Second Earth Orientation Parameters Prediction Comparison Campaign (2nd EOP PCC): Overview
Publicado en línea: 05 ene 2023
Páginas: 237 - 253
Recibido: 14 jun 2022
Aceptado: 17 nov 2022
DOI: https://doi.org/10.2478/arsa-2022-0021
Palabras clave
© 2022 Justyna Śliwińska et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.
Real-time positioning and navigation with the means of Global Navigation Satellite Systems (GNSS) require accurate measurements and predictions of earth orientation parameters (EOP). EOP, comprising polar motion (PM), difference between universal time and universal coordinated time (UT1-UTC) or its time-derivative length-of-day (LoD) variation, and corrections dX and dY to the conventional precession–nutation model IAU 2000/2006, i.e., celestial pole offsets (CPO), are necessary elements of transformation matrices from the celestial reference frame to the terrestrial reference frame (IERS Conventions, 2010, Chapter 5). Due to unavoidable delays in providing accurate EOP estimates caused by latencies in processing space geodetic observations and in acquiring necessary correction models, EOP short-term prediction has become a subject of increased attention within the international geodetic community.
Apart from the International Earth Rotation and Reference Systems Service (IERS) Rapid Service/Prediction Centre that regularly generates EOP forecasts (McCarthy and Luzum, 1991), there are many other research groups around the world working on EOP predicting (e.g., Akyilmaz et al., 2011, Belda et al., 2018, Chin et al., 2004, Dill et al., 2019, Modiri et al., 2018, Nastula et al., 2020, Shen et al., 2017, Stamatakos et al., 2011, Wang et al., 2018, Xu et al., 2012). However, the forecasts delivered by these institutes differ in many aspects such as input data, predicting method, and forecast horizon, which results in different levels of accuracy for individual predictions. As shown in the study of Luzum (2010), EOP forecasting might benefit from improvements in terms of processing and delivering near-real-time EOP data, modelling of diurnal and semidiurnal tides, forecasting geophysical excitation of PM, and ameliorating real-time prediction procedures.
A first thorough comparison and evaluation of various EOP forecasts was conducted between 2006 and 2008 as part of the EOP Prediction Comparison Campaign (EOP PCC, Kalarus et al., 2010), organised by Vienna University of Technology and Centrum Badań Kosmicznych Polskiej Akademii Nauk (CBK PAN) and under the auspices of the IERS. The aim of this past campaign was to find the most optimal method for forecasting EOP as well as to develop a combined series of EOP predictions. The results of the first EOP PCC showed that it was useful as an initial attempt to evaluate the various existing prediction techniques under the same rules and conditions. The advantages of combination of submitted solutions were presented. It was also noted that accuracy of the predictions also benefits from using atmospheric forecasts data as an input. However, the best prediction technique was different for each parameter and prediction interval, i.e., no prediction technique was superior to others.
More than ten years after the end of the EOP PCC, noticeable progress has been made in the methods of processing geodetic observations for EOP estimation (Bizouard et al., 2019, Karbon et al., 2017, Nilsson et al., 2014) and in understanding the impact of the Earth’s surficial fluid layers (atmosphere, oceans, hydrosphere) on orientation changes of the solid Earth (Bizouard, 2020, Chen et al., 2017, Dill et al., 2013, Gross, 2015, Nastula et al. 2019, Quinn et al., 2017). The number of research groups that are actively working on developing new advanced forecasting methods has also increased. In view of those improvements, it is now timely to re-evaluate the quality of present-day EOP predictions that are available so far.
The importance of this issue for the international community has been confirmed by the IERS which established a working group (WG) dedicated to conducting second EOP Prediction Comparison Campaign (2nd EOP PCC) (
The main idea of the 2nd EOP PCC is to compare the various methods, models, and strategies that can be used to predict EOP. The campaign will to some extent repeat the efforts made during the first EOP PCC, considering similar evaluation procedures and parameters, but also aims at going beyond the past efforts by incorporating new evaluation metrics and time-series analysis schemes. All the campaign details and updates are publicly available on the campaign’s website (
This article is the first work about the 2nd EOP PCC; therefore, it does not contain a detailed discussion of the results, as this will be included in the forthcoming papers prepared after the campaign ends. Instead, the current work provides information on the technical preparations of the campaign, most important events related to the campaign, and various statistics on the participants and EOP predictions received so far.
