GFZTD: A Multimodal Fusion-Driven 3-D Tropospheric Delay Prediction Model Coupling Self-Attention and ConvLSTM

Tropospheric delay, for which water vapor is a major cause, is a significant source of error in Global Navigation Satellite System (GNSS). This paper presents the GFZTD (Gray Figure-based Zenith Tropospheric Delay prediction) model, which is built on Convolutional Long Short-Term Memory Networks (ConvLSTM) and self-attention mechanisms. The model converts three-dimensional (3-D) zenith tropospheric delay (ZTD) grid products into multi-layer two-dimensional grayscale images for predictive analysis. Utilizing Global Forecast System (GFS) and ERA5 data from southeastern China and its adjacent seas in 2023, the GFZTD model is trained through seasonal slicing and stratification by altitude. This approach generates high spatio-temporal resolution ZTD 3-D grid products in near real-time. To evaluate the grid prediction results, ERA5 is used as the truth, with an overall RMSE of 1.35 cm, representing improvements of 26.5% and 71.0% over ZTD derived from GFS and GPT3 (Global Pressure and Temperature 3), respectively. The model also successfully mitigates regional extreme prediction errors in complex terrain environments for GFS. Additionally, when using VMF3 (Vienna Mapping Functions 3) post-processing products to assess ZTD prediction values at various stations, the GFZTD model shows an average root mean square error (RMSE) of 1.49 cm. This result indicates improvements of 13.1% and 69.4% compared to GFS and GPT3, respectively, underscoring the model's applicability at the station scale.