Real-time high-precision zenith tropospheric delay stable mapping strategy for sparse stations

Zenith tropospheric delay (ZTD) represents the signal retardation of electromagnetic waves propagating through the neutral atmosphere, serving as both a critical error source in satellite navigation and a valuable parameter for meteorological applications. Global Navigation Satellite System (GNSS) technology provides high-precision ZTD estimation, but sparse station coverage poses fundamental challenges for real-time ZTD mapping, particularly in regions with complex terrain where conventional interpolation methods exhibit limited accuracy due to inadequate characterization of ZTD’s vertical stratification. Here we present a hierarchical framework incorporating two methods: ZTD-ER, combining a three-dimensional voxel empirical model (EZTD) with radial basis function interpolation, and ZTD-GR, integrating Global Forecast System (GFS) data with radial basis function interpolation. The respective average RMSE values are 6.85 mm and 5.90 mm. We found that this represents accuracy improvements of 46–67 % compared to traditional polynomial and spherical harmonic methods, while the EZTD-based approach maintains near-optimal performance (6.85 mm RMSE) even when GFS data is unavailable, demonstrating superior robustness across different elevations and seasons. Our results provide a reliable solution for high-precision real-time ZTD mapping in challenging regions where GNSS networks are sparse. This strategy addresses critical limitations in current tropospheric modeling capabilities, offering enhanced spatial resolution for real-time GNSS meteorological monitoring and improved atmospheric corrections for precision satellite navigation applications. The framework’s operational flexibility and demonstrated accuracy make it particularly valuable for extreme weather early warning systems in sparse stations areas around the world.