Global 3D ionospheric shape function modeling with kriging

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.