Earth Orientation Parameters Predictions Research Articles

Prospects of Predicting the Polar Motion Based on the Results of the Second Earth Orientation Parameters Prediction Comparison Campaign

AbstractGrowing interest in Earth Orientation Parameters (EOP) resulted in various approaches to the EOP prediction algorithms, as well as in the exploitation of distinct input data, including the observed EOP values from various operational data centers and modeled effective angular momentum functions. Considering these developments and recently emerged new methodologies, the Second Earth Orientation Parameters Prediction Comparison Campaign (2nd EOP PCC) was pursued in 2021–2022. The campaign was led by Centrum Badań Kosmicznych Polskiej Akademii Nauk in cooperation with Deutsches GeoForschungsZentrum and under the auspices of the International Earth Rotation and Reference Systems Service. This paper provides the analysis and evaluation of the polar motion predictions submitted during the 2nd EOP PCC with the prediction horizons between 10 and 30 days. Our analysis shows that predictions are highly reliable with only a few occasional discrepancies identified in the submitted files. We demonstrate the accuracy of EOP predictions by (a) calculating the mean absolute error relative to polar motion observations from September 2021 through December 2022 and (b) assessing the stability of the predictions in time. The analysis shows unequal results for the x and y components of polar motion (PMx and PMy, respectively). Predictions of PMy are usually more accurate and have a smaller spread across all submitted files when compared to PMx. We present an analysis of similarity between the participants to indicate what methods and input data give comparable output. We also prepared the ranking of prediction methods for polar motion summarizing the achievements of the campaign.

Ultra-short-term prediction of LOD using LSTM neural networks

Earth orientation parameters (EOPs) are essential in geodesy, linking the terrestrial and celestial reference frames. Due to the time needed for data processing and combining different space geodetic techniques, EOPs of the highest quality suffer latencies from several days to several weeks. However, real-time EOPs are needed for multiple geodetic and geophysical applications. Predictions of EOPs in the ultra-short term can overcome the latency of EOP products to a certain extent. Traditionally, predictions are performed using statistical methods. With the rapid expansion of computing capacity and data volume, the application of deep learning in geodesy has become increasingly promising in recent years. In particular, the Long Short-Term Memory (LSTM) neural networks, one of the most popular Recurrent Neural Network varieties, are promising for geodetic time series prediction. In this study, we investigate the potential of using LSTM to predict daily length of day (LOD) variations up to ten days in advance, accounting for the contribution of effective angular momentum (EAM). The data are first preprocessed to obtain residuals by combining physical and statistical models. Then, we employ LSTM networks to predict the LOD residuals using both LOD and EAM residuals as input features. Our methods outperform all other state-of-the-art methods in the first eight days with an improvement of up to 43% under the first EOP Prediction Comparison Campaign conditions. In addition, we assess the performance of LOD predictions using more extended time series to consider the improvements of EOP products over the last decade. The results show that extending data volume significantly increases the performance of the methods.

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

Abstract 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.

Earth Rotation Parameters Prediction and Climate Change Indicators in it

Abstract As one of the participants in the Second Earth Orientation Parameters Prediction Comparison Campaign (2nd EOP PCC), we submitted two data files. One is 365 days’ predictions into the future for Earth orientation parameters (EOP) (the position parameters Px and Py, the time parameters UT1-UTC and length of day changes ΔLOD), processed by the traditional least-square and autoregressive (LS + AR) model. Another is 90 days’ predictions by the combined least-square and convolution method (LS + Convolution), with effective angular momentum (EAM) from Earth System Modelling GeoForschungsZentrum in Potsdam (ESMGFZ). Results showed that the LS + Convolution method performed better than the LS + AR model in short-term EOP predictions within 10 days, while the traditional LS + AR model presented higher accuracy in medium-term predictions over 10–90 days. Furthermore, based on the climate change information in Earth’s rotation (mainly in the interannual variations of LOD), the climate change indicators are investigated with ΔLOD observations and long-term predictions. After two intermediate La Nina events were detected in the climate-related ΔLOD observations during the period of 2020–2022, another stronger La Nina phenomenon is indicated in the climate-related ΔLOD long-term predictions.

A new hybrid method to improve the ultra-short-term prediction of LOD

Accurate, short-term predictions of Earth orientation parameters (EOP) are needed for many real-time applications including precise tracking and navigation of interplanetary spacecraft, climate forecasting, and disaster prevention. Out of the EOP, the LOD (length of day), which represents the changes in the Earth’s rotation rate, is the most challenging to predict since it is largely affected by the torques associated with changes in atmospheric circulation. In this study, the combination of Copula-based analysis and singular spectrum analysis (SSA) method is introduced to improve the accuracy of the forecasted LOD. The procedure operates as follows: First, we derive the dependence structure between LOD and the Z component of the effective angular momentum (EAM) arising from atmospheric, hydrologic, and oceanic origins (AAM + HAM + OAM). Based on the fitted theoretical Copula, we then simulate LOD from the Z component of EAM data. Next, the difference between LOD time series and its Copula-based estimation is modeled using SSA. Multiple sets of short-term LOD prediction have been done based on the IERS 05 C04 time series to assess the capability of our hybrid model. The results illustrate that the proposed method can efficiently predict LOD.

