Accurate prediction of Global Navigation Satellite System-derived precipitable water vapor (GNSS-PWV), which is a crucial indicator for climate change monitoring, holds significant scientific value for climate disaster prevention and mitigation. In the study of GNSS-PWV prediction, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm within a decomposition–integration framework effectively addresses the non-stationarity and complexity of PWV sequences, enhancing prediction accuracy. However, residual noise and pseudo-modes from decomposition can distort signals, reducing the predictor system’s reliability. Additionally, independent modeling of all decomposed components decreases computational efficiency. To address these challenges, this paper proposes a hybrid model combining the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), autoregressive integrated moving average (ARIMA), and long short-term memory (LSTM) networks. Enhanced by local mean optimization and adaptive noise regulation, the ICEEMDAN algorithm effectively suppresses pseudo-modes and minimizes residual noise, enabling its decomposed intrinsic mode functions (IMFs) to more accurately capture the multi-scale features of GNSS-PWV. Sample entropy (SE) is used to quantify the complexity of IMFs, and components with similar entropy values are reconstructed into the following three sub-sequences: high-frequency, low-frequency, and trend. This process significantly reduces modeling complexity and improves computational efficiency. We propose different modeling strategies tailored to the dynamics of various subsequences. For the nonlinear and non-stationary high-frequency components, the LSTM network is used to effectively capture their complex patterns. The LSTM’s gating mechanism and memory cell design proficiently address the long-term dependency issue. For the stationary and weakly nonlinear low-frequency and trend components, linear patterns are extracted using ARIMA. Differencing eliminates trends and moving average operations capture random fluctuations, effectively addressing periodicity and trends in the time series. Finally, the prediction results of the three components are linearly combined to obtain the final prediction value. To validate the model performance, experiments were conducted using measured GNSS-PWV data from several stations in Hong Kong. The results demonstrate that the proposed model reduces the root mean square error by 56.81%, 37.91%, and 13.58% at the 1 h scale compared to the LSTM, EMD-LSTM, and ICEEMDAN-SE-LSTM benchmark models, respectively. Furthermore, it exhibits strong robustness in cross-month forecasts (accounting for seasonal influences) and multi-step predictions over the 1–6 h period. By improving the accuracy and efficiency of PWV predictions, this model provides reliable technical support for the real-time monitoring and early warning of extreme weather events in Hong Kong while offering a universal methodological reference for multi-scale modeling of geophysical parameters.

Zenith Tropospheric Delay (ZTD) is a significant source of atmospheric error in the Global Navigation Satellite System (GNSS). Developing a high-accuracy ZTD prediction model is essential for both GNSS positioning and GNSS meteorology. To address the challenges of incomplete information extraction and gradient explosion present in current single and combined neural network models that utilize serial ensemble learning, this study proposes a VMD-Informer-BiLSTM-EAA hybrid model based on a parallel ensemble learning strategy. Additionally, it takes into account the non-stationarity of the ZTD sequence. The model employs the Variational Mode Decomposition (VMD) method to address the non-stationarity of ZTD. It utilizes both the informer and Bidirectional Long Short-Term Memory (BiLSTM) architectures to learn ZTD data in parallel, effectively capturing both long-term trends and short-term dynamic changes. The features are then fused using the Efficient Additive Attention (EAA) mechanism, which assigns weights to create a more comprehensive representation of the ZTD data. This enhanced representation ultimately leads to improved predictions of ZTD values. We fill in the missing parts of the GNSS-derived ZTD using the ZTD data from ERA5, sourced from the IGS stations in the Australian region, specifically at 12 IGS stations. These interpolated data are then used to develop a VMD-Informer-BiLSTM-EAA hybrid model for ZTD predictions with a one-year forecast horizon. We applied this model to predict the ZTD for each IGS station in our study area for the year 2021. The numerical results indicate that our model outperforms several comparative models, such as VMD–Informer, Transformer, BiLSTM and GPT3, based on the following key metrics: a Root Mean Square Error (RMSE) of 1.43 cm, a Mean Absolute Error (MAE) of 1.15 cm, a Standard Deviation (STD) of 1.33 cm and a correlation coefficient (R) of 0.96. Furthermore, our model reduces the training time by 8.2% compared to the Transformer model, demonstrating superior prediction performance and robustness in long-term ZTD forecasting. This study introduces a novel approach for high-accuracy ZTD modeling, which is significantly beneficial for precise GNSS positioning and the detection of water vapor content.