Additionally, in this study, we use the IERS 14 C04 EOP data (abbreviated here as C04) to assess a number of potential reference EOP solutions which are planned to be used in a final evaluation of EOP predictions. For this purpose, we use International VLBI Service (IVS) rapid data, rapid and final solutions from International Global Navigation Satellite Systems Service (IGS), solutions provided by International Laser Ranging Service (ILRS), data from Bulletin A provided by the IERS, and SPACE solution delivered by Jet Propulsion Laboratory (JPL). For precession-nutation, data from United States Naval Observatory (USNO) and Goddard Space Flight Center (GSFC) are used. These analyses are performed for the period between January 2020 and December 2021 to assess various reference EOP solutions.
This paper is organized as follows: In Section 2, we present campaign overview. In particular, Section 2.1 describes the preparation to the campaign; Section 2.2 presents some technical aspects regarding the format of prediction files and their submission; Section 2.3 shows the campaign statistics about, e.g., input data and prediction methods. In Section 3, we compare selected reference EOP series with IERS C04 (for PM in Section 3.1, for UT1-UTC and LoD in Section 3.2, and for precession-nutation in Section 3.3). Finally, Section 4 concludes the paper and gives an outlook.
At the international level, our activities started with the establishment of the IERS Working Group on the 2nd EOP PCC (IERS WG on 2nd EOP PCC), which was officially announced in March 2021 via IERS message no. 425 (
In June 2021, the pre-operational phase of the campaign began, which aimed at testing all technical matters. During that stage, interested participants had an opportunity to submit their predictions for testing purposes, and in response, the Office provided feedback on primarily formal issues (data formats, timeliness of submissions, file name conventions, etc.). Predictions submitted during the pre-operational phase were not taken into account in the official evaluation.
In July 2021, the call for participation in the operational phase of the 2nd EOP PCC was announced via IERS message no. 437 (
Figure 1.
Deadlines and milestones of the 2nd EOP PCC: blue – preparation phase, green – pre-operational phase (test phase), and red – operational phase
All technical details including instructions for candidate registration, data submission rules, naming, and file formats convention have been made publicly available in the document with general rules for participation (
Details on the 1st and 2nd EOP PCC participants and methods
| 1st EOP PCC | 2nd EOP PCC | |
|---|---|---|
| Number of registered participants (institutes or groups of institutes) | 13 | 19 |
| Number of institutes | 10 | 24 |
| Number of countries of participants origin | 7 | 8 |
| Total number of all teams members | No data | 58 |
| Number of registered prediction methods (IDs) | 20 (+1 combined prediction series) | 38 |
| Number of active participants | 11 | 16 |
The EOP PCC Office has defined two formats of forecasts with a defined naming convention including individual candidate ID to enable automatic data processing. The file formats allow sending all of the EOP or only one parameter per file using the appropriate suffix in the name. The purpose of providing two forecast file formats is to allow the choice of the most convenient way to prepare forecast files.
Each participant must submit the forecasts on Wednesday before 20:00 UTC. The predictions are sent to a server in CBK PAN, from which they are then transferred to a repository available only to the EOP PCC Office. This prevents the data from being modified or replaced after the submission deadline. Subsequently, the forecast files are manually inspected by the EOP PCC Office for possible errors in formatting, i.e., file names or dates. Thus we have no automatic interference in the file format – any changes, e.g., in the name of the file, to be in line with our rules, are introduced manually with the consent of the participants. We do not interfere in any way with the values of the sent forecasts – these remain unchanged after submission. All approved files are loaded into the prediction database. During this stage, files are checked once again, e.g., if there is an appropriate number of columns with data or if the first forecast is given for the corresponding submission day. Only after successfully passing this quality check, we update statistics published on the campaign website.
