Short-term prediction of UT1-UTC and LOD via Dynamic Mode Decomposition and combination of least-squares and vector autoregressive model
Marcin Ligas 1, A-F
More details
Hide details
Department of Integrated Geodesy and Cartography, Faculty of Geo-Data Science, Geodesy, and Environmental Engineering, AGH University of Krakow, al. Adama Mickiewicza 30, 30-059 Kraków
These authors had equal contribution to this work
A - Research concept and design; B - Collection and/or assembly of data; C - Data analysis and interpretation; D - Writing the article; E - Critical revision of the article; F - Final approval of article
Submission date: 2023-11-07
Final revision date: 2024-02-20
Acceptance date: 2024-02-20
Publication date: 2024-03-06
Corresponding author
Maciej Michalczak   

Department of Integrated Geodesy and Cartography, Faculty of Geo-Data Science, Geodesy, and Environmental Engineering, AGH University of Krakow, al. Adama Mickiewicza 30, 30-059, Krakow, Poland
Reports on Geodesy and Geoinformatics 2024;117:45-54
This study presents a short-term forecast of UT1-UTC and LOD using two methods, i.e. Dynamic Mode Decomposition (DMD) and combination of Least-Squares and Vector Autoregression (LS+VAR). The prediction experiments were performed separately for yearly time spans, 2018-2022. The prediction procedure started on January 1 and ended on December 31, with 7-day shifts between subsequent 30-day forecasts. Atmospheric Angular Momentum data (AAM) were used as an auxiliary time series to potentially improve the prediction accuracy of UT1-UTC and LOD in LS+VAR procedure. An experiment was also conducted with and without elimination of effect of zonal tides from UT1-UTC and LOD time series. Two approaches to using the best steering parameters for the methods were applied:. First, an adaptive approach, which observes the rule that before every single forecast, a preliminary one must be performed on the pre-selected sets of parameters, and the one with the smallest prediction error is then used for the final prediction; and second, an averaged approach, whereby several forecasts are made with different sets of parameters (the same parameters as in adaptive approach) and the final values are calculated as the averages of these predictions. Depending on the method and data combination mean absolute prediction errors (MAPE) for UT1-UTC vary from 0.63 ms to 1.43 ms for the 10th day and from 3.07 ms to 8.05 ms for the 30th day of the forecast. Corresponding values for LOD vary from 0.110 ms to 0.245 ms for the 10th day and from 0.148 ms to 0.325 ms for the 30th day.
Research project supported by program „Excellence initiative – research university” for the AGH University of Krakow. The paper is a result of research on geospatial methods carried out within the statutory research grant no. at the Department of Integrated Geodesy and Cartography, AGH University of Krakow. We gratefully acknowledge Poland’s high-performance computing infrastructure PLGrid (HPC Centers: ACK Cyfronet AGH) for providing computer facilities and support within computational grant Nos. PLG/2022/015968 and PLG/2023/016281. Intermediate results are available on the website accompanying this article: home.agh.edu.pl/mmichalc
Bizouard, C., Lambert, S., Gattano, C., Becker, O., and Richard, J.-Y. (2018). The IERS EOP 14C04 solution for earth orientation parameters consistent with ITRF 2014. Journal of Geodesy, 93(5):621–633, doi:10.1007/s00190-018-1186-3.
Dick, W. R. and Thaller, D. (2020). IERS Annual Report 2018. Technical report, International Earth Rotation and Reference Systems Service, Central Bureau.
Dill, R., Dobslaw, H., and Thomas, M. (2018). Improved 90-day Earth orientation predictions from angular momentum forecasts of atmosphere, ocean, and terrestrial hydrosphere. Journal of Geodesy, 93(3):287–295, doi:10.1007/s00190-018-1158-7.
Dobslaw, H. and Dill, R. (2018). Predicting Earth orientation changes from global forecasts of atmosphere-hydrosphere dynamics. Advances in Space Research, 61(4):1047–1054, doi:10.1016/j.asr.2017.11.044.
Gambis, D. and Luzum, B. (2011). Earth rotation monitoring, UT1 determination and prediction. Metrologia, 48(4):S165–S170, doi:10.1088/0026-1394/48/4/s06.
Gross, R. S., Eubanks, T., Steppe, J., Freedman, A., Dickey, J., and Runge, T. (1998). A Kalman-filter-based approach to combining independent Earth-orientation series. Journal of Geodesy, 72:215–235, doi:10.1007/s001900050162.
Gross, R. S., Fukumori, I., Menemenlis, D., and Gegout, P. (2004). Atmospheric and oceanic excitation of length-of-day variations during 1980–2000. Journal of Geophysical Research: Solid Earth, 109(B1), doi:10.1029/2003jb002432.
Guessoum, S., Belda, S., Ferrandiz, J. M., Modiri, S., Raut, S., Dhar, S., Heinkelmann, R., and Schuh, H. (2022). The short-term prediction of Length of Day using 1D convolutional neural networks (1D CNN). Sensors, 22(23):9517, doi:10.3390/s22239517.
