A Refined Zenith Tropospheric Delay Model Based on a Generalized Regression Neural Network and the GPT3 Model in Europe

Abstract

An accurate model of the Zenith Tropospheric Delay (ZTD) plays a crucial role in Global Navigation Satellite System (GNSS) precise positioning, water vapor retrieval, and meteorological research. Current empirical models (such as the GPT3 model) can only reflect the approximate change trend of ZTD but cannot accurately reflect nonlinear changes such as rapid fluctuations in ZTD. In recent years, the application of machine learning methods in the modeling and prediction of ZTD has gained prominence, yielding commendable results. Utilizing the ZTD products from 53 International GNSS Service (IGS) stations in Europe during the year 2021 as a foundational dataset, a Generalized Regression Neural Network (GRNN) is employed to model IGS ZTD while considering spatiotemporal factors and its association with GPT3 ZTD. This endeavor culminates in the development of a refined GRNN model. To verify the performance of the model, the prediction results are compared with two other ZTD values. One is obtained based on the European Centre for Medium-Range Weather Forecasts Reanalysis 5 (ERA5) data, and the other is obtained by the GPT3 model. The results show that the bias of the GRNN refined model is almost 0 mm, and the average Root-Mean-Square Error (RMSE) and Mean Absolute Error (MAE) are 18.33 mm and 14.08 mm, respectively. Compared with ERA5 ZTD and GPT3 ZTD, the RMSE of GRNN ZTD has decreased by 19.5% and 63.4%, respectively, and the MAE of GRNN ZTD has decreased by 24.8% and 67.1%. Compared with the other two models, the GRNN refined model has better performance in reflecting the rapid fluctuations of ZTD. In addition, also discussed is the impact of spatial factors and time factors on modeling. The findings indicate that modeling accuracy within the central region of the modeling area surpasses that at the periphery by approximately 17.8%. The period from June to October is associated with the lowest accuracy, whereas the optimal accuracy is typically observed from January to April. The most substantial differences in accuracy were observed at station OP71 (Paris, France), with the highest accuracy recorded (9.51 mm) in April and the lowest (24.00 mm) in September.