Timely zenith hydrostatic delay (ZHD) and weighted mean temperature ($T_{m}$) are critical for real-time GNSS precipitable water vapor (PWV) retrieval. However, for GNSS stations without collocated meteorological sensors, ZHD and$T_{m}$data are often inaccessible. Although atmospheric reanalysis offers an accurate alternative, its latency impedes real-time GNSS PWV retrieval. In this study, we propose a novel model, HDTM, capable of providing hourly updated ZHD and$T_{m}$forecast grids using freely available numerical weather predictions (NWPs), NCEP-GFS, and ECMWF-IFS. The HDTM model was validated over land and ocean regions in China, utilizing data from ERA5 reanalysis, 953 GNSS/meteorological stations, 64 radiosonde stations, and oceanic in situ pressure measurements. The results demonstrate that: 1) the HDTM model outperforms the traditional models, particularly in capturing the diurnal variations of ZHD and$T_{m}$, with ZHD root mean square (rms) errors of 3.2 mm (1.9 mm over oceans) and$T_{m}$rms error of 1.5 K; 2) PWV values retrieved using HDTM exhibit negligible discrepancies from those retrieved using in situ meteorological parameters, with a mean rms of 0.9 mm across China; and 3) in two extreme rainfall events, HDTM demonstrated superior accuracy in capturing ZHD and$T_{m}$and retrieved highly variable PWV with an rms of 1.1 mm. Overall, HDTM can provide high-quality ZHD and$T_{m}$forecasts under both stable and turbulent weather conditions, facilitating precise real-time GNSS PWV monitoring over both land and ocean without relying on collocated meteorological sensors.

The assimilation of ground-based Global Navigation Satellite Systems (GNSS) zenith total delays (ZTDs) has been demonstrated to benefit meteorological applications such as weather forecasting and monitoring. However, their effects are limited by the restricted three-dimensional spatial resolution especially in the vertical direction. Fortunately, the fast-developing unmanned aerial vehicle (UAV) market offers an opportunity to obtain airborne GNSS ZTDs that contain atmospheric information at different locations. Given their unprecedented vertical coverage and spatial resolution, it is promising to assimilate them and further improve numerical weather predictions (NWPs), which, however, has not been investigated and thus still unclear to the community. In this paper, we obtained UAV-based GNSS ZTDs and assimilated them using the WRFDA package, with ERA5 and radiosonde as references to evaluate ZTD and relative humidity (RH) accuracy. Our results show that assimilating airborne GNSS ZTDs improved the humidity field, with RMSE and bias decreasing by up to 22% and 57%, respectively, compared to merely assimilating ground-based GNSS ZTDs. The improvements are more significant with a higher spatial-temporal resolution of the airborne observations. This study contributes to further expanding the application of GNSS meteorology and offers initial ideas for using airborne GNSS to benefit weather forecasts.

Global Navigation Satellite Systems (GNSS), such as the American Global Positioning System (GPS) and the European Galileo system, are capable of monitoring tropospheric properties. An important parameter describing the tropospheric impact on GNSS is zenith wet delay (ZWD), which is highly correlated to the amount of water vapour in the troposphere and thus interesting for atmospheric and climate research. This work demonstrates how GNSS observations help to sense the atmosphere and its dynamics by using a newly developed machine learning-based ZWD model. The model provides ZWD globally for the years 2010 to 2023 with a positive trend in the Northern Hemisphere and a negative trend in the Southern Hemisphere. Furthermore, the global average ZWD anomaly follows alternating trends, strongly correlated with the El Niño Southern Oscillation (ENSO) index, increasing up to a correlation coefficient of 0.74 when introducing a time lag of two months.

The ionosphere is a significant error source in space-geodetic techniques, such as the Global Navigation Satellite System (GNSS) and satellite radar altimetry. This is especially pronounced for single-frequency receivers, as ionospheric delays cannot be mitigated by ionosphere-free combinations. Therefore, for high-precision space applications, we need an accurate ionospheric model to provide ionospheric corrections at desired times and locations, such as global ionospheric maps (GIMs) that depict the global distribution of vertical total electron content (VTEC). In this study, we propose a neural network (NN)-based global ionospheric model to predict global VTEC with higher accuracy compared with conventional GIMs. We first determined VTEC based on the carrier-to-code leveling method using multi-GNSS observations from global IGS stations. The derived VTEC time series for all training station-satellite pairs were then used to train the NN-based model. During our experiment in April 2022, a period of high solar activity, the average mean absolute error of VTEC predictions at 47 global test stations was 1.7 TECU. The performance of the NN-based models were also evaluated by single-frequency precise point positioning and compared with GIMs provided by the Chinese Academy of Sciences since the same differential code bias products were used. The NN-based models demonstrated a noteworthy enhancement in the positioning precision at 47 test stations, achieving improvements of 12%, 20%, and 8% for the east, north, and up components, respectively.

