This contribution implements the Kriging interpolation in predicting the tropospheric wet delays using global navigation satellite system networks. The predicted tropospheric delays can be used in strengthening the precise point positioning models and numerical weather prediction models. In order to evaluate the performances of the Kriging interpolation, a sparse network with 8 stations and a dense network with 19 stations from continuously operating reference stations (CORS) of the Netherlands are selected as the reference. In addition, other 15 CORS stations are selected as users, which are divided into three blocks: 5 stations located approximately in the center of the networks, 5 stations on the edge of the networks and 5 stations outside the networks. The zenith tropospheric wet delays are estimated at the network and user stations through the ionosphere-free positioning model; meanwhile, the predicted wet delays at the user stations are generated by the Kriging interpolation in the use of the tropospheric estimations at the network. The root mean square errors (RMSE) are calculated by comparing the predicted wet delays and estimated wet delays at the same user station. The results show that RMSEs of the stations inside the network are at a sub-centimeter level with an average value of 0.74 cm in the sparse network and 0.69 cm in the dense network. The stations on edge and outside the network can also achieve 1-cm level accuracy, which overcomes the limitation that accurate interpolations can only be attained inside the network. This contribution also presents an insignificant improvement of the prediction accuracy from the sparse network to the dense network over 1-year’s data processing and a seasonal effect on the tropospheric wet delay predictions.

中文翻译：

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对流层湿延迟建模中的克里格插值

该贡献使用全球导航卫星系统网络在预测对流层湿延迟中实现了克里格插值。预计的对流层延迟可用于加强精确的点定位模型和数值天气预报模型。为了评估Kriging插值的性能，从荷兰的连续运行参考站（CORS）中选择了具有8个站点的稀疏网络和具有19个站点的密集网络作为参考。此外，还选择了其他15个CORS站作为用户，分为三个块：5个站位于网络中心附近，5个站位于网络边缘和5个站位于网络外部。天顶对流层湿延迟是通过无电离层定位模型在网络和用户站估算的；同时，利用网络上的对流层估计，通过克里格插值法生成用户站的预测湿延迟。均方根误差（RMSE）是通过比较同一用户站上的预测湿延迟和估计湿延迟来计算的。结果表明，网络内部站点的RMSE处于亚厘米级别，在稀疏网络中平均值为0.74 cm，在密集网络中平均值为0.69 cm。网络边缘和外部的站也可以达到1厘米级别的精度，这克服了只能在网络内部实现精确插值的限制。