AGFS: a two-step real-time tropospheric delay model by integrating GNSS, ERA5, and GFS

Tropospheric delay is a major error source in high-precision positioning with global navigation satellite systems (GNSS). However, accurately modeling tropospheric delay remains challenging, particularly for real-time applications in regions with sparse GNSS coverage and large elevation differences. In this study, we propose a two-step real-time tropospheric delay model that accounts for sparse stations and topographic variations. The model integrates GNSS tropospheric delays with the fifth-generation European Center for Medium-Range Weather Forecasts (ECMWF) reanalysis dataset (ERA5) and the Global Forecast System (GFS), resulting in the augmented-GFS (AGFS). The AGFS model enhances ERA5 tropospheric delays with GNSS data (GERA5), models the residual differences with GFS using trigonometric functions, and applies the corrections to GFS to generate real-time tropospheric delay estimates. In addition, the vertical stratification of tropospheric delay is modeled using ERA5 pressure-level data. The model was trained using data from 1385 GNSS stations in the Plate Boundary Observatory (PBO) network across the United States from 2020 to 2022, and validated using 154 GNSS stations in 2023. The results demonstrate that the AGFS model significantly outperforms GFS and Vienna Mapping Functions 3 Forecast (VMF3-FC), achieving improvements of over 35% in root mean square error (RMSE) for zenith hydrostatic delay (ZHD), with an RMSE of 3.12 mm. For zenith wet delay (ZWD), the model achieves over 13% improvement, with an RMSE of 12.03 mm. Temporally, AGFS exhibits stable performance across all seasons, with particularly notable improvements in summer (54.7% for ZHD and 11.8% for ZWD compared to GFS). Spatially, AGFS performs better than GFS and VMF3-FC at all validated stations, especially those at higher elevations. In kinematic precise point positioning (PPP) tests, AGFS reduced convergence time by 17.3% compared to standard PPP, exceeding GFS (15.5%) and VMF3 (14.1%). These results demonstrate that AGFS provides accurate real-time tropospheric corrections and enhances precise GNSS positioning.