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.