On the Probability Distribution of Earth Orientation Parameters Data
Earth Orientation Parameters (EOPs), i.e. pole coordinates (xp, yp), Universal Time (UT1-UTC), and celestial pole offsets (dX, dY), are the transformation parameters between the International Terrestrial Reference Frame (ITRF) and the International Celestial Reference Frame (ICRF). It is customarily assumed that each of the EOP time series follows the normal distribution. The normality assumption has been used specifically in EOP prediction studies. The objective of this paper is to investigate the normality hypothesis in detail. We analysed the daily time series of xp, yp, UT1-UTC, length-of-day (Δ), dX, and dY in the time interval from 01.01.1962 to 31.12.2008. The UT1-UTC data were transformed to UT1R-TAI by removing leap seconds and the tidal signal using the IERS model. The tidal effects δΔ were also removed from the Δ time series and Δ - δΔ data were obtained. Furthermore, we constructed the residuals of these time series using least-squares fit. We evaluated the skewness and kurtosis and tested their statistical significance by the D'Agostino and the Anscombe-Glynn tests, respectively. In addition, the Anderson-Darling test for the normal distribution was applied. It was found that the xp, yp time series and their residuals slightly depart from the normal distribution, but this departure is rather due to marginal flattening/narrowing of the probability density function than due to extreme values. The UT1R-TAI time series and its residuals were also classified as non-Gaussian, however, the deviations from the normal distribution are again slight. The similar results hold for the Δ - δΔ data, but some of its residuals were found to be Gaussian. We noticed that the celestial pole offsets, dX and dY, tend to deviate from the Gaussian distribution. In addition, we examined the determination errors of EOP data and found them to depart significantly from the normal distribution.
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Akyilmaz O. Kutterer H. (2004) Prediction of Earth rotation parameters by fuzzy inference systems Journal of Geodesy 78 82-93.
Anscombe F.J. Glynn W.J. (1983) Distribution of kurtosis statistic for normal statistics Biometrika 70 227-234.
Consolini G. De Michelis P. (1998) Non-Gaussian distribution functions of AE-index fluctuations: Evidence of time intermittency Geophysical Research Letters 25 4087-4090.
D'Agostino R.B. (1970) Transformation to Normality of the Null Distribution of G1 Biometrika 57 679-681.
Eubanks T.M. (1993) Variations in the Orientation of the Earth Contributions of Space Geodesy to Geodynamics: Earth Dynamics Smith D.E. Turcotte D.L. (eds) AGU Geodynamics Series 1-54.
Freedman A.P. Steppe J.A. Dickey J.O. Eubanks T.M. Sung L.Y. (1994) The shortterm prediction of universal time and length of day using atmospheric angular momentum Journal of Geophysical Research 99 (B4) 6981-6996.
Kalarus M. Kosek W. (2004) Prediction of Earth orientation parameters by artificial neural networks. Artificial Satellite 39 175-184.
Kosek W. McCarthy D.D. Luzum B.J. (1998) Possible improvement of Earth orientation forecast using autocovariance prediction procedures Journal of Geodesy 72 189-199.
Kosek W. Kalarus M. Johnson T.J. Wooden W.H. McCarthy D.D. Popiński W. (2005) A comparison of LOD and UT1-UTC forecasts by different combination prediction techniques Artificial Satellites 40 119-125.
McCarthy D.D. Petit G. eds. (2004) IERS Conventions 2003 IERS Technical Note No. 32 Verlag des Bundesamts für Kartographie und Geodäsie Frankfurt am Main.
Niedzielski T. Kosek W. (2008) Prediction of UT1-UTC LOD and AAM X3 by combination of least-squares and multivariate stochastic methods Journal of Geodesy 82 83-92.
Petrov S. Brzeziński A. Gubanov V. (1995) On application of the Kalman filter and the least squares collocation in Earth rotation investigations Proc. Journées 1995 Systémes de Référence Spatio-Temporels Capitaine N. et al. (eds) Warsaw 125-128.
Schuh H. Ulrich M. Egger D. Mueller J. Schwegmann W. (2002) Prediction of Earth orientation parameters by artificial neural networks Journal of Geodesy 76 247-258.
Stoyko N. (1937) Sur la periodicite dans l'irregularite de la rotation de la Terre Comptes rendus des Seances de l'Academie des Sciences Paris 205 79.