Abstract
Earth rotation can be described using Earth Orientation Parameters (EOP). As key parameters connecting the celestial and terrestrial reference frames, EOP constitute important spatiotemporal datum parameters. Due to latency in observational data processing, real-time applications of EOP must be realized through prediction sequences, which hold significant application value in areas such as space vehicle orbit determination, guidance, and deep space exploration. Based on the combined solution from the International Earth Rotation and Reference Systems Service and China's independently observed rapid solution, an EOP combined series is formed, climate variability is introduced into the fitting model, and 365-day long-term predictions are conducted. For the recent two-year period, prediction accuracy is statistically analyzed and compared with forecast products maintained by the United States Naval Observatory (USNO). The results indicate that the EOP prediction series generated based on China's independently observed combined series exhibits slightly lower accuracy in the short term compared to USNO products, yet demonstrates advantages in the medium to long term. In particular, the medium to long-term prediction accuracy for Universal Time parameters has improved by 20%–30%, reflecting technological progress in China's independent EOP observation, solution calculation, and forecast data service capabilities.
Full Text
Preamble
Vol. 43, No. 3
September 2025
PROGRESS IN ASTRONOMY Vol. 43, No. 3 Sept., 2025 doi: 10.3969/j.issn.1000-8349.2025.03.08
Long-term Forecast and Accuracy Evaluation of EOP Based on China's Autonomous Observations
XU Xueqing¹², GUO Li¹²³, ZHOU Weili¹³, ZHANG Zhibin¹²⁴, SONG Suli¹², WANG Guangli¹²³, QI Zhaoxiang¹²
(1. Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China; 2. School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China; 3. Shanghai Key Laboratory of Space Navigation and Positioning Techniques, Shanghai 200030, China; 4. State Key Laboratory of Radio Astronomy and Technology, Beijing 100101, China)
Abstract
Earth's rotation can be described using Earth Orientation Parameters (EOP), which serve as crucial spatiotemporal reference parameters linking the celestial and terrestrial reference frames. Due to latency in observational data processing, real-time applications of EOP require forecast sequences, which hold significant value in spacecraft orbit determination, guidance, and deep space exploration. This study constructs a hybrid EOP sequence by combining the International Earth Rotation and Reference Systems Service (IERS) combined solution with China's autonomously observed rapid solution. Climate variability is incorporated into the fitting model to conduct 365-day long-term forecasts. Focusing on the most recent two-year period, we statistically evaluate forecast accuracy and compare it with forecast products maintained by the United States Naval Observatory (USNO). Results demonstrate that while the short-term forecast accuracy of EOP based on China's autonomous observations is slightly lower than USNO products, it exhibits advantages in medium- to long-term forecasts. In particular, the medium- to long-term forecast accuracy for Universal Time parameters improves by 20%–30%, reflecting China's technological advancement in autonomous EOP observation, solution, and forecast data services.
Keywords: Earth rotation variation; Earth orientation parameters; high-precision forecast; rapid UT1 solution; rapid polar motion solution
1 Introduction
Earth's rotation characterizes the coupling processes between the solid Earth and the atmosphere, oceans, mantle, and core across various spatial and temporal scales, and can be intuitively described using Earth Orientation Parameters (EOP). As transformation parameters between the International Celestial Reference Frame (ICRF) and International Terrestrial Reference Frame (ITRF), EOP are essential for deep space exploration and satellite precision orbit determination. Earth's rotation is extremely complex and highly time-varying, necessitating integrated observations from multiple space geodetic techniques for monitoring. Conventional space geodetic methods primarily include Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging (SLR), Global Navigation Satellite System (GNSS), and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) [1–3].
The celestial reference frame, terrestrial reference frame, and their connecting parameters (EOP) constitute the primary elements of the spatial datum, serving as the reference benchmark for all ground- and space-based activities and representing key technologies for China to independently conduct space programs. Figure 1 illustrates the components of EOP and their connection to celestial and terrestrial reference frames. As shown, EOP typically comprises three components: (1) precession and nutation, describing the motion of Earth's rotation axis in space resulting from gravitational effects of the Sun, Moon, and planets on Earth's equatorial bulge; (2) polar motion, representing the motion of the rotation axis relative to the Earth's crust; and (3) variations in length of day, reflecting changes in Earth's rotation rate. Since precession and nutation can be precisely calculated using models and length-of-day variations can be derived from Universal Time, EOP in this paper refers specifically to polar motion (including Px and Py components) and the difference between Universal Time and Coordinated Universal Time (UT1-UTC), sometimes abbreviated as UT1.
