A high-precision zenith tropospheric delay forecasting model using ET-based spatial interpolation compensation and CNN-LSTM multi-step time series prediction

Zenith Tropospheric Delay (ZTD) plays a vital role in high-precision navigation, positioning and precipitable water vapor retrieval using the Global Navigation Satellite System (GNSS). Based on the ERA5 data and hourly ZTD data provided by the Crustal Movement Observation Network of China (CMONOC) from 2011 to 2018, along with the most recent 24-hour data, this study proposes a high-precision ZTD forecasting model (ECLtrop). This new model can forecast the next 24-hour ZTDs at any spacial point in the study area (i.e., the Chinese mainland). Our new model integrates spatial interpolation, long-term Fourier prediction, and short-term time series forecasting (TSF). Specifically, historical data from 2011 to 2018 is first reconstructed using spatial interpolation, with an Extra Trees (ET) model compensating for discrepancies between ERA5-derived and GNSS-derived ZTDs. Then a long-term ZTD prediction (EFtrop) can be obtained by fitting these historical data with Fourier time-series functions. Finally, short-term corrections are applied using TSF models. Two types of TSF models are tested: Long Short-Term Memory (LSTM) and CNN-LSTM, resulting in ELtrop and ECLtrop, respectively. To test the validation of our new model, two sets of test stations are randomly chosen. Results show that the ET-based spatial interpolation compensation method effectively remove the systematic bias between ERA5-derived ZTD and GNSS-derived ZTD. Meanwhile, EFtrop (RMSE: 3.33cm, 3.67cm), ELtrop (RMSE: 2.30cm, 2.48cm) and ECLtrop (RMSE: 2.19cm, 2.38cm) demonstrate average improvements of 4%, 34%, and 37%, respectively, compared to GPT3 (RMSE: 3.52cm, 3.77cm). The results highlight the effectiveness of TSF models, particularly CNN-LSTM, in enhancing ZTD prediction accuracy.