A comparison of LOD and UT1-UTC forecasts by different combined prediction techniques

Abstract

Stochastic prediction techniques including autocovariance, autoregressive, autoregressive moving average, and neural networks were applied to the UT1-UTC and Length of Day (LOD) International Earth Rotation and Reference Systems Service (IERS) EOPC04 time series to evaluate the capabilities of each method. All known effects such as leap seconds and solid Earth zonal tides were first removed from the observed values of UT1-UTC and LOD. Two combination procedures were applied to predict the resulting LODR time series: 1) the combination of the least-squares (LS) extrapolation with a stochastic prediction method, and 2) the combination of the discrete wavelet transform (DWT) filtering and a stochastic prediction method. The results of the combination of the LS extrapolation with different stochastic prediction techniques were compared with the results of the UT1-UTC prediction method currently used by the IERS Rapid Service/Prediction Centre (RS/PC). It was found that the prediction accuracy depends on the starting prediction epochs, and for the combined forecast methods, the mean prediction errors for 1 to about 70 days in the future are of the same order as those of the method used by the IERS RS/PC. 1. THE CAUSE OF PREDICTION ERRORS OF UT1-UTC AND LOD Modern navigational and positioning systems require accurate universal time (UT1), a measure of the angle about the rotation axis through which the solid Earth has rotated. Many of these systems need near real-time estimates of UT1 with predictions into the future and, as these systems improve, so must our ability to determine and predict UT1. Therefore, research and development efforts are required to improve the accuracy of the estimated UT1, reduce prediction errors, and improve computation speeds. This study will examine different stochastic prediction techniques and compare their performance to UT1-UTC prediction method currently used by the IERS RS/PC. The Length of Day variations (LOD) represent the changes in the Earth’s rotation rate. LOD is related to the first derivative of UT1-TAI. UT1R-TAI and LODR represent UT1-TAI and LOD, respectively, after the removal of the well-known solid Earth tides. Currently, the mean observational error of UT1-UTC is of the order of 0.006 ms, which corresponds to about 2.8 mm on the Earth’s surface. This represents, on average, the best that we can observe UT1R and this error is introduced into the prediction. Therefore, the prediction errors, resulting from any prediction method used, represent the accuracy of that prediction method and the effects of the observational errors. Usually the prediction error even for a few days in the future is several times greater than the observational error. The prediction errors of UT1-UTC increase with the prediction length due to the capabilities of the prediction method used and to variable amplitudes and phases of subseasonal, semiannual and annual oscillations. To compute the prediction of UT1-UTC using the IERS EOPC04 series (IERS 2004), all known effects such as leap seconds and solid Earth zonal tides (McCarthy and Petit 2003) were first removed from the observed values of UT1-UTC. The time-frequency Fourier transform band pass filter (FTBPF) (Kosek 1995) amplitude spectrum of the LODR shows variable amplitudes of the annual, semiannual and shorter period oscillations (Fig. 1). Fig. 1. The time-frequency FTBPF amplitude spectrum of the LODR time series. 2. STOCHASTIC PREDICTION TECHNIQUES APPLIED In the autocovariance prediction (AC) the first predicted value is determined by the principle that the autocovariance of the extended time series coincide as closely as possible with the autocovariance estimated from the given series (Kosek et al. 1998, 2003). The second prediction point can be computed in the same way after the first one is added at the end of the time series. The following predictions are computed in a similar fashion. The autoregressive prediction (AR) is computed from the following autoregressive model: xn+l = â1xn+l−1 + ... + âmxn−m−l, (1) where the estimates of the autoregressive coefficients can be derived using the algorithm given by Friedlander and Porat (1984). These estimates are computed using the modified Yule-Walker equations:   â1 â2 .. âm   =   ĉ1,1 ĉ1,2 · · · ĉ1,m ĉ1,2 ĉ2,2 · · · ĉ2,m .. .. . . . .. ĉ1,m ĉ2,m · · · ĉm,m   −1 .   ĉ1,0 ĉ2,0 .. ĉm,0   , (2) where the autocovariance estimation is given by