For scientific assessments of the submitted predictions, the EOP reference series data are periodically updated on the basis of the EOP C04 files made available by IERS on its website. However, this data are available with a delay of several weeks, so that rapid solutions are also used for more timely checks. Those preliminary analyses are summarised in bi-monthly reports that are being shared with the participants in order to provide timely feedback. In addition, the results are discussed in dedicated workshops and presented at international conferences.
Until February 9th, 2022, the EOP PCC Office has received over 2,000 individual predictions, the most of which are forecasts for PM (497 predictions) and UT1-UTC (442 predictions). In turn, the fewest files were obtained for forecasts of precession-nutation given in dPsi and dEps components (41 predictions) (Table 2). The most frequently predicted parameters, depending on the number of participants and number of methods (denoted with IDs), are also presented in Table 2. It is noticeable that the most often forecasted parameter is PM, predicted by 16 participants with 25 different methods (IDs). UT1-UTC is also forecasted by more than a half of all participants and methods (15 participants and 21 different IDs). On the other hand, precession-nutation is considered by only very few research groups.
Number of predictions submitted to the Office (as of February 9, 2022) with respect to the number of participants and the number of IDs
| x pole | y pole | UT1-UTC | LoD | dPsi | dEps | dX | dY | Total | |
|---|---|---|---|---|---|---|---|---|---|
| Total number of predictions | 497 | 497 | 442 | 348 | 41 | 41 | 142 | 142 | 2150 |
| Number of participants | 16 | 16 | 15 | 10 | 2 | 2 | 6 | 6 | 19 |
| Number of IDs | 25 | 25 | 21 | 17 | 2 | 2 | 7 | 7 | 38 |
The campaign Office collects information about the input data and forecasting methods used by participants to compute predictions. This information will be used in the final evaluation of all forecasts when analysing the effect of these factors on the prediction accuracy. As it can be seen from Figure 2, the diversity of observational data exploited in EOP forecasting is quite high. In terms of geodetic measurements used, data delivered by the IERS (both C04 final data and daily solutions) dominate as 23 out of 38 registered users declared the use of those solutions.
Figure 2.
Input data used by participants to make the predictions
However, EOP observations provided by other data centres, such as SYstèmes de Référence Temps Espace (SYRTE) department of Paris Observatory, JPL, ILRS, IGS, European Space Agency (ESA), Goddard Space Flight Center Very Long Baseline Interferometry (GSFC VLBI) Group, are also applied in some prediction procedures. It can be also seen that most IDs use effective angular momentum (EAM) data (atmospheric angular momentum – AAM, oceanic angular momentum – OAM, hydrological angular momentum – HAM, sea-level angular momentum – SLAM) as an additional input.
An overview about the most popular methods is presented in Figure 3. Although there are a wide variety of algorithms exploited, two main groups of algorithms dominate, i.e., machine learning and least squares collocation. Both methods are used alone or in combination with other methodologies like, e.g., autoregression or convolution. When it comes to the programming languages used by participants to process EOP predictions, MATLAB and FORTRAN are the most frequently used (7 and 6 participants, respectively). Python is used by 4 participants and there are single users of C, Perl, and Julia.
Figure 3.
Methods used by participants to make the predictions
The EOP PCC Office regularly monitors the exact timing of data submissions as only files sent before the deadline (Wednesday 20:00 UTC) will be further processed. The histogram in Figure 4 shows that most of the predictions are delivered on time. A large part of the forecasts are submitted in the afternoon, between 16:30 and 19:00 UTC.
Figure 4.
Times of submitting EOP forecasts by participants to the campaign Office
In contrast to the previous campaign, in the 2nd EOP PCC, participants are not required to send predictions of a specific length. The choice of the prediction horizon is up to each group, and the only requirement of the EOP PCC Office is that the forecasts should not be longer than a year into the future. The analysis of the length of files sent by participants shows that in the case of PM, UT1-UTC, and LoD, the most popular prediction horizon is 90 days into the future, and the second most popular prediction horizon is one year (Figure 5). For precession-nutation, the Office usually receives forecasts for 11 days, 3 months, 6 months, and 12 months into the future.
