A refined tropospheric zenith wet delay model for GNSS applications over the Tibetan Plateau

Significant spatial heterogeneity of tropospheric water vapor over the Tibetan Plateau, particularly along the vertical dimension, presents a major challenge to traditional tropospheric wet delay models used in GNSS applications across large height ranges. To address this issue, we developed a refined Tibetan zenith wet delay (ZWD) model based on pressure-level ERA5 reanalysis data with a spatial resolution of 0.25°, providing ZWD estimates at arbitrary times and heights. The model adopts an improved vertical correction in which ZWD vertical profiles are represented by a cubic polynomial height-correction function. The polynomial coefficients are estimated at each ERA5 grid node using ERA5-derived ZWD profiles and are further parameterized using harmonics up to the semidiurnal term to characterize temporal variability. ZWD at user locations is obtained through bilinear interpolation of the four surrounding grid nodes, ensuring continuous spatial and vertical coverage over Tibet. Validation using ERA5- and radiosonde-derived ZWDs shows that the TZ model achieves lower bias and reduced root-mean-square error (RMSE) than the widely used GPT3 model at both surface and elevated layers. These results indicate stable performance of the model across the full altitude range. The proposed model can be readily integrated into GNSS positioning frameworks. In precise point positioning (PPP), it may be introduced as a virtual observation of ZWD, with the model RMSE used to define the initial measurement-noise covariance. As the model provides a priori information rather than true observations, a time-varying down-weighting strategy is applied so that the ZWD estimation progressively relies on actual GNSS observations. In network real-time kinematic (NRTK) applications with large height differences, model-derived ZWD combined with mapping functions can be used to mitigate height-dependent double-differenced tropospheric delay residuals. This improves positioning accuracy, especially in the vertical component.