Accurate tropospheric delay forecasts are imperative for microwave-based remote sensing techniques, playing a pivotal role in early warning and forecasting of natural disasters such as tsunamis, heavy rains, and hurricanes. Nevertheless, conventional methods for forecasting tropospheric delays entail substantial computational resources and high network transmission speeds, thereby restricting their real-time applicability in remote sensing operations. In this study, we introduce a novel approach to derive forecasted tropospheric delays using artificial intelligence (AI) weather forecast foundation models (FMs), exemplified by Huawei Cloud Pangu-Weather, Google DeepMind GraphCast, and Shanghai AI Lab FengWu. We assess the accuracy of these forecasts on a global scale employing fifth-generation ECMWF atmospheric re-analysis of the global climate (ERA5) (European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5), ground-based Global Navigation Satellite System (GNSS), and in situ radiosonde (RS) measurements as reference data. Our results show that the FM-based scheme outperforms traditional methods in both forecast accuracy and length, with the ability to provide high-accuracy tropospheric delay parameters locally for 15-day forecasts at any location within minutes. Furthermore, the FM scheme still maintains accuracy better than empirical models when forecasting up to ten days in advance. This research demonstrates the potential of AI weather forecast FMs in delivering high-precision tropospheric delay medium-range forecasts and improvements for real-time remote sensing applications.

Layer precipitable water (LPW), a water vapor product similar to precipitable water vapor (PWV), reports partial moisture content within a specified vertical range. Compared with PWV data, the latest LPW products can describe more refined distributions and variations in water vapor in the troposphere. Global Navigation Satellite Systems (GNSSs), as a powerful water vapor sensing tool, only provide the opportunity to retrieve all-weather PWV, not LPW products. To this end, we develop the first deep-learning-assisted, global water vapor stratification (GWVS) model to estimate the GNSS LPW within any given vertical range. The proposed model is trained and tested using the global radiosonde data, with the training and testing root mean square error (RMSE) of 0.94 and 1.10 mm for radiosonde LPW, indicating the excellent generalization of the GWVS model. Furthermore, the model is comprehensively validated using the data from the two regional GNSS networks and one global network. The RMSEs of the predicted GNSS LPW from the three GNSS networks compared with the co-located radiosonde LPW are 1.52, 1.80, and 1.54 mm, respectively. To study potential applications, we use the model-derived GNSS LPW products to calibrate Geostationary Operational Environmental Satellite-16 (GOES-16) LPW products and improve the GNSS water vapor tomography technique. Results show that the accuracy of three GOES-16 LPW products is improved by 31.3%, 23.3%, and 17.9%, respectively, and the RMSE of the tomography results is reduced from 2.28 to$1.67~\text {g}/\text {m}^{3}$. Both validation and application results highlight that the GWVS model retrieves the required GNSS LPW products and provides additional value for water-vapor-related studies.

The Global Navigation Satellite System (GNSS) is a well-recognized tool to probe the Earth’s atmosphere. This contribution highlights how GNSS data collected from smartphones of voluntary contributors can be used to determine parameters of the troposphere and ionosphere. In this regard, the application of machine learning (ML) to characterize the quality of the crowd-sourced data and model atmospheric parameters is discussed. We demonstrate that in certain cases, GNSS data from smartphones can reach a precision that would allow such data to densify observations from existing geodetic infrastructures.

Effective Angular Momentum (EAM) functions and their predictions are essential geophysical information in describing the changes in earth's orientation. We present the frame-work for the prediction of EAM functions developed at the Chair of Space Geodesy at ETH Zurich. The framework functioning and its underlying methods are explained. In addition, the comparative prediction performance of the methods of the framework with respect to the ones provided by the German Research Centre for Geosciences GFZ is analyzed. The best-performing method is a linear recursive forecasting approach. It manages to improve the EAM predictions between 18 to 64%. The highest improvement could be obtained for the Atmospheric Angular Momentum (AAM) components, with an average improvement of > 50%.

Highly accurate time series prediction in the field of geodesy is both important and a demanding task. For this problem we have investigated the potentiality of deep transformers, a deep learning approach. We have slightly modified the original network architecture and the optimization procedure of this model and thus have created a deep learning regression framework. We have applied the method for time series prediction of more than 18000 GNSS stations. We show that this approach performs better than traditional statistical methods by 21.5% in prediction accuracy. Furthermore, we show that it outperforms other machine learning algorithms by at least 2.7%. We demonstrate that millimeter accuracy can be expected for the prediction.