Total water storage anomalies (TWSAs) describe the variations of the terrestrial water cycle, which is essential for understanding our climate system. This study proposes a self-supervised data assimilation model with a new loss function to provide global TWSAs with a spatial resolution of 0.5°. The model combines hydrological simulations as well as measurements from the Gravity Recovery and Climate Experiment (GRACE) and its follow-on (GRACE-FO) satellite missions. The efficiency of the high-resolution information is proved by closing the water balance equation in small basins while preserving large-scale accuracy inherited from the GRACE(-FO) measurements. The product contributes to monitoring natural hazards locally and shows potential for better understanding the impacts of natural and anthropogenic activities on the water cycle. We anticipate our approach to be generally applicable to other TWSA data sources and the resulting products to be valuable for the geoscience community and society.

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.

Growing 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.

The International GNSS Service analysis centers provide orbit products of GPS satellites with weekly, daily, and sub-daily latency. The most frequent ultra-rapid products, which include 24 h of orbits derived from observations and 24 h of orbit predictions, are vital for real-time applications. However, the predicted part of the ultra-rapid orbits is less accurate than the estimated part and has deviations of several decimeters with respect to the final products. In this study, we investigate the potential of applying machine-learning (ML) and deep-learning (DL) algorithms to further enhance physics-based orbit predictions. We employed multiple ML/DL algorithms and comprehensively compared the performances of different models. Since the prediction errors of the physics-based propagators accumulate with time and have sequential characteristics, specific sequential modeling algorithms, such as Long Short-Term Memory (LSTM), show superiority. Our approach shows promising results with average improvements of 47% in 3D RMS within the 24-hour prediction interval of the ultra-rapid products. In the end, we applied the orbit predictions improved by LSTM to kinematic precise point positioning and demonstrated the benefits of LSTM-improved orbit predictions for positioning applications. The accuracy of the station coordinates estimated based on these products is improved by 16% on average compared to those using ultra-rapid orbit predictions.

The gravimetry measurements from the Gravity Recovery and Climate Experiment (GRACE) and its follow-on (GRACE-FO) mission provide an essential way to monitor changes in ocean bottom pressure ( $$p_b$$ p b ), which is a critical variable in understanding ocean circulation. However, the coarse spatial resolution of the GRACE(-FO) fields blurs important spatial details, such as $$p_b$$ p b gradients. In this study, we employ a self-supervised deep learning algorithm to downscale global monthly $$p_b$$ p b anomalies derived from GRACE(-FO) observations to an equal-angle 0.25 $$ ^{\circ }$$ ∘ grid in the absence of high-resolution ground truth. The optimization process is realized by constraining the outputs to follow the large-scale mass conservation contained in the gravity field estimates while learning the spatial details from two ocean reanalysis products. The downscaled product agrees with GRACE(-FO) solutions over large ocean basins at the millimeter level in terms of equivalent water height and shows signs of outperforming them when evaluating short spatial scale variability. In particular, the downscaled $$p_b$$ p b product has more realistic signal content near the coast and exhibits better agreement with tide gauge measurements at around 80% of 465 globally distributed stations. Our method presents a novel way of combining the advantages of satellite measurements and ocean models at the product level, with potential downstream applications for studies of the large-scale ocean circulation, coastal sea level variability, and changes in global geodetic parameters.

Forecasts of Earth’s Effective Angular Momentum functions (EAM) are used for different applications, including prediction of Earth Orientation Parameters (EOPs). Since May 2021, the Chair of Space Geodesy at ETH Zurich has been operationally providing accurate EAM forecasts. These forecasts cover the domain of atmosphere, ocean, hydrology, and sea level. They are based on the EAM forecasts by GFZ Potsdam but are corrected and extended to cover a forecasting horizon of two weeks using machine learning techniques. Here, we present a summary of the methodology and the results achieved during the past two years. We demonstrate the enhanced accuracy of our improved EAM functions of up to 50%. Furthermore, we demonstrate the impact on the potential application of utilizing EAM forecasts in the form of ultra-short-term prediction of length of day, where an improved accuracy of up to 19% has been achieved. The improved EAM forecasting product is updated daily and available at https://gpc.ethz.ch/EAM/.