## 4 Discussion  
Interpolation of the ZWD value with a high accuracy makes significant contributions to applications in GNSS meteorology and positioning applications with the GNSS technique. For the interpolation of wet troposphere delay, analyses were carried out using the ANN, IDW, and LIN methods. Six different artificial neural network models were designed for the ANN model. In the formation of these models, the latitude, longitude, and altitude parameters, as well as meteorological parameters (temperature, pressure, water vapor pressure, and weighted mean temperature), were used. The artificial neural network model which was designed by including all parameters provided a 40% improvement compared to the two-parameter ANN model. The seven-parameter ANN model RMSE values were 5.2 mm for the 40-station network, 5.8 mm for the 30-station network and 6.7 mm for the 20-station network. The mean RMSE values of the IDW method were 11.5, 12.1, and 14.4 mm for the 40-station, 30-station, and 20-station network, respectively. The mean RMSE values of the LIN method were 11.6 mm for the 40-station network, 13.5 mm for the 30-station network, and 15.2 mm for the 20-station network. The distance between stations of the 40-station network (30-40 km) allows interpolation to be carried out at the level of a 1 cm accuracy by conventional methods. The RMSE values obtained in the 20-station network for the IDW and LIN methods increased by 16% and 11%, respectively, when compared to the 30-station network. The RMSE values obtained from the 20-station network increased by 24% for the LIN method and 20% for the IDW method compared to the 40-station network. For the ANN model, these rates were 14% and 23%. The contribution of meteorological parameters was used in the ANN model and the accuracy of ZWD interpolation was around 40%. According to these results, it could be observed that conventional methods provide an approximately 1 cm accuracy in networks with a distance between stations between 30 and 40 km and 1.5 cm for longer distances. However, in the ANN model, ZWD interpolation with an RMSE of around 6 mm can be achieved, even in networks where the distance between stations reaches 70-80 km. This contribution to the accuracy over increasing distances may help for positioning and weather forecast applications in sparse GNSS networks. In addition, the conversion factor used to calculate the PWV value from the ZWD value was approximately 0.16. Accordingly, for the ZWD with an RMSE of 6 mm, the PWV value can be obtained with an accuracy of approximately 1 mm. It has been demonstrated in previous studies that the threshold value for meteorological studies is 2-3 mm [34]. Therefore, it can be said that the accuracy of ZWD interpolation obtained by the ANN model is sufficient for meteorological estimations. According to the results, the proposed ANN model based on meteorological parameters improves the ZWD interpolation accuracy by more than 50% compared with the conventional methods. As a result, ANN algorithms can be successfully applied to meteorological estimations by choosing the optimal parameters as the input of the model. Moreover, using the ability of artificial neural networks based on different architectures may help to improve the water vapor estimation accuracy on a global scale. In future studies, regional T\({}_{\text{M}}\) models can be used instead of the Bevis model, which has limitations due to the latitude dependency, in order to obtain a more accurate ANN structure. Furthermore, the proposed ANN model can be tested on GNSS networks located in different climatic regions of the world.  
**Acknowledgments:** The author thanks [PERSON] and [PERSON] from the Geodesy and Geo Information Department of the Vienna University of Technology for providing the data of the TAWES and EPOSA networks.  
**Conflicts of Interest:** The author declares that there are no conflicts of interest regarding the publication of this paper.