Enhancing the accuracy of GNSS tomography with an empirical stochastic model

Global Navigation Satellite Systems (GNSS) tomography is a modern technique that leverages GNSS satellites and ground-based network stations for meteorological applications, with a particular focus on studying the dynamics of water vapor. Over the past two decades, various approaches have been proposed, but assessing the accuracy of these methods remains challenging. In this study, we introduce an empirical stochastic model for GNSS tomography. This model is formulated as a fully populated covariance-variance matrix that incorporates the variance of the GNSS-Integrated Water Vapor (IWV) solution, the spherical distance between station-satellite signal paths, and an empirical covariance-variance function. Our findings indicate that combining the functional model with the stochastic model significantly improves the estimation of unknown parameters, suggesting a method for enhancing the accuracy and reliability of GNSS tomographic solutions. We compared the standard tomography solution, both with and without stochastic information, with data from radiosondes, ERA5 reanalysis, and the WRF model. The results demonstrate that incorporating the empirical stochastic model can improve the solution accuracy by 10%. More importantly, it provides a valuable tool for evaluating the trustworthiness of tomographic solutions.