# Kriging Interpolation in Modelling Tropospheric Wet Delay
## 3 Experiments in Sparse and Dense Network
Meanwhile, the other three stations VLIS, RIL2 and SASG were located closely with each other and, thus, have similar accuracies. RIL2 had the lowest RMS value among 5 stations outside the network because it had the shortest distance to the network station, and one  
Figure 1:0 RMSEs of the prediction errors for the user stations on the edge of the (**a**) sparse network and (**b**) dense network. Figure 1:1 Average RMSE of the user stations in sparse network. The unit is m.  
newly added reference stations in the dense network were also close to RIL2, which improved the accuracy of this user station. Table 2 presents the statistics of the average RMSEs of all user stations. One can see that stations inside the network had sub-centimeter level accuracy, while stations on edge or outside the network attained the RMSEs around 1 cm. It is worth noting that the stations outside the network can also achieve 1 cm level accuracy, which was much better than the polynomial interpolation normally used in predicting the zenith wet delays. However, the benefits of the dense network were not evident because the water vapor content was spatially stable most of the time. The improvements offered by the dense network are 6.8%, 12.5% and 6.8% for the stations inside the network, on the edge of the network and outside the network, respectively. Figure 1:2 Average RMSE of the user stations in (**a**) the sparse and (**b**) the dense network. Stations from the left to the right are sequential 5 inside the network, 5 on the edge of the network and 5 outside the network. Figure 1:3 RMSEs of the prediction errors for the user stations outside the (**a**) sparse network and (**b**) dense network. The violin plot [46] aims to summarize a batch of data by displaying several main features other than the average value. As shown in Figure 12 the violin plot of the RMSE values of all user stations in the sparse and dense network, it contains the fusiform of the density trace graphically showing the distributional characteristics of RMSEs for each user station and the circle showing the position of a typical central value. These two features summary the univariate data on spread and location. As for the user stations inside the network, the lower adjacent values of three station LITH, HOOG and ADR2 in the dense network were smaller than those of the sparse network, indicating that the dense network can help provide more accurate predictions for the inland stations (i.e., the other two stations LELY and LWRD among 5 users stations inside the network were close to larger water area). Besides, most of the outliers in the dense network have disappeared because of the stable predictions during summer period. The RMSEs distribution of station WARM in the dense network saw a significant improvement, in that, the first quartile was much lower than that of the sparse network, even though their central values were almost at the same accuracy level. Other two stations on the edge of the network TERS and DZYL had better performances in the case of the dense network in terms of the lower adjacent value and the first quartile. However, the patterns of the stations outside the network did not change much between the dense or sparse network, indicating a low sensitivity of the stations outside the network to the number of the references.