Zenith Wet Delay Modeling in Local-Scale with Large Elevation Differences Using Random Forest and LSTM

Objectives: In the complex meteorological environment of mountainous regions, the rapid and accurate modeling of zenith wet delay (ZWD) is of vital importance for Continuously Operating Reference Station (CORS) to ensure stable and reliable high-precision positioning services. ZWD is highly sensitive to atmospheric water vapor variations and exhibits significant temporal and spatial variability, particularly in regions with large elevation differences. However, most existing ZWD modelling approaches, are developed for large-scale domains and rely on long-term historical datasets, which limits their applicability to localized, short-term and high-frequency modelling scenarios. Methods: To address this limitation, we selected the northwestern region of Sichuan Province, China, as the target area. This region is characterized by complex terrain and substantial elevation differences. Utilizing 21 consecutive days of GNSS observational data from CORS stations and measurements of temperature, humidity, and atmospheric pressure from nearby surface meteorological stations, we first performed temporal and spatial alignment of the two datasets to ensure data consistency across all stations and epochs. Based on correlation and sensitivity analyses, a set of representative input features was identified, and the appropriate sequence length required for establishing temporal dependencies in the Long Short-Term Memory (LSTM) model was also determined. We then investigated two data-driven approaches for rapid ZWD modeling: the Random Forest (RF) algorithm and the LSTM neural network. After determining the appropriate hyperparameters for each model and completing rapid training, the models were further applied for the prediction and analysis focusing on temporal and spatial generalization. Results: Experimental results demonstrate that both RF and LSTM models significantly outperform the global pressure and temperature 3 (GPT3) model in terms of representational and predictive capabilities. (1) In terms of model fitting performance, the RF model exhibits no evident systematic bias, with a mean bias of -0.27 mm compared to GPT3’s large bias of -22.78 mm. Its root mean squared error (RMSE) reaches 17.60 mm, representing a 57.5% improvement over GPT3. The LSTM model shows a slightly larger bias of 2.33 mm than RF, yet achieves a lower RMSE of 14.29 mm. (2) For short-term forecasting, a 10-day time window was adopted, and the models were used to predict the ZWD of the following day in a sliding manner. The RF and LSTM models achieved near-zero mean biases of -1.67 mm and -0.48 mm, respectively, compared with GPT3’s large bias of -16.32 mm. Their RMSE values are 25.06 mm and 30.12 mm, reflecting improvements of 25.6% and 10.6% over GPT3. These results show that both models can capture short-term ZWD variability. Notably, the RF model demonstrated relatively high modeling speed than the LSTM model. Using the same input data, the average training time per prediction cycle for RF was approximately 0.23 seconds—about 300 times faster than that of LSTM. Moreover, the RF model offers greater ease of implementation, as it has a lower dependence on temporal data structures. (3) In terms of spatial generalization performance, three independent CORS stations were selected for validation. Both the RF and LSTM models show advantages in bias reduction compared with the GPT3 model, with improvements of 8.9% and 26.6%, respectively. The LSTM model exhibits better overall performance, achieving a 26.5% improvement in RMSE compared with GPT3. Conclusions: We proposed two machine learning-based modeling strategies for ZWD estimation in small-scale regions using the RF and LSTM algorithms Overall, both models demonstrate strong capability in predicting high-frequency and time-varying ZWD under limited data conditions. These results suggest that RF and LSTM have considerable potential for application in rapid ZWD modeling across small-scale and complex environments such as mountainous regions, with the RF model being particularly advantageous for fast-response scenarios.