Vertical variation modeling of the tropospheric horizontal gradient

Accurate modeling of the horizontal and vertical variation of the tropospheric horizontal gradient is crucial for correcting space-geodetic tropospheric delays and retrieving atmospheric water vapor. To date, the horizontal variation in the gradient has been well represented by the operational grid-wise products, such as grid-wise GRAD. However, for vertical variation, the relative methods and models are unavailable, which limits the accuracy of the grid-wise products by ignoring the vertical variation from grid height to target height. In this contribution, we analyze the variation characteristics of the asymmetric delay and the horizontal gradient using ERA5 data and the ray-tracing technique, and confirm their significant reductions with height. Then, we introduce a new height-correction method that adjusts for vertical variation in the horizontal gradient based on its characteristic behavior, and the results demonstrate that accounting for height variation can significantly reduce residuals in horizontal gradient modeling. Finally, we developed a global model using this method and validated it against the grid-wise GRAD products, with the site-wise GRAD products as the reference. The results demonstrate that the height-correction model can significantly improve the accuracy of grid-wise GRAD at high-altitude locations, making it suitable for high-altitude stations and unmanned aerial vehicle applications.