Analysis and prediction of EOP time series using LSHE+ARMA method

Document Type : Research Article


1 Associate Professor, Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran

2 .Sc. Student, Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran

3 Ph.D. Graduated, Department of Geomatics Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan, Iran

4 Professor, Department of Geomatics Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan, Iran


The rotation of the solid Earth with respect to inertial space is not constant due to the changes of external gravitational forces and internal dynamics. Earth orientation parameters (EOP), including, the Earth’s polar motion (PM), Anomalies in the Earth’s angular velocity and celestial pole offsets (CPO), describe these irregularities in the Earth’s rotation. Anomalies in the axis defined by the celestial intermediate pole (CIP) with respect to the Z axis of the terrestrial reference system are named as PM. The CPO are expressed as the deviations, dX and dY, between the observed CIP and the conventional CIP position. The difference between the smoothed principal form of universal time UT1 and the coordinated universal time UTC denotes the Earth’s rotation angle, which together with the xp, yp terrestrial pole coordinates, forms a set of Earth orientation parameters (EOP). In addition to the other EOP, the length of day (LOD) is used to model the Anomalies in the Earth’s rotation rate. LOD is the difference between the duration of the day measured by space geodesy and nominal day of 86,400 s duration.
Generally, EOP are the parameters that provide the rotation of the International Terrestrial Reference System (ITRS) to the International Celestial Reference System (ICRS) as a function of time. However, the EOP are computed using the modern space geodetic techniques such as Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), Satellite Laser Ranging (SLR), Very Long Baseline Interferometry (VLBI) and the Global Navigation Satellite System (GNSS), they are unavailable to the real-time applications due to the data processing complexities. Accurate and rapid EOP predictions are required for different fields like precise orbit determinations of artificial Earth satellites, positional astronomy, space navigation and geophysical phenomena.
There are many different methods for analysis and prediction of EOP time series including deep learning methods, least square (LS) with autoregressive (AR) and also Singular Spectrum Analysis as a non-parametric method.
In this research Least Square Harmonic Estimation analysis is used to investigate the frequencies of EOP. First, the solid and ocean tide terms are modeled based on IERS technical notes. These effects are removed from LOD time series. The remained time series are named as LODR time series. The univariate time series analysis is then applied to the LODR time series and multivariate analysis is used for detecting the PM periodic patterns. Applying these methods to the 40 years of observations of EOP (since 1 January 1980 to 31 December 2020) revealed the Chandler, annual, semi Chandler, semi-annual and annual signals as the main periodic signals in the EOP time series. The functional model is then formed using all detected signals in order to model the deterministic variations of EOP time series.
In order to model the remained non-deterministic variations, an ARMA (Autoregressive Moving Average) model is fitted to the least square residuals. The Akaike's Information Criterion (AIC) is used to investigate the optimized order of ARMA model.
The EOP is then predicted for the first 20 days of 2021, using the pre-identified functional model for the deterministic part and the ARMA model for the non-deterministic part of the time series variations. For the prediction of LOD time series, after creating the functional model of LODR time series, the solid and ocean tide terms are added to the functional model of LODR.
Finally, in order to validate the accuracy of the proposed method, a comparison is made with an EOP prediction study that used the ANN (Artificial Neural Network) and ANFIS (Adaptive Network Based Fuzzy Inference System) methods for short term prediction of EOP.
The result shows that the accuracy of the proposed method is better than the previous study and the method can be used for accurate prediction of EOP time series.


