Tropospheric delay is one of the major error sources in GNSS (Global Navigation Satellite Systems) positioning. Over the years, many approaches have been devised which aim at accurately modeling tropospheric delays, so-called troposphere models. Using the troposphere data of over 16,000 global stations in the last 10 years, as calculated by the Nevada Geodetic Laboratory (NGL), this paper evaluates the performance of the empirical troposphere model GPT3, which is the latest version of the GPT (Global Pressure and Temperature) series model. Owing to the large station number, long time-span and diverse station distribution, the spatiotemporal properties of the empirical model were analyzed using the average deviation (BIAS) and root mean square (RMS) error as indicators. The experimental results demonstrate that: (1) the troposphere products of NGL have the same accuracy as the IGS (International GNSS Service) products and can be used as a reference for evaluating general troposphere models. (2) The global average BIAS of the ZTD (zenith total delay) estimated by GPT3 is −0.99 cm and the global average RMS is 4.41 cm. The accuracy of the model is strongly correlated with latitude and ellipsoidal height, showing obviously seasonal variations. (3) The global average RMS of the north gradient and east gradient estimated by GPT3 is 0.77 mm and 0.73 mm, respectively, which are strongly correlated with each other, with values increasing from the equator to lower latitudes and decreasing from lower to higher latitudes.

A regional zenith tropospheric delay (ZTD) empirical model, referred to as SHAtropE (SHanghai Astronomical observatory tropospheric delay model—Extended), is developed and provides tropospheric propagation delay corrections for users in China and the surrounding areas with improved accuracy. The SHAtropE model was developed based on the ZTD time series of the continuous GNSS sites from the Crustal Movement Observation Network of China (CMONOC) and GNSS sites of surrounding areas. It combines the exponential and periodical functions and is provided as regional grids with a resolution of 2.5° × 2.0° in longitude and latitude. At each grid point, the exponential function converts the ZTD from the site height to the ellipsoid, and the periodical terms, including both annual and semi-annual periods, describe ZTD’s temporal variation. Moreover, SHAtropE also provides the predicted ZTD uncertainty, which is valuable in Precise Point Positioning (PPP) with ZTD being constrained for faster convergence. The data of 310 GNSS sites over 7 years were used to validate the new model. Results show that the SHAtropE ZTD has an accuracy of 3.5 cm in root mean square (RMS) quantity, which has a mean improvement of 35.2% and 5.4% over the UNB3m (5.4 cm) and GPT3 (3.7 cm) models, respectively. The predicted uncertainty of SHAtropE ZTD shows seasonal variations, where the values are larger in summer than in winter. By applying the SHAtropE model in the static PPP, the convergence time of GPS-only and BDS-only solutions are reduced by 8.1% and 14.5% respectively compared to the UNB3m model, and the reductions are 6.9% and 11.2% respectively for the GPT3 model. As no meteorological data are required for the implementation of the model, the SHAtropE could thus be a refined tropospheric model for GNSS users in mainland China and the surrounding areas. The method of modeling the ZTD uncertainty can also be used in further global tropospheric delay modeling.

Precipitable water vapor (PWV) is an important component in the climate system and plays a pivotal role in the global water and energy cycles. Over the years, many approaches have been devised to accurately estimate the PWV. Among them, global navigation satellite systems (GNSS) have become one of the most promising and fastest-growing PWV acquisition methods because of its high accuracy, high temporal and spatial resolution, and ability to acquire PWV in all weather and in near real time. We compared GNSS-derived PWV with a 5 min resolution globally distributed over 14,000 stations from the Nevada Geodetic Laboratory (NGL) from 1994 to 2020 with global radiosonde (RS) data, temperature anomalies, and sea height variations. Then, we examined the temporal and spatial variability of the global PWV and analyzed its climate implications. On a global scale, the average bias and root mean square error (RMSE) between GNSS PWV and RS PWV were ~0.72 ± 1.29 mm and ~2.56 ± 1.13 mm, respectively. PWV decreased with increasing latitude, and the rate of this decrease slowed down at latitudes greater than 35°, with standard deviation (STD) values reaching a maximum at latitudes less than 35°. The global average linear trend was ~0.64 ± 0.81 mm/decade and strongly correlated with temperature and sea height variations. For each 1 °C and 1 mm change, PWV increased by ~2.075 ± 0.765 mm and ~0.015 ± 0.005 mm, respectively. For the time scale, the PWV content peaked ~40 days after the maximum solar radiation of the year (the summer solstice), and the delay was ~40 days relative to the summer solstice.

Numerical weather models (NWMs) are important data sources for space geodetic techniques. Additionally, the Global Navigation Satellite System (GNSS) provides many observations to continuously improve and enhance the NWM. Existing comparative analysis experiments on NWM tropospheric and GNSS tropospheric delays suffer from being conducted in highly specific regions with limited spatial coverage; furthermore, the length of time for the experiment is too short for analyzing seasonal characteristics, and the insufficient number of stations limits spatial density, making it difficult to obtain the equipment-dependent distribution characteristics. After strict quality control and data preprocessing, we have calculated and compared the bias and standard deviation of tropospheric delay for approximately 7000 selected Nevada Geodetic Laboratory (NGL) GNSS stations in 2020 with the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5) hourly ray-traced tropospheric delay for the same group of stations. Characterizations in time, space, and linkage to receivers and antennas reveal positive biases of approximately 4 mm in the NGL zenith tropospheric delay (ZTD) relative to the NWM ZTD over most of the globe; moreover, there is a seasonal amplitude reaching 6 mm in the bias, and an antenna-related mean bias of approximately 1.6 mm in the NGL tropospheric delay. The obtained results can be used to provide a priori tropospheric delays with appropriate uncertainties; additionally, they can be applied to assess the suitability of using NWMs for real-time positioning solutions.

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 (FM), 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 ERA5 (European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5), ground-based GNSS (Global Navigation Satellite System) and in-situ radiosonde 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 10 days in advance. This research demonstrates the potential of AI weather forecast foundation models in delivering high-precision tropospheric delay medium-range forecasts, improvements for real-time remote sensing applications.

High-quality precipitable water vapor (PWV) plays a vital role in climate change and weather prediction studies. This research introduces a novel scheme for retrieving high-resolution surface-domain PWV with real-time and forecasting capabilities with global coverage, utilizing weather forecast foundation models represented by Huawei Cloud Pangu-Weather, Google DeepMind GraphCast, and Shanghai AI Lab FengWu. The accuracy of the new scheme is cross-validated against PWVs from radiosondes, Global Navigation Satellite Systems (GNSSs), and the fifth generation ECMWF reanalysis (ERA5). Results show the new scheme achieves 3.01 mm global root mean square error (RMSE) in real-time, and the value reduce to 2.25 mm when focusing only on land areas, which is more accurate than most existing methods that rely on post-processed surface-domain data. The poor accuracy in low-latitude and mid-latitude ocean regions limits the accuracy of the new scheme and future integration of GNSS PWV data from ocean sources is expected to improve it. Overall, the proposed scheme demonstrates very satisfactory global PWV accuracy and has the potential for further improvement with the development of artificial intelligence.