A global refractive index structure constant model for enhanced tropospheric simulations of space geodetic observations

Simulation studies are an essential tool in space geodesy. They support the optimization of ground and space networks, the exploration of innovative concepts, and the advancement of technological developments. Beyond measurement noise, realistic simulations must incorporate various error sources, including atmospheric effects, clock drift, and technology-related issues. For many space geodetic techniques, accurate simulations of tropospheric effects, particularly incorporating spatio-temporal correlations, are essential in this context. 

Traditionally, high-quality tropospheric simulations popular in the Very Long Baseline Interferometry (VLBI) technology rely on Kolmogorov turbulence theory combined with the frozen flow assumption. These simulations are parameterized using the refractive index structure constant (C_n), alongside auxiliary parameters like wind velocity and troposphere height. Although C_n values can be derived from Global Navigation Satellite System (GNSS) observations, most existing studies assume a generalized average troposphere, largely independent of specific locations or seasonal variations. Only a few incorporate location-based conditions, often through a simplistic latitude-based interpolation. Furthermore, reliance on GNSS data limits the ability to test potential network extensions when such observations are not available. 

This work enhances tropospheric simulations by introducing a global, three-dimensional (latitude, longitude, time) C_n model. The model is trained using zenith wet delay (ZWD) estimates from 21,000 globally distributed GNSS stations (2000–2023) and leverages meteorological data from the ERA5 reanalysis, including specific humidity across 11 pressure levels (1000 to 300 hPa) and wind velocity as features. Utilizing the XGBoost algorithm, the model supports short-term prediction scenarios with HRES weather forecasts and provides model uncertainty through an ensemble strategy. The proposed model is able to effectively capture the spatio-temporal patterns in the input data and provides high accuracy, allowing for enhanced simulations of space geodetic observations operating at radio frequencies such as VLBI and GNSS. Additionally, global monthly average estimates on a 0.25° x 0.25° latitude, longitude grid can be derived, offering a practical solution with sufficient accuracy for most simulation studies.