Empirical tropospheric zenith wet delay models with strong generalization capability based on a robust machine learning fusion algorithm

Jiahao Zhang, Qin Liang, Yunqing Huang,
Empirical tropospheric zenith wet delay models with strong generalization capability based on a robust machine learning fusion algorithm,
Geodesy and Geodynamics,
2025,
,
ISSN 1674-9847,
https://doi.org/10.1016/j.geog.2025.06.004.
(https://www.sciencedirect.com/science/article/pii/S1674984725000680)
Abstract: Tropospheric zenith wet delay (ZWD) plays a vital role in the analysis of space geodetic observations. In recent years, machine learning methods have been increasingly applied to improve the accuracy of ZWD calculations. However, a single machine learning model has limited generalization capabilities. To address these limitations, this study introduces a novel machine learning fusion (MLF) algorithm with stronger generalization capabilities to enhance ZWD modeling and prediction accuracy. The MLF algorithm utilizes a two-layer structure integrating extra trees (ET), backpropagation neural network (BPNN), and linear regression models. By comparing the root mean square error (RMSE) of these models, we found that both ET-based and MLF-based models outperform RF-based and BPNN-based models in terms of internal and external accuracy, across both surface meteorological data-based and blind models. The improvement in external accuracy is particularly significant in the blind models. Our results show that the MLF (with an RMSE of 3.93 cm) and ET (3.99 cm) models outperform the traditional GPT3 model (4.07 cm), while the RF (4.21 cm) and BPNN (4.14 cm) have worse external accuracies than the GPT3 model. It is worth noting that the BPNN suffered from overfitting during external accuracy tests, which was avoided by the MLF. In summary, regardless of the availability of surface meteorological data, the MLF-based empirical models demonstrate superior internal and external accuracy compared to the other tested models in this study.
Keywords: Tropospheric zenith wet delay; Machine learning; Extra trees; Machine learning fusion algorithm; Empirical models