Main Subjects

Akyilmaz, O. and Kutterer, H., 2004, Prediction of Earth Rotation Parameters by Fuzzy Inference Systems, Journal of Geodesy 78(1–2), doi: 10.1007/s00190-004-0374-5.
Akyilmaz, O., Kutterer, H., Shum, C. and Ayan, T., 2011, Fuzzy-Wavelet Based Prediction of Earth Rotation Parameters, Applied Soft Computing, 11(1), 837–41, doi: 10.1016/j.asoc.2010.01.003.
Amiri Simkooei, A. and Asgari, J., 2012, Harmonic analysis of total electron contents time series: Methodology and results. GPS Solutions, 16(1), 77–88.
Amiri Simkooei, A., 2007, Least-Squares Variance Component Estimation, Theory and GPS Applications, Delft: NCG.
Amiri Simkooei, A. 2009, Noise in Multivariate GPS Position Time-Series, J Geod 83, 175–187. Https://Doi.Org/10.1007/S00190-008-0251-8.
Angermann, D., Seitz, M. and Drewes, H., 2010, Analysis of the DORIS Contributions to IRTF2008. Adv Space Res, 46(12), 1633–1647.
Barnes, R., Raymond, H., White, A. and Wilson, C., 1983, Atmospheric Angular Momentum Fluctuations, Length-of-Day Changes and Polar Motion’. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 387(1792), 31–73. doi: 10.1098/rspa.1983.0050.
Chen, J. and Wilson, C. 2005, Hydrological Excitations of Polar Motion, 1993–2002, Geophysical Journal International, 160(3), 833–39. doi: 10.1111/j.1365-246X.2005.02522.x.
Coulot, D., Pollet, A., Collilieux, X. and Berio, P., 2010, Global Optimization of Core Station Networks for Space Geodesy: Application to the Referencing of the STR EOP with Respect to ITRF. J Geod 84(1), 31.
Dickey, J., Newhall, X. and Williams, J., 1985, Earth Orientation from Lunar Laser Ranging and an Error Analysis Polar Motion Services. J Geophys Res Solid Earth, 90(B11), 9353–9362.
Dow, J., Nelan, R. And Rizos, C., 2009, The International GNSS Service in a Changing Landscape of Global Navigation Satellite Systems. J Geod83 (3–4), 191–198.
Freedman, A., Steppe, J., Dickey, J., Eubanks, T. and Sung, L.Y., 1994, The short-term prediction of universal time and length of day using atmospheric angular momentum. J Geophys Res Solid Earth 99(B4), 6981–6996.
Iz, H., 2008, Polar Motion Modeling, Analysis, and Prediction with Time Dependent Harmonic Coefficients, Journal of Geodesy 82(12), 871–81. doi: 10.1007/s00190-008-0215-z.
Jin, X., Liu, X., Cuo, J. and Shen, Y. 2021, Analysis and Prediction of Polar Motion Using MSSA Method. Earth, Planets and Space 73(1):147. doi: 10.1186/s40623-021-01477-2.
Kalarus, M., Schuh, H., Kosek, W., Akyilmaz, O., Bizouard, Ch., Gambis, D., Gross, R., Jovanović, B., Kumakshev, S., Kutterer, H., Mendes Cerveira, P. J., Pasynok, S., and Zotov, L., 2010, Achievements of the Earth Orientation Parameters Prediction Comparison Campaign, Journal of Geodesy 84(10), 587–96. doi: 10.1007/s00190-010-0387-1.
Kong, Q., Zhang, L., Han, L., Guo, J., Zhang, D.  and Fang, W. 2020, Analysis of 25 Years of Polar Motion Derived from the DORIS Space Geodetic Technique Using FFT and SSA Methods. Sensors 20(10), 2823. doi: 10.3390/s20102823.
Kosek, W., 2012, Future Improvements in EOP Prediction, Pp. 513–20 in Geodesy for Planet Earth. Vol. 136, International Association of Geodesy Symposia, edited by S. Kenyon, M. C. Pacino, and U. Marti. Berlin, Heidelberg: Springer Berlin Heidelberg.
Kosek, W., Kalarus, M., Johnson, T. J., Wooden, W. H., McCarthy, D. D., and Popiński, W., 2005, A comparison of LOD and UT1-UTC forecasts by different combined prediction techniques, Artificial Satellites 40 (2), 119–125.
Malkin, Z. and Miller N., 2010, Chandler Wobble: Two More Large Phase Jumps Revealed’. Earth, Planets and Space 62(12):943–47. doi: 10.5047/eps.2010.11.002.
Mathews, P. M., Buffett, B. A., Herring, T. A. and Shapiro, I. I., 1991, Forced Nutations of the Earth: Influence of Inner Core Dynamics 1. Theory, Journal of Geophysical Research 96(B5), 8219–42.
McCarthy, D. and. Luzum, B., 1991, Prediction of Earth Orientation’. Bulletin Géodésique 65(1), 18–21. doi: 10.1007/BF00806338.
Modiri, S., Belda, S., Hoseini, M., Heinkelmann, R., Ferrándiz, JM. and Schuh, H. 2020, A New Hybrid Method to Improve the Ultra-Short-Term Prediction of LOD’. Journal of Geodesy 94(2):23. doi: 10.1007/s00190-020-01354-y.
Nastula, J., Chin, T., Gross, R., Śliwińska, J. and Wińska, M., 2020, Smoothing and Predicting Celestial Pole Offsets Using a Kalman Filter and Smoother. Journal of Geodesy 94(3), 29. doi: 10.1007/s00190-020-01349-9.
Petit, G. and Luzum, B., 2010, (IERS Technical Note; No. 36, (36), 179.
Priestley, M. B., 1981, Spectral Analysis and Time Series: Probability and Mathematical Statistics, No. 04; QA280, P7.
Schuh, H., Ulrich, M., Egger, D., Müller, J. and Schwegmann, W., 2002, Prediction of Earth Orientation Parameters by Artificial Neural Networks, Journal of Geodesy 76(5), 247–58. doi: 10.1007/s00190-001-0242-5.
Schuh, H. and Schmitz-Hübsch, H., 2000, Short Period Variations in Earth Rotation as Seen by VLBI.Surv Geophys 21(5–6), 499–520.
Shen, Y., Guo, J., Liu, X., Kong, Q., Guo, L. and Li, W., 2018, Long-Term Prediction of Polar Motion Using a Combined SSA and ARMA Model, Journal of Geodesy 92(3), 333–43. doi: 10.1007/s00190-017-1065-3.
Wu, F., Chang, G. and Deng, K., 2021, One-Step Method for Predicting LOD Parameters Based on LS+AR Model, Journal of Spatial Science 66(2), 317–28. doi: 10.1080/14498596.2019.1618401.
Zhao, D. and Lei, Y., 2019, Possible Enhancement of Earth’s Polar Motion Predictions Using a Wavelet-Based Preprocessing Procedure, Studia Geophysica et Geodaetica 63(1), 83–94. doi: 10.1007/s11200-018-1026-1.
Zhao, D. and Lei, Y., 2020, A Technique to Reduce the Edge Effect in Least Squares Extrapolation for Enhanced Earth Orientation Prediction, Studia Geophysica et Geodaetica 64(3), 293–305. doi: 10.1007/s11200-021-0546-2.