Effective Angular Momentum Research Articles

Assessment of length-of-day and universal time predictions based on the results of the Second Earth Orientation Parameters Prediction Comparison Campaign

Predicting Earth Orientation Parameters (EOP) is crucial for precise positioning and navigation both on the Earth’s surface and in space. In recent years, many approaches have been developed to forecast EOP, incorporating observed EOP as well as information on the effective angular momentum (EAM) derived from numerical models of the atmosphere, oceans, and land-surface dynamics. The Second Earth Orientation Parameters Prediction Comparison Campaign (2nd EOP PCC) aimed to comprehensively evaluate EOP forecasts from many international participants and identify the most promising prediction methodologies. This paper presents the validation results of predictions for universal time and length-of-day variations submitted during the 2nd EOP PCC, providing an assessment of their accuracy and reliability. We conduct a detailed evaluation of all valid forecasts using the IERS 14 C04 solution provided by the International Earth Rotation and Reference Systems Service (IERS) as a reference and mean absolute error as the quality measure. Our analysis demonstrates that approaches based on machine learning or the combination of least squares and autoregression, with the use of EAM information as an additional input, provide the highest prediction accuracy for both investigated parameters. Utilizing precise EAM data and forecasts emerges as a pivotal factor in enhancing forecasting accuracy. Although several methods show some potential to outperform the IERS forecasts, the current standard predictions disseminated by IERS are highly reliable and can be fully recommended for operational purposes.

Research on Methods to Improve Length of Day Precision by Combining with Effective Angular Momentum

Due to the high correlation between Effective Angular Momentum (EAM) and Length of Day (LOD) data, and the wide application of LOD prediction, this study proposes to combine EAM data with Global Navigation Satellite System (GNSS) LOD data to obtain a more accurate LOD series and attempt to provide a reasonable formal error for the EAM dataset. Firstly, tidal corrections are applied to the LOD data. A first-order difference method is proposed to identify outliers in GNSS LODR (tidal corrected LOD) data, and the EAM data are converted into LODR data using the Liouville equation. Then, the residual term and the fitted term are obtained by least squares fitting. Finally, the fitted residual terms of GNSS LODR and EAM LODR are combined by using the Kalman combination method. In this study, EAM data from the German Research Centre for Geosciences (GFZ) (2019–2022), as well as LOD data from Wuhan University (WHU) and Jet Propulsion Laboratory (JPL), are used for the Kalman combination algorithm experiment. In the Kalman combination, we consider weighted combination based on formal error. However, none of the computing centers provide an uncertainty estimation for the EAM dataset. Therefore, we simulate the combination experiment of LOD and EAM with formal error ranging from 0 to 100 us. The experiment shows that using reasonable formal error for the EAM dataset can improve the accuracy of LOD. Finally, when the formal error of EAM is 2–5 times that of the GNSS LOD formal error, i.e., the EAM formal error is between 10 and 30 us, the accuracy of the combined LOD can be improved by 10–20%.

ESMGFZ EAM Products for EOP Prediction: Toward the Quantification of Time Variable EAM Forecast Errors

Abstract Since more than 10 years, the Earth system modeling group at GFZ (ESMGFZ) provides effective angular momentum (EAM) functions for Earth orientation parameter assessment on a routinely daily basis. In addition to EAM of the individual Earth’s subsystems atmosphere, ocean, and hydrology, the global mass balance is calculated as barystatic sea level variation by solving explicitly the sea-level equation. ESMGFZ provides also 6-day forecasts for all of these EAM products. EAM forecasts are naturally degraded by forecast errors that typically grow with increasing forecast length, but they also show recurring patterns with occasionally higher errors at very short forecast horizons. To characterize such errors which are not randomly distributed in time, we divided the errors into a systematic and a stochastic contribution. In an earlier study, we were able to detect and remove the large systematic fraction occurring in the atmospheric angular momentum (AAM) wind term forecast errors with a cascading forward neural network model, thereby reducing the total forecast error by about 50%. In contrast, we were not able to remove the random error component assed in this study. Nevertheless, we show that machine learning methods are able to predict quasi-daily variations in time variable EAM forecasts error levels. We plan to provide these forecast error estimates along with the deterministic EAM forecast products for subsequent use in, for example, EOP Kalman filter prediction schemes.

