Enhancing GNSS water vapor tomography using machine learning-generated virtual tropospheric delays

The accuracy of ground-based Global Navigation Satellite System (GNSS) tomography is constrained by the ill-posed inverse problem, particularly in regions with sparse station coverage. To address this limitation, this study proposes an augmented tomography framework that introduces virtual observations to improve the observation geometry. A LightGBM model, incorporating Digital Elevation Model (DEM) data and ERA5 priors, was developed to predict virtual Slant Wet Delay (SWD) values. These virtual rays are integrated into the tomographic system to provide constraints for voxels unprobed by real signals, thereby reducing reliance on empirical smoothing constraints. Validation against radiosonde profiles and ERA5 data across four station density scenarios (S1–S4) yields two primary results. First, the proposed method improves reconstruction accuracy compared to the traditional approach. The sparse scenario (S4, 40 real stations) achieved an RMSE of 9.08 mm/km, outperforming the traditional benchmark (123 real stations, RMSE 11.51 mm/km) by approximately 21%. Notably, the method reduced the systematic negative bias in the Planetary Boundary Layer (0–2 km) from −11.16 to −5.67 mm/km. Second, a comparison between scenarios reveals that the reduced network (S2) marginally outperformed the dense network (S1). This suggests that once the observation geometry is stabilized by virtual rays, mitigating geometric conflicts from redundant observations contributes more to solution quality than maximizing station density. These findings indicate that the proposed framework is an effective approach for high-resolution water vapor reconstruction in data-sparse regions.