Improved empirical zenith tropospheric wet delay models based on a novel machine learning fusion algorithm

Zenith tropospheric 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. The most widely used approaches are random forest (RF) and back propagation neural network (BPNN) models, both of which have shown promising results in terms of internal accuracy (where test stations are included in the training set). However, the external accuracy (where test stations are excluded from the training set) of these models still requires improvement. To address this issue, this study introduces two new methods: Extra Trees (ET) and a novel machine learning fusion (MLF) algorithm, aimed at enhancing ZWD accuracy. The MLF algorithm utilizes a two-layer structure that integrates ET, BPNN, and linear regression models. By comparing the root mean squared 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 (4.21cm) and BPNN (4.14cm) have worse external accuracies than the GPT3 model. 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.