Figure 5.
Prediction horizons used by participants in the forecasts and the number of methods in which a given forecast horizon is exploited
An essential part of our analysis is comparing submitted predictions against subsequently available final EOP estimates based on geodetic observations. For the sake of obtaining quick results, we usually use rapid solutions provided by IERS (
Details on EOP reference solutions compared in this study
| Solution | Starting date | Provided EOP | Provider |
|---|---|---|---|
| C04 | 1 January 1962 | x pole, y pole, UT1-UTC, LoD, dX, dY, dPsi, dEps | The Earth Orientation Center of the IERS (Bizouard et al. 2019) |
| SPACE | 19 July 1993 | x pole, y pole, UT1-UTC | JPL (Ratcliff and Gross 2019) |
| Bulletin A | 1 September 1996 | x pole, y pole, UT1-UTC | IERS Rapid Service Prediction Centre (Wooden and Gambis 2004) |
| ILRS | 28 December 1997 | x pole, y pole, LoD | ILRS (Sciarletta et al. 2010) |
| IGS rapid | 30 June 1996 | x pole, y pole, UT1-UTC, LoD | IGS (Kouba and Mireault 1998) |
| IGS final | 30 June 1996 | x pole, y pole, UT1-UTC, LoD | IGS (Kouba and Mireault 1998) |
| IVS rapid | 4 January 2002 | x pole, y pole, UT1-UTC, LoD, dX, dY, dPsi, dEps | IVS BKG/DGFI Combination Center (Malkin 2001) |
| GSFC | 4 August 1979 | x pole, y pole, UT1-UTC, LoD, dX, dY, dPsi, dEps | NASA GSFC (Technical description of solution gsf2014a, |
| USNO | 4 August 1979 | x pole, y pole, UT1-UTC, LoD, dX, dY, dPsi, dEps | USNO (Technical description of solution usn2015a, |
The IERS EOP C04 14 solution became the international reference EOP series on February 1, 2017, and it is the combination of operational series provided by the single-technique centres together with EOP solution associated with the International Terrestrial Reference Frame (ITRF) 2014 and operational solutions maintained by several IVS analysis centres and one IGS analysis centre (Bizouard el al. 2019). The C04 has been tied to two guide series, the IVS combination and the ITRF 2014 EOP solution, to ensure consistency with the conventional reference frames: second realization of International Celestial Reference Frame (ICRF2) (Fey et al 2015) and ITRF 2014 (Altamimi et al. 2016). Bizouard el al. (2019) state that the Allan standard deviation of differences between the C04 and the guide series revealed a stability on timescales between 10 days and 3 years below 20 μas for pole coordinates, 30 μas for precession-nutation offsets, and 3 μs for UT1.
The results of preliminary comparison of different reference solutions are presented in the following subsections. All the data sets were accessed from the website of the IERS Earth Orientation Center managed by Paris Observatory (
The plots of differences between C04 14 and other potential reference data for PM are shown in Figure 6, and the statistics for these differences are given in Table 4. For PM, the smallest differences with respect to C04 are present in Bulletin A and SPACE, whereas the highest discrepancies are found for ILRS and IVS solutions (Figure 6). This is confirmed by root mean square (RMS) values shown in Table 4. ILRS and IVS seem to be better compatible with each other for x pole, while in y pole, they are slightly shifted relative to each other. Mean differences between C04 and other possible reference data for x pole are between −0.050 and 0.028 mas, while for y pole, they range between -0.116 and 0.139 mas (Table 4).