Combined SAI-SHAO prediction of Earth Orientation Parameters since 2012 till 2017

As the participants of Earth Orientation Parameters Combination of Prediction Pilot Project (EOPC PPP), Sternberg Astronomical Institute of Moscow State University (SAI) and Shanghai Astronomical Observatory (SHAO) have accumulated ∼1800 days of Earth Orientation Parameters (EOP) predictions since 2012 till 2017, which were up to 90 days into the future, and made by four techniques: auto-regression (AR), least squares collocation (LSC), and neural network (NNET) forecasts from SAI, and least-squares plus auto-regression (LS + AR) forecast from SHAO. The predictions were finally combined into SAI-SHAO COMB EOP prediction. In this work we present five-year real-time statistics of the combined prediction and compare it with the uncertainties of IERS bulletin A predictions made by USNO.

A new method to improve the prediction of the celestial pole offsets

Knowledge of the Earth’s changing rotation is fundamental to positioning objects in space and on the planet. Nowadays, the Earth’s orientation in space is expressed by five Earth Orientation Parameters (EOP). Many applications in astronomy, geosciences, and space missions require accurate EOP predictions. Operational predictions are released daily by the Rapid Service/Prediction Centre of the International Earth Rotation and Reference Systems Service (IERS). The prediction procedures and performances differ for the three EOP classes: polar motion, rotation angle (UT1-UTC), and the two celestial pole offsets (CPO), dX and dY. The IERS Annual Report 2016 shows Rapid Service CPO predictions errors with respect to IERS 08 C04 observations in 2016 ranging from 120 to 140 μas in 40 days for dX, and 100–160 μas for dY. We test a new method for the CPO prediction based on the recent availability of sophisticated empirical models for the Free Core Nutation, a main component of the CPO variations. We found it allows predicting both CPO with error estimates for the period 2000–2016 lower than the 2016 Rapid Service products, reaching about 85 μas after 40 days and near 90 μas after a year. These results would represent a 35–40% improvement.

Prediction of length-of-day using extreme learning machine

Traditional artificial neural networks (ANN) such as back-propagation neural networks (BPNN) provide good predictions of length-of-day (LOD). However, the determination of network topology is difficult and time consuming. Therefore, we propose a new type of neural network, extreme learning machine (ELM), to improve the efficiency of LOD predictions. Earth orientation parameters (EOP) C04 time-series provides daily values from International Earth Rotation and Reference Systems Service (IERS), which serves as our database. First, the known predictable effects that can be described by functional models—such as the effects of solid earth, ocean tides, or seasonal atmospheric variations—are removed a priori from the C04 time-series. Only the residuals after the subtraction of a priori model from the observed LOD data (i.e., the irregular and quasi-periodic variations) are employed for training and predictions. The predicted LOD is the sum of a prior extrapolation model and the ELM predictions of the residuals. Different input patterns are discussed and compared to optimize the network solution. The prediction results are analyzed and compared with those obtained by other machine learning-based prediction methods, including BPNN, generalization regression neural networks (GRNN), and adaptive network-based fuzzy inference systems (ANFIS). It is shown that while achieving similar prediction accuracy, the developed method uses much less training time than other methods. Furthermore, to conduct a direct comparison with the existing prediction techniques, the mean-absolute-error (MAE) from the proposed method is compared with that from the EOP prediction comparison campaign (EOP PCC). The results indicate that the accuracy of the proposed method is comparable with that of the former techniques. The implementation of the proposed method is simple.

Long-term prediction of the Earth Orientation Parameters by the artificial neural network technique

There are increasing demands for EOP predictions in science, deep space navigation, etc. Based on previous research on short-term prediction of Earth Orientation Parameters (EOP) by artificial neural networks (ANN), we extend our attempt to long-term predictions of EOPs, i.e. predictions with a lead time up to 360 days. The basic theory and some special considerations for the ANN forecast of EOPs are presented, and finally our preliminary results and their accuracy estimates are shown and compared with those obtained by other authors.

Analysis of Pole Coordinate Data Predictions in the Earth Orientation Parameters Combination of Prediction Pilot Project

Abstract : In October 2010 the US Naval Observatory together with the Space Research Centre in Warsaw initiated the Earth Orientation Parameters Combination of Prediction Pilot Project, which was accepted by the IERS Directing Board. The goal of this project is to determine the feasibility of combining Earth Orientation Parameters (EOP)predictions on an operational basis. The ensemble predictions of EOPs are more accurate than the results from individual predictions. The pole coordinate data predictions from different prediction contributors and ensemble predictions computed by the U.S. Naval Observatory are studied to determine the statistical properties of polar motion forecasts by looking at second, third and fourth moments about the mean. The increase of prediction errors in pole coordinate data can be due to the change of phase of the annual oscillation in the joint atmospheric-ocean excitation function.

