# Kriging Interpolation in Modelling Tropospheric Wet Delay
## 3 Experiments in Sparse and Dense Network
Overall, 84.38% of the RMSEs of the sparse network were less than 1 cm, and 88.49% of those for the dense network, which provide an adequate capability of predicting the zenith wet delay. In order to justify the influences of the individual network on the predictions, the values of the predicted zenith wet delays at particular locations of the sparse and dense network during the winter period (1 st February) and summer period (1 st August) are presented in Figures 6 and 7, respectively. Figure 6 presents that the pattern of the predicted zenith wet delays had a smooth surface so that a receiver at the same location of the sparse and dense network would have a similar predicted value. This indicated that the spatial variations of the water vapor were small and also explained the similar performances of the sparse and dense network under stable weather conditions. Figure 4: Sample variogram for the dense network (square symbols) with fitted model (solid curve). Figure 5: RMSEs of the prediction errors for the user stations inside the (**a**) sparse network and (**b**) dense network. On the contrary, the predicted zenith wet delays in the dense network were different from those at the same locations of the sparse network during the summer period, as shown in Figure 7. Since most of the newly added reference stations were inside the network, the elaborated description of the predicted zenith wet delays was presented as compared to the sparse network with fewer reference stations. Therefore, the predicted zenith wet delays are more accurate in the dense network than those of in the sparse network. Figure 8 presents the RMSEs of the user stations on the edge of the network which were varying individually to each other. On the one hand, the zenith wet delay predictions of three stations HHOL, OLDE and DZYL were at the same accuracy level as the stations inside the network; and on the other hand, station WARM and TERS had significantly larger RMSE values than the others, as can be seen in Figure 9. This is because some of their nearby reference stations, shown in Figures 1 and 2, were located in the coastal area or the islands, and, thus, the zenith wet delay estimations may change dramatically due to the water evaporation of the large water area. Besides, the seasonal variation was not significant for the stations WARM and TERS due to the inaccurate predictions. Figure 6: Values of the predicted zenith wet delays at particular locations (the smaller circle) in the local area by using the sparse and dense network (the bigger circle) on 1 February 2019. The unit is m.  
Figure 7: Values of the predicted zenith wet delays at particular locations (the smaller circle) in the local area by using the sparse and dense network (the bigger circle) on 1 August 2019. The unit is m.  
Figure 9 indicates one exception of station HHOL which is located at the coastline while having small RMSE value. This was probably because the evaporation of the sea does not significantly affect the water vapor content above HHOL due to its location that one side was oriented towards the land. Comparatively, station TERS was on an island and WARM was on a \"peninsula\" between North Sea and Markermeer & IJmeer Lake. The large water area may disturb the smooth distribution of a local area, and, therefore, influenced the accuracy of the predicted zenith wet delays. Figure 10 presents the RMSEs of the user stations that are outside the network. The patterns are likewise similar with an unobvious seasonal effect for both the sparse and dense network, which indicated that the number of reference stations had an insignificant impact on the stations outside the network. This was because the Kriging interpolation is a distance-based method, and the performances of the stations outside the network mainly depend on the closest reference station. For instance, as shown in Figure 11 the histogram of the average RMSE of user stations, KERK and MSTR have similar values because they have approximately the same distance to the reference station (as can be seen in Figure 1).