Accurate Earth orientation parameter (EOP) predictions are needed for many applications, e.g., for the tracking and navigation of interplanetary spacecraft missions. One of the most difficult parameters to forecast is the length of day (LOD), which represents the variation in the Earth’s rotation rate since it is primarily affected by the torques associated with changes in atmospheric circulation. In this study, a new-generation time-series prediction algorithm is developed. The one-dimensional convolutional neural network (1D CNN), which is one of the deep learning methods, is introduced to model and predict the LOD using the IERS EOP 14 C04 and axial Z component of the atmospheric angular momentum (AAM), which was taken from the German Research Centre for Geosciences (GFZ) since it is strongly correlated with the LOD changes. The prediction procedure operates as follows: first, we detrend the LOD and Z-component series using the LS method, then, we obtain the residual series of each one to be used in the 1D CNN prediction algorithm. Finally, we analyze the results before and after introducing the AAM function. The results prove the potential of the proposed method as an optimal algorithm to successfully reconstruct and predict the LOD for up to 7 days.

Accurate prediction of Earth orientation parameters (EOPs) is critical for astro-geodynamics, high-precision space navigation, and positioning. However, the current model prediction accuracy for EOPs is significantly lower than the geodetic technical solutions, which can adversely affect certain high-precision real-time users. Deep learning neural networks, precisely one-dimensional convolutional neural networks (1DCNN), and long short-term memory (LSTM) can automatically learn arbitrary complex mappings from inputs to outputs and support multiple inputs and outputs. These are powerful features that offer a lot of promise for time series forecasting, which makes this method suitable to predict simultaneously the Earth rotation parameters (ERP). The computational strategy follows multiple steps. First, using the singular spectrum analysis SSA, the deterministic time-varying signal of the ERP time series can be more precisely and reasonably detected and modeled. Then the reconstructed series and its corresponding residuals are used for 1DCNN training and prediction. However, first, we develop a multivariate multi-step 1DCNN model with a multi-output strategy using three different scenarios including the ocean angular momentum (OAM), atmospheric angular momentum (AAM), and hydrological angular momentum (HAM), to predict both the deterministic and the stochastic part for (PMx, PMy) components of PM. Then the best case with fewer errors is chosen to predict the ERP at the same time in the short term. The results of 3 years of prediction experiments based on the EOP 14 C04 series using 1DCNN are compared with LSTM and show that the proposed model can predict both the deterministic and the stochastic parts for the three parameters at the same time with significant improvements in the ERP for short-term prediction. Compared with alternative methods analyzed in the Second EOP Prediction Comparison Campaign (2nd EOP PCC), the 1DCNN model achieves comparable or even better results: 0.26 mas for PMx, 0.28 mas for PMy, and 0.022 ms for LOD on the first day of prediction, and 1.93 mas for PMx, 1.28 mas for PMy, and 0.13 ms for LOD for the last day of prediction horizon. Graphical abstract

