Hybrid Machine-Learning Framework for Slant Wet Delay Modeling

Tropospheric wet delay remains a key error source for space geodesy, including GNSS, VLBI, and InSAR. Empirical models such as GPT3 are widely used, yet they rely on simplified parameterizations and fixed coefficient tables that limit modeling capacity. Frequent updates are difficult because the entire archive must be reprocessed. With the rapid progress of machine learning, it is natural to seek ML-based tropospheric models that improve both accuracy and efficiency. To date, most work has focused on zenith wet delay (ZWD), which is essentially one-dimensional, while fully data-driven slant modeling has been largely unexplored. Slant wet delays (SWD) are inherently anisotropic, which makes the task more challenging.

We propose a hybrid ML framework that embeds a physical layer inside the network to predict SWD end-to-end and yields consistent ZWD and wet mapping function as internal outputs. Training uses hundreds of millions of ERA5 ray-traced samples from 2018 to 2022 with global coverage. The resulting ML model outperforms GPT3 for SWD, with markedly lower errors over continental regions where most space-geodetic stations operate and with the largest gains at low elevation angles and along coasts. The learned mapping is asymmetric in elevation and azimuth, which removes the need for explicit horizontal gradients. As ancillary products, the framework provides ZWD that surpasses GPT3 and a wet mapping function that exceeds the symmetric GPT3 variant and is comparable to the asymmetric one. We also develop augmented variants that accept surface temperature and water vapor pressure as inputs and obtain further accuracy gains. To our knowledge, this is the first ML-based model that directly predicts SWD. The model is compact and faster than GPT3 when applied to large sample sets. The hybrid design supports efficient fine-tuning with new observations and provides a practical path to maintainable routine processing and continued advances in space-geodetic troposphere modeling.