[FIGURE:1] EOP and their connection to celestial and terrestrial reference frames
High-precision EOP data are typically determined based on the terrestrial reference frame definition through weighted integration of multiple space geodetic data with certain constraints, known as EOP combined solutions. Due to complex data processing procedures, high-precision EOP combined solutions experience approximately a four-week delay. Data for the most recent month are usually supplemented using GNSS-observed polar motion and VLBI-observed Universal Time, forming EOP rapid solutions. Currently, EOP combined solutions are released by the International Earth Rotation and Reference Systems Service (IERS), while organizations providing EOP rapid solutions include the United States Naval Observatory (USNO) and the European Space Agency (ESA). China currently lacks such domestic products [4–8]. Presently, most global satellite navigation systems and space exploration missions heavily rely on EOP data released by IERS. With China's comprehensive national strength enhancement and changing international circumstances, there is an urgent need to establish an independent EOP observation, solution, and forecast data service system [9].
Combining EOP combined solutions with rapid solutions enables backward extrapolation to obtain forecast data, for which high-precision EOP forecasts have critical practical application demands. Numerous scholars have conducted research on EOP forecasting in recent years. Among various forecasting methods, the least squares extrapolation and auto-regressive (LS+AR) model has been recognized as the most reliable EOP forecasting method since its proposal due to its simplicity and effectiveness [10,11]. This combined method has been validated through two EOP Prediction Comparison Campaigns (EOP PCC) [12,13] and serves as the primary method for obtaining IERS Bulletin forecast data [14]. Meanwhile, extensive research demonstrates that Effective Angular Momentum (EAM) from atmospheric and oceanic fluids constitutes the primary excitation factor for Earth rotation variations, with its equatorial and axial components corresponding to excitations of the two polar motion components and rotation rate parameters, respectively. The German Research Centre for Geosciences (GFZ) releases daily EAM fundamental datasets with a one-day delay and six-day forecast sequences, providing a foundation for ultra-high-precision 1–10 day EOP forecasts [15–18]. Recent studies combining EAM data with mathematical models for EOP forecasting have consistently shown that introducing fluid excitation can effectively improve short-term forecast accuracy [19–23].
However, the aforementioned work is based on international EOP data, primarily focusing on short-term forecasts within 30 days for polar motion parameters, with limited research on UT1-UTC parameters and medium- to long-term EOP forecasts, and lacking forecast analysis based on autonomously observed and solved EOP data. Furthermore, EAM can only improve ultra-short-term EOP forecast accuracy and has no effect on medium- to long-term forecasts. Addressing this situation, this work employs autonomously observed and solved EOP data from the most recent 30 days, combined with IERS combined solutions to form a hybrid sequence, then uses the LS+AR model for 365-day long-term EOP forecasts. Given that EAM cannot improve medium- to long-term EOP forecasts, and considering research on climate change representation in EOP [24–30], we incorporate interannual variability cycles related to climate in the fitting model and adopt newly solved geophysical parameters to improve medium- to long-term EOP forecast accuracy.
2 Accuracy Assessment of Autonomous Rapid EOP
To meet the urgent demand for autonomous determination and forecasting of EOP (particularly Universal Time UT1) for China's major projects, the Shanghai Astronomical Observatory established a rapid EOP and UT1 measurement team in early May 2022. Leveraging previously constructed VLBI stations and GNSS monitoring stations, the team initiated rapid EOP products and services using a combination of domestic autonomous observations and international collaborative measurements. To compensate for the delay in IERS combined solutions, the most recent 30-day EOP observation sequence is obtained by integrating autonomous observation data (SESHAN 13-m, TIANMA 13-m, URUMQI-13-m VLBI antennas, and the Shanghai Astronomical Observatory GNSS center) with international station data.
Simple data preprocessing is required to fuse EOP combined solutions with autonomous rapid solutions. First, GNSS rapid polar motion data at daily UTC 12h must be interpolated to daily UTC 24h to align with the IERS C04 series. Second, VLBI rapid UT1 sequence time points are irregular; this paper employs intensive interpolation to output daily UTC 24h point values forming the rapid UT1 sequence. Using the first quarter of 2023 as an example, Figure 2 shows the residual sequence of autonomously observed and solved EOP relative to the IERS C04 combined solution and its accuracy statistics, using Mean Absolute Error (MAE) as the accuracy metric.
[FIGURE:2] Residual sequence and accuracy statistics of autonomously observed and solved EOP relative to IERS C04 combined solution
Figure 2 demonstrates that the residual sequence of autonomously observed and solved EOP is generally concentrated compared to high-precision post-processed combined solutions, indicating good accuracy stability. For comparison, this paper also statistics the accuracy of USNO-solved rapid EOP sequences for the same period, with polar motion component MAE values of 0.033 mas and 0.028 mas, and UT1-UTC parameter MAE of 0.019 ms. These results reveal that the accuracy of autonomous rapid EOP solutions still lags behind USNO's rapid EOP solutions.