Root mean square (RMS), mean, minimum, and maximum of differences between C04 and Bulletin A, SPACE, IGS rapid, IGS final, ILRS, and IVS rapid solutions for x pole and y pole
| Solution | RMS | Mean | Min | Max | ||||
|---|---|---|---|---|---|---|---|---|
| x pole (mas) | y pole (mas) | x pole (mas) | y pole (mas) | x pole (mas) | y pole (mas) | x pole (mas) | y pole (mas) | |
| C04 – Bulletin A | 0.052 | 0.045 | 0.001 | 0.001 | −0.312 | −0.242 | 0.152 | 0.139 |
| C04 – SPACE | 0.066 | 0.051 | 0.035 | −0.025 | −0.307 | −0.228 | 0.214 | 0.122 |
| C04 – IGS rapid | 0.084 | 0.070 | 0.006 | −0.001 | −0.413 | −0.257 | 0.247 | 0.254 |
| C04 – IGS final | 0.080 | 0.065 | 0.001 | 0.000 | −0.419 | −0.254 | 0.227 | 0.194 |
| C04 – ILRS | 0.214 | 0.241 | −0.050 | −0.116 | −1.656 | −0.772 | 0.600 | 0.673 |
| C04 – IVS rapid | 0.360 | 0.299 | 0.028 | 0.139 | -1.441 | -1.144 | 2.268 | 1.263 |
Figure 6.
Differences between C04 and: IVS rapid, ILRS, IGS rapid, IGS final, Bulletin A, and SPACE solutions for x pole (a-c) and y pole (d-f). Note that for better visibility, the scale on y axis varies depending on the solution
In the case of UT1-UTC and LoD, the agreement with C04 is on a very good level for all solutions except IVS over the whole time span (Figure 7). All solutions are very stable, with the mean difference very close to zero (Table 5). Isolated anomalies and deviations from C04 series are found in the ILRS solution in the case of LoD, which could introduce systematic errors into the final evaluation. For UT1-UTC, the highest agreement with C04 is provided by SPACE and Bulletin A, while for LoD, the smallest deviation from C04 is observed for SPACE as well as final and rapid IGS solutions.
Figure 7.
Differences between C04 and IVS rapid, ILRS, IGS rapid, IGS final, and SPACE solutions for LoD (a-c); differences between C04 and IVS rapid, IGS rapid, IGS final, Bulletin A, and SPACE solutions for UT1-UTC (d-f). Note that for better visibility, the scale on y axis varies depending on the solution
Root mean square (RMS), mean, minimum, and maximum of differences between C04 and ILRS, SPACE, IGS rapid, IGS final, IVS rapid, and Bulletin A solutions for LoD and UT1-UTC
| Solution | LoD | UT1-UTC | ||||||
|---|---|---|---|---|---|---|---|---|
| RMS (ms) | Mean (ms) | Min (ms) | Max (ms) | RMS (ms) | Mean (ms) | Min (ms) | Max (ms) | |
| C04 – ILRS | 0.035 | 0.000 | −0.077 | 0.290 | × | × | × | × |
| C04 – SPACE | 0.015 | −0.001 | −0.054 | 0.050 | 0.019 | −0.005 | −0.113 | 0.082 |
| C04 – IGS rapid | 0.011 | 0.000 | −0.039 | 0.034 | 0.051 | −0.008 | −0.167 | 0.153 |
| C04 – IGS final | 0.010 | −0.001 | −0.037 | 0.028 | 0.043 | −0.006 | −0.147 | 0.140 |
| C04 – IVS rapid | 0.098 | −0.005 | −0.391 | 0.502 | 0.212 | −0.001 | −1.035 | 0.744 |
| C04 – Bulletin A | × | × | × | × | 0.020 | −0.004 | −0.110 | 0.087 |
Although it is evident that IVS solution strongly differs from the others in case of PM, UT1-UTC, and LoD (Figures 6 and 7), the IVS series are fully in agreement with C04 data for precession-nutation (both dX, dY and dPsi, dEpsilon) which is shown in Figures 8 and 9, and indicated by very low RMS values in Table 6.
Figure 8.
Differences between C04 and: USNO, GSFC, and IVS rapid solutions for dX (a-c), dY (d-f) components of precession-nutation
Figure 9.
