The 3D ionosphere structure is of interest in many fields such as radio frequency communication and global navigation satellite system (GNSS) applications. However, the limited temporal and spatial coverage of measurements poses a challenge for 3D electron density modeling. To overcome this challenge, we explore the use of kriging interpolation technique. The kriging interpolation is performed to obtain 3D representation of the ionosphere over electron density measurements retrieved by GNSS radio-occultation (RO) data. RO measurements are first reduced to “shape function,” the ratio of electron density to vertical total electron content (VTEC), aiming to create a background model. Then, the empirical residual semivariogram is analyzed for variation characteristics of the shape functions under different solar geomagnetic conditions. Finally, 3D kriging is adopted for shape function interpolation. Compared to the modeling results without kriging, the maximum root mean square error (RMSE) reduction reaches \(3.4\times {10}^{-4}~\text {km}^{-1}\), which amounts to \(3.4\times {10}^{11}~\text {el/m}^{3}\) of electron density when VTEC is assumed as 100 TECU. This improvement accounts for 17.8% of root mean square (RMS) of shape function.

3D 电离层结构在许多领域都受到关注，例如射频通信和全球导航卫星系统 （GNSS） 应用。然而，测量的有限时间和空间覆盖范围对 3D 电子密度建模构成了挑战。为了克服这一挑战，我们探索了克里金插值技术的使用。执行克里金插值以获得电离层在 GNSS 射掩星 （RO） 数据检索的电子密度测量值上的 3D 表示。RO 测量首先简化为“形状函数”，即电子密度与垂直总电子含量 （VTEC） 的比率，旨在创建一个背景模型。然后，分析了不同太阳地磁条件下形状函数变化特征的经验残差半变异函数。最后，采用 3D Kriging 进行形函数插值。与没有克里金法的建模结果相比，当 VTEC 假设为 100 TECU 时，最大均方根误差 （RMSE） 减少达到 \（3.4\times {10}^{-4}~\text {km}^{-1}\），相当于电子密度的 \（3.4\times {10}^{11}~\text {el/m}^{3}\）。这种改进占形状函数均方根 （RMS） 的 17.8%。