# Kriging Interpolation in Modelling Tropospheric Wet Delay
## 4 Conclusions and Discussions  
This contribution investigates the performances of the Kriging interpolation in predicting the zenith tropospheric wet delays in the use of GNSS networks. The zenith wet delay was estimated in PPP data processing with the IF combination model at the selected Netherlands CORS stations. A sparse network with 8 reference stations and a dense network with 19 reference stations were selected and used to predict the zenith wet delays at 15 user stations, including 5 inside the network, 5 on the edge of the network and 5 outside the network. The entire year's data of 2019 were processed to evaluate the quality of the zenith wet delay predictions from the Kriging interpolation, and the RMSEs were calculated by comparing the predicted delays and the estimated delays at each user station. The RMSEs of 5 user stations inside the network were at sub-centimeter level, in which average values were 0.74 cm with the sparse network and 0.69 cm with the dense network. The stations on the edge of the network achieve 1 cm accuracy level with 1.12 cm of the sparse network and 0.98 cm of the dense network. The statistics of RMSE were 1.17 cm with the sparse and 1.09 cm with the dense when user stations were outside the network. The seasonal effects can be seen in the user stations inside the network that the accuracy of predicted zenith wet delays is relatively worse in summer period because water vapor content would change rapidly in space with the rising temperature. Results also show that the benefits of the dense network are not evident for the average RMSE over the year as the water vapor content is spatially stable most of the time. Compared to the sparse network, the number of dense network stations is doubled; meanwhile, the average RMSE is reduced by around 10%. The advantages of the dense network are mainly in the summer period and the stations that are encountered complex weather conditions. As for the user stations inside or on the edge of the network, the performances of the inland stations are usually better than those of coastal because of the inland smooth water vapor disturbances. The prediction accuracy of the stations outside the network mainly depends on the distance to the nearby reference station, therefore it is not sensitive to the number of reference stations. The predicted zenith wet delays can be used in strengthening the PPP models to improve the positioning accuracy and reduce the convergence time and used in NWP models to help identify model biases and forecast weather conditions. Although the Kriging interpolation has been confirmed for a certain level of accuracy for predicting the zenith wet delays using a GNSS network, the conclusions of this contribution are restricted by the number of CORS stations and the area of the Netherlands. More stations or a larger area might be needed in further investigation of the Kriging interpolation in predicting the zenith wet delays or other GNSS applications. Conceptualization, H.M. and S.V. ; methodology, H.M.; software, H.M.; validation, Q.Z. ; formal analysis, H.M. and D.P. ; investigation, H.M. and H.D. ; writing--original draft preparation, H.M.; writing--review and editing, S.V., Q.Z., D.P. and H.D. ; visualization, H.M.; supervision, S.V. and Q.Z. ; All authors have read and agreed to the published version of the manuscript. The first and fourth authors have received funding from the European Union's Horizon 2020 research and innovation programme under the Marie-Sklodowska Grant No 722023. This research was also partially supported by National Natural Science Foundation of China (Grant No 41774035). The authors would like to thank The Netherlands Cadastre, Land Registry and Mapping Agency (Kadaster) for maintaining the Netherlands GNSS network. The authors are thankful to the Center for Orbit Determination in Europe for providing the precise satellite orbits. The authors declare no conflict of interest.