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<p>Short-term spatio-temporal forecasting of zenith tropospheric delay (ZTD) is beneficial for high-precision global navigation satellite system (GNSS) positioning and meteorological applications. Therefore, it is necessary to develop a short-term spatio-temporal model for ZTD forecasting over a 1–24&#xa0;h horizon. A spatio-temporal iterative ZTD forecasting model combining the convolutional long short-term memory neural network (ConvLSTM) and a periodic model is proposed based on the European Centre for Medium-range Weather Forecast (ECMWF) Reanalysis 5 (ERA5) data and the GNSS data from the Crustal Movement Observation Network of China (CMONOC) during 2019–2023. Firstly, an ERA5 ZTD modified model is constructed based on the back propagation neural network (BPNN) and GNSS ZTD. Secondly, the Lomb-Scargle (LS) method is used to detect long-term periodicities of modified ERA5 (modERA5) ZTD and the periodic model is constructed using Fourier fitting. Then the ZTD residuals are obtained by subtracting the periodic model from the modERA5 ZTD, and the spatio-temporal variations of the ZTD residuals are learned and predicted based on ConvLSTM. For ConvLSTM training, the input consists of the ZTD residual sequence from the preceding 24&#xa0;h, and the ZTD residual of the subsequent hour is used as the output. Finally, the forecasted ZTD residuals are combined with the periodic model to obtain the final forecasted ZTD. The results indicate that the Bias of the modERA5 ZTD is 0.01&#xa0;mm, which proves that the modified model effectively eliminates the systematic deviation. The ConvLSTM 1-h ZTD forecasting model has an RMSE of 2.82&#xa0;mm and an STD of 2.81&#xa0;mm. The ZTD forecasting model proposed in this study exhibits strong performance with RMSE values ranging from 2.9&#xa0;mm to 9.8&#xa0;mm when the forecasting horizon is between 1 and 12&#xa0;h. The forecasting accuracy will decrease as the forecast step increases, and the forecasting accuracy is about 15&#xa0;mm when the forecast step reaches 24&#xa0;h. The findings also reveal that the iterative forecasting strategy enhances multi-step predictions. The proposed model outperforms existing site-based ZTD forecasting approaches by jointly considering temporal and spatial variations while ensuring high predictive accuracy. Additionally, the inclusion of a periodic component improves model interpretability, providing new insights and potential advances for GNSS meteorology.</p>

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A hybrid deep learning and empirical model for short-term spatio-temporal ZTD forecasting for China

  • 期刊论文

  • 发表日期：

    2026年4月17日

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  • Xiongwei Ma,
  • Haoran Huang,
  • Qi Zhang,
  • Bao Zhang,
  • Qingzhi Zhao,
  • Xiaohu Lin,
  • Yunzheng Huang,
  • Yiyang Zhao,
  • Yibin Yao

摘要

Short-term spatio-temporal forecasting of zenith tropospheric delay (ZTD) is beneficial for high-precision global navigation satellite system (GNSS) positioning and meteorological applications. Therefore, it is necessary to develop a short-term spatio-temporal model for ZTD forecasting over a 1–24 h horizon. A spatio-temporal iterative ZTD forecasting model combining the convolutional long short-term memory neural network (ConvLSTM) and a periodic model is proposed based on the European Centre for Medium-range Weather Forecast (ECMWF) Reanalysis 5 (ERA5) data and the GNSS data from the Crustal Movement Observation Network of China (CMONOC) during 2019–2023. Firstly, an ERA5 ZTD modified model is constructed based on the back propagation neural network (BPNN) and GNSS ZTD. Secondly, the Lomb-Scargle (LS) method is used to detect long-term periodicities of modified ERA5 (modERA5) ZTD and the periodic model is constructed using Fourier fitting. Then the ZTD residuals are obtained by subtracting the periodic model from the modERA5 ZTD, and the spatio-temporal variations of the ZTD residuals are learned and predicted based on ConvLSTM. For ConvLSTM training, the input consists of the ZTD residual sequence from the preceding 24 h, and the ZTD residual of the subsequent hour is used as the output. Finally, the forecasted ZTD residuals are combined with the periodic model to obtain the final forecasted ZTD. The results indicate that the Bias of the modERA5 ZTD is 0.01 mm, which proves that the modified model effectively eliminates the systematic deviation. The ConvLSTM 1-h ZTD forecasting model has an RMSE of 2.82 mm and an STD of 2.81 mm. The ZTD forecasting model proposed in this study exhibits strong performance with RMSE values ranging from 2.9 mm to 9.8 mm when the forecasting horizon is between 1 and 12 h. The forecasting accuracy will decrease as the forecast step increases, and the forecasting accuracy is about 15 mm when the forecast step reaches 24 h. The findings also reveal that the iterative forecasting strategy enhances multi-step predictions. The proposed model outperforms existing site-based ZTD forecasting approaches by jointly considering temporal and spatial variations while ensuring high predictive accuracy. Additionally, the inclusion of a periodic component improves model interpretability, providing new insights and potential advances for GNSS meteorology.