Prediction Analysis of UT1-UTC Time Series by Combination of the Least-Squares and Multivariate Autoregressive Method

  • Tomasz NiedzielskiEmail author
  • Wiesław Kosek
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 137)


The objective of this paper is to extensively discuss the theory behind the multivariate autoregressive prediction technique used elsewhere for forecasting Universal Time (UT1-UTC) and to characterise its performance depending on input geodetic and geophysical data. This method uses the bivariate time series comprising length-of-day and the axial component of atmospheric angular momentum data and needs to be combined with a least-squares extrapolation of a polynomial-harmonic model. Two daily length-of-day time series, i.e. EOPC04 and EOPC04_05 spanning the time interval from 04.01.1962 to 02.05.2007, are utilised. These time series are corrected for tidal effects following the IERS Conventions model. The data on the axial component of atmospheric angular momentum are processed to gain the 1-day sampling interval and cover the time span listed above. The superior performance of the multivariate autoregressive prediction in comparison to autoregressive forecasting is noticed, in particular during El Niño and La Niña events. However, the accuracy of the multivariate predictions depends on a particular solution of input length-of-day time series. Indeed, for EOPC04-based analysis the multivariate autoregressive predictions are more accurate than for EOPC04_05-based one. This finding can be interpreted as the meaningful influence of smoothing on forecasting performance.


Atmospheric angular momentum El Niño/Southern Ociallation Length of day Multivariate autoregressive model Prediction 



The research was financed from the Polish science funds for the period of 2009-2011 provided by Polish Ministry of Science and Higher Education through the grant no. N N526 160136 under leadership of Dr Tomasz Niedzielski at the Space Research Centre of Polish Academy of Sciences. The first author was also supported by EU EuroSITES project. The authors of R 2.9.0 – A Language and Environment and additional packages are acknowledged.


  1. Abarca del Rio A, Gambis D, Salstein DA (2000) Interannual signals in length of day and atmospheric angular momentum. Annales Geophysicae 18:347–364CrossRefGoogle Scholar
  2. Akyilmaz O, Kutt erer H (2004) Prediction of Earth rotation parameters by fuzzy inference systems. J Geodes 78:82–93Google Scholar
  3. Freedman AP, Steppe JA, Dickey JO, Eubanks TM, Sung LY (1994) The short-term prediction of universal time and length of day using atmospheric angular momentum. J Geophys Res 99(B4):6981–6996Google Scholar
  4. Gross RS, Eubanks TM, Steppe JA, Freedman AP, Dickey JO, Runge TF (1998) A Kalman filter-based approach to combining independent Earth-orientation series. J Geodes 72:215–235CrossRefGoogle Scholar
  5. Gross RS, Marcus SL, Eubanks TM, Dickey JO, Keppenne CL (1996) Detection of an ENSO signal in seasonal length-of-day variations. Geophys Res Lett 23:3373–3376CrossRefGoogle Scholar
  6. Johnson T, Luzum BJ, Ray JR (2005) Improved near-term Earth rotation predictions using atmospheric angular momentum analysis and forecasts. J Geodyn 39:209–221CrossRefGoogle Scholar
  7. Kalarus M, Kosek W (2004) Prediction of Earth orientation parameters by artificial neural networks. Artificial Satellites 39:175–184Google Scholar
  8. Kalnay E, Kanamitsu M, Kistler R, Collins W, Deaven D, Gandin L, Iredell M, Saha S, White G, Woollen J, Zhu Y, Leetmaa A, Reynolds B, Chelliah M, Ebisuzaki W, Higgins W, Janowiak J, Mo KC, Ropelewski C, Wang J, Jenne R, Joseph D (1996) The NCEP/NCAR 40-year reanalysis project. Bull Am Meteorol Soc 77:437–471CrossRefGoogle Scholar
  9. Kosek W (1992) Short periodic autoregressive prediction of the Earth rotation parameters. Artificial Satellites 27:9–17Google Scholar
  10. Kosek W, Kalarus M, Johnson TJ, Wooden WH, McCarthy DD, Popiński W(2005) A comparison of LOD and UT1-UTC forecasts by different combination prediction techniques. Artificial Satellites 40:119–125Google Scholar
  11. Kosek W, McCarthy DD, Luzum BJ (1998) Possible improvement of Earth orientation forecast using autocovariance prediction procedures. J Geodes 72:189–199CrossRefGoogle Scholar
  12. McCarthy DD, Petit G (eds) (2004) IERS Conventions 2003 IERS Technical Note No. 32, Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am MainGoogle Scholar
  13. Neumaier A, Schneider T (2001) Estimation of parameters and eigenmodes of multivariate autoregressive models. ACM Trans Math Software 27:27–57CrossRefGoogle Scholar
  14. Niedzielski T, Kosek W (2008) Prediction of UT1-UTC, LOD and AAM χ3 by combination of least-squares and multivariate stochastic methods. J Geodes 82:83–92CrossRefGoogle Scholar
  15. Niedzielski T, Sen AK, Kosek W (2009) On the probability distribution of Earth orientation parameters data. Artficial Satellites 44:33–41CrossRefGoogle Scholar
  16. Rosen RD, Salstein DA, Eubanks TM, Dickey JO, Steppe JA (1984) An El Niño signal in atmoshperic angular momentum and Earth rotation. Science 27:411–414CrossRefGoogle Scholar
  17. Schuh H, Ulrich M, Egger D, Müller J, Schwegmann W (2002) Prediction of Earth orientation parameters by artificial neural networks. J Geodes 76:247–258CrossRefGoogle Scholar
  18. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464CrossRefGoogle Scholar
  19. Zhao J, Han Y (2008) The relationship between the interannual variation of Earth’s rotation and El Niño events. Pure Appl Geophys 165:1435–1443CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Space Research CentrePolish Academy of SciencesWarsawPoland
  2. 2.Institute of Geography and Regional DevelopmentUniversity of WrocławWrocławPoland
  3. 3.OceanlabUniversity of AberdeenNewburghUK
  4. 4.Department of Land SurveyingUniversity of Agriculture in KrakówKrakówPoland

Personalised recommendations