Accurate prediction of Earth orientation parameters (EOPs) is critical for astro-geodynamics, high-precision space navigation, and positioning, and deep space exploration. However, the current models' prediction accuracy for EOPs is significantly lower than that of geodetic technical solutions, which can adversely affect certain high-precision real-time users. In this study, we introduce a simultaneous prediction approach for Polar Motion (PM) and Celestial Pole Offsets (CPO) employing deep neural networks, aiming to deliver precise predictions for both parameters.The methodology comprises three components, with the first being feature interaction and selection. The process of feature selection within the context of deep learning differs from traditional methods for machine learning, and may not be directly applicable to theme since they are designed to automatically learn relevant features. Consequently, we propose in this step a solution based on feature engineering to select the best set of variables that can keep the model as simple as possible but with enough precision and accuracy using recursive feature elimination and the SHAP value algorithm, aiming to investigate the influence of FCN (Free Core Nutation) with its amplitude and phase on the CPO forecasting. This investigation is crucial since FCN is the main source of variance of the CPO series. Considering the role represented by the effective Angular Momentum functions (EAM), and their direct influence on the Earth's rotation, it is logical to assess numerically the impact of EAM on the Polar motion and FCN excitations. SHAP value aids in comprehending how each feature contributes to final predictions, highlighting the significance of each feature relative to others, and revealing the model's dependency on feature interactions.During the second phase, we formulate two deep-learning methods for each parameter. The first Neural Network incorporates all features, while the second focuses on the subset of features identified in the initial step. This stage primarily involves exploring feature and hyperparameter tuning to enhance model performance. The SHAP value algorithm is also used in this stage for interpretation. In the final phase, we construct a multi-task deep learning model designed to simultaneously predict ( CPO ) and ( PM ). This model is built using the optimal set of features and hyperparameters identified in the preceding steps. To validate the methodology, we employ the most recent version of the time series from the International Earth Rotation and Reference Systems Service (IERS), namely IERS 20 C04 and EAM provided by the German Research Center for Geosciences (GFZ). We focus on a forecasting horizon of 90 days, the practical forecasting horizon needed in space-geodetic applications.In the end, we conclude that the developed model is proficient in simultaneously predicting ( CPO ) and ( PM ). The incorporation of ( EAM ), sheds light on its role in CPO excitations and Polar Motion predictions.

Knowledge of the Earth orientation parameters (EOP) is essential for numerous practical and scientific applications including, positioning and navigating in space and on Earth.The LOD (length of day), which represents the variation in the Earth's rotation rate, is the most difficult to forecast since it is primarily affected by the torques associated with changes in atmospheric circulation. Therefore, accurate LOD predictions are an ongoing challenge and are the focus of this work.Consequently, there is a compelling need to identify next-generation time series prediction algorithms to be integrated into an operational processing chain. Of specific interest is the emergence of deep learning methods.  These methods tend to behave as highly adaptive and versatile fitting algorithms and can thus replace conventional fitting functions for enabling more accurate predictions.In this study, the 1D-Convolutional Neural Networks (1D-CNN) is introduced to model and to predict the LOD using the IERS EOP 14 C04 and the axial Z component of the atmospheric angular momentum (AAM) taken from the German Research Centre for Geosciences (GFZ), since it is strongly correlated with the LOD changes. The prediction procedure operates as follows: First, we detrend the LOD and Z-component series by using the LS method, then, we obtain the residuals series of each one to be used in the 1D-CNN prediction algorithm. Finally,  we analyzed the results before and after introducing the AAM function. These results prove the potential of the proposed method as an optimal algorithm to successfully reconstruct and predict LOD for up to 7 days.Keywords1D-Convolutional Neural Networks (1D-CNN);  Length of the day;  atmospheric angular momentum(AAM) function; prediction

Polar Motion is the movement of the Earth's rotational axis relative to its crust, reflecting the influence of the material exchange and mess redistribution of each layer of the Earth on the Earth's rotation axis.The real-time estimation of Polar Motion (PM) is needed for the navigation of Earth satellites and interplanetary spacecraft. However, it is impossible to have real-time information due to the complexity of the measurement model and data processing.Various prediction methods have been developed. However, the accuracy of PM prediction is still not satisfactory even for a few days in the future. Therefore, a new technique or a combination of the existing methods needs to be investigated for improving the accuracy of the prediction PM.In this study, we combine the 1D Convolutional Neural Network with the Singular Spectrum Analysis (SSA). The computational strategy follows multiple steps, first, we model the predominant trend of the PM time series using SSA. Then, the difference between the PM time series and its SSA estimation is modeled using the 1D Convolution Neural Network. However, we developed a Multivariate Multi step 1D-CNN Model with a Multi-output strategy to predict at the same time both components (Xp, Yp) of the PM. . We introduce to the Model: the Ocean Angular Momentum, Atmospheric Angular Momentum, and Hydrological Angular Momentum (OAM+AAM+HAM) to improve the results. Multiple sets of PM predictions which range between 1 and 10 days have been performed based on an IERS 14 C04 time series to assess the capability of our hybrid Model. Our results illustrate that the proposed method can efficiently predict both (Xp, Yp) of PM.