Differences between C04 and USNO, GSFC, and IVS rapid solutions for dPsi (a-c), dEpsilon (d-f) components of precession-nutation
Root mean square (RMS), mean, minimum, and maximum of differences between C04 and: USNO, GSFC, and IVS rapid solutions for dX, dY and dPsi, dEps components of precession-nutation
| Solution | RMS | Mean | Min | Max | ||||
|---|---|---|---|---|---|---|---|---|
| dX (mas) | dY (mas) | dX (mas) | dY (mas) | dX (mas) | dY (mas) | dX (mas) | dY (mas) | |
| C04 – USNO | 0.178 | 0.117 | −0.001 | 0.018 | −0.913 | −0.455 | 2.952 | 1.658 |
| C04 – GSFC | 0.114 | 0.146 | −0.034 | 0.027 | −0.885 | -1.262 | 0.946 | 2.002 |
| C04 – IVS rapid | 0.018 | 0.008 | 0.001 | 0.000 | −0.231 | −0.055 | 0.159 | 0.076 |
| C04 – USNO | 0.130 | 0.139 | 0.010 | −0.031 | −0.466 | −0.642 | 1.608 | 1.086 |
| C04 – GSFC | 0.135 | 0.181 | −0.019 | −0.024 | −0.878 | −1.297 | 0.954 | 1.965 |
| C04 – IVS rapid | 0.078 | 0.117 | 0.009 | −0.008 | −0.414 | −0.634 | 0.440 | 0.498 |
This simple analysis reveals possible differences between various EOP series, which might affect the results of the predictions evaluation. IERS solutions as the official products will be central to the routine analysis performed as a part of the ongoing campaign. However, we believe that the additional consideration of other solutions might be essential for a proper understanding of the performance of individual contributions, which might be more tailored to reference solutions other than C04. Despite the high variances of differences for some single-technique solutions visible in the figures, we aim at adopting those data as the study of the impact of the choice of reference data on prediction accuracy is one of the objectives of the 2nd EOP PCC.
The 2nd EOP PCC is conducted under the auspices of IERS from September 2021. The campaign registration is open to all interested scientists, and new submissions may be entered at any time until the expected end of the campaign in December 2022. Submissions of all different kinds of EOP for up to one year in the future are welcome. It is also possible for individual institutions to submit more than one forecast with sufficiently distinct methods.
A first summary of the statistics on the 2nd EOP PCC participants and predictions shows high interest in the campaign by the scientific community. We recorded a higher number of participating groups and forecasting methods used than in the previous campaign, which was carried out in the years 2006 to 2008. The presented statistics indicate a large variety of EOP forecasts in terms of the input data, forecasting methods, programming languages, and the forecast horizon. In terms of input data used, IERS C04 solutions are dominant. The most often forecasted parameter is PM, predicted by 16 participants with 25 different methods, wherein two main groups of algorithms dominate, i.e., machine learning and least squares collocation.
During the course of the campaign, we will continue evaluating the quality of predictions against various reference data and for different prediction horizons. A preliminary comparison of potential reference series for EOP prediction validation reveals some discrepancies that merit further scrutiny. RMS values for differences between IERS 14 C04 and selected EOP solutions show discrepancies at the level:
for PM from 0.04 mas for Bulletin A to 0.36 mas for IVS rapid; for LoD from 0.01 ms for IGS to 0.10 ms for IVS rapid; for UT1-UTC from 0.02 ms for SPACE and Bulletin A to 0.21 ms for IVS rapid; for dX, dY components of precession-nutation from 0.01 mas for IVS rapid to 0.18 mas for USNO; for dPsi, dEps components of precession-nutation from 0.08 mas for IVS rapid to 0.18 mas for GSFC.
In the upcoming articles with detailed campaign results, we will focus more on the basic features of the input data and predicting methods used by participants, and their impact on the prediction accuracy. We will also study in detail various reference solutions, especially the way they are constructed, the time span of records and predictions, their uncertainties, and limitations. This will help to objectively assess the impact of the observational data used on the accuracy of the forecasts. The campaign will continue to discuss preliminary results with participants and other interested scientists in a series of online meetings and workshops. All details of these events will be announced publicly via https://eoppcc.cbk.waw.pl.