Spatiotemporal Forecasting Method for GNSS Water Vapor Integrating an Empirical Periodic Model and ConvLSTM

Objectives: Atmospheric precipitable water vapor (PWV) plays a crucial role in natural atmospheric processes. Its accurate monitoring and forecasting are of great importance for extreme weather early warning and for correcting signal delays in satellite-based Earth observation. Methods: A regional recursive forecasting model for GNSS-derived PWV is developed by integrating an empirical periodic model with a Convolutional Long ShortTerm Memory (ConvLSTM) neural network, using observations collected from the Kunming Continuously Operating Reference Station (CORS) network during 2023-2024. Meanwhile, the Lomb-Scargle (LS) method is introduced to detect periodic signals in the PWV time series, and a Fourier series is employed to establish an empirical periodic model characterizing PWV variations in the Kunming region. Second, the periodic component is separated from the original PWV observations collected in 2023, and a PWV residual field without evident periodic patterns is obtained. ConvLSTM is then used to learn the spatiotemporal variation characteristics of the PWV residual field and to construct a residual-based recursive forecasting model. Finally, the empirical periodic model iscombined with the ConvLSTM residual forecasting model to obtain a short-term regional recursive PWV forecasting model for Kunming. Compared with purely black-box models, the proposed method achieves satisfactory fitting performance while offering stronger interpretability. Results: The forecasting accuracy is evaluated using independent observations from 2024. The results show that the root mean square error (RMSE) of the one-hourahead PWV forecast is 0.86 mm. It is further demonstrated by the recursive forecasting experiments that the RMSE remains below 1.27 mm for forecast horizons of up to 12 h. Conclusions: Although the forecasting performance gradually decreases with increasing forecast horizon, the proposed model still outperforms the direct forecasting strategy. The integrated method provides a new approach for two-dimensional PWV field forecasting, with forecast products supporting meteorological disaster early warning and high-precision positioning.