Space weather describes varying conditions between the Sun and Earth that can degrade Global Navigation Satellite Systems (GNSS) operations. Thus, these effects should be precisely and timely corrected for accurate and reliable GNSS applications. That can be modeled with the Vertical Total Electron Content (VTEC) in the Earth’s ionosphere. This study investigates different learning algorithms to approximate nonlinear space weather processes and forecast VTEC for 1 h and 24 h in the future for low-, mid- and high-latitude ionospheric grid points along the same longitude. VTEC models are developed using learning algorithms of Decision Tree and ensemble learning of Random Forest, Adaptive Boosting (AdaBoost), and eXtreme Gradient Boosting (XGBoost). Furthermore, ensemble models are combined into a single meta-model Voting Regressor. Models were trained, optimized, and validated with the time series cross-validation technique. Moreover, the relative importance of input variables to the VTEC forecast is estimated. The results show that the developed models perform well in both quiet and storm conditions, where multi-tree ensemble learning outperforms the single Decision Tree. In particular, the meta-estimator Voting Regressor provides mostly the lowest RMSE and the highest correlation coefficients as it averages predictions from different well-performing models. Furthermore, expanding the input dataset with time derivatives, moving averages, and daily differences, as well as modifying data, such as differencing, enhances the learning of space weather features, especially over a longer forecast horizon.

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.

This paper introduces a new learning algorithm for accurate, physically driven time series prediction. The fundamental assumption behind the method is that the phenomena follow Ordinary Differential Equations. We investigate the general case where the time series follows an ODE of degree . The resulting method is a learning algorithm based on the finite differences between the values of time series. We present the application of the method in the field of geodesy for polar motion prediction, the main objective of the present paper. We show that in this application, the linear form of the method is sufficient and offers competitive predictive performance. We present a baseline solution, in which we use historical polar motion time series from 1976 to predict up to the year 2020. The prediction horizon in this case is short‐term (up to 10 days into the future). In addition, we compare the prediction accuracy in the short‐term horizon with the results of the best performing model in the first Earth Orientation Prediction Comparison Campaign. On average, a 53% improvement in prediction performance is achieved. In further analyses, we compare the prediction accuracy for both short‐term and long‐term against the results of state‐of‐the‐art methods, namely Multichannel Singular Spectrum Analysis, and a combination of Singular Spectrum Analysis and Copula sampling. We show that the proposed method in this paper can outperform the mentioned two methods in both short and long‐term horizons, with an average improvement of the prediction performance of 54% and 52%, respectively.

Radio signals transmitted by Global Navigation Satellite System (GNSS) satellites experience tropospheric delays. While the hydrostatic part, referred to as zenith hydrostatic delay (ZHD) when mapped to the zenith direction, can be analytically modelled with sufficient accuracy, the wet part, referred to as zenith wet delay (ZWD), is much more difficult to determine and needs to be estimated. Thus, there exist several ZWD models which are used for various applications such as positioning and climate research. In this study, we present a data-driven, global model of the spatial ZWD field, based on the Extreme Gradient Boosting (XGBoost). The model takes the geographical location, the time, and a number of meteorological variables (in particular, specific humidity at several pressure levels) as input, and can predict ZWD anywhere on Earth as long as the input features are available. It was trained on ZWDs at 10718 GNSS stations and tested on ZWDs at 2684 GNSS stations for the year 2019. Across all test stations and all observations, the trained model achieved a mean absolute error of 6.1 mm, respectively, a root mean squared error of 8.1 mm. Comparisons of the XGBoost-based ZWD predictions with independently computed ZWDs and baseline models underline the good performance of the proposed model. Moreover, we analysed regional and monthly models, as well as the seasonal behaviour of the ZWD predictions in different climate zones, and found that the global model exhibits a high predictive skill in all regions and across all months of the year.