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Short-term prediction of UT1-UTC and LOD via Dynamic Mode Decomposition and combination of least-squares and vector autoregressive model

Michalczak Maciej, Ligas Marcin

Reports on Geodesy and Geoinformatics

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2024

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Vol. 117

45--54

EN

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.

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Second Earth Orientation Parameters Prediction Comparison Campaign (2nd EOP PCC): Overview

Śliwińska Justyna, Kur Tomasz, Wińska Małgorzata, Nastula Jolanta, Dobslaw Henryk, Partyka Aleksander

Artificial Satellites : Journal of Planetary Geodesy

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2022

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Vol. 57, Special Issue 1

237--253

EN

Precise positioning and navigation on the Earth’s surface and in space require accurate earth orientation parameters (EOP) data and predictions. In the last few decades, EOP prediction has become a subject of increased attention within the international geodetic community, e.g., space agencies, satellite operators, researchers studying Earth rotation dynamics, and users of navigation systems. Due to this fact, many research centres from around the world have developed dedicated methods for the forecasting of EOP. An assessment of the various EOP prediction capabilities is currently being pursued in the frame of the Second Earth Orientation Parameters Prediction Comparison Campaign (2nd EOP PCC), which began in September 2021 and will be continued until the end of the year 2022. The new campaign was prepared by the EOP PCC Office run by Centrum Badań Kosmicznych Polskiej Akademii Nauk (CBK PAN) in Warsaw, Poland, in cooperation with GeoForschungsZentrum (GFZ) and under the auspices of the International Earth Rotation and Reference Systems Service (IERS). In this paper, we provide an overview of the 2nd EOP PCC five months after its start. We discuss the technical aspects and present statistics about the participants and valid prediction files received so far. Additionally, we present the results of preliminary comparisons of different reference solutions with respect to the official IERS 14 C04 EOP series. Root mean square values for different solutions for polar motion, length of day, and precession-nutation components show discrepancies at the level from 0.04 to 0.36 mas, from 0.01 to 0.10 ms, and from 0.01 to 0.18 mas, respectively.

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Prediction of Earth Rotation Parameters With the Use of Rapid Products From IGS, Code and GFZ Data Centres Using ARIMA and Kriging - A Comparison

Michalczak Maciej, Ligas Marcin, Kudrys Jacek

Artificial Satellites : Journal of Planetary Geodesy

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2022

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Vol. 57, Special Issue 1

275--289

EN

Real-time prediction of Earth Orientation Parameters is necessary for many advanced geodetic and astronomical tasks including positioning and navigation on Earth and in space. Earth Rotation Parameters (ERP) are a subset of EOP, consisting of coordinates of the Earth’s pole (PMx, PMy) and UT1-UTC (or Length of Day - LOD). This paper presents the ultra-short-term (up to 15 days into the future) and short-term (up to 30 days into the future) ERP prediction using geostatistical method of ordinary kriging and autoregressive integrated moving average (ARIMA) model. This contribution uses rapid GNSS products EOP 14 12h from IGS, CODE and GFZ and also IERS final products - IERS EOP 14 C04 12h (IAU2000A). The results indicate that the accuracy of ARIMA prediction for each ERP is better for ultra-short prediction. The maximum differences between methods for first few days of 15-day predictions are around 0.32 mas (PMx), 0.23 mas (PMy) and 0.004 ms (LOD) in favour of ARIMA model. The maximum differences of Mean Absolute Prediction Errors (MAPEs) on the last few days of 30-day predictions are 1.91 mas (PMx), 0.30 mas (PMy) and 0.026 ms (LOD) with advantage to kriging method. For all ERPs the differences of MAPEs for time series from various analysis centres are not significant and vary up to maximum value of around 0.05 mas (PMx), 0.04 mas (PMy) and 0.005 ms (LOD).

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ESMGFZ Products for Earth Rotation Prediction

Dill Robert, Dobslaw Henryk, Thomas Maik

Artificial Satellites : Journal of Planetary Geodesy

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2022

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Vol. 57, Special Issue 1

254--261

EN

The Earth System Modelling Group of GeoForschungsZentrum Potsdam (ESMGFZ) provides geodetic products for gravity variations, Earth rotation excitations, and Earth surface deformations related to mass redistributions and mass loads in the atmosphere, ocean, and terrestrial water storage. Earth rotation excitation compiled as effective angular momentum (EAM) functions for each Earth subsystem (atmosphere, ocean, continental hydrology) are important for Earth rotation prediction. Especially the 6-day forecasts extending the model analysis runs offer essential information for the improvement of ultra-short-term Earth rotation predictions. In addition to the individual effective angular momentum function of each subsystem, ESMGFZ calculates a combined EAM prediction product. Adjusted to the official Earth orientation parameter (EOP) products IERS 14C04 and Bulletin A, this EAM prediction product allows to extrapolate the polar motion and Length-of-Day parameter time series for 90 days into the future via the Liouville equation. ESMGFZ submits such an EOP prediction to the 2nd EOPPCC campaign.