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.

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.

ESMGFZ Products for Earth Rotation Prediction

Abstract 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.

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.

Predicting Earth orientation changes from global forecasts of atmosphere-hydrosphere dynamics

Effective Angular Momentum (EAM) functions obtained from global numerical simulations of atmosphere, ocean, and land surface dynamics are routinely processed by the Earth System Modelling group at Deutsches GeoForschungsZentrum. EAM functions are available since January 1976 with up to 3 h temporal resolution. Additionally, 6 days-long EAM forecasts are routinely published every day. Based on hindcast experiments with 305 individual predictions distributed over 15 months, we demonstrate that EAM forecasts improve the prediction accuracy of the Earth Orientation Parameters at all forecast horizons between 1 and 6 days. At day 6, prediction accuracy improves down to 1.76 mas for the terrestrial pole offset, and 2.6 mas for ΔUT1, which correspond to an accuracy increase of about 41% over predictions published in Bulletin A by the International Earth Rotation and Reference System Service.

INFLUENCE OF THE ATMOSPHERE ON EARTH ROTATION: WHAT NEW CAN BE LEARNED FROM THE RECENT ATMOSPHERIC ANGULAR MOMENTUM ESTIMATES?

The interaction between the atmosphere and the underlying solid mantle is one of the most important sources of changes in all three components of the Earth's rotation vector on different time scales. In this paper the NCEP/NCAR reanalysis time series of four times daily atmospheric effective angular momentum (EAM) estimates is used to investigate some selected aspects of the atmospheric influence on Earth rotation. Emphasis is placed on the controversial features which were difficult or impossible to study using the operational EAM data, such as excitation of the free oscillations in polar motion, the Chandler wobble (CW) and the free core nutation (FCN), or the roles of diurnal and semidiurnal atmospheric tides and atmospheric normal modes in the rotational dynamics of the Earth.

Diurnal atmospheric forcing and temporal variations of the nutation amplitudes

A 29-year time-series of four-times-daily atmospheric effective angular momentum (EAM) estimates is used to study the atmospheric influence on nutation. The most important atmospheric contributions are found for the prograde annual (77 μas), retrograde annual (53 as), prograde semiannual (45 as), and for the constant offset of the pole (δψsinɛ0=−86 as, δɛ=77 as). Among them only the prograde semiannual component is driven mostly by the wind term of the EAM function, while in all other cases the pressure term is dominant. These are nonnegligible quantities which should be taken into account in the new theory of nutation. Comparison with the VLBI corrections to the IAU 1980 nutation model taking into account the ocean tide contribution yields good agreement for the prograde annual and semiannual nutations. We also investigated time variability of the atmospheric contribution to the nutation amplitudes by performing the sliding-window least-squares analysis of both the atmospheric excitation and VLBI nutation data. Almost all detected variations of atmospheric origin can be attributed to the pressure term, the biggest being the in-phase annual prograde component (about 30 as) and the retrograde one (as much as 100200 as). These variations, if physical, limit the precision of classical modeling of nutation to the level of 0.1 mas. Comparison with the VLBI data shows significant correlation for the retrograde annual nutation after 1989, while for the prograde annual term there is a high correlation in shape but the size of the atmospherically driven variations is about three times less than deduced from the VLBI data. This discrepancy in size can be attributed either to inaccuracy of the theoretical transfer function or the frequency-dependent ocean response to the pressure variations. Our comparison also yields a considerably better agreement with the VLBI nutation data when using the EAM function without the IB correction for ocean response, which indicates that this correction is not adequate for nearly diurnal variations.