Holton, J. R. and Dmowska, R. (1989). El Niño, La Niña, and the southern oscillation. Academic press, Cambridge, MA, USA.
Höpfner, J. (1998). Seasonal variations in length of day and atmospheric angular momentum. Geophysical Journal International, 135(2):407–437, doi:10.1046/j.1365-246X.1998.00648.x.
Kalarus, M., Schuh, H., Kosek, W., Akyilmaz, O., Bizouard, C., 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):587–596, doi:10.1007/s00190-010-0387-1.
Kiani Shahvandi, M., Schartner, M., and Soja, B. (2022). Neural ODE differential learning and its application in polar motion prediction. Journal of Geophysical Research: Solid Earth, 127(11), doi:10.1029/2022jb024775.
Kur, T., Dobslaw, H., Śliwińska, J., Nastula, J., Wińska, M., and Partyka, A. (2022). Evaluation of selected short-term predictions of UT1-UTC and LOD collected in the second earth orientation parameters prediction comparison campaign. Earth, Planets and Space, 74(1), doi:10.1186/s40623-022-01753-9.
Lei, Y., Cai, H., and Zhao, D. (2017). Improvement of the prediction accuracy of polar motion using empirical mode decomposition. Geodesy and Geodynamics, 8(2):141–146, doi:10.1016/j.geog.2016.09.007.
Liao, D., Wang, Q., Zhou, Y., Liao, X., and Huang, C. (2012). Long-term prediction of the Earth Orientation Parameters by the artificial neural network technique. Journal of Geodynamics, 62:87– 92, doi:10.1016/j.jog.2011.12.004.
Michalczak, M. and Ligas, M. (2021). Kriging-based prediction of the Earth’s pole coordinates. Journal of Applied Geodesy, 15(3):233–241, doi:10.1515/jag-2021-0007.
Michalczak, M. and Ligas, M. (2022). The (ultra) short term prediction of length-of-day using kriging. Advances in Space Research, 70(3):610–620, doi:10.1016/j.asr.2022.05.007.
Modiri, S., Belda, S., Hoseini, M., Heinkelmann, R., Ferrándiz, J. M., and Schuh, H. (2020). A new hybrid method to improve the ultra-short-term prediction of LOD. Journal of Geodesy, 94(2), doi:10.1007/s00190-020-01354-y.
Nastula, J., Chin, T. M., 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), doi:10.1007/s00190-020-01349-9.
Niedzielski, T. and Kosek, W. (2011). Prediction Analysis of UT1-UTC Time Series by Combination of the Least-Squares and Multivariate Autoregressive Method, pages 153–157. Springer Berlin Heidelberg, doi:10.1007/978-3-642-22078-4_23.
Okhotnikov, G. and Golyandina, N. (2019). EOP time series prediction using singular spectrum analysis. In Corpetti, T., Ienco, D., and Interdonato, R., editors, Proceedings of MACLEAN: MAChine learning for Earth observation workshop, RWTH Aahen University, CEUR Workshop Proceedings.
Petit, G. and Luzum, B. (2010). IERS conventions. Technical report, IERS Technical Note 36, Verlag des Bundesamts für Kartographie und Geodäsie Frankfurt am Main, Germany.
Schmid, P. J. (2010). Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics, 656:5–28, doi:10.1017/s0022112010001217.
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):247–258, doi:10.1007/s00190-001-0242-5.
Soffel, M. (2013). Space-Time Reference Systems. SpringerLink. Springer, Berlin. Description based upon print version of record.
Tirunagari, S., Kouchaki, S., Poh, N., Bober, M., and Windridge, D. (2017). Dynamic mode decomposition for univariate time series: analysing trends and forecasting. hal-01463744f.
Tu, J. H., Rowley, W. C., Luchtenburg, D. M., Brunton, S. L., and Kutz, J. N. (2014). On dynamic mode decomposition: Theory and applications. Journal of Computational Dynamics, 1(2):391–421, doi:10.3934/jcd.2014.1.391.
Xu, X., Zhou, Y., and Liao, X. (2012). Short-term Earth orientation parameters predictions by combination of the least-squares, AR model and Kalman filter. Journal of Geodynamics, 62:83–86, doi:10.1016/j.jog.2011.12.001.
Xu, X., Zhou, Y., and XU, C. (2022a). Earth rotation parameters prediction and climate change indicators in it. Artificial Satellites, 57(s1):262–273, doi:10.2478/arsa-2022-0023.
Xu, X.-Q., Zhou, Y.-H., Duan, P.-S., Fang, M., Kong, Z.-Y., Xu, C.-C., and An, X.-R. (2022b). Contributions of oceanic and continental AAM to interannual variation in ∆LOD with the detection of 2020–2021 La Nina event. Journal of Geodesy, 96(6), doi:10.1007/s00190-022-01632-x.
Śliwińska, J., Kur, T., Wińska, M., Nastula, J., Dobslaw, H., and Partyka, A. (2022). Second Earth Orientation Parameters prediction comparison campaign (2nd EOP PCC): Overview. Artificial Satellites, 57(s1):237–253, doi:10.2478/arsa-2022-0021.
Journals System - logo
Scroll to top