Achievements of the Earth orientation parameters prediction comparison campaign

Precise transformations between the international celestial and terrestrial reference frames are needed for many advanced geodetic and astronomical tasks including positioning and navigation on Earth and in space. To perform this transformation at the time of observation, that is for real-time applications, accurate predictions of the Earth orientation parameters (EOP) are needed. The Earth orientation parameters prediction comparison campaign (EOP PCC) that started in October 2005 was organized for the purpose of assessing the accuracy of EOP predictions. This paper summarizes the results of the EOP PCC after nearly two and a half years of operational activity. The ultra short-term (predictions to 10 days into the future), short-term (30 days), and medium-term (500 days) EOP predictions submitted by the participants were evaluated by the same statistical technique based on the mean absolute prediction error using the IERS EOP 05 C04 series as a reference. A combined series of EOP predictions computed as a weighted mean of all submissions available at a given prediction epoch was also evaluated. The combined series is shown to perform very well, as do some of the individual series, especially those using atmospheric angular momentum forecasts. A main conclusion of the EOP PCC is that no single prediction technique performs the best for all EOP components and all prediction intervals.

Improved UT1 predictions through low-latency VLBI observations

The quality of predictions of Earth orientation parameters (EOPs) in general, and of Universal Time (UT1) in particular, depends strongly on the time delay between the last observation available and the first prediction. Since 30 September 2007 (MJD 54373), the latency of UT1 results from a subset of single baseline VLBI observations running once per week (Mondays) has been decreased from 2 to 3 days to about 8 h. This was achieved by transmitting the raw VLBI data of 1-h duration from the observing sites in Tsukuba (Japan), Wettzell (Germany) and Ny-Alesund (Norway) to the correlator of the Max-Planck-Institute for Radio Astronomy and the German Federal Agency of Cartography and Geodesy at Bonn, Germany, by high-speed Internet connections (e-Transfer). The reduced latency of the observations has improved the accuracy of the combined International Earth Rotation and Reference Systems Service (IERS) Rapid Service/Prediction Center (RS/PC) UT1-UTC solution by roughly 50% on the days when the data are available. Because this combination is an input to the UT1-UTC prediction process, the improved latency is also responsible for a roughly 21% improvement in the accuracy of short-term IERS RS/PC UT1-UTC predictions on the days where the data are available.

Employing Combination Procedures to Short-Time Eop Prediction

Employing Combination Procedures to Short-Time Eop Prediction A well known problem with Earth Orientation Parameters (EOP) prediction is that a prediction strategy proved to be the best for some testing time span and prediction length may not remain the same for other time intervals. In this paper, we consider possible strategies to combine EOP predictions computed using different analysis techniques to obtain a final prediction with the best accuracy corresponding to the smallest prediction error of input predictions. It was found that this approach is most efficient for ultra-short-term EOP forecast.

Dynamical Modeling and Excitation Reconstruction as Fundamental of Earth Rotation Prediction

Dynamical Modeling and Excitation Reconstruction as Fundamental of Earth Rotation Prediction Though pure mathematical approximations such as regression models and neural networks show good results in Earth rotation forecasting, dynamical modeling remains the only base for the physically meaningful prediction. That assumes the knowledge of cause-effect relationships and physical model of the rotating Earth. Excitation reconstruction from the observed Earth orientation parameters (EOP) is a crucial stage, needed for comparison with known causes, such as tidal forcing, atmospheric (AAM), oceanic (OAM) angular momentum changes, and uncovering unknown ones. We demonstrate different approaches, which can be used to avoid ill-conditionality and amplification of noises during the inversion. We present amplitude and phase studies of the model and reconstructed excitations of Chandler wobble. We found out, that modulation of Chandler excitation is synchronous with 18-yr tidal effects in the Earth's rotation rate changes. The results of the study can be used for excitation and EOP forecast. The key issues of the EOP prediction are discussed.

Weights for prediction of Earth orientation Parameters

The most important factor in getting accurate predictions of Earth orientation parameters (EOP) is choosing suitable input data. Also, we must choose a proper statistical model for the noise in these data. The weights of the data are determined on the basis of these models. Finally, we must determine suitable values of parameters in the computation of EOP predictions.

Predicting Earth orientation

Predictions of Earth orientation parameters are affected by the accuracy of the input data, the quality of the statistical models, and the delay between the last observed data and the date of the first prediction. The accuracy of the prediction of polar motion is adequate to meet most user needs, but the prediction of UT1-UTC is more difficult. Extended forecasts of polar motion and the rotational time can also be made with useful accuracies.