MSWD: A Hybrid Machine-Learning Framework for Slant Wet Delay Modeling

Space geodetic techniques such as Global Navigation Satellite Systems (GNSS) and Very Long Baseline Interferometry (VLBI) are limited by direction-dependent tropospheric delays, with the slant wet delay (SWD) being the most variable component and a major source of error. Accurate SWD priors can accelerate convergence, stabilize parameter estimation, and improve positioning and atmospheric retrievals. Existing global empirical models, such as the state-of-the-art GPT3 model, reconstruct SWD through a fixed pipeline of zenith wet delay (ZWD), wet mapping function (MFw), and wet horizontal gradients. They rely on simplified parameterizations and fixed coefficient tables, and because re-estimating the full set of parameters is burdensome, products are rarely updated to reflect current conditions. In this paper, we present a hybrid machine-learning (ML) framework that embeds the established tilting mapping function formulation directly into the network, enabling end-to-end prediction of SWD. To our knowledge, this is the first ML model that outputs SWD directly. We also developed augmented variants that accept temperature and water vapor pressure as optional inputs for higher accuracy. Trained on five years of globally distributed ERA5-based SWD samples, the model delivers markedly lower errors than GPT3 over continental regions, where most space-geodetic stations operate. As ancillary products it can also output ZWD and MFw, with ZWD surpassing GPT3 and MFw exceeding the performance of the symmetric GPT3 variant while remaining slightly below that of the asymmetric variant. Besides the performance gains, this hybrid ML framework streamlines model maintenance and advances SWD modeling in space geodesy.