Accurate tropospheric delays from Numerical Weather Models (NWM) are an important input to space geodetic techniques, especially for precise real‐time Global Navigation Satellite Systems, which are indispensable to earthquake and tsunami early warning systems as well as weather forecasting. The NWM‐based tropospheric delays are currently provided either site‐specific with a limited spatial coverage, or on two‐dimensional grids close to the Earth surface, which cannot be used for high altitudes. We introduce a new method of representing NWM‐derived tropospheric zenith hydrostatic and wet delays. A large volume of NWM‐derived data is parameterized with surface values and additional two or three coefficients for their vertical scaling to heights up to 14 km. A precision of 1–2 mm is achieved for reconstructing delays to the NWM‐determined delays at any altitudes. The method can efficiently deliver NWM‐derived tropospheric delays to a broader community of space geodetic techniques.

The performance of precise point positioning (PPP) has been significantly improved thanks to the continuous improvements in satellite orbit, clock, and ambiguity resolution (AR) technologies, but the convergence speed remains a limiting factor in real-time PPP applications. To improve the PPP precision and convergence time, tropospheric delays from a regional network can be modeled to provide precise correction for users. We focus on the precise modeling of zenith wet delay (ZWD) over a wide area with large altitude variations for improving PPP-AR. By exploiting the water vapor exponential vertical decrease, we develop a modified optimal fitting coefficients (MOFC) model based on the traditional optimal fitting coefficients (OFC) model. The proposed MOFC model provides a precision better than 1.5 cm under sparse inter-station distances over the Europe region, with a significant improvement of 70% for high-altitude stations compared to the OFC model. The MOFC model with different densities of reference stations is further evaluated in GPS and Galileo kinematic PPP-AR solutions. Compared to the PPP-AR solutions without tropospheric delay augmentation, the positioning precision of those with 100-km inter-station spacing MOFC and OFC is improved by 25.7% and 17.8%, respectively, and the corresponding time to first fix (TTFF) is improved by 36.9% and 33.0% in the high-altitude areas. On the other hand, the OFC model only slightly improves the TTFF and positioning accuracy when using the 200 km inter-station spacing modeling and even degrades the positioning for high-altitude stations, whereas using the MOFC model, the PPP-AR solutions always improve. Moreover, the positioning precision improvement of MOFC compared with OFC is about 22.1%, 21.7%, and 25.7% for the Galileo-only, GPS-only, and GPS + Galileo PPP-AR solutions, respectively.

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.

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.