A High-Accuracy GNSS Tropospheric Wet Delay Forecasting Algorithm via PINN-LSTM Integration Tailored to Complex Mountainous Terrain and Urban Environments: Methodology and Validation

Abstract

The rapid expansion of low-altitude uncrewed aerial system (UAS) operations in complex mountainous urban environments have created urgent demand for high spatiotemporal resolution water vapor observations to support safe flight, precise navigation, and growth of the low-altitude economy. To address this unmet need, this study develops and validates a framework for the refined construction and forecasting of zenith wet delay (ZWD)—a core metric for precipitable water vapor estimation—across discrete atmospheric pressure levels, using Chongqing, China, a representative complex mountainous urban region, as a case study. We integrate in situ meteorological station observations with multilevel pressure ERA5 reanalysis data to retrieve ZWD values at the surface, 900 and 800 hPa levels using the Askne and Nordius model, followed by a comprehensive assessment of retrieval data reliability. We then develop a random forest interpolation algorithm to generate continuous, layered ZWD fields at 1 km spatial resolution across the study domain. Finally, we design a hybrid physics-informed neural network and long short-term memory (PINN-LSTM) model to produce high-accuracy ZWD forecasts for each target pressure level. Experimental results demonstrate three key findings: first, station-retrieved ZWD values show strong agreement with both Vienna Mapping Function (VMF) and radiosonde reference datasets, with correlation coefficients exceeding 0.95 for all validation comparisons and consistent variation trends, confirming the suitability of the retrieved data for multilevel ZWD forecasting research. Second, ZWD high-value and low-value zones exhibit distinct spatial distribution patterns across different seasons and pressure levels. Overall, ZWD decreases systematically as atmospheric pressure declines (i.e., at increasing altitude). Third, the PINN-LSTM model significantly outperformed both PINN and LSTM in predicting ZWD at different pressure levels across meteorological stations, demonstrating superior predictive accuracy, stability, and generalization capability. Compared with PINN and LSTM, PINN-LSTM reduced the average RMSE from 3.86 and 2.88 cm, respectively, to 1.51 cm, and decreased the average MAE from 2.83 cand 2.01 cm, respectively, to 1.01 cm. The layered ZWD construction and forecasting framework proposed in this study markedly improves the refined representation and predictive capability of low-altitude water vapor parameters in complex topographical regions. These findings provide critical support for meteorological assurance for UAS low-altitude flight, Global Navigation Satellite System navigation error correction, and the safe operation of the low-altitude economy.