These gaps can be summarized as follows: (1) All three residual sequences exhibit semi-monthly variation terms, likely related to the omission of smaller variation terms in tidal models during autonomous solution [3,5,9]; (2) Polar motion residual sequences also show certain linear biases, primarily due to reliance on single GNSS technology for autonomous rapid data; (3) Universal time residual sequences exhibit locally dispersed observation points, possibly related to the distribution of some participating stations. Therefore, future improvements in autonomous EOP rapid solution accuracy can focus on two aspects: (1) Increasing globally distributed stations to reduce solution errors caused by insufficient baseline lengths; (2) Improving rapid EOP integrated processing schemes to eliminate systematic biases and reduce tidal model error impacts.
3 Improving Medium- to Long-term EOP Forecasts by Incorporating Climate Variability
This work constructs an EOP joint observation sequence by combining the IERS combined solution (EOP C04 series) from January 1, 1962 to present with autonomously observed and solved rapid solutions. Based on this sequence, forecasts are performed using the LS+AR method. Regular terms in the EOP sequence (primarily trend and periodic components) are forecasted through model fitting and extrapolation, while remaining residual terms are forecasted using an autoregressive model. Combining both yields 1–365 day EOP forecast sequences. The fitting and autoregressive models are expressed as follows:
$$
\begin{align}
\text{EOP}{\text{rg}}(t) &= a + bt + \sum + \phi_k\right) \}^{p} c_k \cos\left(\frac{2\pi t}{T_k
\text{EOP}{\text{rs}}(t) &= \sum(t-l)}^{q} \alpha_l \text{EOP}_{\text{rs}
\end{align}
$$
where $\text{EOP}{\text{rg}}$ and $\text{EOP}$ represent regular and residual terms, respectively; $a, b, c_k, T_k, \phi_k$ are fitting model parameters; and $p, \alpha_l$ are autoregressive model parameters [29].}
Research indicates that Earth Angular Momentum (EAM) significantly improves ultra-short-term EOP forecasts but has virtually no impact on medium- to long-term forecasts [20–24]. Therefore, this work does not introduce EAM for long-term EOP forecasting. Additionally, recent studies investigating climate change signatures in Earth rotation variations have confirmed that EOP sequences have undergone trend changes in recent years [24,26]. Figure 3 shows EOP observation sequences from 1962 to present, with red boxes marking periods of anomalies.
[FIGURE:3] EOP observation sequences from 1962–2024
Figures 3a and 3b display the $P_x$ and $P_y$ observation sequences, revealing that Earth polar motion sequence amplitudes decreased sharply during 2012–2021. Latest research indicates this amplitude attenuation resulted from anti-phase excitation by the atmosphere and oceans, reflecting changes in ocean-atmosphere coupling patterns [26]. Figure 3c shows the UT1-UTC sequence, with breaks indicating leap seconds due to Earth's long-term rotation slowdown. The decreasing trend of the UT1-UTC sequence changed in 2020, reversing to an increasing trend. This trend reversal indicates Earth has recently entered a rotation acceleration phase, with the triple La Niña event during 2020–2023 contributing approximately 9% to this acceleration [29]. These changes in EOP sequences affect their medium- to long-term forecasts and must be considered.
Based on the above research on climate change indicators in EOP sequences, this work incorporates climate variability into the EOP forecast model to improve medium- to long-term forecast accuracy. Specific improvements include: (1) To accurately fit complex variations in the universal time sequence, the model incorporates not only conventional annual, semi-annual, and 1/3-year periodic terms but also several interannual variation cycles (approximately 2, 3, 6, and 7-year periods), thereby improving fitting accuracy for long-term variation terms [27–29]; (2) To accommodate recent amplitude changes in polar motion sequences, fluid excitation data are introduced to re-estimate the Chandler wobble period (approximately 432.4 days; specific solution methods详见文献 [31]). These data introductions and updates consider recent climate change impacts on Earth rotation variations, collectively referred to as climate variability in this paper.
Based on these improvements, 1–365 day EOP forecast data can be obtained from the joint observation sequence. This data file is generated monthly and uploaded to a data platform for user download. Accumulating two years of forecast data files since May 2022 enables accuracy evaluation. This paper selects forecast data from May 2022 to July 2024 for comparison with corresponding EOP observation data, using MAE as the accuracy metric. MAE is expressed as:
$$
\text{MAE} = \frac{1}{n} \sum_{i=1}^{n} |O_i - P_{j,i}|
$$
where $O$ represents EOP observed values, $P$ represents forecast values, $j$ represents forecast span, and $n$ represents the number of points participating in forecast accuracy statistics.