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Comparison of Amplitude Variations of Seasonal and Sub-Seasonal Oscillations in Length of Day and Total Solar Irradiance

Kosek Wiesław, Gabryszuk Justyna

Journal of Ecological Engineering

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2020

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Vol. 21, nr 7

52--57

EN

The aim of the study was to identify and compute oscillations in two different time series with similar amplitude variations using length of day data with tide model removed (LODR) and total solar irradiance (TSI) data. The combination of the Fourier transform band pass filter and Hilbert transform allows detecting amplitude variations as a function of the oscillation period. The amplitude variations in two different time series enable computation of frequency dependent or time-frequency correlation coefficients between them. It allows also identifying such oscillations in two time series which have similar amplitude variations. The method applied to LODR and TSI data, enable to detect a possible relationship between them. This comparison method can be applied to any time series which consist of oscillations with non-constant amplitudes.

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Extreme learning machine for the predictions of length of day

Lei Y., Zhao D., Cai H.

Artificial Satellites : Journal of Planetary Geodesy

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2015

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Vol. 50, No. 1

19--33

EN

This work presents short- and medium-term predictions of length of day (LOD) up to 500 days by means of extreme learning machine (ELM). The EOP C04 time-series with daily values from the International Earth Rotation and Reference Systems Service (IERS) serve as the data basis. The influences of the solid Earth and ocean tides and seasonal atmospheric variations are removed from the C04 series. The residuals are used for training of the ELM. The results of the prediction are compared with those from other prediction methods. The accuracy of the prediction is equal to or even better than that by other approaches. The most striking advantages of employing ELM instead of other algorithms are its noticeably reduced complexity and high computational efficiency.

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Status and prospects for combined GPS LOD and VLBI UT1 measurements

Senior K., Kouba J., Ray .

Artificial Satellites : Journal of Planetary Geodesy

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2010

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Vol. 45, No. 2

57--73

EN

A Kalman filter was developed to combine VLBI estimates of UT1-TAI with biased length of day (LOD) estimates from GPS. The VLBI results are the analyses of the NASA Goddard Space Flight Center group from 24-hr multi-station observing sessions several times per week and the nearly daily 1-hr single-baseline sessions. Daily GPS LOD estimates from the International GNSS Service (IGS) are combined with the VLBI UT1-TAI by modeling the natural excitation of LOD as the integral of a white noise process (i.e., as a random walk) and the UT1 variations as the integration of LOD, similar to the method described by Morabito et al. (1988). To account for GPS technique errors, which express themselves mostly as temporally correlated biases in the LOD measurements, a Gauss-Markov model has been added to assimilate the IGS data, together with a fortnightly sinusoidal term to capture errors in the IGS treatments of tidal effects. Evaluated against independent atmospheric and oceanic axial angular momentum (AAM + OAM) excitations and compared to other UT1/LOD combinations, ours performs best overall in terms of lowest RMS residual and highest correlation with (AAM + OAM) over sliding intervals down to 3 d. The IERS 05C04 and Bulletin A combinations show strong high-frequency smoothing and other problems. Until modified, the JPL SPACE series suffered in the high frequencies from not including any GPS-based LODs. We find, surprisingly, that further improvements are possible in the Kalman filter combination by selective rejection of some VLBI data. The best combined results are obtained by excluding all the 1-hr single-baseline UT1 data as well as those 24-hr UT1 measurements with formal errors greater than 5 μs (about 18% of the multi-baseline sessions). A rescaling of the VLBI formal errors, rather than rejection, was not an effective strategy. These results suggest that the UT1 errors of the 1-hr and weaker 24-hr VLBI sessions are non-Gaussian and more heterogeneous than expected, possibly due to the diversity of observing geometries used, other neglected systematic effects, or to the much shorter observational averaging interval of the single-baseline sessions. UT1 prediction services could benefit from better handling of VLBI inputs together with proper assimilation of IGS LOD products, including using the Ultra-rapid series that is updated four times daily with 15 hr delay.