Evaluation of Tropospheric Delay Interpolation Methods from Scattered GPS Station Observations

This study comprehensively evaluates the effectiveness of five interpolation methods, Kriging, Support Vector Machine (SVM), Random Forest (RF), Natural Neighbor (NN), and Artificial Neural Network (ANN), in estimating Precipitable Water Vapor (PWV) based on GPS data collected from 25 strategically located stations across the diverse geographic region of Los Angeles. The predictors utilized in this study include critical factors such as latitude, longitude, elevation, and tropospheric delay components derived from high-precision GPS observations. The analysis primarily focuses on two representative dates, July 24, 2021 (summer), and January 28, 2022 (winter), specifically chosen for their contrasting meteorological conditions. These dates enable a detailed evaluation of seasonal variability in PWV distribution and provide an opportunity to test the robustness of the selected methods under varying atmospheric conditions.
Tropospheric delay, a key parameter in GNSS-based atmospheric studies, was computed by separating it into its hydrostatic (Zenith Hydrostatic Delay: ZHD) and wet (Zenith Wet Delay: ZWD) components. ZHD was accurately calculated using the well-established Saastamoinen model, which relies on meteorological variables such as surface pressure and station altitude. ZWD was subsequently derived as the difference between ZHD and the Zenith Total Delay (ZTD). The final PWV values were estimated by applying a region-specific coefficient that depends on the weighted mean temperature (T_m). This critical parameter, T_m, was determined using ERA-5 reanalysis data to ensure precise calculations.
The results demonstrate that SVM emerged as the most effective interpolation method, achieving the lowest Root Mean Square Error (RMSE) of 0.6 mm in winter and exhibiting remarkable robustness across diverse spatial and temporal conditions. Kriging, another reliable method, provided accurate results in regions with dense station coverage but encountered difficulties in sparsely populated areas. RF and NN exhibited better performance in winter conditions, benefiting from the reduced atmospheric noise and more stable meteorological conditions during this season. Conversely, ANN, while theoretically capable of modeling complex relationships, was limited in this study by suboptimal network configurations and sensitivity to sparse data distribution. This underscores the importance of careful architectural design and parameter tuning to unlock its full potential.
Seasonal differences in PWV distribution were clearly depicted in the high-resolution maps generated for the selected dates. During summer, PWV values exhibited significant diurnal fluctuations, with peaks in coastal regions during the afternoon due to elevated temperatures and humidity levels. In contrast, the winter maps displayed more stable distributions with lower peak values, reflecting cooler temperatures and reduced atmospheric moisture. These observations highlight the challenges posed by the dynamic summer conditions while emphasizing the critical role of meteorological parameters such as temperature, pressure, and humidity in influencing PWV estimation accuracy.
This study underscores the necessity of selecting appropriate interpolation methods tailored to specific conditions for accurate PWV estimation. SVM demonstrated exceptional capability in handling nonlinear relationships and scattered datasets, making it the most reliable method in this study. Furthermore, while ANN showed room for improvement, its performance could be significantly enhanced with better configurations and deeper architectures specifically tailored for atmospheric complexities. These findings provide valuable insights into GNSS-based atmospheric research and contribute to the advancement of meteorological modeling, weather forecasting, and climate science.