4 Medium- to Long-term EOP Forecast Results and Analysis
To better evaluate the accuracy of our long-term EOP forecast sequence, we compare it with Bulletin A forecast data published by IERS for the same period. Figure 4 shows the comparison of 1–365 day EOP forecast accuracy between our results and Bulletin A from May 2022 to July 2024. Bulletin A files are provided by the United States Naval Observatory (marked as USNO), while our results are marked as SHAO (Shanghai Astronomical Observatory).
[FIGURE:4] Comparison of 365-day EOP forecast accuracy between SHAO and USNO
Figure 4 reveals different performance characteristics between the two organizations across various EOP parameters and forecast spans. For the $P_x$ parameter, SHAO demonstrates superior forecast accuracy between 50–150 days and after 320 days, while USNO performs better within 50 days and between 150–320 days. For the $P_y$ parameter, SHAO shows advantage between 180–260 days, with USNO performing better across other spans. For UT1-UTC parameters, USNO leads within 1–140 days, while SHAO exhibits clear advantage beyond 140 days. According to different application requirements, EOP forecasts are typically categorized as: (1) ultra-short-term (within 10 days); (2) short-term (within 90 days); (3) medium-term (within 180 days); and (4) long-term (within 365 days). For intuitive comparison, Figure 5 shows MAE comparisons across these primary spans, also including short-term forecast accuracy at 30 and 60 days for the three parameters.
[FIGURE:5] Comparison of EOP forecast accuracy across primary spans between SHAO and USNO
Based on the MAE comparisons at fixed spans in Figure 5, several conclusions can be drawn: (1) At the 10-day span, USNO's EOP forecast accuracy is slightly higher than SHAO's; (2) For 30, 60, and 90-day short-term forecasts, SHAO and USNO each show advantages in $P_x$ and $P_y$ components respectively, with USNO leading in the UT1-UTC component; (3) For 180-day medium-term forecasts, SHAO demonstrates advantages in both $P_x$ and UT1-UTC components, while USNO slightly leads in the $P_y$ component; (4) For 365-day long-term forecasts, SHAO substantially leads in $P_y$ and UT1-UTC components, while USNO leads in the $P_x$ component.
In summary, USNO marginally leads in ultra-short- and short-term forecasts, primarily due to higher accuracy in its most recent 30-day rapid EOP solutions. SHAO exhibits accuracy advantages in medium- to long-term forecasts, indicating that rapid solution accuracy for the most recent month only affects forecasts within 90 days, while medium- to long-term forecast accuracy depends primarily on the forecast model. SHAO's advantages in medium-term forecasts simultaneously demonstrate that incorporating climate variability in the forecast model improves accuracy. Particularly for universal time parameters, medium- to long-term forecast accuracy improves by approximately 20%–30%. Additionally, results show that incorporating climate variability yields less significant improvement for polar motion than for UT1-UTC. During the evaluation period (2022–2024), polar motion amplitude attenuation adjustment had completed and returned to normal amplitude stages, thus Chandler period updates had minimal impact on forecasts during this period. However, UT1-UTC's complex variation trends persisted, making the introduction of relevant interannual cycles effective for improving medium- to long-term forecasts.
5 Summary and Outlook
This work preprocesses autonomously observed and solved rapid EOP solutions, then combines them with EOP C04 combined solutions to form a joint observation sequence. Based on this sequence, we incorporate climate variability into the model for the first time to obtain real-time 1–365 day EOP forecast data through backward extrapolation, which are uploaded as data files to serve relevant users. Accuracy evaluation of EOP forecast data generated by SHAO and USNO reveals that each organization shows advantages across different forecast spans. Analysis indicates that SHAO and USNO achieve comparable accuracy levels in rapid EOP solution and 1–365 day EOP forecasting. These results demonstrate that after years of technical accumulation, China has established comprehensive capabilities in multi-technology EOP system construction, observation and solution, data processing, and product services.
To better support China's major project application requirements and scientific research needs, autonomous EOP data services can be improved through: (1) Adopting multi-technology collocation strategies to eliminate station coordinate error effects and enhance VLBI, GNSS, and other station stability; (2) Combining high-resolution data to precisely analyze excitation mechanisms across EOP frequency bands, reducing solid Earth tide and ocean tide model errors; (3) Developing new rapid EOP data processing strategies to eliminate systematic biases from frame inconsistencies; (4) Improving existing Earth rotation theory by introducing comprehensive geophysical excitation factors to further enhance EOP forecast accuracy; (5) Conducting extensive user requirement surveys to provide personalized EOP data services.
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