Zenith tropospheric delay (ZTD) is a significant atmospheric error that impacts the Global Navigation Satellite System (GNSS). Developing a high-precision, long-term forecasting model for ZTD can provide valuable insights into the overall trends of predicted ZTD, which is essential for improving GNSS positioning and analyzing changes in regional climate and water vapor. To address the challenges of incomplete information extraction and gradient explosion in a single neural network when forecasting ZTD long-term, this study introduces an Informer-LSTM Hybrid Prediction Model. This model employs a parallel ensemble learning strategy that combines the strengths of both the Informer and LSTM networks to extract features from ZTD data. The Informer model is effective at capturing the periodicity and long-term trends within the ZTD data, while the LSTM model excels at understanding short-term dependencies and dynamic changes. By merging the features extracted by both models, the prediction capabilities of each can complement one another, allowing for a more comprehensive analysis of the characteristics present in ZTD data. In our research, we utilized ERA5-derived ZTD data from 11 International GNSS Service (IGS) stations in Europe to interpolate the missing portions of GNSS-derived ZTD. We then employed this interpolated data from 2016 to 2020, along with an Informer-LSTM Hybrid Prediction Model, to develop a long-term prediction model for ZTD with a prediction duration of one year. Our numerical results demonstrate that the proposed model outperforms several comparative models, including the LSTM-Informer based on a serial ensemble learning model, as well as the Informer, Transformer, LSTM, and GPT3 empirical ZTD models. The performance metrics indicate a root mean square error (RMSE) of 1.91 cm, a mean absolute error (MAE) of 1.45 cm, a mean absolute percentage error (MAPE) of 0.60, and a correlation coefficient (R) of 0.916. Spatial distribution analysis of the accuracy metrics showed that predictive accuracy was higher in high-latitude regions compared to low-latitude areas, with inland regions demonstrating better performance than those near the ocean. This study introduced a novel methodology for high-precision ZTD modeling, which is significant for improving accurate GNSS positioning and detecting water vapor content.
