2456. https://doi.org/10.1175/JCLI-D-15-0158.1
Rodionov S (2004) A sequential algorithm for testing climate regime shifts. Geophys Res Lett. https://doi.org/10.1029/2004GL019448
Saastamoinen J (1972) Atmospheric correction for the troposphere and stratosphere in radio ranging satellites. Use Artif Satell Geodesy 15:247–251
Schneider T, O’Gorman PA, Levine XJ (2010) Water vapor and the dynamics of climate changes. Rev Geophys. https://doi.org/10.1029/2009RG000302
Sinha A, Harries JE (1997) The earth’s clear-sky radiation budget and water vapor absorption in the far infrared. J Clim 10(7):1601–1614. https://doi.org/10.1175/1520-0442(1997)010%3c1601:Tescsr%3e2.0.Co;2
Van Malderen R, Pottiaux E, Klos A, Bock O, Bogusz J, Chimani B, Elias M, Gruszczynska M, Guijarro J, Kazancı SZ, Ning T (2017) Homogenizing GPS integrated water vapour time series: methodology and benchmarking the algorithms on synthetic datasets. In: Ninth seminar for homogenization and quality control in climatological databases and fourth conference on spatial interpolation techniques in climatology and meteorology, Budapest. pp 104–116
Venema VKC, Mestre O, Aguilar E, Auer I, Guijarro JA, Domonkos P, Vertacnik G, Szentimrey T, Stepanek P, Zahradnicek P, Viarre J, Müller-Westermeier G, Lakatos M, Williams CN, Menne MJ, Lindau R, Rasol D, Rustemeier E, Kolokythas K, Marinova T, Andresen L, Acquaotta F, Fratianni S, Cheval S, Klancar M, Brunetti M, Gruber C, Prohom Duran M, Likso T, Esteban P, Brandsma T (2012) Benchmarking monthly homogenization algorithms. Clim Past 8:89–115. https://doi.org/10.5194/cp-8-89-2012
Vey S, Dietrich R, Fritsche M, Rülke A, Steigenberger P, Rothacher M (2009) On the homogeneity and interpretation of precipitable water time series derived from global GPS observations. J Geophys Res Atmos. https://doi.org/10.1029/2008JD010415
Wang X (2008) Accounting for autocorrelation in detecting mean shifts in climate data series using the penalized maximal t or F test. J Appl Meteorol Climatol 47:2423–2444. https://doi.org/10.1175/2008JAMC1741.1
Wang X, Wen QH, Wu Y (2007) Penalized maximal t test for detecting undocumented mean change in climate data series. J Appl Meteorol Climatol 46:916–931. https://doi.org/10.1175/JAM2504.1
Wang J, Dai A, Mears C (2016) Global water vapor trend from 1988 to 2011 and its diurnal asymmetry based on GPS, radiosonde, and microwave satellite measurements. J Clim 29(14):5205–5222
Williams SDP (2003) Offsets in global positioning system time series. J Geophys Res 108(B6):2310. https://doi.org/10.1029/2002JB002156
Acknowledgements
The Norwegian University of Science and Technology (NTNU), Grant Number 81771107, funded this project. We thank Stefan Heise and Kyriakos Balidakis for providing us with simulated ERA-Interim time series. Thanks also to ECMWF for making publicly available the ERA-Interim data. The first author is very grateful to Yahya AllahTavakoli for his mathematical comments on the research. The authors would like to thank anonymous reviewers for their constructive comments.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Hoseini, M., Alshawaf, F., Nahavandchi, H. et al. Towards a zero-difference approach for homogenizing GNSS tropospheric products. GPS Solut 24, 8 (2020). https://doi.org/10.1007/s10291-019-0915-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10291-019-0915-2